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a1de1.. as prop with payaddr PrGVS.. rights free controlledby PrGVS.. upto 0TMGdp../66c73.. ownership of 822fd.. as prop with payaddr PrGVS.. rights free controlledby PrGVS.. upto 0TMHdQ../ce828.. ownership of c6258.. as prop with payaddr PrGVS.. rights free controlledby PrGVS.. upto 0TMGa3../d4ed6.. ownership of b1ccf.. as prop with payaddr PrGVS.. rights free controlledby PrGVS.. upto 0TMVFP../a214a.. ownership of 6b2d1.. as prop with payaddr PrGVS.. rights free controlledby PrGVS.. upto 0TMG4Y../e58cb.. ownership of 0eb92.. as prop with payaddr PrGVS.. rights free controlledby PrGVS.. upto 0TMT3w../7335c.. ownership of ab174.. as prop with payaddr PrGVS.. rights free controlledby PrGVS.. upto 0TMG3K../0fd2d.. ownership of 2836d.. as prop with payaddr PrGVS.. rights free controlledby PrGVS.. upto 0TMbFB../0c466.. ownership of 3f950.. as prop with payaddr PrGVS.. rights free controlledby PrGVS.. upto 0TMG1z../7c129.. ownership of 36f64.. as prop with payaddr PrGVS.. rights free controlledby PrGVS.. upto 0TMYtA../dcd2a.. ownership of 9601b.. as prop with payaddr PrGVS.. rights free controlledby PrGVS.. upto 0TMFXe../ed8fb.. ownership of b4f37.. as prop with payaddr PrGVS.. rights free controlledby PrGVS.. upto 0TMJNP../18458.. ownership of 0f4cf.. as prop with payaddr PrGVS.. rights free controlledby PrGVS.. upto 0TMFxd../d605c.. ownership of a9210.. as prop with payaddr PrGVS.. rights free controlledby PrGVS.. upto 0TMFDe../25bc0.. ownership of cc285.. as prop with payaddr PrGVS.. rights free controlledby PrGVS.. upto 0TMFUZ../7819e.. ownership of 22432.. as prop with payaddr PrGVS.. rights free controlledby PrGVS.. upto 0TMcH8../9b122.. ownership of c8110.. as prop with payaddr PrGVS.. rights free controlledby PrGVS.. upto 0TMFrt../f449d.. ownership of aefa3.. as prop with payaddr PrGVS.. rights free controlledby PrGVS.. upto 0TMaBL../b35f7.. ownership of 8df67.. as prop with payaddr PrGVS.. rights free controlledby PrGVS.. upto 0TMFRC../a1aed.. ownership of 1cbc7.. as prop with payaddr PrGVS.. rights free controlledby PrGVS.. upto 0TMQxd../5d90e.. ownership of e9d04.. as prop with payaddr PrGVS.. rights free controlledby PrGVS.. upto 0TMFQu../802de.. ownership of f02bb.. as prop with payaddr PrGVS.. rights free controlledby PrGVS.. upto 0TMQva../72667.. ownership of e85be.. as prop with payaddr PrGVS.. rights free controlledby PrGVS.. upto 0TMFN4../b27b0.. ownership of 381ed.. as prop with payaddr PrGVS.. rights free controlledby PrGVS.. upto 0TMLWx../17cc3.. ownership of 181f5.. as prop with payaddr PrGVS.. rights free controlledby PrGVS.. upto 0TMFmW../742fe.. ownership of 8c027.. as prop with payaddr PrGVS.. rights free controlledby PrGVS.. upto 0TMbDt../f9826.. ownership of 8a03e.. as prop with payaddr PrGVS.. rights free controlledby PrGVS.. upto 0TMFh1../81708.. ownership of cd23f.. as prop with payaddr PrGVS.. rights free controlledby PrGVS.. upto 0TMbpU../4eff0.. ownership of 26054.. as prop with payaddr PrGVS.. rights free controlledby PrGVS.. upto 0TMMnT../96dcf.. ownership of cd8e8.. as prop with payaddr PrGVS.. rights free controlledby PrGVS.. upto 0TMUWc../3295f.. ownership of e9b62.. as prop with payaddr PrGVS.. rights free controlledby PrGVS.. upto 0TMFa5../1b7b9.. ownership of f8888.. as prop with payaddr PrGVS.. rights free controlledby PrGVS.. upto 0TMTFJ../368de.. ownership of 40608.. as prop with payaddr PrGVS.. rights free controlledby PrGVS.. upto 0TMEuo../714bd.. ownership of ab27c.. as prop with payaddr PrGVS.. rights free controlledby PrGVS.. upto 0TMM7v../d65dd.. ownership of 96161.. as prop with payaddr PrGVS.. rights free controlledby PrGVS.. upto 0TMdWA../74ab0.. ownership of 2bfdd.. as prop with payaddr PrGVS.. rights free controlledby PrGVS.. upto 0TMcyT../333f4.. ownership of 8e943.. as prop with payaddr PrGVS.. rights free controlledby PrGVS.. upto 0TMdvN../94f92.. ownership of dc9ca.. as prop with payaddr PrGVS.. rights free controlledby PrGVS.. upto 0TMRwy../f77c1.. ownership of 310ac.. as prop with payaddr PrGVS.. rights free controlledby PrGVS.. upto 0TMdVJ../3d89e.. ownership of 9a10f.. as prop with payaddr PrGVS.. rights free controlledby PrGVS.. upto 0TMNX7../c7833.. ownership of 3cfe1.. as prop with payaddr PrGVS.. rights free controlledby PrGVS.. upto 0TMdvJ../f65d6.. ownership of 15092.. as prop with payaddr PrGVS.. rights free controlledby PrGVS.. upto 0TMHyk../57550.. ownership of 1b1cd.. as prop with payaddr PrGVS.. rights free controlledby PrGVS.. upto 0TMdJQ../48b40.. ownership of 4bada.. as prop with payaddr PrGVS.. rights free controlledby PrGVS.. upto 0TMa1h../d3c77.. ownership of fd943.. as prop with payaddr PrGVS.. rights free controlledby PrGVS.. upto 0TMdgp../41528.. ownership of 3677d.. as prop with payaddr PrGVS.. rights free controlledby PrGVS.. upto 0TMTFq../2ba0e.. ownership of 1e132.. as prop with payaddr PrGVS.. rights free controlledby PrGVS.. upto 0TMd4P../7ffe2.. ownership of bd450.. as prop with payaddr PrGVS.. rights free controlledby PrGVS.. upto 0TMa1A../39d6c.. ownership of bae28.. as prop with payaddr PrGVS.. rights free controlledby PrGVS.. upto 0TMcz3../be5e0.. ownership of 07659.. as prop with payaddr PrGVS.. rights free controlledby PrGVS.. upto 0TMHPx../6ba7a.. ownership of 6af13.. as prop with payaddr PrGVS.. rights free controlledby PrGVS.. upto 0TMTqV../aff97.. ownership of 4873e.. as prop with payaddr PrGVS.. rights free controlledby PrGVS.. upto 0TMYyR../f89d5.. ownership of b6244.. as prop with payaddr PrGVS.. rights free controlledby PrGVS.. upto 0TMcWt../90548.. ownership of 50893.. as prop with payaddr PrGVS.. rights free controlledby PrGVS.. upto 0TMWuR../10cef.. ownership of 02161.. as prop with payaddr PrGVS.. rights free controlledby PrGVS.. upto 0TMcHY../b1a51.. ownership of b4a18.. as prop with payaddr PrGVS.. rights free controlledby PrGVS.. upto 0TMXMY../ef531.. ownership of 851fc.. as prop with payaddr PrGVS.. rights free controlledby PrGVS.. upto 0TMc6c../6b5e2.. ownership of 2625c.. as prop with payaddr PrGVS.. rights free controlledby PrGVS.. upto 0TMWbb../ce2b6.. ownership of bf57b.. as prop with payaddr PrGVS.. rights free controlledby PrGVS.. upto 0TMbzv../d7eaa.. ownership of 3165c.. as prop with payaddr PrGVS.. rights free controlledby PrGVS.. upto 0TMZF5../33258.. ownership of 01c82.. as prop with payaddr PrGVS.. rights free controlledby PrGVS.. upto 0TMbur../6deee.. ownership of 9f7c7.. as prop with payaddr PrGVS.. rights free controlledby PrGVS.. upto 0TMT34../ce97e.. ownership of b5971.. as prop with payaddr PrGVS.. rights free controlledby PrGVS.. upto 0TMboC../0dca6.. ownership of 001c8.. as prop with payaddr PrGVS.. rights free controlledby PrGVS.. upto 0TMPdG../e3f82.. ownership of 2829c.. as prop with payaddr PrGVS.. rights free controlledby PrGVS.. upto 0TMbnx../32f37.. ownership of fa49b.. as prop with payaddr PrGVS.. rights free controlledby PrGVS.. upto 0TMd7Q../546c7.. ownership of 3d4b8.. as prop with payaddr PrGVS.. rights free controlledby PrGVS.. upto 0TMbn1../334ef.. ownership of f7d60.. as prop with payaddr PrGVS.. rights free controlledby PrGVS.. upto 0TMHuC../a4fae.. ownership of b788a.. as prop with payaddr PrGVS.. rights free controlledby PrGVS.. upto 0TMbMQ../6d427.. ownership of 6fc01.. as prop with payaddr PrGVS.. rights free controlledby PrGVS.. upto 0TMK6L../6ef3f.. ownership of 93f6d.. as prop with payaddr PrGVS.. rights free controlledby PrGVS.. upto 0TMbkp../4c173.. ownership of 33063.. as prop with payaddr PrGVS.. rights free controlledby PrGVS.. upto 0TMURR../c19a3.. ownership of 8f339.. as prop with payaddr PrGVS.. rights free controlledby PrGVS.. upto 0TMbCa../d0cfd.. ownership of 5b7cf.. as prop with payaddr PrGVS.. rights free controlledby PrGVS.. upto 0TMQf5../1817f.. ownership of 4c2c3.. as prop with payaddr PrGVS.. rights free controlledby PrGVS.. upto 0TMb56../715e3.. ownership of dfd17.. as prop with payaddr PrGVS.. rights free controlledby PrGVS.. upto 0TMaWD../9ff0b.. ownership of fe1d2.. as prop with payaddr PrGVS.. rights free controlledby PrGVS.. upto 0TMaUN../f6434.. ownership of e3c3e.. as prop with payaddr PrGVS.. rights free controlledby PrGVS.. upto 0TMYVb../6274c.. ownership of 40897.. as prop with payaddr PrGVS.. rights free controlledby PrGVS.. upto 0TMYP5../e2573.. ownership of 63aac.. as prop with payaddr PrGVS.. rights free controlledby PrGVS.. upto 0TMKb7../ba216.. ownership of 94381.. as prop with payaddr PrGVS.. rights free controlledby PrGVS.. upto 0TMarH../af9ef.. ownership of f183e.. as prop with payaddr PrGVS.. rights free controlledby PrGVS.. upto 0TMYXy../8ecb0.. ownership of 1cb1c.. as prop with payaddr PrGVS.. rights free controlledby PrGVS.. upto 0TMait../98ca0.. ownership of 4eb01.. as prop with payaddr PrGVS.. rights free controlledby PrGVS.. upto 0TMYYT../f324e.. ownership of acfe0.. as prop with payaddr PrGVS.. rights free controlledby PrGVS.. upto 0PUe4y../77d6b.. doc published by PrGVS..Known FalseEFalseE : False ⟶ ∀ x0 : ο . x0Known notEnotE : ∀ x0 : ο . not x0 ⟶ x0 ⟶ FalseKnown e3ec9..neq_0_1 : not (0 = 1)Theorem 4eb01.. : ∀ x0 : (ι → ι) → (ι → ι → (ι → ι) → ι) → ι . ∀ x1 : ((ι → ((ι → ι) → ι → ι) → ι → ι) → ι → ι → (ι → ι) → ι → ι) → ((ι → (ι → ι) → ι) → ι) → ι . ∀ x2 : ((ι → ((ι → ι) → ι → ι) → ι → ι → ι) → ι) → (ι → ((ι → ι) → ι) → (ι → ι) → ι) → ι → ι . ∀ x3 : ((((ι → ι → ι) → ι → ι) → ι) → (ι → ι → ι) → ι) → ι → ι . (∀ x4 x5 x6 . ∀ x7 : (ι → ι) → ι . x3 (λ x9 : ((ι → ι → ι) → ι → ι) → ι . λ x10 : ι → ι → ι . x2 (λ x11 : ι → ((ι → ι) → ι → ι) → ι → ι → ι . 0) (λ x11 . λ x12 : (ι → ι) → ι . λ x13 : ι → ι . setsum (Inj1 (Inj0 0)) (x10 (Inj1 0) (Inj0 0))) (x0 (λ x11 . x11) (λ x11 x12 . λ x13 : ι → ι . setsum (x1 (λ x14 : ι → ((ι → ι) → ι → ι) → ι → ι . λ x15 x16 . λ x17 : ι → ι . λ x18 . 0) (λ x14 : ι → (ι → ι) → ι . 0)) (setsum 0 0)))) (x2 (λ x9 : ι → ((ι → ι) → ι → ι) → ι → ι → ι . setsum (x3 (λ x10 : ((ι → ι → ι) → ι → ι) → ι . λ x11 : ι → ι → ι . 0) x5) (x2 (λ x10 : ι → ((ι → ι) → ι → ι) → ι → ι → ι . x7 (λ x11 . 0)) (λ x10 . λ x11 : (ι → ι) → ι . λ x12 : ι → ι . setsum 0 0) (x0 (λ x10 . 0) (λ x10 x11 . λ x12 : ι → ι . 0)))) (λ x9 . λ x10 : (ι → ι) → ι . λ x11 : ι → ι . x9) x4) = setsum x5 x4) ⟶ (∀ x4 : (ι → (ι → ι) → ι) → ι . ∀ x5 x6 x7 . x3 (λ x9 : ((ι → ι → ι) → ι → ι) → ι . λ x10 : ι → ι → ι . 0) 0 = setsum 0 (x4 (λ x9 . λ x10 : ι → ι . 0))) ⟶ (∀ x4 : ι → (ι → ι) → (ι → ι) → ι → ι . ∀ x5 : ι → ι → (ι → ι) → ι . ∀ x6 . ∀ x7 : ι → ι . x2 (λ x9 : ι → ((ι → ι) → ι → ι) → ι → ι → ι . x0 (λ x10 . 0) (λ x10 x11 . λ x12 : ι → ι . Inj0 (Inj0 (setsum 0 0)))) (λ x9 . λ x10 : (ι → ι) → ι . λ x11 : ι → ι . setsum (x0 (λ x12 . setsum x12 (x1 (λ x13 : ι → ((ι → ι) → ι → ι) → ι → ι . λ x14 x15 . λ x16 : ι → ι . λ x17 . 0) (λ x13 : ι → (ι → ι) → ι . 0))) (λ x12 x13 . λ x14 : ι → ι . setsum (setsum 0 0) (Inj1 0))) (setsum 0 (setsum (setsum 0 0) (x3 (λ x12 : ((ι → ι → ι) → ι → ι) → ι . λ x13 : ι → ι → ι . 0) 0)))) (x4 (x3 (λ x9 : ((ι → ι → ι) → ι → ι) → ι . λ x10 : ι → ι → ι . 0) (setsum (Inj0 0) 0)) (λ x9 . setsum 0 (Inj0 0)) (λ x9 . setsum 0 (setsum 0 (x5 0 0 (λ x10 . 0)))) (x1 (λ x9 : ι → ((ι → ι) → ι → ι) → ι → ι . λ x10 x11 . λ x12 : ι → ι . λ x13 . 0) (λ x9 : ι → (ι → ι) → ι . 0))) = x0 (λ x9 . x0 (λ x10 . 0) (λ x10 x11 . λ x12 : ι → ι . setsum (x1 (λ x13 : ι → ((ι → ι) → ι → ι) → ι → ι . λ x14 x15 . λ x16 : ι → ι . λ x17 . 0) (λ x13 : ι → (ι → ι) → ι . 0)) (Inj1 x11))) (λ x9 x10 . λ x11 : ι → ι . setsum (x7 (setsum x10 (x1 (λ x12 : ι → ((ι → ι) → ι → ι) → ι → ι . λ x13 x14 . λ x15 : ι → ι . λ x16 . 0) (λ x12 : ι → (ι → ι) → ι . 0)))) 0)) ⟶ (∀ x4 : (ι → (ι → ι) → ι → ι) → ((ι → ι) → ι) → ι . ∀ x5 x6 x7 . x2 (λ x9 : ι → ((ι → ι) → ι → ι) → ι → ι → ι . setsum 0 (setsum (setsum (x2 (λ x10 : ι → ((ι → ι) → ι → ι) → ι → ι → ι . 0) (λ x10 . λ x11 : (ι → ι) → ι . λ x12 : ι → ι . 0) 0) (x3 (λ x10 : ((ι → ι → ι) → ι → ι) → ι . λ x11 : ι → ι → ι . 0) 0)) 0)) (λ x9 . λ x10 : (ι → ι) → ι . λ x11 : ι → ι . setsum (setsum 0 x7) (x1 (λ x12 : ι → ((ι → ι) → ι → ι) → ι → ι . λ x13 x14 . λ x15 : ι → ι . λ x16 . x3 (λ x17 : ((ι → ι → ι) → ι → ι) → ι . λ x18 : ι → ι → ι . x15 0) x13) (λ x12 : ι → (ι → ι) → ι . Inj1 (x1 (λ x13 : ι → ((ι → ι) → ι → ι) → ι → ι . λ x14 x15 . λ x16 : ι → ι . λ x17 . 0) (λ x13 : ι → (ι → ι) → ι . 0))))) 0 = x4 (λ x9 . λ x10 : ι → ι . λ x11 . x3 (λ x12 : ((ι → ι → ι) → ι → ι) → ι . λ x13 : ι → ι → ι . x13 (x1 (λ x14 : ι → ((ι → ι) → ι → ι) → ι → ι . λ x15 x16 . λ x17 : ι → ι . λ x18 . x2 (λ x19 : ι → ((ι → ι) → ι → ι) → ι → ι → ι . 0) (λ x19 . λ x20 : (ι → ι) → ι . λ x21 : ι → ι . 0) 0) (λ x14 : ι → (ι → ι) → ι . 0)) (Inj0 0)) (x10 0)) (λ x9 : ι → ι . 0)) ⟶ (∀ x4 : (ι → ι → ι → ι) → ι . ∀ x5 x6 . ∀ x7 : (ι → ι → ι → ι) → ι . x1 (λ x9 : ι → ((ι → ι) → ι → ι) → ι → ι . λ x10 x11 . λ x12 : ι → ι . λ x13 . x10) (λ x9 : ι → (ι → ι) → ι . setsum 0 (setsum (x7 (λ x10 x11 x12 . x9 0 (λ x13 . 0))) (setsum (setsum 0 0) (x9 0 (λ x10 . 0))))) = x5) ⟶ (∀ x4 : (((ι → ι) → ι → ι) → ι → ι → ι) → ι → ι → ι . ∀ x5 : ((ι → ι) → ι) → ι . ∀ x6 : ι → ι . ∀ x7 : ι → ((ι → ι) → ι) → (ι → ι) → ι → ι . x1 (λ x9 : ι → ((ι → ι) → ι → ι) → ι → ι . λ x10 x11 . λ x12 : ι → ι . λ x13 . setsum (x2 (λ x14 : ι → ((ι → ι) → ι → ι) → ι → ι → ι . setsum (Inj1 0) (x2 (λ x15 : ι → ((ι → ι) → ι → ι) → ι → ι → ι . 0) (λ x15 . λ x16 : (ι → ι) → ι . λ x17 : ι → ι . 0) 0)) (λ x14 . λ x15 : (ι → ι) → ι . λ x16 : ι → ι . x2 (λ x17 : ι → ((ι → ι) → ι → ι) → ι → ι → ι . x15 (λ x18 . 0)) (λ x17 . λ x18 : (ι → ι) → ι . λ x19 : ι → ι . x2 (λ x20 : ι → ((ι → ι) → ι → ι) → ι → ι → ι . 0) (λ x20 . λ x21 : (ι → ι) → ι . λ x22 : ι → ι . 0) 0) (x15 (λ x17 . 0))) (Inj0 (x12 0))) x10) (λ x9 : ι → (ι → ι) → ι . x9 0 (λ x10 . 0)) = x4 (λ x9 : (ι → ι) → ι → ι . λ x10 x11 . x1 (λ x12 : ι → ((ι → ι) → ι → ι) → ι → ι . λ x13 x14 . λ x15 : ι → ι . λ x16 . setsum (Inj1 0) (x3 (λ x17 : ((ι → ι → ι) → ι → ι) → ι . λ x18 : ι → ι → ι . x2 (λ x19 : ι → ((ι → ι) → ι → ι) → ι → ι → ι . 0) (λ x19 . λ x20 : (ι → ι) → ι . λ x21 : ι → ι . 0) 0) (Inj1 0))) (λ x12 : ι → (ι → ι) → ι . x3 (λ x13 : ((ι → ι → ι) → ι → ι) → ι . λ x14 : ι → ι → ι . setsum (x13 (λ x15 : ι → ι → ι . λ x16 . 0)) (setsum 0 0)) (setsum (Inj1 0) (Inj1 0)))) (x3 (λ x9 : ((ι → ι → ι) → ι → ι) → ι . λ x10 : ι → ι → ι . x0 (λ x11 . x9 (λ x12 : ι → ι → ι . λ x13 . x1 (λ x14 : ι → ((ι → ι) → ι → ι) → ι → ι . λ x15 x16 . λ x17 : ι → ι . λ x18 . 0) (λ x14 : ι → (ι → ι) → ι . 0))) (λ x11 x12 . λ x13 : ι → ι . x0 (λ x14 . x0 (λ x15 . 0) (λ x15 x16 . λ x17 : ι → ι . 0)) (λ x14 x15 . λ x16 : ι → ι . setsum 0 0))) (setsum (Inj1 0) (x6 (x7 0 (λ x9 : ι → ι . 0) (λ x9 . 0) 0)))) (x5 (λ x9 : ι → ι . setsum 0 0))) ⟶ (∀ x4 . ∀ x5 : ι → ι . ∀ x6 : ι → ((ι → ι) → ι) → ι . ∀ x7 : (ι → (ι → ι) → ι) → ι → (ι → ι) → ι . x0 (λ x9 . x3 (λ x10 : ((ι → ι → ι) → ι → ι) → ι . λ x11 : ι → ι → ι . 0) (setsum 0 (Inj0 (x2 (λ x10 : ι → ((ι → ι) → ι → ι) → ι → ι → ι . 0) (λ x10 . λ x11 : (ι → ι) → ι . λ x12 : ι → ι . 0) 0)))) (λ x9 x10 . λ x11 : ι → ι . x2 (λ x12 : ι → ((ι → ι) → ι → ι) → ι → ι → ι . 0) (λ x12 . λ x13 : (ι → ι) → ι . λ x14 : ι → ι . setsum (x2 (λ x15 : ι → ((ι → ι) → ι → ι) → ι → ι → ι . 0) (λ x15 . λ x16 : (ι → ι) → ι . λ x17 : ι → ι . 0) (x13 (λ x15 . 0))) (Inj1 (x1 (λ x15 : ι → ((ι → ι) → ι → ι) → ι → ι . λ x16 x17 . λ x18 : ι → ι . λ x19 . 0) (λ x15 : ι → (ι → ι) → ι . 0)))) 0) = x2 (λ x9 : ι → ((ι → ι) → ι → ι) → ι → ι → ι . setsum (x9 0 (λ x10 : ι → ι . λ x11 . Inj1 (Inj0 0)) (setsum 0 (x3 (λ x10 : ((ι → ι → ι) → ι → ι) → ι . λ x11 : ι → ι → ι . 0) 0)) (Inj0 (Inj0 0))) (x1 (λ x10 : ι → ((ι → ι) → ι → ι) → ι → ι . λ x11 x12 . λ x13 : ι → ι . λ x14 . Inj0 0) (λ x10 : ι → (ι → ι) → ι . Inj1 (x3 (λ x11 : ((ι → ι → ι) → ι → ι) → ι . λ x12 : ι → ι → ι . 0) 0)))) (λ x9 . λ x10 : (ι → ι) → ι . λ x11 : ι → ι . setsum (x2 (λ x12 : ι → ((ι → ι) → ι → ι) → ι → ι → ι . 0) (λ x12 . λ x13 : (ι → ι) → ι . λ x14 : ι → ι . Inj1 (x2 (λ x15 : ι → ((ι → ι) → ι → ι) → ι → ι → ι . 0) (λ x15 . λ x16 : (ι → ι) → ι . λ x17 : ι → ι . 0) 0)) (x7 (λ x12 . λ x13 : ι → ι . setsum 0 0) (x2 (λ x12 : ι → ((ι → ι) → ι → ι) → ι → ι → ι . 0) (λ x12 . λ x13 : (ι → ι) → ι . λ x14 : ι → ι . 0) 0) (λ x12 . x9))) (x10 (λ x12 . Inj1 (x0 (λ x13 . 0) (λ x13 x14 . λ x15 : ι → ι . 0))))) (x2 (λ x9 : ι → ((ι → ι) → ι → ι) → ι → ι → ι . x5 (x5 (setsum 0 0))) (λ x9 . λ x10 : (ι → ι) → ι . λ x11 : ι → ι . 0) (setsum 0 0))) ⟶ (∀ x4 x5 x6 x7 . x0 (λ x9 . x9) (λ x9 x10 . λ x11 : ι → ι . setsum (Inj0 0) (Inj0 0)) = Inj0 0) ⟶ False (proof)Theorem f183e.. : ∀ x0 : ((ι → (ι → ι) → ι) → ι → (ι → ι) → ι → ι → ι) → (ι → ι → ι) → ι → ι → ι → ι → ι . ∀ x1 : ((ι → (ι → ι → ι) → ι) → ι → ι → ι → ι) → ι → ι . ∀ x2 : (ι → ι) → ι → (ι → ι) → ι . ∀ x3 : (ι → ι → ((ι → ι) → ι) → ι) → ι → (((ι → ι) → ι → ι) → ι → ι) → ι . (∀ x4 . ∀ x5 : ((ι → ι) → ι) → ι . ∀ x6 : ((ι → ι → ι) → ι) → ι . ∀ x7 : (ι → ι → ι → ι) → ι → ι . x3 (λ x9 x10 . λ x11 : (ι → ι) → ι . 0) (Inj0 (x5 (λ x9 : ι → ι . 0))) (λ x9 : (ι → ι) → ι → ι . λ x10 . x2 (λ x11 . 0) (x0 (λ x11 : ι → (ι → ι) → ι . λ x12 . λ x13 : ι → ι . λ x14 x15 . setsum (x13 0) (x3 (λ x16 x17 . λ x18 : (ι → ι) → ι . 0) 0 (λ x16 : (ι → ι) → ι → ι . λ x17 . 0))) (λ x11 x12 . x1 (λ x13 : ι → (ι → ι → ι) → ι . λ x14 x15 x16 . Inj0 0) (x1 (λ x13 : ι → (ι → ι → ι) → ι . λ x14 x15 x16 . 0) 0)) 0 (x6 (λ x11 : ι → ι → ι . Inj0 0)) (x3 (λ x11 x12 . λ x13 : (ι → ι) → ι . x10) (x0 (λ x11 : ι → (ι → ι) → ι . λ x12 . λ x13 : ι → ι . λ x14 x15 . 0) (λ x11 x12 . 0) 0 0 0 0) (λ x11 : (ι → ι) → ι → ι . λ x12 . setsum 0 0)) (x1 (λ x11 : ι → (ι → ι → ι) → ι . λ x12 x13 x14 . 0) 0)) (λ x11 . x9 (λ x12 . 0) (x3 (λ x12 x13 . λ x14 : (ι → ι) → ι . x1 (λ x15 : ι → (ι → ι → ι) → ι . λ x16 x17 x18 . 0) 0) 0 (λ x12 : (ι → ι) → ι → ι . λ x13 . x10)))) = x2 (λ x9 . x3 (λ x10 x11 . λ x12 : (ι → ι) → ι . x1 (λ x13 : ι → (ι → ι → ι) → ι . λ x14 x15 x16 . x3 (λ x17 x18 . λ x19 : (ι → ι) → ι . 0) (x1 (λ x17 : ι → (ι → ι → ι) → ι . λ x18 x19 x20 . 0) 0) (λ x17 : (ι → ι) → ι → ι . λ x18 . x2 (λ x19 . 0) 0 (λ x19 . 0))) (x1 (λ x13 : ι → (ι → ι → ι) → ι . λ x14 x15 x16 . x16) 0)) x9 (λ x10 : (ι → ι) → ι → ι . λ x11 . 0)) (x2 (λ x9 . 0) 0 (λ x9 . x6 (λ x10 : ι → ι → ι . Inj0 x9))) (λ x9 . setsum 0 (x5 (λ x10 : ι → ι . Inj1 (x6 (λ x11 : ι → ι → ι . 0)))))) ⟶ (∀ x4 x5 : ι → ι . ∀ x6 x7 . x3 (λ x9 x10 . λ x11 : (ι → ι) → ι . 0) (x4 (x3 (λ x9 x10 . λ x11 : (ι → ι) → ι . 0) (x3 (λ x9 x10 . λ x11 : (ι → ι) → ι . x3 (λ x12 x13 . λ x14 : (ι → ι) → ι . 0) 0 (λ x12 : (ι → ι) → ι → ι . λ x13 . 0)) x7 (λ x9 : (ι → ι) → ι → ι . λ x10 . x1 (λ x11 : ι → (ι → ι → ι) → ι . λ x12 x13 x14 . 0) 0)) (λ x9 : (ι → ι) → ι → ι . λ x10 . setsum (x1 (λ x11 : ι → (ι → ι → ι) → ι . λ x12 x13 x14 . 0) 0) (x2 (λ x11 . 0) 0 (λ x11 . 0))))) (λ x9 : (ι → ι) → ι → ι . x1 (λ x10 : ι → (ι → ι → ι) → ι . λ x11 x12 x13 . setsum (x0 (λ x14 : ι → (ι → ι) → ι . λ x15 . λ x16 : ι → ι . λ x17 x18 . Inj1 0) (λ x14 x15 . x0 (λ x16 : ι → (ι → ι) → ι . λ x17 . λ x18 : ι → ι . λ x19 x20 . 0) (λ x16 x17 . 0) 0 0 0 0) x12 x11 (x3 (λ x14 x15 . λ x16 : (ι → ι) → ι . 0) 0 (λ x14 : (ι → ι) → ι → ι . λ x15 . 0)) (setsum 0 0)) (Inj0 (Inj0 0)))) = x4 x7) ⟶ (∀ x4 : ι → ι → ι . ∀ x5 : (((ι → ι) → ι) → ι) → ι → ι . ∀ x6 : ι → (ι → ι) → ι → ι . ∀ x7 : ι → ι → ι . x2 (λ x9 . setsum (x7 (x6 (Inj1 0) (λ x10 . x9) (x2 (λ x10 . 0) 0 (λ x10 . 0))) (x7 0 0)) (setsum (x5 (λ x10 : (ι → ι) → ι . setsum 0 0) 0) (Inj1 (x2 (λ x10 . 0) 0 (λ x10 . 0))))) (Inj1 0) (λ x9 . Inj1 (x5 (λ x10 : (ι → ι) → ι . x1 (λ x11 : ι → (ι → ι → ι) → ι . λ x12 x13 x14 . x0 (λ x15 : ι → (ι → ι) → ι . λ x16 . λ x17 : ι → ι . λ x18 x19 . 0) (λ x15 x16 . 0) 0 0 0 0) (setsum 0 0)) 0)) = x4 (setsum (setsum (x2 (λ x9 . x5 (λ x10 : (ι → ι) → ι . 0) 0) (x7 0 0) (λ x9 . 0)) (x5 (λ x9 : (ι → ι) → ι . x6 0 (λ x10 . 0) 0) 0)) (x0 (λ x9 : ι → (ι → ι) → ι . λ x10 . λ x11 : ι → ι . λ x12 x13 . 0) (λ x9 x10 . setsum x10 x10) 0 (x5 (λ x9 : (ι → ι) → ι . Inj1 0) (x7 0 0)) (x3 (λ x9 x10 . λ x11 : (ι → ι) → ι . 0) 0 (λ x9 : (ι → ι) → ι → ι . λ x10 . Inj0 0)) (Inj0 (x5 (λ x9 : (ι → ι) → ι . 0) 0)))) (x1 (λ x9 : ι → (ι → ι → ι) → ι . λ x10 x11 x12 . Inj1 (x2 (λ x13 . x2 (λ x14 . 0) 0 (λ x14 . 0)) x12 (λ x13 . x12))) 0)) ⟶ (∀ x4 : ((ι → ι → ι) → ι) → ι → ι . ∀ x5 x6 . ∀ x7 : (ι → ι) → ι . x2 (λ x9 . x9) (x7 (λ x9 . 0)) (λ x9 . x5) = x7 (λ x9 . x3 (λ x10 x11 . λ x12 : (ι → ι) → ι . 0) x5 (λ x10 : (ι → ι) → ι → ι . λ x11 . x0 (λ x12 : ι → (ι → ι) → ι . λ x13 . λ x14 : ι → ι . λ x15 x16 . x14 (Inj0 0)) (λ x12 x13 . 0) (x2 (λ x12 . x1 (λ x13 : ι → (ι → ι → ι) → ι . λ x14 x15 x16 . 0) 0) (setsum 0 0) (λ x12 . 0)) (setsum (x0 (λ x12 : ι → (ι → ι) → ι . λ x13 . λ x14 : ι → ι . λ x15 x16 . 0) (λ x12 x13 . 0) 0 0 0 0) (x1 (λ x12 : ι → (ι → ι → ι) → ι . λ x13 x14 x15 . 0) 0)) (setsum 0 (x0 (λ x12 : ι → (ι → ι) → ι . λ x13 . λ x14 : ι → ι . λ x15 x16 . 0) (λ x12 x13 . 0) 0 0 0 0)) (setsum (x1 (λ x12 : ι → (ι → ι → ι) → ι . λ x13 x14 x15 . 0) 0) (setsum 0 0))))) ⟶ (∀ x4 x5 : ι → ι . ∀ x6 : (((ι → ι) → ι) → ι → ι → ι) → ι . ∀ x7 : ι → ι . x1 (λ x9 : ι → (ι → ι → ι) → ι . λ x10 x11 x12 . 0) (Inj0 (x5 0)) = setsum 0 (Inj1 0)) ⟶ (∀ x4 . ∀ x5 : ι → ι . ∀ x6 x7 . x1 (λ x9 : ι → (ι → ι → ι) → ι . λ x10 x11 x12 . x1 (λ x13 : ι → (ι → ι → ι) → ι . λ x14 x15 x16 . setsum 0 (Inj1 (Inj0 0))) x11) (x3 (λ x9 x10 . λ x11 : (ι → ι) → ι . setsum x9 (Inj1 (x1 (λ x12 : ι → (ι → ι → ι) → ι . λ x13 x14 x15 . 0) 0))) 0 (λ x9 : (ι → ι) → ι → ι . λ x10 . x7)) = x3 (λ x9 x10 . λ x11 : (ι → ι) → ι . setsum (x1 (λ x12 : ι → (ι → ι → ι) → ι . λ x13 x14 x15 . x15) x7) (x2 (λ x12 . x10) (x0 (λ x12 : ι → (ι → ι) → ι . λ x13 . λ x14 : ι → ι . λ x15 x16 . 0) (λ x12 x13 . 0) (Inj1 0) (x1 (λ x12 : ι → (ι → ι → ι) → ι . λ x13 x14 x15 . 0) 0) (x1 (λ x12 : ι → (ι → ι → ι) → ι . λ x13 x14 x15 . 0) 0) x7) (λ x12 . x12))) (x1 (λ x9 : ι → (ι → ι → ι) → ι . λ x10 x11 x12 . x12) 0) (λ x9 : (ι → ι) → ι → ι . λ x10 . x3 (λ x11 x12 . λ x13 : (ι → ι) → ι . x1 (λ x14 : ι → (ι → ι → ι) → ι . λ x15 x16 x17 . x0 (λ x18 : ι → (ι → ι) → ι . λ x19 . λ x20 : ι → ι . λ x21 x22 . 0) (λ x18 x19 . x1 (λ x20 : ι → (ι → ι → ι) → ι . λ x21 x22 x23 . 0) 0) (x0 (λ x18 : ι → (ι → ι) → ι . λ x19 . λ x20 : ι → ι . λ x21 x22 . 0) (λ x18 x19 . 0) 0 0 0 0) x15 (x2 (λ x18 . 0) 0 (λ x18 . 0)) (x14 0 (λ x18 x19 . 0))) (x2 (λ x14 . 0) 0 (λ x14 . x14))) x10 (λ x11 : (ι → ι) → ι → ι . λ x12 . setsum (setsum (x0 (λ x13 : ι → (ι → ι) → ι . λ x14 . λ x15 : ι → ι . λ x16 x17 . 0) (λ x13 x14 . 0) 0 0 0 0) (x0 (λ x13 : ι → (ι → ι) → ι . λ x14 . λ x15 : ι → ι . λ x16 x17 . 0) (λ x13 x14 . 0) 0 0 0 0)) (x0 (λ x13 : ι → (ι → ι) → ι . λ x14 . λ x15 : ι → ι . λ x16 x17 . Inj0 0) (λ x13 x14 . x13) (setsum 0 0) (x0 (λ x13 : ι → (ι → ι) → ι . λ x14 . λ x15 : ι → ι . λ x16 x17 . 0) (λ x13 x14 . 0) 0 0 0 0) x10 x12)))) ⟶ (∀ x4 : ι → ι → ι → ι → ι . ∀ x5 x6 x7 . x0 (λ x9 : ι → (ι → ι) → ι . λ x10 . λ x11 : ι → ι . λ x12 x13 . 0) (λ x9 x10 . setsum (setsum (x2 (λ x11 . x7) x10 (λ x11 . Inj1 0)) (x2 (λ x11 . x11) 0 (λ x11 . x11))) (setsum 0 (x1 (λ x11 : ι → (ι → ι → ι) → ι . λ x12 x13 x14 . x14) (setsum 0 0)))) 0 (x4 (Inj1 (x1 (λ x9 : ι → (ι → ι → ι) → ι . λ x10 x11 x12 . Inj0 0) 0)) x5 x5 (x4 0 (x2 (λ x9 . x7) 0 (λ x9 . x7)) 0 (x3 (λ x9 x10 . λ x11 : (ι → ι) → ι . x0 (λ x12 : ι → (ι → ι) → ι . λ x13 . λ x14 : ι → ι . λ x15 x16 . 0) (λ x12 x13 . 0) 0 0 0 0) (Inj1 0) (λ x9 : (ι → ι) → ι → ι . λ x10 . x2 (λ x11 . 0) 0 (λ x11 . 0))))) (setsum (setsum x7 (setsum x7 (x2 (λ x9 . 0) 0 (λ x9 . 0)))) (Inj1 (x1 (λ x9 : ι → (ι → ι → ι) → ι . λ x10 x11 x12 . 0) (x3 (λ x9 x10 . λ x11 : (ι → ι) → ι . 0) 0 (λ x9 : (ι → ι) → ι → ι . λ x10 . 0))))) (setsum 0 0) = Inj0 x5) ⟶ (∀ x4 : (((ι → ι) → ι) → (ι → ι) → ι → ι) → ((ι → ι) → ι) → ι . ∀ x5 : (((ι → ι) → ι) → ι) → ι . ∀ x6 x7 . x0 (λ x9 : ι → (ι → ι) → ι . λ x10 . λ x11 : ι → ι . λ x12 x13 . setsum 0 (x2 (λ x14 . x2 (λ x15 . Inj1 0) x12 (λ x15 . x14)) x13 (λ x14 . 0))) (λ x9 x10 . setsum (x3 (λ x11 x12 . λ x13 : (ι → ι) → ι . Inj0 (x13 (λ x14 . 0))) (x1 (λ x11 : ι → (ι → ι → ι) → ι . λ x12 x13 x14 . Inj0 0) (Inj1 0)) (λ x11 : (ι → ι) → ι → ι . λ x12 . setsum (x1 (λ x13 : ι → (ι → ι → ι) → ι . λ x14 x15 x16 . 0) 0) 0)) 0) (x3 (λ x9 x10 . λ x11 : (ι → ι) → ι . x2 (λ x12 . x12) 0 (λ x12 . x2 (λ x13 . x13) (x2 (λ x13 . 0) 0 (λ x13 . 0)) (λ x13 . x0 (λ x14 : ι → (ι → ι) → ι . λ x15 . λ x16 : ι → ι . λ x17 x18 . 0) (λ x14 x15 . 0) 0 0 0 0))) (Inj1 (x5 (λ x9 : (ι → ι) → ι . x3 (λ x10 x11 . λ x12 : (ι → ι) → ι . 0) 0 (λ x10 : (ι → ι) → ι → ι . λ x11 . 0)))) (λ x9 : (ι → ι) → ι → ι . λ x10 . setsum (x2 (λ x11 . x3 (λ x12 x13 . λ x14 : (ι → ι) → ι . 0) 0 (λ x12 : (ι → ι) → ι → ι . λ x13 . 0)) (x1 (λ x11 : ι → (ι → ι → ι) → ι . λ x12 x13 x14 . 0) 0) (λ x11 . x3 (λ x12 x13 . λ x14 : (ι → ι) → ι . 0) 0 (λ x12 : (ι → ι) → ι → ι . λ x13 . 0))) 0)) (x3 (λ x9 x10 . λ x11 : (ι → ι) → ι . x10) (Inj1 (x4 (λ x9 : (ι → ι) → ι . λ x10 : ι → ι . λ x11 . x11) (λ x9 : ι → ι . 0))) (λ x9 : (ι → ι) → ι → ι . λ x10 . x1 (λ x11 : ι → (ι → ι → ι) → ι . λ x12 x13 x14 . 0) (x2 (λ x11 . 0) 0 (λ x11 . x9 (λ x12 . 0) 0)))) 0 0 = x3 (λ x9 x10 . λ x11 : (ι → ι) → ι . x3 (λ x12 x13 . λ x14 : (ι → ι) → ι . 0) (setsum (x0 (λ x12 : ι → (ι → ι) → ι . λ x13 . λ x14 : ι → ι . λ x15 x16 . x3 (λ x17 x18 . λ x19 : (ι → ι) → ι . 0) 0 (λ x17 : (ι → ι) → ι → ι . λ x18 . 0)) (λ x12 x13 . x13) (x2 (λ x12 . 0) 0 (λ x12 . 0)) x9 x10 (x1 (λ x12 : ι → (ι → ι → ι) → ι . λ x13 x14 x15 . 0) 0)) (x2 (λ x12 . x11 (λ x13 . 0)) 0 (λ x12 . 0))) (λ x12 : (ι → ι) → ι → ι . λ x13 . x2 (λ x14 . 0) (x1 (λ x14 : ι → (ι → ι → ι) → ι . λ x15 x16 x17 . x0 (λ x18 : ι → (ι → ι) → ι . λ x19 . λ x20 : ι → ι . λ x21 x22 . 0) (λ x18 x19 . 0) 0 0 0 0) (x11 (λ x14 . 0))) (λ x14 . Inj0 (x11 (λ x15 . 0))))) (x5 (λ x9 : (ι → ι) → ι . 0)) (λ x9 : (ι → ι) → ι → ι . λ x10 . x7)) ⟶ False (proof)Theorem 63aac.. : ∀ x0 : (ι → ι → ι → ι) → ι → ι → ι → ι . ∀ x1 : (ι → (ι → ι) → ι) → (ι → ι → ι → ι → ι) → ι . ∀ x2 : (ι → (ι → ι) → ((ι → ι) → ι) → (ι → ι) → ι → ι) → (ι → ι) → ι . ∀ x3 : (ι → ι) → ι → ι → ι . (∀ x4 x5 x6 x7 . x3 (λ x9 . x3 (λ x10 . x7) (x3 (λ x10 . x7) 0 (Inj0 0)) x5) 0 (setsum (Inj0 (setsum (x0 (λ x9 x10 x11 . 0) 0 0 0) x5)) (x1 (λ x9 . λ x10 : ι → ι . x2 (λ x11 . λ x12 : ι → ι . λ x13 : (ι → ι) → ι . λ x14 : ι → ι . λ x15 . setsum 0 0) (λ x11 . x11)) (λ x9 x10 x11 x12 . x2 (λ x13 . λ x14 : ι → ι . λ x15 : (ι → ι) → ι . λ x16 : ι → ι . λ x17 . x15 (λ x18 . 0)) (λ x13 . x13)))) = setsum (x0 (λ x9 x10 x11 . 0) x6 0 (setsum 0 (Inj0 (Inj1 0)))) x7) ⟶ (∀ x4 : ((ι → ι) → (ι → ι) → ι → ι) → ι . ∀ x5 : (((ι → ι) → ι → ι) → ι → ι) → ι → (ι → ι) → ι . ∀ x6 : (((ι → ι) → ι) → (ι → ι) → ι) → ι . ∀ x7 . x3 (λ x9 . x6 (λ x10 : (ι → ι) → ι . λ x11 : ι → ι . x2 (λ x12 . λ x13 : ι → ι . λ x14 : (ι → ι) → ι . λ x15 : ι → ι . λ x16 . 0) (λ x12 . x10 (λ x13 . x1 (λ x14 . λ x15 : ι → ι . 0) (λ x14 x15 x16 x17 . 0))))) (setsum (setsum 0 0) (x5 (λ x9 : (ι → ι) → ι → ι . λ x10 . x2 (λ x11 . λ x12 : ι → ι . λ x13 : (ι → ι) → ι . λ x14 : ι → ι . λ x15 . 0) (λ x11 . setsum 0 0)) (x3 (λ x9 . x9) x7 (Inj1 0)) (λ x9 . 0))) (x3 (λ x9 . x6 (λ x10 : (ι → ι) → ι . λ x11 : ι → ι . x3 (λ x12 . Inj0 0) (x11 0) (x2 (λ x12 . λ x13 : ι → ι . λ x14 : (ι → ι) → ι . λ x15 : ι → ι . λ x16 . 0) (λ x12 . 0)))) (x6 (λ x9 : (ι → ι) → ι . λ x10 : ι → ι . setsum 0 (x0 (λ x11 x12 x13 . 0) 0 0 0))) (setsum (x5 (λ x9 : (ι → ι) → ι → ι . λ x10 . x9 (λ x11 . 0) 0) (setsum 0 0) (λ x9 . x1 (λ x10 . λ x11 : ι → ι . 0) (λ x10 x11 x12 x13 . 0))) (Inj0 0))) = Inj0 (x2 (λ x9 . λ x10 : ι → ι . λ x11 : (ι → ι) → ι . λ x12 : ι → ι . λ x13 . x2 (λ x14 . λ x15 : ι → ι . λ x16 : (ι → ι) → ι . λ x17 : ι → ι . λ x18 . 0) (λ x14 . x11 (λ x15 . x12 0))) (λ x9 . 0))) ⟶ (∀ x4 : ι → ι . ∀ x5 x6 x7 . x2 (λ x9 . λ x10 : ι → ι . λ x11 : (ι → ι) → ι . λ x12 : ι → ι . λ x13 . Inj1 (Inj1 0)) (λ x9 . x5) = Inj0 (x3 Inj1 (setsum (setsum (x1 (λ x9 . λ x10 : ι → ι . 0) (λ x9 x10 x11 x12 . 0)) (x2 (λ x9 . λ x10 : ι → ι . λ x11 : (ι → ι) → ι . λ x12 : ι → ι . λ x13 . 0) (λ x9 . 0))) (x2 (λ x9 . λ x10 : ι → ι . λ x11 : (ι → ι) → ι . λ x12 : ι → ι . λ x13 . x13) (λ x9 . x1 (λ x10 . λ x11 : ι → ι . 0) (λ x10 x11 x12 x13 . 0)))) (x3 (λ x9 . x2 (λ x10 . λ x11 : ι → ι . λ x12 : (ι → ι) → ι . λ x13 : ι → ι . λ x14 . 0) (λ x10 . x2 (λ x11 . λ x12 : ι → ι . λ x13 : (ι → ι) → ι . λ x14 : ι → ι . λ x15 . 0) (λ x11 . 0))) (x2 (λ x9 . λ x10 : ι → ι . λ x11 : (ι → ι) → ι . λ x12 : ι → ι . λ x13 . x12 0) (λ x9 . x9)) (setsum (x0 (λ x9 x10 x11 . 0) 0 0 0) (x2 (λ x9 . λ x10 : ι → ι . λ x11 : (ι → ι) → ι . λ x12 : ι → ι . λ x13 . 0) (λ x9 . 0)))))) ⟶ (∀ x4 : (ι → (ι → ι) → ι → ι) → ι → ι → ι → ι . ∀ x5 : ((ι → ι) → (ι → ι) → ι) → ((ι → ι) → ι → ι) → (ι → ι) → ι → ι . ∀ x6 x7 . x2 (λ x9 . λ x10 : ι → ι . λ x11 : (ι → ι) → ι . λ x12 : ι → ι . λ x13 . Inj0 (x11 (λ x14 . Inj0 (x0 (λ x15 x16 x17 . 0) 0 0 0)))) (λ x9 . x7) = Inj1 (setsum 0 (setsum x7 x6))) ⟶ (∀ x4 x5 . ∀ x6 : ι → (ι → ι) → ι → ι → ι . ∀ x7 : (ι → ι → ι) → ι → ι . x1 (λ x9 . λ x10 : ι → ι . 0) (λ x9 x10 x11 x12 . x9) = setsum (Inj0 0) (x1 (λ x9 . λ x10 : ι → ι . x3 (λ x11 . x1 (λ x12 . λ x13 : ι → ι . x2 (λ x14 . λ x15 : ι → ι . λ x16 : (ι → ι) → ι . λ x17 : ι → ι . λ x18 . 0) (λ x14 . 0)) (λ x12 x13 x14 x15 . x13)) (setsum (setsum 0 0) (x2 (λ x11 . λ x12 : ι → ι . λ x13 : (ι → ι) → ι . λ x14 : ι → ι . λ x15 . 0) (λ x11 . 0))) 0) (λ x9 x10 x11 x12 . Inj0 (x0 (λ x13 x14 x15 . x12) (setsum 0 0) 0 (x3 (λ x13 . 0) 0 0))))) ⟶ (∀ x4 . ∀ x5 : (ι → ι) → ι → (ι → ι) → ι . ∀ x6 : ι → ((ι → ι) → ι → ι) → ι . ∀ x7 : ((ι → ι) → ι → ι → ι) → ι → ι . x1 (λ x9 . λ x10 : ι → ι . setsum 0 0) (λ x9 x10 x11 x12 . x12) = x6 (setsum (x5 (λ x9 . 0) (setsum 0 (Inj1 0)) (λ x9 . x9)) 0) (λ x9 : ι → ι . λ x10 . x1 (λ x11 . λ x12 : ι → ι . x11) (λ x11 x12 x13 x14 . x3 (λ x15 . x2 (λ x16 . λ x17 : ι → ι . λ x18 : (ι → ι) → ι . λ x19 : ι → ι . λ x20 . x18 (λ x21 . 0)) (λ x16 . Inj0 0)) x11 (setsum x11 0)))) ⟶ (∀ x4 : (ι → (ι → ι) → ι → ι) → ι . ∀ x5 . ∀ x6 : ι → ι . ∀ x7 : (((ι → ι) → ι → ι) → ι) → ι . x0 (λ x9 x10 x11 . x9) (x6 (x0 (λ x9 x10 x11 . setsum x11 x11) 0 0 (x4 (λ x9 . λ x10 : ι → ι . λ x11 . x11)))) (x1 (λ x9 . λ x10 : ι → ι . 0) (λ x9 x10 x11 x12 . setsum x10 (x0 (λ x13 x14 x15 . x14) x10 x11 0))) (x7 (λ x9 : (ι → ι) → ι → ι . 0)) = setsum (x7 (λ x9 : (ι → ι) → ι → ι . 0)) (setsum (Inj0 0) 0)) ⟶ (∀ x4 x5 . ∀ x6 : ι → ι → ι → ι → ι . ∀ x7 : (ι → ι) → ((ι → ι) → ι) → ι . x0 (λ x9 x10 x11 . setsum (x3 (λ x12 . 0) (x3 (λ x12 . Inj1 0) x9 (x3 (λ x12 . 0) 0 0)) (x3 (λ x12 . 0) (setsum 0 0) x9)) 0) (x0 (λ x9 x10 x11 . x11) 0 (x2 (λ x9 . λ x10 : ι → ι . λ x11 : (ι → ι) → ι . λ x12 : ι → ι . λ x13 . 0) (λ x9 . 0)) (x1 (λ x9 . λ x10 : ι → ι . Inj0 (setsum 0 0)) (λ x9 x10 x11 x12 . setsum x10 (setsum 0 0)))) (x1 (λ x9 . λ x10 : ι → ι . x0 (λ x11 x12 x13 . 0) (Inj0 0) (x2 (λ x11 . λ x12 : ι → ι . λ x13 : (ι → ι) → ι . λ x14 : ι → ι . λ x15 . x12 0) (λ x11 . x11)) (Inj0 0)) (λ x9 x10 x11 x12 . x3 (λ x13 . x1 (λ x14 . λ x15 : ι → ι . x2 (λ x16 . λ x17 : ι → ι . λ x18 : (ι → ι) → ι . λ x19 : ι → ι . λ x20 . 0) (λ x16 . 0)) (λ x14 x15 x16 x17 . x3 (λ x18 . 0) 0 0)) x10 x10)) 0 = setsum (setsum x5 0) 0) ⟶ False (proof)Theorem e3c3e.. : ∀ x0 : ((ι → (ι → ι) → ι) → ι) → ι → ι → ι . ∀ x1 : (((ι → ι → ι) → (ι → ι → ι) → ι → ι) → ((ι → ι → ι) → (ι → ι) → ι) → ι → ι → ι) → ι → ((ι → ι → ι) → ι) → ι . ∀ x2 : (ι → ((ι → ι) → ι → ι) → ((ι → ι) → ι → ι) → ι) → ι → ((ι → ι) → ι) → ι . ∀ x3 : ((((ι → ι) → (ι → ι) → ι) → ι) → ι → (ι → ι → ι) → ι) → (ι → ι → (ι → ι) → ι) → (((ι → ι) → ι → ι) → ι) → ι . (∀ x4 x5 . ∀ x6 : (((ι → ι) → ι → ι) → ι → ι) → ι → ι → ι . ∀ x7 : ι → ι → (ι → ι) → ι → ι . x3 (λ x9 : ((ι → ι) → (ι → ι) → ι) → ι . λ x10 . λ x11 : ι → ι → ι . x9 (λ x12 x13 : ι → ι . x12 (x11 (x0 (λ x14 : ι → (ι → ι) → ι . 0) 0 0) 0))) (λ x9 x10 . λ x11 : ι → ι . 0) (λ x9 : (ι → ι) → ι → ι . 0) = x5) ⟶ (∀ x4 : ι → ι . ∀ x5 : (((ι → ι) → ι) → ι) → ι → ι . ∀ x6 x7 . x3 (λ x9 : ((ι → ι) → (ι → ι) → ι) → ι . λ x10 . λ x11 : ι → ι → ι . x1 (λ x12 : (ι → ι → ι) → (ι → ι → ι) → ι → ι . λ x13 : (ι → ι → ι) → (ι → ι) → ι . λ x14 x15 . x13 (λ x16 x17 . x16) (λ x16 . x16)) (setsum (x9 (λ x12 x13 : ι → ι . setsum 0 0)) 0) (λ x12 : ι → ι → ι . x9 (λ x13 x14 : ι → ι . Inj1 (x0 (λ x15 : ι → (ι → ι) → ι . 0) 0 0)))) (λ x9 x10 . λ x11 : ι → ι . x2 (λ x12 . λ x13 x14 : (ι → ι) → ι → ι . Inj1 0) (x3 (λ x12 : ((ι → ι) → (ι → ι) → ι) → ι . λ x13 . λ x14 : ι → ι → ι . 0) (λ x12 x13 . λ x14 : ι → ι . 0) (λ x12 : (ι → ι) → ι → ι . x2 (λ x13 . λ x14 x15 : (ι → ι) → ι → ι . x2 (λ x16 . λ x17 x18 : (ι → ι) → ι → ι . 0) 0 (λ x16 : ι → ι . 0)) (x12 (λ x13 . 0) 0) (λ x13 : ι → ι . 0))) (λ x12 : ι → ι . 0)) (λ x9 : (ι → ι) → ι → ι . setsum (Inj1 x6) (Inj1 (setsum (x0 (λ x10 : ι → (ι → ι) → ι . 0) 0 0) 0))) = Inj0 x6) ⟶ (∀ x4 . ∀ x5 : ((ι → ι) → ι → ι) → ι . ∀ x6 x7 : ι → ι . x2 (λ x9 . λ x10 x11 : (ι → ι) → ι → ι . x3 (λ x12 : ((ι → ι) → (ι → ι) → ι) → ι . λ x13 . λ x14 : ι → ι → ι . x13) (λ x12 x13 . λ x14 : ι → ι . 0) (λ x12 : (ι → ι) → ι → ι . setsum (x0 (λ x13 : ι → (ι → ι) → ι . 0) (x11 (λ x13 . 0) 0) (x11 (λ x13 . 0) 0)) 0)) (x0 (λ x9 : ι → (ι → ι) → ι . x7 0) (setsum 0 0) (Inj1 0)) (λ x9 : ι → ι . setsum (x7 (Inj0 (x5 (λ x10 : ι → ι . λ x11 . 0)))) (Inj0 (x3 (λ x10 : ((ι → ι) → (ι → ι) → ι) → ι . λ x11 . λ x12 : ι → ι → ι . setsum 0 0) (λ x10 x11 . λ x12 : ι → ι . setsum 0 0) (λ x10 : (ι → ι) → ι → ι . Inj1 0)))) = setsum (x5 (λ x9 : ι → ι . λ x10 . x3 (λ x11 : ((ι → ι) → (ι → ι) → ι) → ι . λ x12 . λ x13 : ι → ι → ι . 0) (λ x11 x12 . λ x13 : ι → ι . x11) (λ x11 : (ι → ι) → ι → ι . x9 (x0 (λ x12 : ι → (ι → ι) → ι . 0) 0 0)))) (setsum (x0 (λ x9 : ι → (ι → ι) → ι . x9 (x0 (λ x10 : ι → (ι → ι) → ι . 0) 0 0) (λ x10 . x3 (λ x11 : ((ι → ι) → (ι → ι) → ι) → ι . λ x12 . λ x13 : ι → ι → ι . 0) (λ x11 x12 . λ x13 : ι → ι . 0) (λ x11 : (ι → ι) → ι → ι . 0))) (Inj0 (x0 (λ x9 : ι → (ι → ι) → ι . 0) 0 0)) (x7 (setsum 0 0))) (setsum (x0 (λ x9 : ι → (ι → ι) → ι . setsum 0 0) (Inj0 0) (x7 0)) (setsum (x5 (λ x9 : ι → ι . λ x10 . 0)) 0)))) ⟶ (∀ x4 : (ι → ι) → ι → ι . ∀ x5 : (ι → (ι → ι) → ι) → ι . ∀ x6 : ι → ι . ∀ x7 : (ι → ι) → ι . x2 (λ x9 . λ x10 x11 : (ι → ι) → ι → ι . x2 (λ x12 . λ x13 x14 : (ι → ι) → ι → ι . x12) (setsum 0 (setsum (setsum 0 0) 0)) (λ x12 : ι → ι . Inj0 (x12 0))) (x4 (λ x9 . x3 (λ x10 : ((ι → ι) → (ι → ι) → ι) → ι . λ x11 . λ x12 : ι → ι → ι . x10 (λ x13 x14 : ι → ι . x11)) (λ x10 x11 . λ x12 : ι → ι . x0 (λ x13 : ι → (ι → ι) → ι . 0) x10 0) (λ x10 : (ι → ι) → ι → ι . x9)) 0) (λ x9 : ι → ι . Inj0 (x0 (λ x10 : ι → (ι → ι) → ι . x3 (λ x11 : ((ι → ι) → (ι → ι) → ι) → ι . λ x12 . λ x13 : ι → ι → ι . 0) (λ x11 x12 . λ x13 : ι → ι . x2 (λ x14 . λ x15 x16 : (ι → ι) → ι → ι . 0) 0 (λ x14 : ι → ι . 0)) (λ x11 : (ι → ι) → ι → ι . x7 (λ x12 . 0))) (setsum 0 (setsum 0 0)) 0)) = x2 (λ x9 . λ x10 x11 : (ι → ι) → ι → ι . x0 (λ x12 : ι → (ι → ι) → ι . x2 (λ x13 . λ x14 x15 : (ι → ι) → ι → ι . x15 (λ x16 . 0) (x3 (λ x16 : ((ι → ι) → (ι → ι) → ι) → ι . λ x17 . λ x18 : ι → ι → ι . 0) (λ x16 x17 . λ x18 : ι → ι . 0) (λ x16 : (ι → ι) → ι → ι . 0))) x9 (λ x13 : ι → ι . x1 (λ x14 : (ι → ι → ι) → (ι → ι → ι) → ι → ι . λ x15 : (ι → ι → ι) → (ι → ι) → ι . λ x16 x17 . 0) 0 (λ x14 : ι → ι → ι . x1 (λ x15 : (ι → ι → ι) → (ι → ι → ι) → ι → ι . λ x16 : (ι → ι → ι) → (ι → ι) → ι . λ x17 x18 . 0) 0 (λ x15 : ι → ι → ι . 0)))) (x0 (λ x12 : ι → (ι → ι) → ι . setsum (x11 (λ x13 . 0) 0) (Inj0 0)) (Inj1 (x1 (λ x12 : (ι → ι → ι) → (ι → ι → ι) → ι → ι . λ x13 : (ι → ι → ι) → (ι → ι) → ι . λ x14 x15 . 0) 0 (λ x12 : ι → ι → ι . 0))) (Inj1 0)) (x1 (λ x12 : (ι → ι → ι) → (ι → ι → ι) → ι → ι . λ x13 : (ι → ι → ι) → (ι → ι) → ι . λ x14 x15 . setsum (x12 (λ x16 x17 . 0) (λ x16 x17 . 0) 0) (Inj0 0)) (setsum x9 0) (λ x12 : ι → ι → ι . x1 (λ x13 : (ι → ι → ι) → (ι → ι → ι) → ι → ι . λ x14 : (ι → ι → ι) → (ι → ι) → ι . λ x15 x16 . setsum 0 0) 0 (λ x13 : ι → ι → ι . x2 (λ x14 . λ x15 x16 : (ι → ι) → ι → ι . 0) 0 (λ x14 : ι → ι . 0))))) (setsum (setsum (x3 (λ x9 : ((ι → ι) → (ι → ι) → ι) → ι . λ x10 . λ x11 : ι → ι → ι . 0) (λ x9 x10 . λ x11 : ι → ι . 0) (λ x9 : (ι → ι) → ι → ι . 0)) 0) (x7 (λ x9 . setsum x9 (x5 (λ x10 . λ x11 : ι → ι . 0))))) (λ x9 : ι → ι . setsum (x7 (λ x10 . 0)) (Inj0 (Inj0 (x2 (λ x10 . λ x11 x12 : (ι → ι) → ι → ι . 0) 0 (λ x10 : ι → ι . 0)))))) ⟶ (∀ x4 : ((ι → ι) → ι → ι) → ι . ∀ x5 : ((ι → ι → ι) → ι → ι) → ι → ι . ∀ x6 x7 . x1 (λ x9 : (ι → ι → ι) → (ι → ι → ι) → ι → ι . λ x10 : (ι → ι → ι) → (ι → ι) → ι . λ x11 x12 . x2 (λ x13 . λ x14 x15 : (ι → ι) → ι → ι . 0) (x9 (λ x13 x14 . x14) (λ x13 x14 . 0) (Inj0 (x1 (λ x13 : (ι → ι → ι) → (ι → ι → ι) → ι → ι . λ x14 : (ι → ι → ι) → (ι → ι) → ι . λ x15 x16 . 0) 0 (λ x13 : ι → ι → ι . 0)))) (λ x13 : ι → ι . x3 (λ x14 : ((ι → ι) → (ι → ι) → ι) → ι . λ x15 . λ x16 : ι → ι → ι . 0) (λ x14 x15 . λ x16 : ι → ι . setsum (Inj1 0) (setsum 0 0)) (λ x14 : (ι → ι) → ι → ι . Inj1 (x2 (λ x15 . λ x16 x17 : (ι → ι) → ι → ι . 0) 0 (λ x15 : ι → ι . 0))))) (x3 (λ x9 : ((ι → ι) → (ι → ι) → ι) → ι . λ x10 . λ x11 : ι → ι → ι . setsum (Inj1 (x11 0 0)) 0) (λ x9 x10 . λ x11 : ι → ι . x1 (λ x12 : (ι → ι → ι) → (ι → ι → ι) → ι → ι . λ x13 : (ι → ι → ι) → (ι → ι) → ι . λ x14 x15 . x15) 0 (λ x12 : ι → ι → ι . x10)) (λ x9 : (ι → ι) → ι → ι . x1 (λ x10 : (ι → ι → ι) → (ι → ι → ι) → ι → ι . λ x11 : (ι → ι → ι) → (ι → ι) → ι . λ x12 x13 . x12) x6 (λ x10 : ι → ι → ι . setsum (x3 (λ x11 : ((ι → ι) → (ι → ι) → ι) → ι . λ x12 . λ x13 : ι → ι → ι . 0) (λ x11 x12 . λ x13 : ι → ι . 0) (λ x11 : (ι → ι) → ι → ι . 0)) 0))) (λ x9 : ι → ι → ι . 0) = x2 (λ x9 . λ x10 x11 : (ι → ι) → ι → ι . Inj1 (setsum (x0 (λ x12 : ι → (ι → ι) → ι . x12 0 (λ x13 . 0)) 0 (x2 (λ x12 . λ x13 x14 : (ι → ι) → ι → ι . 0) 0 (λ x12 : ι → ι . 0))) (x3 (λ x12 : ((ι → ι) → (ι → ι) → ι) → ι . λ x13 . λ x14 : ι → ι → ι . Inj0 0) (λ x12 x13 . λ x14 : ι → ι . x11 (λ x15 . 0) 0) (λ x12 : (ι → ι) → ι → ι . x1 (λ x13 : (ι → ι → ι) → (ι → ι → ι) → ι → ι . λ x14 : (ι → ι → ι) → (ι → ι) → ι . λ x15 x16 . 0) 0 (λ x13 : ι → ι → ι . 0))))) (setsum (x2 (λ x9 . λ x10 x11 : (ι → ι) → ι → ι . Inj1 (setsum 0 0)) x7 (λ x9 : ι → ι . Inj0 (setsum 0 0))) (Inj0 (x5 (λ x9 : ι → ι → ι . λ x10 . Inj1 0) 0))) (λ x9 : ι → ι . x1 (λ x10 : (ι → ι → ι) → (ι → ι → ι) → ι → ι . λ x11 : (ι → ι → ι) → (ι → ι) → ι . λ x12 x13 . x13) (Inj0 0) (λ x10 : ι → ι → ι . x7))) ⟶ (∀ x4 . ∀ x5 : (ι → ι → ι → ι) → ι → (ι → ι) → ι . ∀ x6 : ι → ι . ∀ x7 : (((ι → ι) → ι → ι) → (ι → ι) → ι) → ι . x1 (λ x9 : (ι → ι → ι) → (ι → ι → ι) → ι → ι . λ x10 : (ι → ι → ι) → (ι → ι) → ι . λ x11 x12 . x2 (λ x13 . λ x14 x15 : (ι → ι) → ι → ι . setsum (x14 (λ x16 . 0) (x14 (λ x16 . 0) 0)) (x15 (λ x16 . Inj0 0) (x1 (λ x16 : (ι → ι → ι) → (ι → ι → ι) → ι → ι . λ x17 : (ι → ι → ι) → (ι → ι) → ι . λ x18 x19 . 0) 0 (λ x16 : ι → ι → ι . 0)))) (x0 (λ x13 : ι → (ι → ι) → ι . 0) (setsum x11 (x10 (λ x13 x14 . 0) (λ x13 . 0))) (x1 (λ x13 : (ι → ι → ι) → (ι → ι → ι) → ι → ι . λ x14 : (ι → ι → ι) → (ι → ι) → ι . λ x15 x16 . 0) (x10 (λ x13 x14 . 0) (λ x13 . 0)) (λ x13 : ι → ι → ι . 0))) (λ x13 : ι → ι . x0 (λ x14 : ι → (ι → ι) → ι . setsum 0 (x0 (λ x15 : ι → (ι → ι) → ι . 0) 0 0)) (x1 (λ x14 : (ι → ι → ι) → (ι → ι → ι) → ι → ι . λ x15 : (ι → ι → ι) → (ι → ι) → ι . λ x16 x17 . Inj0 0) (Inj1 0) (λ x14 : ι → ι → ι . 0)) (setsum (x1 (λ x14 : (ι → ι → ι) → (ι → ι → ι) → ι → ι . λ x15 : (ι → ι → ι) → (ι → ι) → ι . λ x16 x17 . 0) 0 (λ x14 : ι → ι → ι . 0)) 0))) 0 (λ x9 : ι → ι → ι . 0) = setsum (x2 (λ x9 . λ x10 x11 : (ι → ι) → ι → ι . x0 (λ x12 : ι → (ι → ι) → ι . Inj0 (Inj1 0)) (setsum (setsum 0 0) (setsum 0 0)) (x2 (λ x12 . λ x13 x14 : (ι → ι) → ι → ι . x3 (λ x15 : ((ι → ι) → (ι → ι) → ι) → ι . λ x16 . λ x17 : ι → ι → ι . 0) (λ x15 x16 . λ x17 : ι → ι . 0) (λ x15 : (ι → ι) → ι → ι . 0)) (x7 (λ x12 : (ι → ι) → ι → ι . λ x13 : ι → ι . 0)) (λ x12 : ι → ι . 0))) (x6 0) (λ x9 : ι → ι . setsum (x2 (λ x10 . λ x11 x12 : (ι → ι) → ι → ι . setsum 0 0) 0 (λ x10 : ι → ι . x3 (λ x11 : ((ι → ι) → (ι → ι) → ι) → ι . λ x12 . λ x13 : ι → ι → ι . 0) (λ x11 x12 . λ x13 : ι → ι . 0) (λ x11 : (ι → ι) → ι → ι . 0))) (x2 (λ x10 . λ x11 x12 : (ι → ι) → ι → ι . x10) (setsum 0 0) (λ x10 : ι → ι . x9 0)))) 0) ⟶ (∀ x4 : ι → ι → ι . ∀ x5 : (ι → ι → ι) → ι → ι . ∀ x6 : ι → ι . ∀ x7 . x0 (λ x9 : ι → (ι → ι) → ι . 0) (x5 (λ x9 x10 . setsum x9 0) 0) (Inj1 (setsum (x3 (λ x9 : ((ι → ι) → (ι → ι) → ι) → ι . λ x10 . λ x11 : ι → ι → ι . x2 (λ x12 . λ x13 x14 : (ι → ι) → ι → ι . 0) 0 (λ x12 : ι → ι . 0)) (λ x9 x10 . λ x11 : ι → ι . x9) (λ x9 : (ι → ι) → ι → ι . x9 (λ x10 . 0) 0)) (Inj1 (x0 (λ x9 : ι → (ι → ι) → ι . 0) 0 0)))) = x5 (λ x9 x10 . x6 (x1 (λ x11 : (ι → ι → ι) → (ι → ι → ι) → ι → ι . λ x12 : (ι → ι → ι) → (ι → ι) → ι . λ x13 x14 . x1 (λ x15 : (ι → ι → ι) → (ι → ι → ι) → ι → ι . λ x16 : (ι → ι → ι) → (ι → ι) → ι . λ x17 x18 . x2 (λ x19 . λ x20 x21 : (ι → ι) → ι → ι . 0) 0 (λ x19 : ι → ι . 0)) (Inj0 0) (λ x15 : ι → ι → ι . x13)) (x1 (λ x11 : (ι → ι → ι) → (ι → ι → ι) → ι → ι . λ x12 : (ι → ι → ι) → (ι → ι) → ι . λ x13 x14 . x2 (λ x15 . λ x16 x17 : (ι → ι) → ι → ι . 0) 0 (λ x15 : ι → ι . 0)) (Inj0 0) (λ x11 : ι → ι → ι . x3 (λ x12 : ((ι → ι) → (ι → ι) → ι) → ι . λ x13 . λ x14 : ι → ι → ι . 0) (λ x12 x13 . λ x14 : ι → ι . 0) (λ x12 : (ι → ι) → ι → ι . 0))) (λ x11 : ι → ι → ι . x9))) (x4 0 (Inj1 0))) ⟶ (∀ x4 x5 . ∀ x6 x7 : ι → ι . x0 (λ x9 : ι → (ι → ι) → ι . x2 (λ x10 . λ x11 x12 : (ι → ι) → ι → ι . x3 (λ x13 : ((ι → ι) → (ι → ι) → ι) → ι . λ x14 . λ x15 : ι → ι → ι . Inj1 (x2 (λ x16 . λ x17 x18 : (ι → ι) → ι → ι . 0) 0 (λ x16 : ι → ι . 0))) (λ x13 x14 . λ x15 : ι → ι . x1 (λ x16 : (ι → ι → ι) → (ι → ι → ι) → ι → ι . λ x17 : (ι → ι → ι) → (ι → ι) → ι . λ x18 x19 . x18) 0 (λ x16 : ι → ι → ι . x2 (λ x17 . λ x18 x19 : (ι → ι) → ι → ι . 0) 0 (λ x17 : ι → ι . 0))) (λ x13 : (ι → ι) → ι → ι . 0)) (x6 0) (λ x10 : ι → ι . x10 0)) (x3 (λ x9 : ((ι → ι) → (ι → ι) → ι) → ι . λ x10 . λ x11 : ι → ι → ι . x9 (λ x12 x13 : ι → ι . 0)) (λ x9 x10 . λ x11 : ι → ι . x9) (λ x9 : (ι → ι) → ι → ι . x6 0)) 0 = x2 (λ x9 . λ x10 x11 : (ι → ι) → ι → ι . setsum (setsum x9 (x3 (λ x12 : ((ι → ι) → (ι → ι) → ι) → ι . λ x13 . λ x14 : ι → ι → ι . x2 (λ x15 . λ x16 x17 : (ι → ι) → ι → ι . 0) 0 (λ x15 : ι → ι . 0)) (λ x12 x13 . λ x14 : ι → ι . x11 (λ x15 . 0) 0) (λ x12 : (ι → ι) → ι → ι . setsum 0 0))) 0) (x2 (λ x9 . λ x10 x11 : (ι → ι) → ι → ι . setsum 0 0) (x6 0) (λ x9 : ι → ι . setsum (x0 (λ x10 : ι → (ι → ι) → ι . x2 (λ x11 . λ x12 x13 : (ι → ι) → ι → ι . 0) 0 (λ x11 : ι → ι . 0)) 0 0) (x6 (x6 0)))) (λ x9 : ι → ι . Inj1 (x2 (λ x10 . λ x11 x12 : (ι → ι) → ι → ι . x10) (x0 (λ x10 : ι → (ι → ι) → ι . setsum 0 0) 0 (Inj0 0)) (λ x10 : ι → ι . setsum (setsum 0 0) (x6 0))))) ⟶ False (proof)Theorem dfd17.. : ∀ x0 : (((((ι → ι) → ι → ι) → ι) → (ι → ι) → ι) → ι → ι → (ι → ι) → ι → ι) → ((ι → (ι → ι) → ι) → ι → ι) → ι . ∀ x1 : ((((ι → ι) → ι → ι → ι) → ι → ι) → ι → ι) → (((ι → ι) → ι) → ι) → (((ι → ι) → ι) → ι) → ι . ∀ x2 : (ι → ι) → ((ι → ι → ι) → ι) → (ι → ι) → (ι → ι) → ι . ∀ x3 : (ι → ι → ι) → ((ι → (ι → ι) → ι → ι) → ι) → (ι → ι) → (ι → ι) → ι . (∀ x4 : (ι → ι) → ι . ∀ x5 : ι → ((ι → ι) → ι) → ι . ∀ x6 x7 . x3 (λ x9 x10 . x1 (λ x11 : ((ι → ι) → ι → ι → ι) → ι → ι . λ x12 . Inj0 (x11 (λ x13 : ι → ι . λ x14 x15 . x1 (λ x16 : ((ι → ι) → ι → ι → ι) → ι → ι . λ x17 . 0) (λ x16 : (ι → ι) → ι . 0) (λ x16 : (ι → ι) → ι . 0)) (x2 (λ x13 . 0) (λ x13 : ι → ι → ι . 0) (λ x13 . 0) (λ x13 . 0)))) (λ x11 : (ι → ι) → ι . 0) (λ x11 : (ι → ι) → ι . x2 (λ x12 . 0) (λ x12 : ι → ι → ι . x3 (λ x13 x14 . x14) (λ x13 : ι → (ι → ι) → ι → ι . x3 (λ x14 x15 . 0) (λ x14 : ι → (ι → ι) → ι → ι . 0) (λ x14 . 0) (λ x14 . 0)) (λ x13 . setsum 0 0) (λ x13 . setsum 0 0)) (λ x12 . x3 (λ x13 x14 . x14) (λ x13 : ι → (ι → ι) → ι → ι . x3 (λ x14 x15 . 0) (λ x14 : ι → (ι → ι) → ι → ι . 0) (λ x14 . 0) (λ x14 . 0)) (λ x13 . 0) (λ x13 . Inj0 0)) (λ x12 . 0))) (λ x9 : ι → (ι → ι) → ι → ι . Inj0 (x1 (λ x10 : ((ι → ι) → ι → ι → ι) → ι → ι . λ x11 . Inj0 (setsum 0 0)) (λ x10 : (ι → ι) → ι . x9 (x3 (λ x11 x12 . 0) (λ x11 : ι → (ι → ι) → ι → ι . 0) (λ x11 . 0) (λ x11 . 0)) (λ x11 . 0) x7) (λ x10 : (ι → ι) → ι . x1 (λ x11 : ((ι → ι) → ι → ι → ι) → ι → ι . λ x12 . x1 (λ x13 : ((ι → ι) → ι → ι → ι) → ι → ι . λ x14 . 0) (λ x13 : (ι → ι) → ι . 0) (λ x13 : (ι → ι) → ι . 0)) (λ x11 : (ι → ι) → ι . x1 (λ x12 : ((ι → ι) → ι → ι → ι) → ι → ι . λ x13 . 0) (λ x12 : (ι → ι) → ι . 0) (λ x12 : (ι → ι) → ι . 0)) (λ x11 : (ι → ι) → ι . x7)))) (λ x9 . 0) (λ x9 . setsum 0 x7) = x1 (λ x9 : ((ι → ι) → ι → ι → ι) → ι → ι . λ x10 . setsum (x0 (λ x11 : (((ι → ι) → ι → ι) → ι) → (ι → ι) → ι . λ x12 x13 . λ x14 : ι → ι . λ x15 . x1 (λ x16 : ((ι → ι) → ι → ι → ι) → ι → ι . λ x17 . Inj0 0) (λ x16 : (ι → ι) → ι . x0 (λ x17 : (((ι → ι) → ι → ι) → ι) → (ι → ι) → ι . λ x18 x19 . λ x20 : ι → ι . λ x21 . 0) (λ x17 : ι → (ι → ι) → ι . λ x18 . 0)) (λ x16 : (ι → ι) → ι . x0 (λ x17 : (((ι → ι) → ι → ι) → ι) → (ι → ι) → ι . λ x18 x19 . λ x20 : ι → ι . λ x21 . 0) (λ x17 : ι → (ι → ι) → ι . λ x18 . 0))) (λ x11 : ι → (ι → ι) → ι . λ x12 . x10)) (x0 (λ x11 : (((ι → ι) → ι → ι) → ι) → (ι → ι) → ι . λ x12 x13 . λ x14 : ι → ι . λ x15 . 0) (λ x11 : ι → (ι → ι) → ι . λ x12 . x10))) (λ x9 : (ι → ι) → ι . Inj1 0) (λ x9 : (ι → ι) → ι . Inj0 (setsum (x2 (λ x10 . x3 (λ x11 x12 . 0) (λ x11 : ι → (ι → ι) → ι → ι . 0) (λ x11 . 0) (λ x11 . 0)) (λ x10 : ι → ι → ι . 0) (λ x10 . x6) (λ x10 . setsum 0 0)) x6))) ⟶ (∀ x4 : ι → ((ι → ι) → ι → ι) → ι . ∀ x5 x6 . ∀ x7 : (ι → ι → ι → ι) → ((ι → ι) → ι) → ι → ι → ι . x3 (λ x9 x10 . x3 (λ x11 x12 . x0 (λ x13 : (((ι → ι) → ι → ι) → ι) → (ι → ι) → ι . λ x14 x15 . λ x16 : ι → ι . λ x17 . x2 (λ x18 . 0) (λ x18 : ι → ι → ι . x0 (λ x19 : (((ι → ι) → ι → ι) → ι) → (ι → ι) → ι . λ x20 x21 . λ x22 : ι → ι . λ x23 . 0) (λ x19 : ι → (ι → ι) → ι . λ x20 . 0)) (λ x18 . x0 (λ x19 : (((ι → ι) → ι → ι) → ι) → (ι → ι) → ι . λ x20 x21 . λ x22 : ι → ι . λ x23 . 0) (λ x19 : ι → (ι → ι) → ι . λ x20 . 0)) (λ x18 . setsum 0 0)) (λ x13 : ι → (ι → ι) → ι . λ x14 . 0)) (λ x11 : ι → (ι → ι) → ι → ι . x0 (λ x12 : (((ι → ι) → ι → ι) → ι) → (ι → ι) → ι . λ x13 x14 . λ x15 : ι → ι . λ x16 . x1 (λ x17 : ((ι → ι) → ι → ι → ι) → ι → ι . λ x18 . x18) (λ x17 : (ι → ι) → ι . Inj0 0) (λ x17 : (ι → ι) → ι . x0 (λ x18 : (((ι → ι) → ι → ι) → ι) → (ι → ι) → ι . λ x19 x20 . λ x21 : ι → ι . λ x22 . 0) (λ x18 : ι → (ι → ι) → ι . λ x19 . 0))) (λ x12 : ι → (ι → ι) → ι . λ x13 . setsum (x0 (λ x14 : (((ι → ι) → ι → ι) → ι) → (ι → ι) → ι . λ x15 x16 . λ x17 : ι → ι . λ x18 . 0) (λ x14 : ι → (ι → ι) → ι . λ x15 . 0)) 0)) (λ x11 . x11) (λ x11 . 0)) (λ x9 : ι → (ι → ι) → ι → ι . x0 (λ x10 : (((ι → ι) → ι → ι) → ι) → (ι → ι) → ι . λ x11 x12 . λ x13 : ι → ι . λ x14 . Inj0 (x13 0)) (λ x10 : ι → (ι → ι) → ι . λ x11 . x3 (λ x12 x13 . x12) (λ x12 : ι → (ι → ι) → ι → ι . 0) (λ x12 . Inj1 x11) (λ x12 . Inj1 (x2 (λ x13 . 0) (λ x13 : ι → ι → ι . 0) (λ x13 . 0) (λ x13 . 0))))) (λ x9 . setsum x6 (setsum 0 (x0 (λ x10 : (((ι → ι) → ι → ι) → ι) → (ι → ι) → ι . λ x11 x12 . λ x13 : ι → ι . λ x14 . x1 (λ x15 : ((ι → ι) → ι → ι → ι) → ι → ι . λ x16 . 0) (λ x15 : (ι → ι) → ι . 0) (λ x15 : (ι → ι) → ι . 0)) (λ x10 : ι → (ι → ι) → ι . λ x11 . setsum 0 0)))) (λ x9 . Inj1 0) = setsum 0 x6) ⟶ (∀ x4 . ∀ x5 : ((ι → ι → ι) → ι → ι → ι) → (ι → ι) → ι . ∀ x6 x7 . x2 (λ x9 . x0 (λ x10 : (((ι → ι) → ι → ι) → ι) → (ι → ι) → ι . λ x11 x12 . λ x13 : ι → ι . λ x14 . setsum (Inj0 x14) x14) (λ x10 : ι → (ι → ι) → ι . λ x11 . x9)) (λ x9 : ι → ι → ι . 0) (λ x9 . Inj0 (x0 (λ x10 : (((ι → ι) → ι → ι) → ι) → (ι → ι) → ι . λ x11 x12 . λ x13 : ι → ι . λ x14 . 0) (λ x10 : ι → (ι → ι) → ι . λ x11 . Inj1 (Inj1 0)))) (λ x9 . x0 (λ x10 : (((ι → ι) → ι → ι) → ι) → (ι → ι) → ι . λ x11 x12 . λ x13 : ι → ι . λ x14 . x2 (λ x15 . x1 (λ x16 : ((ι → ι) → ι → ι → ι) → ι → ι . λ x17 . x3 (λ x18 x19 . 0) (λ x18 : ι → (ι → ι) → ι → ι . 0) (λ x18 . 0) (λ x18 . 0)) (λ x16 : (ι → ι) → ι . 0) (λ x16 : (ι → ι) → ι . x16 (λ x17 . 0))) (λ x15 : ι → ι → ι . x2 (λ x16 . 0) (λ x16 : ι → ι → ι . x13 0) (λ x16 . x14) (λ x16 . x15 0 0)) (λ x15 . x15) (λ x15 . x2 (λ x16 . 0) (λ x16 : ι → ι → ι . x3 (λ x17 x18 . 0) (λ x17 : ι → (ι → ι) → ι → ι . 0) (λ x17 . 0) (λ x17 . 0)) (λ x16 . 0) (λ x16 . 0))) (λ x10 : ι → (ι → ι) → ι . λ x11 . x2 (λ x12 . 0) (λ x12 : ι → ι → ι . setsum (x12 0 0) (x10 0 (λ x13 . 0))) (λ x12 . x3 (λ x13 x14 . x13) (λ x13 : ι → (ι → ι) → ι → ι . 0) (λ x13 . x10 0 (λ x14 . 0)) (λ x13 . x10 0 (λ x14 . 0))) (λ x12 . 0))) = setsum x4 0) ⟶ (∀ x4 . ∀ x5 : ι → ((ι → ι) → ι → ι) → ι . ∀ x6 : ι → ι . ∀ x7 . x2 (λ x9 . x5 (x3 (λ x10 x11 . Inj0 0) (λ x10 : ι → (ι → ι) → ι → ι . 0) (λ x10 . x1 (λ x11 : ((ι → ι) → ι → ι → ι) → ι → ι . λ x12 . Inj0 0) (λ x11 : (ι → ι) → ι . Inj0 0) (λ x11 : (ι → ι) → ι . x0 (λ x12 : (((ι → ι) → ι → ι) → ι) → (ι → ι) → ι . λ x13 x14 . λ x15 : ι → ι . λ x16 . 0) (λ x12 : ι → (ι → ι) → ι . λ x13 . 0))) (λ x10 . 0)) (λ x10 : ι → ι . λ x11 . 0)) (λ x9 : ι → ι → ι . setsum (x9 (x6 0) (x6 (x9 0 0))) (x5 x7 (λ x10 : ι → ι . λ x11 . Inj1 (x9 0 0)))) (λ x9 . x6 (setsum (x3 (λ x10 x11 . 0) (λ x10 : ι → (ι → ι) → ι → ι . x7) (λ x10 . x3 (λ x11 x12 . 0) (λ x11 : ι → (ι → ι) → ι → ι . 0) (λ x11 . 0) (λ x11 . 0)) (λ x10 . x2 (λ x11 . 0) (λ x11 : ι → ι → ι . 0) (λ x11 . 0) (λ x11 . 0))) (x0 (λ x10 : (((ι → ι) → ι → ι) → ι) → (ι → ι) → ι . λ x11 x12 . λ x13 : ι → ι . λ x14 . 0) (λ x10 : ι → (ι → ι) → ι . λ x11 . x3 (λ x12 x13 . 0) (λ x12 : ι → (ι → ι) → ι → ι . 0) (λ x12 . 0) (λ x12 . 0))))) (λ x9 . 0) = setsum (x2 (λ x9 . x7) (λ x9 : ι → ι → ι . x7) (λ x9 . x5 x9 (λ x10 : ι → ι . λ x11 . Inj0 0)) (λ x9 . 0)) (setsum (x5 (x0 (λ x9 : (((ι → ι) → ι → ι) → ι) → (ι → ι) → ι . λ x10 x11 . λ x12 : ι → ι . λ x13 . 0) (λ x9 : ι → (ι → ι) → ι . λ x10 . x7)) (λ x9 : ι → ι . λ x10 . x3 (λ x11 x12 . x9 0) (λ x11 : ι → (ι → ι) → ι → ι . 0) (λ x11 . 0) (λ x11 . Inj1 0))) (x0 (λ x9 : (((ι → ι) → ι → ι) → ι) → (ι → ι) → ι . λ x10 x11 . λ x12 : ι → ι . λ x13 . x11) (λ x9 : ι → (ι → ι) → ι . λ x10 . x10)))) ⟶ (∀ x4 . ∀ x5 : (ι → ι) → ι → ι → ι → ι . ∀ x6 : ((ι → ι → ι) → (ι → ι) → ι → ι) → ι → ι . ∀ x7 : (ι → ι) → ((ι → ι) → ι → ι) → ι → ι → ι . x1 (λ x9 : ((ι → ι) → ι → ι → ι) → ι → ι . λ x10 . Inj1 (x0 (λ x11 : (((ι → ι) → ι → ι) → ι) → (ι → ι) → ι . λ x12 x13 . λ x14 : ι → ι . λ x15 . 0) (λ x11 : ι → (ι → ι) → ι . λ x12 . Inj0 0))) (λ x9 : (ι → ι) → ι . x7 (λ x10 . 0) (λ x10 : ι → ι . x7 (λ x11 . x9 (λ x12 . Inj1 0)) (λ x11 : ι → ι . λ x12 . 0) (setsum (x7 (λ x11 . 0) (λ x11 : ι → ι . λ x12 . 0) 0 0) (x1 (λ x11 : ((ι → ι) → ι → ι → ι) → ι → ι . λ x12 . 0) (λ x11 : (ι → ι) → ι . 0) (λ x11 : (ι → ι) → ι . 0)))) (x2 (λ x10 . x6 (λ x11 : ι → ι → ι . λ x12 : ι → ι . λ x13 . Inj0 0) (x9 (λ x11 . 0))) (λ x10 : ι → ι → ι . x3 (λ x11 x12 . 0) (λ x11 : ι → (ι → ι) → ι → ι . x0 (λ x12 : (((ι → ι) → ι → ι) → ι) → (ι → ι) → ι . λ x13 x14 . λ x15 : ι → ι . λ x16 . 0) (λ x12 : ι → (ι → ι) → ι . λ x13 . 0)) (λ x11 . x11) (λ x11 . x7 (λ x12 . 0) (λ x12 : ι → ι . λ x13 . 0) 0 0)) (λ x10 . x7 (λ x11 . x1 (λ x12 : ((ι → ι) → ι → ι → ι) → ι → ι . λ x13 . 0) (λ x12 : (ι → ι) → ι . 0) (λ x12 : (ι → ι) → ι . 0)) (λ x11 : ι → ι . λ x12 . 0) (Inj1 0) (x1 (λ x11 : ((ι → ι) → ι → ι → ι) → ι → ι . λ x12 . 0) (λ x11 : (ι → ι) → ι . 0) (λ x11 : (ι → ι) → ι . 0))) (λ x10 . x0 (λ x11 : (((ι → ι) → ι → ι) → ι) → (ι → ι) → ι . λ x12 x13 . λ x14 : ι → ι . λ x15 . setsum 0 0) (λ x11 : ι → (ι → ι) → ι . λ x12 . setsum 0 0))) (x0 (λ x10 : (((ι → ι) → ι → ι) → ι) → (ι → ι) → ι . λ x11 x12 . λ x13 : ι → ι . λ x14 . 0) (λ x10 : ι → (ι → ι) → ι . λ x11 . setsum (x7 (λ x12 . 0) (λ x12 : ι → ι . λ x13 . 0) 0 0) (x2 (λ x12 . 0) (λ x12 : ι → ι → ι . 0) (λ x12 . 0) (λ x12 . 0))))) (λ x9 : (ι → ι) → ι . x9 (λ x10 . x6 (λ x11 : ι → ι → ι . λ x12 : ι → ι . λ x13 . setsum (x3 (λ x14 x15 . 0) (λ x14 : ι → (ι → ι) → ι → ι . 0) (λ x14 . 0) (λ x14 . 0)) 0) 0)) = Inj1 x4) ⟶ (∀ x4 . ∀ x5 : ((ι → ι) → ι → ι) → ι . ∀ x6 x7 . x1 (λ x9 : ((ι → ι) → ι → ι → ι) → ι → ι . λ x10 . x6) (λ x9 : (ι → ι) → ι . x1 (λ x10 : ((ι → ι) → ι → ι → ι) → ι → ι . λ x11 . setsum (x10 (λ x12 : ι → ι . λ x13 x14 . x2 (λ x15 . 0) (λ x15 : ι → ι → ι . 0) (λ x15 . 0) (λ x15 . 0)) x7) (Inj0 x7)) (λ x10 : (ι → ι) → ι . x3 (λ x11 x12 . Inj0 (x3 (λ x13 x14 . 0) (λ x13 : ι → (ι → ι) → ι → ι . 0) (λ x13 . 0) (λ x13 . 0))) (λ x11 : ι → (ι → ι) → ι → ι . Inj0 (Inj1 0)) (λ x11 . Inj0 (x2 (λ x12 . 0) (λ x12 : ι → ι → ι . 0) (λ x12 . 0) (λ x12 . 0))) (λ x11 . 0)) (λ x10 : (ι → ι) → ι . 0)) (λ x9 : (ι → ι) → ι . 0) = Inj0 x6) ⟶ (∀ x4 : (((ι → ι) → ι) → ι) → (ι → ι) → ι . ∀ x5 x6 x7 . x0 (λ x9 : (((ι → ι) → ι → ι) → ι) → (ι → ι) → ι . λ x10 x11 . λ x12 : ι → ι . λ x13 . Inj1 (setsum (Inj0 (Inj0 0)) x13)) (λ x9 : ι → (ι → ι) → ι . λ x10 . 0) = x7) ⟶ (∀ x4 : (ι → ι → ι) → ι . ∀ x5 x6 . ∀ x7 : ι → (ι → ι → ι) → ι . x0 (λ x9 : (((ι → ι) → ι → ι) → ι) → (ι → ι) → ι . λ x10 x11 . λ x12 : ι → ι . λ x13 . 0) (λ x9 : ι → (ι → ι) → ι . λ x10 . setsum (x1 (λ x11 : ((ι → ι) → ι → ι → ι) → ι → ι . λ x12 . x12) (λ x11 : (ι → ι) → ι . 0) (λ x11 : (ι → ι) → ι . setsum 0 (x1 (λ x12 : ((ι → ι) → ι → ι → ι) → ι → ι . λ x13 . 0) (λ x12 : (ι → ι) → ι . 0) (λ x12 : (ι → ι) → ι . 0)))) 0) = x4 (λ x9 x10 . x7 (x0 (λ x11 : (((ι → ι) → ι → ι) → ι) → (ι → ι) → ι . λ x12 x13 . λ x14 : ι → ι . λ x15 . x14 0) (λ x11 : ι → (ι → ι) → ι . Inj1)) (λ x11 x12 . 0))) ⟶ False (proof)Theorem 5b7cf.. : ∀ x0 : ((ι → (ι → ι) → (ι → ι) → ι → ι) → ι → ι) → ((((ι → ι) → ι → ι) → (ι → ι) → ι → ι) → ι → ι → ι) → (((ι → ι) → ι → ι) → ι) → ι . ∀ x1 : ((ι → ι) → ι) → ((ι → ι) → ι) → ι . ∀ x2 : (((((ι → ι) → ι) → ι → ι → ι) → ι) → ι → ((ι → ι) → ι) → (ι → ι) → ι → ι) → (ι → (ι → ι → ι) → ι → ι → ι) → (((ι → ι) → ι → ι) → ι) → (ι → ι → ι) → ι . ∀ x3 : ((ι → ι) → ι) → (ι → ι) → ι . (∀ x4 : ι → ((ι → ι) → ι) → ι . ∀ x5 x6 x7 . x3 (λ x9 : ι → ι . x0 (λ x10 : ι → (ι → ι) → (ι → ι) → ι → ι . λ x11 . 0) (λ x10 : ((ι → ι) → ι → ι) → (ι → ι) → ι → ι . λ x11 x12 . x10 (λ x13 : ι → ι . λ x14 . x12) (λ x13 . Inj0 0) 0) (λ x10 : (ι → ι) → ι → ι . x3 (λ x11 : ι → ι . x9 (Inj0 0)) (λ x11 . x11))) (λ x9 . x0 (λ x10 : ι → (ι → ι) → (ι → ι) → ι → ι . λ x11 . 0) (λ x10 : ((ι → ι) → ι → ι) → (ι → ι) → ι → ι . λ x11 x12 . x2 (λ x13 : (((ι → ι) → ι) → ι → ι → ι) → ι . λ x14 . λ x15 : (ι → ι) → ι . λ x16 : ι → ι . λ x17 . Inj0 (x1 (λ x18 : ι → ι . 0) (λ x18 : ι → ι . 0))) (λ x13 . λ x14 : ι → ι → ι . λ x15 x16 . 0) (λ x13 : (ι → ι) → ι → ι . x1 (λ x14 : ι → ι . Inj0 0) (λ x14 : ι → ι . x3 (λ x15 : ι → ι . 0) (λ x15 . 0))) (λ x13 x14 . x14)) (λ x10 : (ι → ι) → ι → ι . 0)) = x0 (λ x9 : ι → (ι → ι) → (ι → ι) → ι → ι . λ x10 . Inj1 (x2 (λ x11 : (((ι → ι) → ι) → ι → ι → ι) → ι . λ x12 . λ x13 : (ι → ι) → ι . λ x14 : ι → ι . λ x15 . x0 (λ x16 : ι → (ι → ι) → (ι → ι) → ι → ι . λ x17 . 0) (λ x16 : ((ι → ι) → ι → ι) → (ι → ι) → ι → ι . λ x17 x18 . 0) (λ x16 : (ι → ι) → ι → ι . Inj1 0)) (λ x11 . λ x12 : ι → ι → ι . λ x13 x14 . setsum x14 0) (λ x11 : (ι → ι) → ι → ι . x7) (λ x11 x12 . x9 (x1 (λ x13 : ι → ι . 0) (λ x13 : ι → ι . 0)) (λ x13 . x1 (λ x14 : ι → ι . 0) (λ x14 : ι → ι . 0)) (λ x13 . 0) (x0 (λ x13 : ι → (ι → ι) → (ι → ι) → ι → ι . λ x14 . 0) (λ x13 : ((ι → ι) → ι → ι) → (ι → ι) → ι → ι . λ x14 x15 . 0) (λ x13 : (ι → ι) → ι → ι . 0))))) (λ x9 : ((ι → ι) → ι → ι) → (ι → ι) → ι → ι . λ x10 x11 . setsum 0 (x3 (λ x12 : ι → ι . setsum x11 0) (λ x12 . x0 (λ x13 : ι → (ι → ι) → (ι → ι) → ι → ι . λ x14 . setsum 0 0) (λ x13 : ((ι → ι) → ι → ι) → (ι → ι) → ι → ι . λ x14 x15 . x12) (λ x13 : (ι → ι) → ι → ι . x2 (λ x14 : (((ι → ι) → ι) → ι → ι → ι) → ι . λ x15 . λ x16 : (ι → ι) → ι . λ x17 : ι → ι . λ x18 . 0) (λ x14 . λ x15 : ι → ι → ι . λ x16 x17 . 0) (λ x14 : (ι → ι) → ι → ι . 0) (λ x14 x15 . 0))))) (λ x9 : (ι → ι) → ι → ι . Inj1 x6)) ⟶ (∀ x4 . ∀ x5 : ι → ι . ∀ x6 x7 . x3 (λ x9 : ι → ι . x6) (λ x9 . x5 0) = x6) ⟶ (∀ x4 x5 . ∀ x6 : ((ι → ι) → ι → ι → ι) → ι . ∀ x7 : ι → ι . x2 (λ x9 : (((ι → ι) → ι) → ι → ι → ι) → ι . λ x10 . λ x11 : (ι → ι) → ι . λ x12 : ι → ι . λ x13 . x13) (λ x9 . λ x10 : ι → ι → ι . λ x11 x12 . 0) (λ x9 : (ι → ι) → ι → ι . 0) (λ x9 x10 . x9) = x6 (λ x9 : ι → ι . λ x10 x11 . Inj0 (setsum (Inj0 (x7 0)) x11))) ⟶ (∀ x4 x5 . ∀ x6 : (ι → ι) → ι . ∀ x7 . x2 (λ x9 : (((ι → ι) → ι) → ι → ι → ι) → ι . λ x10 . λ x11 : (ι → ι) → ι . λ x12 : ι → ι . λ x13 . 0) (λ x9 . λ x10 : ι → ι → ι . λ x11 x12 . 0) (λ x9 : (ι → ι) → ι → ι . 0) (λ x9 x10 . 0) = x6 (λ x9 . x3 (λ x10 : ι → ι . 0) (λ x10 . setsum (Inj0 x7) (x0 (λ x11 : ι → (ι → ι) → (ι → ι) → ι → ι . λ x12 . x2 (λ x13 : (((ι → ι) → ι) → ι → ι → ι) → ι . λ x14 . λ x15 : (ι → ι) → ι . λ x16 : ι → ι . λ x17 . 0) (λ x13 . λ x14 : ι → ι → ι . λ x15 x16 . 0) (λ x13 : (ι → ι) → ι → ι . 0) (λ x13 x14 . 0)) (λ x11 : ((ι → ι) → ι → ι) → (ι → ι) → ι → ι . λ x12 x13 . x1 (λ x14 : ι → ι . 0) (λ x14 : ι → ι . 0)) (λ x11 : (ι → ι) → ι → ι . x10))))) ⟶ (∀ x4 : (ι → (ι → ι) → ι → ι) → (ι → ι) → ι . ∀ x5 : ι → ι → (ι → ι) → ι → ι . ∀ x6 x7 : ι → ι . x1 (λ x9 : ι → ι . 0) (λ x9 : ι → ι . x9 (setsum (Inj0 (x6 0)) (x0 (λ x10 : ι → (ι → ι) → (ι → ι) → ι → ι . λ x11 . setsum 0 0) (λ x10 : ((ι → ι) → ι → ι) → (ι → ι) → ι → ι . λ x11 x12 . x10 (λ x13 : ι → ι . λ x14 . 0) (λ x13 . 0) 0) (λ x10 : (ι → ι) → ι → ι . 0)))) = Inj0 (setsum (x3 (λ x9 : ι → ι . Inj1 (x3 (λ x10 : ι → ι . 0) (λ x10 . 0))) (λ x9 . x5 (Inj1 0) (x1 (λ x10 : ι → ι . 0) (λ x10 : ι → ι . 0)) (λ x10 . x1 (λ x11 : ι → ι . 0) (λ x11 : ι → ι . 0)) (Inj0 0))) (Inj1 0))) ⟶ (∀ x4 . ∀ x5 : ι → ι . ∀ x6 : ι → (ι → ι) → (ι → ι) → ι . ∀ x7 : (((ι → ι) → ι → ι) → (ι → ι) → ι → ι) → (ι → ι) → (ι → ι) → ι . x1 (λ x9 : ι → ι . x0 (λ x10 : ι → (ι → ι) → (ι → ι) → ι → ι . λ x11 . x2 (λ x12 : (((ι → ι) → ι) → ι → ι → ι) → ι . λ x13 . λ x14 : (ι → ι) → ι . λ x15 : ι → ι . λ x16 . 0) (λ x12 . λ x13 : ι → ι → ι . λ x14 x15 . 0) (λ x12 : (ι → ι) → ι → ι . x0 (λ x13 : ι → (ι → ι) → (ι → ι) → ι → ι . λ x14 . 0) (λ x13 : ((ι → ι) → ι → ι) → (ι → ι) → ι → ι . λ x14 x15 . x1 (λ x16 : ι → ι . 0) (λ x16 : ι → ι . 0)) (λ x13 : (ι → ι) → ι → ι . x11)) (λ x12 x13 . x3 (λ x14 : ι → ι . 0) (λ x14 . setsum 0 0))) (λ x10 : ((ι → ι) → ι → ι) → (ι → ι) → ι → ι . λ x11 x12 . x11) (λ x10 : (ι → ι) → ι → ι . x6 (x0 (λ x11 : ι → (ι → ι) → (ι → ι) → ι → ι . λ x12 . x11 0 (λ x13 . 0) (λ x13 . 0) 0) (λ x11 : ((ι → ι) → ι → ι) → (ι → ι) → ι → ι . λ x12 x13 . x2 (λ x14 : (((ι → ι) → ι) → ι → ι → ι) → ι . λ x15 . λ x16 : (ι → ι) → ι . λ x17 : ι → ι . λ x18 . 0) (λ x14 . λ x15 : ι → ι → ι . λ x16 x17 . 0) (λ x14 : (ι → ι) → ι → ι . 0) (λ x14 x15 . 0)) (λ x11 : (ι → ι) → ι → ι . setsum 0 0)) (λ x11 . 0) (λ x11 . setsum (x3 (λ x12 : ι → ι . 0) (λ x12 . 0)) (x10 (λ x12 . 0) 0)))) (λ x9 : ι → ι . 0) = Inj1 (x7 (λ x9 : (ι → ι) → ι → ι . λ x10 : ι → ι . λ x11 . x3 (λ x12 : ι → ι . x0 (λ x13 : ι → (ι → ι) → (ι → ι) → ι → ι . λ x14 . setsum 0 0) (λ x13 : ((ι → ι) → ι → ι) → (ι → ι) → ι → ι . λ x14 x15 . x1 (λ x16 : ι → ι . 0) (λ x16 : ι → ι . 0)) (λ x13 : (ι → ι) → ι → ι . x3 (λ x14 : ι → ι . 0) (λ x14 . 0))) (λ x12 . Inj0 0)) (λ x9 . x0 (λ x10 : ι → (ι → ι) → (ι → ι) → ι → ι . λ x11 . x11) (λ x10 : ((ι → ι) → ι → ι) → (ι → ι) → ι → ι . λ x11 x12 . 0) (λ x10 : (ι → ι) → ι → ι . x0 (λ x11 : ι → (ι → ι) → (ι → ι) → ι → ι . λ x12 . Inj0 0) (λ x11 : ((ι → ι) → ι → ι) → (ι → ι) → ι → ι . λ x12 x13 . 0) (λ x11 : (ι → ι) → ι → ι . x9))) (λ x9 . setsum (x2 (λ x10 : (((ι → ι) → ι) → ι → ι → ι) → ι . λ x11 . λ x12 : (ι → ι) → ι . λ x13 : ι → ι . λ x14 . x11) (λ x10 . λ x11 : ι → ι → ι . λ x12 x13 . 0) (λ x10 : (ι → ι) → ι → ι . x1 (λ x11 : ι → ι . 0) (λ x11 : ι → ι . 0)) (λ x10 x11 . x10)) (setsum 0 0)))) ⟶ (∀ x4 : ι → ι . ∀ x5 : ι → (ι → ι → ι) → ι . ∀ x6 x7 . x0 (λ x9 : ι → (ι → ι) → (ι → ι) → ι → ι . λ x10 . x6) (λ x9 : ((ι → ι) → ι → ι) → (ι → ι) → ι → ι . λ x10 x11 . x9 (λ x12 : ι → ι . λ x13 . x2 (λ x14 : (((ι → ι) → ι) → ι → ι → ι) → ι . λ x15 . λ x16 : (ι → ι) → ι . λ x17 : ι → ι . λ x18 . 0) (λ x14 . λ x15 : ι → ι → ι . λ x16 x17 . x1 (λ x18 : ι → ι . 0) (λ x18 : ι → ι . x18 0)) (λ x14 : (ι → ι) → ι → ι . 0) (λ x14 x15 . 0)) (setsum x10) (setsum (Inj1 0) (setsum (setsum 0 0) (x3 (λ x12 : ι → ι . 0) (λ x12 . 0))))) (λ x9 : (ι → ι) → ι → ι . 0) = setsum 0 (setsum (Inj0 (x0 (λ x9 : ι → (ι → ι) → (ι → ι) → ι → ι . λ x10 . setsum 0 0) (λ x9 : ((ι → ι) → ι → ι) → (ι → ι) → ι → ι . λ x10 x11 . 0) (λ x9 : (ι → ι) → ι → ι . x9 (λ x10 . 0) 0))) 0)) ⟶ (∀ x4 : ι → ι . ∀ x5 : ((ι → ι → ι) → ι) → ι . ∀ x6 . ∀ x7 : (((ι → ι) → ι) → ι) → ι → (ι → ι) → ι → ι . x0 (λ x9 : ι → (ι → ι) → (ι → ι) → ι → ι . λ x10 . x2 (λ x11 : (((ι → ι) → ι) → ι → ι → ι) → ι . λ x12 . λ x13 : (ι → ι) → ι . λ x14 : ι → ι . λ x15 . Inj1 (x2 (λ x16 : (((ι → ι) → ι) → ι → ι → ι) → ι . λ x17 . λ x18 : (ι → ι) → ι . λ x19 : ι → ι . λ x20 . x20) (λ x16 . λ x17 : ι → ι → ι . λ x18 x19 . x3 (λ x20 : ι → ι . 0) (λ x20 . 0)) (λ x16 : (ι → ι) → ι → ι . setsum 0 0) (λ x16 x17 . x14 0))) (λ x11 . λ x12 : ι → ι → ι . λ x13 x14 . 0) (λ x11 : (ι → ι) → ι → ι . setsum 0 (x9 (setsum 0 0) (λ x12 . 0) (λ x12 . x9 0 (λ x13 . 0) (λ x13 . 0) 0) (setsum 0 0))) (λ x11 x12 . x12)) (λ x9 : ((ι → ι) → ι → ι) → (ι → ι) → ι → ι . λ x10 x11 . 0) (λ x9 : (ι → ι) → ι → ι . 0) = setsum (x0 (λ x9 : ι → (ι → ι) → (ι → ι) → ι → ι . λ x10 . setsum 0 (x1 (λ x11 : ι → ι . x7 (λ x12 : (ι → ι) → ι . 0) 0 (λ x12 . 0) 0) (λ x11 : ι → ι . x10))) (λ x9 : ((ι → ι) → ι → ι) → (ι → ι) → ι → ι . λ x10 x11 . x10) (λ x9 : (ι → ι) → ι → ι . setsum 0 (x0 (λ x10 : ι → (ι → ι) → (ι → ι) → ι → ι . λ x11 . x2 (λ x12 : (((ι → ι) → ι) → ι → ι → ι) → ι . λ x13 . λ x14 : (ι → ι) → ι . λ x15 : ι → ι . λ x16 . 0) (λ x12 . λ x13 : ι → ι → ι . λ x14 x15 . 0) (λ x12 : (ι → ι) → ι → ι . 0) (λ x12 x13 . 0)) (λ x10 : ((ι → ι) → ι → ι) → (ι → ι) → ι → ι . λ x11 x12 . Inj0 0) (λ x10 : (ι → ι) → ι → ι . x10 (λ x11 . 0) 0)))) 0) ⟶ False (proof)Theorem 33063.. : ∀ x0 : (((ι → ι → ι → ι) → ι) → ι) → ι → ι . ∀ x1 : ((ι → ι) → ι) → (((ι → ι → ι) → ι → ι) → ι) → ι . ∀ x2 : (ι → ι) → (ι → (ι → ι → ι) → ι → ι → ι) → ι . ∀ x3 : (ι → ι) → ι → ι → ι . (∀ x4 : ι → ι . ∀ x5 x6 x7 . x3 (λ x9 . Inj1 (x1 (λ x10 : ι → ι . x9) (λ x10 : (ι → ι → ι) → ι → ι . setsum 0 (x2 (λ x11 . 0) (λ x11 . λ x12 : ι → ι → ι . λ x13 x14 . 0))))) x7 0 = setsum (x0 (λ x9 : (ι → ι → ι → ι) → ι . x2 (λ x10 . setsum 0 x7) (λ x10 . λ x11 : ι → ι → ι . λ x12 x13 . x0 (λ x14 : (ι → ι → ι → ι) → ι . x3 (λ x15 . 0) 0 0) (setsum 0 0))) (setsum (Inj1 x6) x6)) 0) ⟶ (∀ x4 . ∀ x5 : ((ι → ι) → ι → ι → ι) → ι . ∀ x6 . ∀ x7 : ι → ι → ι . x3 (λ x9 . setsum x9 x9) 0 (x2 (λ x9 . x2 (λ x10 . x7 (setsum 0 0) (x3 (λ x11 . 0) 0 0)) (λ x10 . λ x11 : ι → ι → ι . λ x12 x13 . 0)) (λ x9 . λ x10 : ι → ι → ι . λ x11 x12 . Inj0 (setsum (Inj1 0) x9))) = x2 (λ x9 . x0 (λ x10 : (ι → ι → ι → ι) → ι . x0 (λ x11 : (ι → ι → ι → ι) → ι . 0) 0) 0) (λ x9 . λ x10 : ι → ι → ι . λ x11 x12 . x10 (x1 (λ x13 : ι → ι . x10 0 0) (λ x13 : (ι → ι → ι) → ι → ι . 0)) 0)) ⟶ (∀ x4 : ι → ι → ι → ι . ∀ x5 x6 x7 : ι → ι . x2 (λ x9 . 0) (λ x9 . λ x10 : ι → ι → ι . λ x11 x12 . Inj1 (setsum (setsum (setsum 0 0) 0) (x10 (x2 (λ x13 . 0) (λ x13 . λ x14 : ι → ι → ι . λ x15 x16 . 0)) 0))) = x7 (Inj1 (x1 (λ x9 : ι → ι . 0) (λ x9 : (ι → ι → ι) → ι → ι . x1 (λ x10 : ι → ι . x7 0) (λ x10 : (ι → ι → ι) → ι → ι . x0 (λ x11 : (ι → ι → ι → ι) → ι . 0) 0))))) ⟶ (∀ x4 . ∀ x5 : ι → ((ι → ι) → ι) → ι . ∀ x6 : (ι → ι) → ι → ι . ∀ x7 : ((ι → ι → ι) → ι) → ι . x2 (λ x9 . 0) (λ x9 . λ x10 : ι → ι → ι . λ x11 x12 . x10 (x10 (setsum (setsum 0 0) (setsum 0 0)) (x2 (λ x13 . 0) (λ x13 . λ x14 : ι → ι → ι . λ x15 x16 . x14 0 0))) 0) = setsum (x3 (λ x9 . x5 (Inj1 0) (λ x10 : ι → ι . x10 0)) (x2 (setsum (setsum 0 0)) (λ x9 . λ x10 : ι → ι → ι . λ x11 x12 . 0)) (setsum (x3 (λ x9 . x9) (x0 (λ x9 : (ι → ι → ι → ι) → ι . 0) 0) (x2 (λ x9 . 0) (λ x9 . λ x10 : ι → ι → ι . λ x11 x12 . 0))) 0)) (x6 (λ x9 . 0) (x6 (λ x9 . x6 (λ x10 . x3 (λ x11 . 0) 0 0) (x3 (λ x10 . 0) 0 0)) (x5 (x0 (λ x9 : (ι → ι → ι → ι) → ι . 0) 0) (λ x9 : ι → ι . setsum 0 0))))) ⟶ (∀ x4 x5 . ∀ x6 : (ι → ι) → (ι → ι → ι) → (ι → ι) → ι . ∀ x7 . x1 (λ x9 : ι → ι . setsum (x9 (x6 (λ x10 . x0 (λ x11 : (ι → ι → ι → ι) → ι . 0) 0) (λ x10 x11 . x0 (λ x12 : (ι → ι → ι → ι) → ι . 0) 0) (λ x10 . 0))) (x6 (λ x10 . x9 0) (λ x10 x11 . 0) (λ x10 . x10))) (λ x9 : (ι → ι → ι) → ι → ι . x2 (λ x10 . x9 (λ x11 x12 . setsum 0 0) 0) (λ x10 . λ x11 : ι → ι → ι . λ x12 x13 . Inj1 (x0 (λ x14 : (ι → ι → ι → ι) → ι . 0) (x11 0 0)))) = x2 (λ x9 . x5) (λ x9 . λ x10 : ι → ι → ι . λ x11 x12 . x10 (x0 (λ x13 : (ι → ι → ι → ι) → ι . Inj1 (x2 (λ x14 . 0) (λ x14 . λ x15 : ι → ι → ι . λ x16 x17 . 0))) x12) 0)) ⟶ (∀ x4 x5 x6 x7 . x1 (λ x9 : ι → ι . setsum 0 0) (λ x9 : (ι → ι → ι) → ι → ι . x5) = x5) ⟶ (∀ x4 : ι → ι → ι → ι . ∀ x5 . ∀ x6 : ι → ι . ∀ x7 . x0 (λ x9 : (ι → ι → ι → ι) → ι . setsum x5 (Inj0 0)) x7 = x7) ⟶ (∀ x4 x5 x6 x7 . x0 (λ x9 : (ι → ι → ι → ι) → ι . x7) x5 = x5) ⟶ False (proof)Theorem 6fc01.. : ∀ x0 : (ι → ι → ((ι → ι) → ι) → ι) → ι → ι → ι . ∀ x1 : (ι → (ι → ι) → ι) → ι → ι . ∀ x2 : (((ι → ι) → (ι → ι → ι) → ι) → (ι → (ι → ι) → ι) → ι → ι) → (ι → ι) → ι . ∀ x3 : ((ι → (ι → ι → ι) → ι → ι) → ι) → ι → (ι → ι → ι → ι) → ι → ι . (∀ x4 . ∀ x5 : ι → ι . ∀ x6 . ∀ x7 : (ι → (ι → ι) → ι) → ι . x3 (λ x9 : ι → (ι → ι → ι) → ι → ι . x1 (λ x10 . λ x11 : ι → ι . setsum 0 x10) 0) 0 (λ x9 x10 x11 . 0) (x1 (λ x9 . λ x10 : ι → ι . x6) (setsum (x0 (λ x9 x10 . λ x11 : (ι → ι) → ι . setsum 0 0) 0 (x5 0)) (setsum (x2 (λ x9 : (ι → ι) → (ι → ι → ι) → ι . λ x10 : ι → (ι → ι) → ι . λ x11 . 0) (λ x9 . 0)) (x5 0)))) = setsum 0 x6) ⟶ (∀ x4 . ∀ x5 : ι → ι → ι . ∀ x6 : ι → ι . ∀ x7 : ι → (ι → ι → ι) → ι . x3 (λ x9 : ι → (ι → ι → ι) → ι → ι . setsum (x0 (λ x10 x11 . λ x12 : (ι → ι) → ι . x2 (λ x13 : (ι → ι) → (ι → ι → ι) → ι . λ x14 : ι → (ι → ι) → ι . λ x15 . x3 (λ x16 : ι → (ι → ι → ι) → ι → ι . 0) 0 (λ x16 x17 x18 . 0) 0) (λ x13 . x12 (λ x14 . 0))) (x3 (λ x10 : ι → (ι → ι → ι) → ι → ι . x7 0 (λ x11 x12 . 0)) (Inj0 0) (λ x10 x11 x12 . 0) 0) 0) (x0 (λ x10 x11 . λ x12 : (ι → ι) → ι . 0) (setsum (x6 0) (Inj1 0)) (x2 (λ x10 : (ι → ι) → (ι → ι → ι) → ι . λ x11 : ι → (ι → ι) → ι . λ x12 . x11 0 (λ x13 . 0)) (λ x10 . x1 (λ x11 . λ x12 : ι → ι . 0) 0)))) (x0 (λ x9 x10 . λ x11 : (ι → ι) → ι . x3 (λ x12 : ι → (ι → ι → ι) → ι → ι . x10) (setsum (x7 0 (λ x12 x13 . 0)) (x3 (λ x12 : ι → (ι → ι → ι) → ι → ι . 0) 0 (λ x12 x13 x14 . 0) 0)) (λ x12 x13 x14 . 0) x9) (x0 (λ x9 x10 . λ x11 : (ι → ι) → ι . 0) x4 (x7 (x2 (λ x9 : (ι → ι) → (ι → ι → ι) → ι . λ x10 : ι → (ι → ι) → ι . λ x11 . 0) (λ x9 . 0)) (λ x9 x10 . x2 (λ x11 : (ι → ι) → (ι → ι → ι) → ι . λ x12 : ι → (ι → ι) → ι . λ x13 . 0) (λ x11 . 0)))) (setsum (setsum (setsum 0 0) 0) (x0 (λ x9 x10 . λ x11 : (ι → ι) → ι . x9) (setsum 0 0) (x3 (λ x9 : ι → (ι → ι → ι) → ι → ι . 0) 0 (λ x9 x10 x11 . 0) 0)))) (λ x9 x10 x11 . 0) 0 = x0 (λ x9 x10 . λ x11 : (ι → ι) → ι . setsum 0 (x2 (λ x12 : (ι → ι) → (ι → ι → ι) → ι . λ x13 : ι → (ι → ι) → ι . λ x14 . x3 (λ x15 : ι → (ι → ι → ι) → ι → ι . x1 (λ x16 . λ x17 : ι → ι . 0) 0) 0 (λ x15 x16 x17 . x3 (λ x18 : ι → (ι → ι → ι) → ι → ι . 0) 0 (λ x18 x19 x20 . 0) 0) 0) (λ x12 . x3 (λ x13 : ι → (ι → ι → ι) → ι → ι . x10) (Inj0 0) (λ x13 x14 x15 . setsum 0 0) 0))) (x2 (λ x9 : (ι → ι) → (ι → ι → ι) → ι . λ x10 : ι → (ι → ι) → ι . λ x11 . 0) (λ x9 . setsum 0 0)) (x6 (x1 (λ x9 . λ x10 : ι → ι . 0) (Inj1 (x1 (λ x9 . λ x10 : ι → ι . 0) 0))))) ⟶ (∀ x4 : (((ι → ι) → ι → ι) → ι → ι) → ι → ι . ∀ x5 : ι → ι → ι . ∀ x6 : ι → ι → ι → ι → ι . ∀ x7 : (ι → (ι → ι) → ι → ι) → ι . x2 (λ x9 : (ι → ι) → (ι → ι → ι) → ι . λ x10 : ι → (ι → ι) → ι . λ x11 . x11) (λ x9 . 0) = x4 (λ x9 : (ι → ι) → ι → ι . λ x10 . Inj0 (x9 (λ x11 . setsum (x1 (λ x12 . λ x13 : ι → ι . 0) 0) (x2 (λ x12 : (ι → ι) → (ι → ι → ι) → ι . λ x13 : ι → (ι → ι) → ι . λ x14 . 0) (λ x12 . 0))) (x7 (λ x11 . λ x12 : ι → ι . λ x13 . 0)))) 0) ⟶ (∀ x4 x5 x6 . ∀ x7 : (((ι → ι) → ι) → ι) → ι . x2 (λ x9 : (ι → ι) → (ι → ι → ι) → ι . λ x10 : ι → (ι → ι) → ι . λ x11 . x1 (λ x12 . λ x13 : ι → ι . setsum (Inj1 (setsum 0 0)) (x13 (setsum 0 0))) 0) (λ x9 . 0) = Inj1 0) ⟶ (∀ x4 : ι → ι . ∀ x5 . ∀ x6 x7 : ι → ι . x1 (λ x9 . λ x10 : ι → ι . x1 (λ x11 . λ x12 : ι → ι . 0) (setsum (Inj0 0) (x6 (x7 0)))) 0 = Inj0 (x0 (λ x9 x10 . λ x11 : (ι → ι) → ι . setsum (x1 (λ x12 . λ x13 : ι → ι . 0) 0) (x3 (λ x12 : ι → (ι → ι → ι) → ι → ι . 0) (x2 (λ x12 : (ι → ι) → (ι → ι → ι) → ι . λ x13 : ι → (ι → ι) → ι . λ x14 . 0) (λ x12 . 0)) (λ x12 x13 x14 . x2 (λ x15 : (ι → ι) → (ι → ι → ι) → ι . λ x16 : ι → (ι → ι) → ι . λ x17 . 0) (λ x15 . 0)) (x7 0))) x5 (x4 (x2 (λ x9 : (ι → ι) → (ι → ι → ι) → ι . λ x10 : ι → (ι → ι) → ι . λ x11 . 0) (λ x9 . setsum 0 0))))) ⟶ (∀ x4 : ι → ι . ∀ x5 . ∀ x6 : ι → ι → ι . ∀ x7 : ι → ι . x1 (λ x9 . λ x10 : ι → ι . Inj1 (x7 (x2 (λ x11 : (ι → ι) → (ι → ι → ι) → ι . λ x12 : ι → (ι → ι) → ι . λ x13 . x13) (λ x11 . 0)))) (setsum 0 (x4 0)) = x7 (Inj1 (x2 (λ x9 : (ι → ι) → (ι → ι → ι) → ι . λ x10 : ι → (ι → ι) → ι . λ x11 . x7 0) (λ x9 . x0 (λ x10 x11 . λ x12 : (ι → ι) → ι . 0) (x3 (λ x10 : ι → (ι → ι → ι) → ι → ι . 0) 0 (λ x10 x11 x12 . 0) 0) (x1 (λ x10 . λ x11 : ι → ι . 0) 0))))) ⟶ (∀ x4 x5 x6 . ∀ x7 : (ι → ι) → ι → (ι → ι) → ι . x0 (λ x9 x10 . λ x11 : (ι → ι) → ι . Inj0 (x2 (λ x12 : (ι → ι) → (ι → ι → ι) → ι . λ x13 : ι → (ι → ι) → ι . λ x14 . Inj0 (x11 (λ x15 . 0))) (λ x12 . Inj0 (setsum 0 0)))) (x7 (λ x9 . x1 (λ x10 . λ x11 : ι → ι . Inj0 (setsum 0 0)) (setsum (setsum 0 0) (Inj1 0))) x5 (λ x9 . 0)) (x3 (λ x9 : ι → (ι → ι → ι) → ι → ι . x1 (λ x10 . λ x11 : ι → ι . x3 (λ x12 : ι → (ι → ι → ι) → ι → ι . x11 0) 0 (λ x12 x13 x14 . 0) (x0 (λ x12 x13 . λ x14 : (ι → ι) → ι . 0) 0 0)) x5) 0 (λ x9 x10 x11 . 0) x4) = x3 (λ x9 : ι → (ι → ι → ι) → ι → ι . x3 (λ x10 : ι → (ι → ι → ι) → ι → ι . Inj0 (x9 0 (λ x11 x12 . Inj0 0) 0)) (x7 (λ x10 . x9 x10 (λ x11 x12 . setsum 0 0) (x3 (λ x11 : ι → (ι → ι → ι) → ι → ι . 0) 0 (λ x11 x12 x13 . 0) 0)) (x2 (λ x10 : (ι → ι) → (ι → ι → ι) → ι . λ x11 : ι → (ι → ι) → ι . λ x12 . x9 0 (λ x13 x14 . 0) 0) (λ x10 . x10)) (λ x10 . x6)) (λ x10 x11 x12 . x0 (λ x13 x14 . λ x15 : (ι → ι) → ι . 0) (x0 (λ x13 x14 . λ x15 : (ι → ι) → ι . x15 (λ x16 . 0)) x10 x12) x12) x6) x6 (λ x9 x10 x11 . setsum (Inj0 (setsum 0 x11)) (x3 (λ x12 : ι → (ι → ι → ι) → ι → ι . 0) (Inj0 (x7 (λ x12 . 0) 0 (λ x12 . 0))) (λ x12 x13 . x3 (λ x14 : ι → (ι → ι → ι) → ι → ι . setsum 0 0) 0 (λ x14 x15 x16 . x15)) (setsum (Inj0 0) (x0 (λ x12 x13 . λ x14 : (ι → ι) → ι . 0) 0 0)))) (x3 (λ x9 : ι → (ι → ι → ι) → ι → ι . 0) (setsum 0 (Inj0 (x1 (λ x9 . λ x10 : ι → ι . 0) 0))) (λ x9 x10 x11 . x7 (λ x12 . x2 (λ x13 : (ι → ι) → (ι → ι → ι) → ι . λ x14 : ι → (ι → ι) → ι . λ x15 . 0) (λ x13 . x13)) 0 (λ x12 . x11)) (x0 (λ x9 x10 . λ x11 : (ι → ι) → ι . setsum 0 (x1 (λ x12 . λ x13 : ι → ι . 0) 0)) 0 0))) ⟶ (∀ x4 : (ι → ι → ι) → ι → ι → ι . ∀ x5 : (((ι → ι) → ι → ι) → ι) → ι . ∀ x6 . ∀ x7 : (((ι → ι) → ι) → ι → ι) → ι . x0 (λ x9 x10 . λ x11 : (ι → ι) → ι . x1 (λ x12 . λ x13 : ι → ι . Inj1 (setsum (setsum 0 0) (Inj0 0))) x9) (x4 (λ x9 x10 . x9) (x0 (λ x9 x10 . λ x11 : (ι → ι) → ι . setsum (Inj1 0) x10) (x0 (λ x9 x10 . λ x11 : (ι → ι) → ι . x0 (λ x12 x13 . λ x14 : (ι → ι) → ι . 0) 0 0) (setsum 0 0) (x0 (λ x9 x10 . λ x11 : (ι → ι) → ι . 0) 0 0)) (x1 (λ x9 . λ x10 : ι → ι . 0) (setsum 0 0))) 0) (setsum (setsum 0 0) 0) = setsum (x5 (λ x9 : (ι → ι) → ι → ι . x6)) (Inj1 (Inj0 (x4 (λ x9 x10 . Inj1 0) (Inj1 0) x6)))) ⟶ False (proof)Theorem f7d60.. : ∀ x0 : (ι → ι) → ι → ι → ι → ι → ι . ∀ x1 : (((ι → (ι → ι) → ι → ι) → ι → ι → ι) → ι → ι → ι → ι) → ((((ι → ι) → ι → ι) → ι → ι → ι) → ι → ι → ι) → ι . ∀ x2 : (((ι → (ι → ι) → ι) → ((ι → ι) → ι) → (ι → ι) → ι → ι) → ι) → ι → ι . ∀ x3 : ((ι → ι) → ι) → ι → ι → ι . (∀ x4 . ∀ x5 : (((ι → ι) → ι → ι) → (ι → ι) → ι → ι) → (ι → ι) → ι . ∀ x6 x7 . x3 (λ x9 : ι → ι . 0) 0 (setsum (setsum (x0 (λ x9 . 0) (x1 (λ x9 : (ι → (ι → ι) → ι → ι) → ι → ι → ι . λ x10 x11 x12 . 0) (λ x9 : ((ι → ι) → ι → ι) → ι → ι → ι . λ x10 x11 . 0)) (setsum 0 0) (x0 (λ x9 . 0) 0 0 0 0) (Inj1 0)) (Inj1 (x0 (λ x9 . 0) 0 0 0 0))) (x1 (λ x9 : (ι → (ι → ι) → ι → ι) → ι → ι → ι . λ x10 x11 x12 . 0) (λ x9 : ((ι → ι) → ι → ι) → ι → ι → ι . λ x10 x11 . x11))) = x4) ⟶ (∀ x4 . ∀ x5 : ι → ((ι → ι) → ι) → ι . ∀ x6 : ι → ι → ι . ∀ x7 . x3 (λ x9 : ι → ι . x2 (λ x10 : (ι → (ι → ι) → ι) → ((ι → ι) → ι) → (ι → ι) → ι → ι . x0 (λ x11 . 0) (x2 (λ x11 : (ι → (ι → ι) → ι) → ((ι → ι) → ι) → (ι → ι) → ι → ι . 0) 0) (x2 (λ x11 : (ι → (ι → ι) → ι) → ((ι → ι) → ι) → (ι → ι) → ι → ι . Inj0 0) (x9 0)) (setsum (setsum 0 0) 0) (setsum 0 (x2 (λ x11 : (ι → (ι → ι) → ι) → ((ι → ι) → ι) → (ι → ι) → ι → ι . 0) 0))) (x3 (λ x10 : ι → ι . 0) (Inj1 (x5 0 (λ x10 : ι → ι . 0))) 0)) (setsum (Inj0 (x0 (λ x9 . 0) x4 0 (x3 (λ x9 : ι → ι . 0) 0 0) x4)) 0) (Inj1 (x3 (λ x9 : ι → ι . 0) (x5 0 (λ x9 : ι → ι . x5 0 (λ x10 : ι → ι . 0))) 0)) = setsum (x6 0 x4) 0) ⟶ (∀ x4 : ι → ι → ι . ∀ x5 : (ι → ι → ι → ι) → ι → (ι → ι) → ι . ∀ x6 : ι → ι . ∀ x7 : (((ι → ι) → ι) → ι) → ι . x2 (λ x9 : (ι → (ι → ι) → ι) → ((ι → ι) → ι) → (ι → ι) → ι → ι . Inj0 0) 0 = x7 (λ x9 : (ι → ι) → ι . x2 (λ x10 : (ι → (ι → ι) → ι) → ((ι → ι) → ι) → (ι → ι) → ι → ι . x9 (λ x11 . x7 (λ x12 : (ι → ι) → ι . 0))) 0)) ⟶ (∀ x4 : ι → ι . ∀ x5 : (ι → ι) → ι → ι . ∀ x6 . ∀ x7 : (ι → ι) → ι . x2 (λ x9 : (ι → (ι → ι) → ι) → ((ι → ι) → ι) → (ι → ι) → ι → ι . x6) (x4 (x7 (λ x9 . x1 (λ x10 : (ι → (ι → ι) → ι → ι) → ι → ι → ι . λ x11 x12 x13 . x0 (λ x14 . 0) 0 0 0 0) (λ x10 : ((ι → ι) → ι → ι) → ι → ι → ι . λ x11 x12 . 0)))) = x6) ⟶ (∀ x4 . ∀ x5 : (ι → ι → ι → ι) → ι → ι . ∀ x6 : (ι → (ι → ι) → ι) → ι → ι . ∀ x7 : ((ι → ι → ι) → ι → ι) → ι . x1 (λ x9 : (ι → (ι → ι) → ι → ι) → ι → ι → ι . λ x10 x11 x12 . setsum (setsum (setsum 0 (x0 (λ x13 . 0) 0 0 0 0)) (x0 (λ x13 . x3 (λ x14 : ι → ι . 0) 0 0) x10 (x2 (λ x13 : (ι → (ι → ι) → ι) → ((ι → ι) → ι) → (ι → ι) → ι → ι . 0) 0) (Inj1 0) (x3 (λ x13 : ι → ι . 0) 0 0))) (Inj1 (Inj1 0))) (λ x9 : ((ι → ι) → ι → ι) → ι → ι → ι . λ x10 x11 . x10) = setsum 0 0) ⟶ (∀ x4 . ∀ x5 : (ι → ι) → ι . ∀ x6 : (ι → (ι → ι) → ι → ι) → ι . ∀ x7 . x1 (λ x9 : (ι → (ι → ι) → ι → ι) → ι → ι → ι . λ x10 x11 x12 . 0) (λ x9 : ((ι → ι) → ι → ι) → ι → ι → ι . λ x10 x11 . Inj1 (x0 (λ x12 . Inj0 x11) (x2 (λ x12 : (ι → (ι → ι) → ι) → ((ι → ι) → ι) → (ι → ι) → ι → ι . x2 (λ x13 : (ι → (ι → ι) → ι) → ((ι → ι) → ι) → (ι → ι) → ι → ι . 0) 0) 0) (x2 (λ x12 : (ι → (ι → ι) → ι) → ((ι → ι) → ι) → (ι → ι) → ι → ι . x1 (λ x13 : (ι → (ι → ι) → ι → ι) → ι → ι → ι . λ x14 x15 x16 . 0) (λ x13 : ((ι → ι) → ι → ι) → ι → ι → ι . λ x14 x15 . 0)) x7) x7 (x9 (λ x12 : ι → ι . λ x13 . x1 (λ x14 : (ι → (ι → ι) → ι → ι) → ι → ι → ι . λ x15 x16 x17 . 0) (λ x14 : ((ι → ι) → ι → ι) → ι → ι → ι . λ x15 x16 . 0)) (setsum 0 0) (x1 (λ x12 : (ι → (ι → ι) → ι → ι) → ι → ι → ι . λ x13 x14 x15 . 0) (λ x12 : ((ι → ι) → ι → ι) → ι → ι → ι . λ x13 x14 . 0))))) = Inj1 (x3 (λ x9 : ι → ι . 0) 0 (setsum (setsum (x5 (λ x9 . 0)) 0) (x5 (λ x9 . x3 (λ x10 : ι → ι . 0) 0 0))))) ⟶ (∀ x4 x5 x6 . ∀ x7 : (ι → ι → ι) → ι . x0 (λ x9 . 0) 0 (x0 (λ x9 . x9) (setsum (x2 (λ x9 : (ι → (ι → ι) → ι) → ((ι → ι) → ι) → (ι → ι) → ι → ι . x0 (λ x10 . 0) 0 0 0 0) x5) 0) (x7 (λ x9 x10 . x7 (λ x11 x12 . x12))) (x3 (λ x9 : ι → ι . x5) x5 0) 0) x4 (setsum x6 (x2 (λ x9 : (ι → (ι → ι) → ι) → ((ι → ι) → ι) → (ι → ι) → ι → ι . x3 (λ x10 : ι → ι . x3 (λ x11 : ι → ι . 0) 0 0) (Inj1 0) (x1 (λ x10 : (ι → (ι → ι) → ι → ι) → ι → ι → ι . λ x11 x12 x13 . 0) (λ x10 : ((ι → ι) → ι → ι) → ι → ι → ι . λ x11 x12 . 0))) (Inj0 x5))) = x0 (λ x9 . Inj1 (Inj0 (Inj1 (setsum 0 0)))) (Inj1 x6) (x0 (λ x9 . 0) 0 0 0 (x0 (λ x9 . x0 (λ x10 . 0) (x7 (λ x10 x11 . 0)) (x7 (λ x10 x11 . 0)) (x0 (λ x10 . 0) 0 0 0 0) (Inj1 0)) 0 x4 x6 x4)) x6 (Inj0 x6)) ⟶ (∀ x4 x5 . ∀ x6 : ι → (ι → ι) → ι → ι → ι . ∀ x7 : (((ι → ι) → ι → ι) → ι) → ι → (ι → ι) → ι . x0 (λ x9 . x1 (λ x10 : (ι → (ι → ι) → ι → ι) → ι → ι → ι . λ x11 x12 x13 . x11) (λ x10 : ((ι → ι) → ι → ι) → ι → ι → ι . λ x11 x12 . Inj0 (x10 (λ x13 : ι → ι . λ x14 . Inj0 0) x9 0))) 0 (setsum (x3 (λ x9 : ι → ι . x2 (λ x10 : (ι → (ι → ι) → ι) → ((ι → ι) → ι) → (ι → ι) → ι → ι . 0) (Inj1 0)) (x6 (x0 (λ x9 . 0) 0 0 0 0) (λ x9 . x7 (λ x10 : (ι → ι) → ι → ι . 0) 0 (λ x10 . 0)) (x3 (λ x9 : ι → ι . 0) 0 0) (setsum 0 0)) x4) (Inj1 (x1 (λ x9 : (ι → (ι → ι) → ι → ι) → ι → ι → ι . λ x10 x11 x12 . 0) (λ x9 : ((ι → ι) → ι → ι) → ι → ι → ι . λ x10 x11 . 0)))) 0 (Inj1 (x1 (λ x9 : (ι → (ι → ι) → ι → ι) → ι → ι → ι . λ x10 x11 x12 . x9 (λ x13 . λ x14 : ι → ι . λ x15 . Inj1 0) 0 0) (λ x9 : ((ι → ι) → ι → ι) → ι → ι → ι . λ x10 x11 . 0))) = Inj1 0) ⟶ False (proof)Theorem fa49b.. : ∀ x0 : (ι → ι) → ι → ι . ∀ x1 : ((ι → ((ι → ι) → ι → ι) → ι) → ι) → (ι → ((ι → ι) → ι → ι) → (ι → ι) → ι → ι) → ι → ι . ∀ x2 : (ι → ι) → (((ι → ι → ι) → ι) → ι) → ι → ((ι → ι) → ι) → ι . ∀ x3 : (ι → (ι → ι → ι) → ι) → (ι → ι → ι → ι) → (ι → ι → ι) → ι . (∀ x4 : ι → ι → (ι → ι) → ι → ι . ∀ x5 x6 x7 . x3 (λ x9 . λ x10 : ι → ι → ι . Inj0 (x3 (λ x11 . λ x12 : ι → ι → ι . x3 (λ x13 . λ x14 : ι → ι → ι . x1 (λ x15 : ι → ((ι → ι) → ι → ι) → ι . 0) (λ x15 . λ x16 : (ι → ι) → ι → ι . λ x17 : ι → ι . λ x18 . 0) 0) (λ x13 x14 x15 . 0) (λ x13 x14 . x11)) (λ x11 x12 x13 . x11) (λ x11 x12 . 0))) (λ x9 x10 x11 . 0) (λ x9 x10 . 0) = x5) ⟶ (∀ x4 x5 x6 x7 . x3 (λ x9 . λ x10 : ι → ι → ι . Inj0 (setsum x9 x9)) (λ x9 x10 x11 . 0) (λ x9 x10 . x0 (λ x11 . x0 (λ x12 . Inj0 0) (x3 (λ x12 . λ x13 : ι → ι → ι . 0) (λ x12 x13 x14 . 0) (λ x12 x13 . x2 (λ x14 . 0) (λ x14 : (ι → ι → ι) → ι . 0) 0 (λ x14 : ι → ι . 0)))) (setsum x7 (Inj1 (setsum 0 0)))) = Inj1 x6) ⟶ (∀ x4 : ι → ι . ∀ x5 : (ι → ι) → ι → (ι → ι) → ι → ι . ∀ x6 : ι → ι . ∀ x7 : ι → ((ι → ι) → ι) → ι . x2 (λ x9 . x5 (λ x10 . x10) (x2 (λ x10 . Inj0 (x7 0 (λ x11 : ι → ι . 0))) (λ x10 : (ι → ι → ι) → ι . x6 (x6 0)) (x5 (λ x10 . x3 (λ x11 . λ x12 : ι → ι → ι . 0) (λ x11 x12 x13 . 0) (λ x11 x12 . 0)) (x7 0 (λ x10 : ι → ι . 0)) (λ x10 . Inj1 0) (x5 (λ x10 . 0) 0 (λ x10 . 0) 0)) (λ x10 : ι → ι . x10 x9)) (x0 (λ x10 . 0)) 0) (λ x9 : (ι → ι → ι) → ι . x1 (λ x10 : ι → ((ι → ι) → ι → ι) → ι . x0 (λ x11 . x1 (λ x12 : ι → ((ι → ι) → ι → ι) → ι . 0) (λ x12 . λ x13 : (ι → ι) → ι → ι . λ x14 : ι → ι . λ x15 . 0) (Inj0 0)) (x1 (λ x11 : ι → ((ι → ι) → ι → ι) → ι . x1 (λ x12 : ι → ((ι → ι) → ι → ι) → ι . 0) (λ x12 . λ x13 : (ι → ι) → ι → ι . λ x14 : ι → ι . λ x15 . 0) 0) (λ x11 . λ x12 : (ι → ι) → ι → ι . λ x13 : ι → ι . λ x14 . x0 (λ x15 . 0) 0) (x7 0 (λ x11 : ι → ι . 0)))) (λ x10 . λ x11 : (ι → ι) → ι → ι . λ x12 : ι → ι . λ x13 . 0) (setsum 0 (setsum (x3 (λ x10 . λ x11 : ι → ι → ι . 0) (λ x10 x11 x12 . 0) (λ x10 x11 . 0)) 0))) 0 (λ x9 : ι → ι . x1 (λ x10 : ι → ((ι → ι) → ι → ι) → ι . x7 (x7 (x3 (λ x11 . λ x12 : ι → ι → ι . 0) (λ x11 x12 x13 . 0) (λ x11 x12 . 0)) (λ x11 : ι → ι . Inj0 0)) (λ x11 : ι → ι . 0)) (λ x10 . λ x11 : (ι → ι) → ι → ι . λ x12 : ι → ι . λ x13 . x13) 0) = x1 (λ x9 : ι → ((ι → ι) → ι → ι) → ι . setsum (x9 0 (λ x10 : ι → ι . λ x11 . Inj1 (x0 (λ x12 . 0) 0))) (Inj1 0)) (λ x9 . λ x10 : (ι → ι) → ι → ι . λ x11 : ι → ι . λ x12 . x11 0) (x0 (λ x9 . x1 (λ x10 : ι → ((ι → ι) → ι → ι) → ι . 0) (λ x10 . λ x11 : (ι → ι) → ι → ι . λ x12 : ι → ι . λ x13 . setsum (x11 (λ x14 . 0) 0) 0) (x6 (x1 (λ x10 : ι → ((ι → ι) → ι → ι) → ι . 0) (λ x10 . λ x11 : (ι → ι) → ι → ι . λ x12 : ι → ι . λ x13 . 0) 0))) (x4 0))) ⟶ (∀ x4 x5 . ∀ x6 : ι → (ι → ι) → (ι → ι) → ι . ∀ x7 : ι → ι → (ι → ι) → ι → ι . x2 (λ x9 . 0) (λ x9 : (ι → ι → ι) → ι . x7 (x0 (λ x10 . x3 (λ x11 . λ x12 : ι → ι → ι . x0 (λ x13 . 0) 0) (λ x11 x12 x13 . Inj0 0) (λ x11 x12 . 0)) (x9 (λ x10 x11 . x2 (λ x12 . 0) (λ x12 : (ι → ι → ι) → ι . 0) 0 (λ x12 : ι → ι . 0)))) 0 (λ x10 . Inj1 0) 0) 0 (λ x9 : ι → ι . 0) = setsum (x3 (λ x9 . λ x10 : ι → ι → ι . 0) (λ x9 x10 x11 . setsum x11 (setsum (Inj0 0) (x7 0 0 (λ x12 . 0) 0))) (λ x9 x10 . x9)) (x0 (λ x9 . 0) (x0 (λ x9 . Inj1 (x6 0 (λ x10 . 0) (λ x10 . 0))) 0))) ⟶ (∀ x4 : ι → ι . ∀ x5 : (((ι → ι) → ι) → ι → ι → ι) → ι → (ι → ι) → ι . ∀ x6 x7 . x1 (λ x9 : ι → ((ι → ι) → ι → ι) → ι . x7) (λ x9 . λ x10 : (ι → ι) → ι → ι . λ x11 : ι → ι . λ x12 . x2 (λ x13 . x11 (Inj0 0)) (λ x13 : (ι → ι → ι) → ι . setsum x12 (setsum (x10 (λ x14 . 0) 0) (x10 (λ x14 . 0) 0))) 0 (λ x13 : ι → ι . setsum 0 0)) 0 = Inj0 (Inj0 (x1 (λ x9 : ι → ((ι → ι) → ι → ι) → ι . x6) (λ x9 . λ x10 : (ι → ι) → ι → ι . λ x11 : ι → ι . λ x12 . setsum (x0 (λ x13 . 0) 0) (setsum 0 0)) (Inj1 (Inj0 0))))) ⟶ (∀ x4 . ∀ x5 : ι → (ι → ι) → ι . ∀ x6 . ∀ x7 : (ι → ι) → ι . x1 (λ x9 : ι → ((ι → ι) → ι → ι) → ι . x7 (λ x10 . x7 (λ x11 . 0))) (λ x9 . λ x10 : (ι → ι) → ι → ι . λ x11 : ι → ι . λ x12 . x2 (λ x13 . 0) (λ x13 : (ι → ι → ι) → ι . 0) (setsum (Inj0 x9) (setsum x12 (x2 (λ x13 . 0) (λ x13 : (ι → ι → ι) → ι . 0) 0 (λ x13 : ι → ι . 0)))) (λ x13 : ι → ι . Inj0 (setsum (x3 (λ x14 . λ x15 : ι → ι → ι . 0) (λ x14 x15 x16 . 0) (λ x14 x15 . 0)) 0))) (x1 (λ x9 : ι → ((ι → ι) → ι → ι) → ι . x7 (λ x10 . Inj1 0)) (λ x9 . λ x10 : (ι → ι) → ι → ι . λ x11 : ι → ι . λ x12 . setsum (Inj1 (x10 (λ x13 . 0) 0)) (Inj0 0)) (x7 (λ x9 . 0))) = x1 (λ x9 : ι → ((ι → ι) → ι → ι) → ι . Inj0 0) (λ x9 . λ x10 : (ι → ι) → ι → ι . λ x11 : ι → ι . λ x12 . setsum (x2 (λ x13 . setsum (x0 (λ x14 . 0) 0) (x2 (λ x14 . 0) (λ x14 : (ι → ι → ι) → ι . 0) 0 (λ x14 : ι → ι . 0))) (λ x13 : (ι → ι → ι) → ι . x3 (λ x14 . λ x15 : ι → ι → ι . Inj0 0) (λ x14 x15 x16 . x16) (λ x14 x15 . x1 (λ x16 : ι → ((ι → ι) → ι → ι) → ι . 0) (λ x16 . λ x17 : (ι → ι) → ι → ι . λ x18 : ι → ι . λ x19 . 0) 0)) 0 (λ x13 : ι → ι . Inj0 (Inj0 0))) (x2 (λ x13 . setsum (x11 0) (x11 0)) (λ x13 : (ι → ι → ι) → ι . Inj1 (Inj1 0)) x9 (λ x13 : ι → ι . Inj0 x12))) (Inj0 0)) ⟶ (∀ x4 : ι → (ι → ι) → ι → ι → ι . ∀ x5 : ι → ι . ∀ x6 . ∀ x7 : ι → ι . x0 (λ x9 . 0) (Inj0 0) = Inj1 (x2 (λ x9 . 0) (λ x9 : (ι → ι → ι) → ι . setsum (x9 (λ x10 x11 . x0 (λ x12 . 0) 0)) 0) (x3 (λ x9 . λ x10 : ι → ι → ι . 0) (λ x9 x10 x11 . x1 (λ x12 : ι → ((ι → ι) → ι → ι) → ι . 0) (λ x12 . λ x13 : (ι → ι) → ι → ι . λ x14 : ι → ι . λ x15 . 0) 0) (λ x9 x10 . x10)) (λ x9 : ι → ι . x2 (λ x10 . x9 (setsum 0 0)) (λ x10 : (ι → ι → ι) → ι . Inj0 (setsum 0 0)) (x7 0) (λ x10 : ι → ι . 0)))) ⟶ (∀ x4 x5 : ι → ι . ∀ x6 . ∀ x7 : (ι → ι) → ι . x0 (λ x9 . setsum (Inj0 (x2 (λ x10 . x6) (λ x10 : (ι → ι → ι) → ι . x10 (λ x11 x12 . 0)) (Inj1 0) (λ x10 : ι → ι . x2 (λ x11 . 0) (λ x11 : (ι → ι → ι) → ι . 0) 0 (λ x11 : ι → ι . 0)))) (setsum (x1 (λ x10 : ι → ((ι → ι) → ι → ι) → ι . 0) (λ x10 . λ x11 : (ι → ι) → ι → ι . λ x12 : ι → ι . λ x13 . x1 (λ x14 : ι → ((ι → ι) → ι → ι) → ι . 0) (λ x14 . λ x15 : (ι → ι) → ι → ι . λ x16 : ι → ι . λ x17 . 0) 0) 0) (x0 (λ x10 . x0 (λ x11 . 0) 0) 0))) (x7 (λ x9 . x3 (λ x10 . λ x11 : ι → ι → ι . 0) (λ x10 x11 x12 . 0) (λ x10 x11 . x7 (λ x12 . x10)))) = setsum 0 (Inj1 (x5 (x0 (λ x9 . x1 (λ x10 : ι → ((ι → ι) → ι → ι) → ι . 0) (λ x10 . λ x11 : (ι → ι) → ι → ι . λ x12 : ι → ι . λ x13 . 0) 0) (setsum 0 0))))) ⟶ False (proof)Theorem 001c8.. : ∀ x0 : ((ι → ι) → ι) → ι → ι . ∀ x1 : ((((ι → ι) → ι) → ι) → ι) → ι → ι . ∀ x2 : (ι → ι) → ((ι → ι → ι → ι) → ι) → ι → ι . ∀ x3 : (ι → ι → ι → ι) → ι → ι . (∀ x4 x5 x6 x7 . x3 (λ x9 x10 x11 . x1 (λ x12 : ((ι → ι) → ι) → ι . x2 (λ x13 . 0) (λ x13 : ι → ι → ι → ι . setsum x11 (Inj0 0)) 0) (x1 (λ x12 : ((ι → ι) → ι) → ι . x3 (λ x13 x14 x15 . 0) 0) 0)) 0 = setsum x4 x6) ⟶ (∀ x4 . ∀ x5 : ι → ι . ∀ x6 x7 . x3 (λ x9 x10 x11 . 0) x6 = Inj1 (Inj0 (x1 (λ x9 : ((ι → ι) → ι) → ι . Inj1 0) (setsum 0 0)))) ⟶ (∀ x4 : (ι → (ι → ι) → ι → ι) → ι . ∀ x5 x6 x7 . x2 (λ x9 . 0) (λ x9 : ι → ι → ι → ι . x9 0 (x1 (λ x10 : ((ι → ι) → ι) → ι . 0) 0) (x3 (λ x10 x11 x12 . x0 (λ x13 : ι → ι . x0 (λ x14 : ι → ι . 0) 0) 0) x5)) 0 = x7) ⟶ (∀ x4 . ∀ x5 : (ι → ι) → ι . ∀ x6 : (ι → ι) → ((ι → ι) → ι) → (ι → ι) → ι → ι . ∀ x7 : (((ι → ι) → ι) → ι) → (ι → ι → ι) → ι → ι . x2 (λ x9 . 0) (λ x9 : ι → ι → ι → ι . 0) (x7 (λ x9 : (ι → ι) → ι . x2 (setsum (x9 (λ x10 . 0))) (λ x10 : ι → ι → ι → ι . 0) (x0 (λ x10 : ι → ι . x0 (λ x11 : ι → ι . 0) 0) 0)) (λ x9 x10 . x6 (λ x11 . x9) (λ x11 : ι → ι . x10) (λ x11 . 0) (setsum (x0 (λ x11 : ι → ι . 0) 0) 0)) 0) = x7 (λ x9 : (ι → ι) → ι . Inj1 (Inj0 (x5 (λ x10 . setsum 0 0)))) (λ x9 x10 . x6 (λ x11 . setsum x11 x10) (λ x11 : ι → ι . x1 (λ x12 : ((ι → ι) → ι) → ι . Inj0 (x1 (λ x13 : ((ι → ι) → ι) → ι . 0) 0)) (x3 (λ x12 x13 x14 . setsum 0 0) (x2 (λ x12 . 0) (λ x12 : ι → ι → ι → ι . 0) 0))) (λ x11 . setsum (x2 (λ x12 . x0 (λ x13 : ι → ι . 0) 0) (λ x12 : ι → ι → ι → ι . x0 (λ x13 : ι → ι . 0) 0) x11) 0) 0) (Inj0 (setsum 0 (setsum (x6 (λ x9 . 0) (λ x9 : ι → ι . 0) (λ x9 . 0) 0) (Inj0 0))))) ⟶ (∀ x4 . ∀ x5 : ι → ((ι → ι) → ι) → ι → ι → ι . ∀ x6 x7 . x1 (λ x9 : ((ι → ι) → ι) → ι . x6) 0 = x6) ⟶ (∀ x4 . ∀ x5 : (ι → (ι → ι) → ι) → ι . ∀ x6 x7 . x1 (λ x9 : ((ι → ι) → ι) → ι . x0 (λ x10 : ι → ι . x2 (λ x11 . x3 (λ x12 x13 x14 . 0) (Inj0 0)) (λ x11 : ι → ι → ι → ι . x0 (λ x12 : ι → ι . Inj1 0) (Inj1 0)) (setsum (Inj0 0) (x2 (λ x11 . 0) (λ x11 : ι → ι → ι → ι . 0) 0))) (x9 (λ x10 : ι → ι . Inj0 0))) (x1 (λ x9 : ((ι → ι) → ι) → ι . x0 (λ x10 : ι → ι . x9 (λ x11 : ι → ι . x11 0)) (x9 (λ x10 : ι → ι . x1 (λ x11 : ((ι → ι) → ι) → ι . 0) 0))) x6) = setsum x7 (Inj0 x6)) ⟶ (∀ x4 : ι → ((ι → ι) → ι) → (ι → ι) → ι → ι . ∀ x5 : ι → ι → ι . ∀ x6 x7 . x0 (λ x9 : ι → ι . setsum (setsum 0 0) (x0 (λ x10 : ι → ι . x3 (λ x11 x12 x13 . x11) 0) (x5 x7 0))) (x2 Inj0 (λ x9 : ι → ι → ι → ι . x3 (λ x10 x11 x12 . x3 (λ x13 x14 x15 . x0 (λ x16 : ι → ι . 0) 0) (Inj1 0)) (x5 0 (setsum 0 0))) 0) = x2 (λ x9 . setsum (x0 (λ x10 : ι → ι . x9) (x3 (λ x10 x11 x12 . 0) (setsum 0 0))) (x1 (λ x10 : ((ι → ι) → ι) → ι . setsum (x3 (λ x11 x12 x13 . 0) 0) 0) 0)) (λ x9 : ι → ι → ι → ι . setsum (x0 (λ x10 : ι → ι . setsum x7 (setsum 0 0)) (x5 x7 (x5 0 0))) x7) (x0 (λ x9 : ι → ι . 0) x7)) ⟶ (∀ x4 : ι → ι . ∀ x5 . ∀ x6 : (((ι → ι) → ι) → ι → ι → ι) → ι → ι . ∀ x7 : ι → ι . x0 (λ x9 : ι → ι . 0) x5 = setsum 0 (x4 0)) ⟶ False (proof)Theorem 9f7c7.. : ∀ x0 : (ι → (ι → ι) → (ι → ι) → ι → ι → ι) → ι → ι → ((ι → ι) → ι → ι) → ι . ∀ x1 : (((ι → (ι → ι) → ι → ι) → ι) → (ι → ι) → (ι → ι → ι) → (ι → ι) → ι) → ι → ι → ι → (ι → ι) → ι → ι . ∀ x2 : ((ι → (ι → ι → ι) → ι) → ι) → ι → ι . ∀ x3 : (ι → ι) → ι → (((ι → ι) → ι) → (ι → ι) → ι) → ι . (∀ x4 x5 . ∀ x6 : (ι → ι) → ι → (ι → ι) → ι → ι . ∀ x7 . x3 (λ x9 . setsum 0 x5) (setsum x5 (x6 (λ x9 . 0) (setsum x5 (x0 (λ x9 . λ x10 x11 : ι → ι . λ x12 x13 . 0) 0 0 (λ x9 : ι → ι . λ x10 . 0))) (λ x9 . setsum (Inj1 0) (x6 (λ x10 . 0) 0 (λ x10 . 0) 0)) 0)) (λ x9 : (ι → ι) → ι . λ x10 : ι → ι . 0) = x4) ⟶ (∀ x4 . ∀ x5 : (ι → ι) → ι . ∀ x6 . ∀ x7 : ι → ι → (ι → ι) → ι . x3 (λ x9 . 0) (setsum (x0 (λ x9 . λ x10 x11 : ι → ι . λ x12 x13 . setsum (Inj1 0) (x1 (λ x14 : (ι → (ι → ι) → ι → ι) → ι . λ x15 : ι → ι . λ x16 : ι → ι → ι . λ x17 : ι → ι . 0) 0 0 0 (λ x14 . 0) 0)) 0 0 (λ x9 : ι → ι . λ x10 . 0)) (x2 (λ x9 : ι → (ι → ι → ι) → ι . setsum (Inj0 0) (setsum 0 0)) x4)) (λ x9 : (ι → ι) → ι . λ x10 : ι → ι . 0) = setsum 0 x4) ⟶ (∀ x4 : (((ι → ι) → ι → ι) → ι) → ι . ∀ x5 : ((ι → ι) → ι) → ι . ∀ x6 : ι → ((ι → ι) → ι) → (ι → ι) → ι → ι . ∀ x7 . x2 (λ x9 : ι → (ι → ι → ι) → ι . x2 (λ x10 : ι → (ι → ι → ι) → ι . 0) 0) 0 = Inj0 (setsum x7 (x5 (λ x9 : ι → ι . x6 0 (λ x10 : ι → ι . 0) (λ x10 . Inj0 0) 0)))) ⟶ (∀ x4 : ι → ι . ∀ x5 : ((ι → ι) → ι → ι) → ι . ∀ x6 : ι → ι . ∀ x7 . x2 (λ x9 : ι → (ι → ι → ι) → ι . 0) (x1 (λ x9 : (ι → (ι → ι) → ι → ι) → ι . λ x10 : ι → ι . λ x11 : ι → ι → ι . λ x12 : ι → ι . x3 (λ x13 . x2 (λ x14 : ι → (ι → ι → ι) → ι . 0) (Inj1 0)) 0 (λ x13 : (ι → ι) → ι . λ x14 : ι → ι . x13 (λ x15 . x15))) (setsum 0 (x6 0)) (x1 (λ x9 : (ι → (ι → ι) → ι → ι) → ι . λ x10 : ι → ι . λ x11 : ι → ι → ι . λ x12 : ι → ι . x12 (x9 (λ x13 . λ x14 : ι → ι . λ x15 . 0))) (x6 (Inj1 0)) 0 (setsum (x2 (λ x9 : ι → (ι → ι → ι) → ι . 0) 0) (x3 (λ x9 . 0) 0 (λ x9 : (ι → ι) → ι . λ x10 : ι → ι . 0))) (λ x9 . x9) 0) (x0 (λ x9 . λ x10 x11 : ι → ι . λ x12 x13 . x11 x12) (x0 (λ x9 . λ x10 x11 : ι → ι . λ x12 x13 . setsum 0 0) 0 x7 (λ x9 : ι → ι . λ x10 . x0 (λ x11 . λ x12 x13 : ι → ι . λ x14 x15 . 0) 0 0 (λ x11 : ι → ι . λ x12 . 0))) 0 (λ x9 : ι → ι . λ x10 . 0)) (λ x9 . x7) (x5 (λ x9 : ι → ι . λ x10 . x9 0))) = setsum (x4 (x1 (λ x9 : (ι → (ι → ι) → ι → ι) → ι . λ x10 : ι → ι . λ x11 : ι → ι → ι . λ x12 : ι → ι . 0) (x2 (λ x9 : ι → (ι → ι → ι) → ι . x1 (λ x10 : (ι → (ι → ι) → ι → ι) → ι . λ x11 : ι → ι . λ x12 : ι → ι → ι . λ x13 : ι → ι . 0) 0 0 0 (λ x10 . 0) 0) (x3 (λ x9 . 0) 0 (λ x9 : (ι → ι) → ι . λ x10 : ι → ι . 0))) (x5 (λ x9 : ι → ι . λ x10 . 0)) (x0 (λ x9 . λ x10 x11 : ι → ι . λ x12 x13 . x1 (λ x14 : (ι → (ι → ι) → ι → ι) → ι . λ x15 : ι → ι . λ x16 : ι → ι → ι . λ x17 : ι → ι . 0) 0 0 0 (λ x14 . 0) 0) (Inj1 0) (setsum 0 0) (λ x9 : ι → ι . λ x10 . x6 0)) (λ x9 . 0) (Inj0 0))) 0) ⟶ (∀ x4 : ι → (ι → ι → ι) → ι → ι . ∀ x5 x6 . ∀ x7 : (ι → ι) → ι . x1 (λ x9 : (ι → (ι → ι) → ι → ι) → ι . λ x10 : ι → ι . λ x11 : ι → ι → ι . λ x12 : ι → ι . x2 (λ x13 : ι → (ι → ι → ι) → ι . 0) (x9 (λ x13 . λ x14 : ι → ι . λ x15 . x15))) (x7 (λ x9 . 0)) (Inj0 (x7 (λ x9 . Inj0 0))) 0 (λ x9 . x3 (λ x10 . x7 (λ x11 . setsum (x2 (λ x12 : ι → (ι → ι → ι) → ι . 0) 0) (x1 (λ x12 : (ι → (ι → ι) → ι → ι) → ι . λ x13 : ι → ι . λ x14 : ι → ι → ι . λ x15 : ι → ι . 0) 0 0 0 (λ x12 . 0) 0))) (setsum x5 (Inj1 (setsum 0 0))) (λ x10 : (ι → ι) → ι . λ x11 : ι → ι . setsum (setsum 0 (x10 (λ x12 . 0))) (x0 (λ x12 . λ x13 x14 : ι → ι . λ x15 x16 . x13 0) (x2 (λ x12 : ι → (ι → ι → ι) → ι . 0) 0) (x0 (λ x12 . λ x13 x14 : ι → ι . λ x15 x16 . 0) 0 0 (λ x12 : ι → ι . λ x13 . 0)) (λ x12 : ι → ι . λ x13 . x1 (λ x14 : (ι → (ι → ι) → ι → ι) → ι . λ x15 : ι → ι . λ x16 : ι → ι → ι . λ x17 : ι → ι . 0) 0 0 0 (λ x14 . 0) 0)))) (x2 (λ x9 : ι → (ι → ι → ι) → ι . 0) x6) = x2 (λ x9 : ι → (ι → ι → ι) → ι . setsum (x0 (λ x10 . λ x11 x12 : ι → ι . λ x13 x14 . x2 (λ x15 : ι → (ι → ι → ι) → ι . 0) (Inj0 0)) (x2 (λ x10 : ι → (ι → ι → ι) → ι . x6) x6) (x7 (λ x10 . 0)) (λ x10 : ι → ι . λ x11 . setsum (x1 (λ x12 : (ι → (ι → ι) → ι → ι) → ι . λ x13 : ι → ι . λ x14 : ι → ι → ι . λ x15 : ι → ι . 0) 0 0 0 (λ x12 . 0) 0) (Inj1 0))) (setsum (Inj1 (x9 0 (λ x10 x11 . 0))) (setsum (setsum 0 0) (x1 (λ x10 : (ι → (ι → ι) → ι → ι) → ι . λ x11 : ι → ι . λ x12 : ι → ι → ι . λ x13 : ι → ι . 0) 0 0 0 (λ x10 . 0) 0)))) x6) ⟶ (∀ x4 x5 x6 x7 . x1 (λ x9 : (ι → (ι → ι) → ι → ι) → ι . λ x10 : ι → ι . λ x11 : ι → ι → ι . λ x12 : ι → ι . x11 (Inj1 (x10 (x12 0))) (setsum (x10 0) (Inj1 0))) x4 0 x7 (λ x9 . setsum x7 (x2 (λ x10 : ι → (ι → ι → ι) → ι . x9) (setsum (x2 (λ x10 : ι → (ι → ι → ι) → ι . 0) 0) (x0 (λ x10 . λ x11 x12 : ι → ι . λ x13 x14 . 0) 0 0 (λ x10 : ι → ι . λ x11 . 0))))) (Inj0 (Inj1 x4)) = setsum (x0 (λ x9 . λ x10 x11 : ι → ι . λ x12 x13 . x11 0) (Inj0 0) (x3 (λ x9 . x7) (x2 (λ x9 : ι → (ι → ι → ι) → ι . x2 (λ x10 : ι → (ι → ι → ι) → ι . 0) 0) 0) (λ x9 : (ι → ι) → ι . λ x10 : ι → ι . Inj1 (Inj0 0))) (λ x9 : ι → ι . λ x10 . Inj0 0)) x4) ⟶ (∀ x4 x5 x6 . ∀ x7 : ι → ι → ι . x0 (λ x9 . λ x10 x11 : ι → ι . λ x12 x13 . x3 (λ x14 . setsum 0 0) (x0 (λ x14 . λ x15 x16 : ι → ι . λ x17 x18 . 0) 0 (setsum (x11 0) 0) (λ x14 : ι → ι . λ x15 . x13)) (λ x14 : (ι → ι) → ι . λ x15 : ι → ι . 0)) (Inj1 (x3 (λ x9 . Inj1 (x3 (λ x10 . 0) 0 (λ x10 : (ι → ι) → ι . λ x11 : ι → ι . 0))) (setsum 0 0) (λ x9 : (ι → ι) → ι . λ x10 : ι → ι . x1 (λ x11 : (ι → (ι → ι) → ι → ι) → ι . λ x12 : ι → ι . λ x13 : ι → ι → ι . λ x14 : ι → ι . x2 (λ x15 : ι → (ι → ι → ι) → ι . 0) 0) (x3 (λ x11 . 0) 0 (λ x11 : (ι → ι) → ι . λ x12 : ι → ι . 0)) 0 (Inj1 0) (λ x11 . 0) 0))) 0 (λ x9 : ι → ι . λ x10 . Inj1 0) = x3 (λ x9 . setsum (x3 (λ x10 . setsum (setsum 0 0) (Inj1 0)) (x0 (λ x10 . λ x11 x12 : ι → ι . λ x13 x14 . x1 (λ x15 : (ι → (ι → ι) → ι → ι) → ι . λ x16 : ι → ι . λ x17 : ι → ι → ι . λ x18 : ι → ι . 0) 0 0 0 (λ x15 . 0) 0) (Inj0 0) (Inj1 0) (λ x10 : ι → ι . λ x11 . x1 (λ x12 : (ι → (ι → ι) → ι → ι) → ι . λ x13 : ι → ι . λ x14 : ι → ι → ι . λ x15 : ι → ι . 0) 0 0 0 (λ x12 . 0) 0)) (λ x10 : (ι → ι) → ι . λ x11 : ι → ι . x2 (λ x12 : ι → (ι → ι → ι) → ι . x10 (λ x13 . 0)) 0)) x6) x5 (λ x9 : (ι → ι) → ι . λ x10 : ι → ι . setsum 0 0)) ⟶ (∀ x4 . ∀ x5 : ι → ι . ∀ x6 : (ι → ι) → ι . ∀ x7 : (ι → ι) → ι → ι → ι → ι . x0 (λ x9 . λ x10 x11 : ι → ι . λ x12 x13 . x0 (λ x14 . λ x15 x16 : ι → ι . λ x17 x18 . x16 0) (Inj1 (setsum x12 (x11 0))) (x11 x12) (λ x14 : ι → ι . λ x15 . Inj1 (x0 (λ x16 . λ x17 x18 : ι → ι . λ x19 x20 . x20) (x1 (λ x16 : (ι → (ι → ι) → ι → ι) → ι . λ x17 : ι → ι . λ x18 : ι → ι → ι . λ x19 : ι → ι . 0) 0 0 0 (λ x16 . 0) 0) (setsum 0 0) (λ x16 : ι → ι . λ x17 . x0 (λ x18 . λ x19 x20 : ι → ι . λ x21 x22 . 0) 0 0 (λ x18 : ι → ι . λ x19 . 0))))) 0 (x0 (λ x9 . λ x10 x11 : ι → ι . λ x12 x13 . setsum (Inj1 (x1 (λ x14 : (ι → (ι → ι) → ι → ι) → ι . λ x15 : ι → ι . λ x16 : ι → ι → ι . λ x17 : ι → ι . 0) 0 0 0 (λ x14 . 0) 0)) (setsum (x0 (λ x14 . λ x15 x16 : ι → ι . λ x17 x18 . 0) 0 0 (λ x14 : ι → ι . λ x15 . 0)) x13)) (x1 (λ x9 : (ι → (ι → ι) → ι → ι) → ι . λ x10 : ι → ι . λ x11 : ι → ι → ι . λ x12 : ι → ι . x11 (Inj0 0) (x2 (λ x13 : ι → (ι → ι → ι) → ι . 0) 0)) 0 0 (x0 (λ x9 . λ x10 x11 : ι → ι . λ x12 x13 . x3 (λ x14 . 0) 0 (λ x14 : (ι → ι) → ι . λ x15 : ι → ι . 0)) (x1 (λ x9 : (ι → (ι → ι) → ι → ι) → ι . λ x10 : ι → ι . λ x11 : ι → ι → ι . λ x12 : ι → ι . 0) 0 0 0 (λ x9 . 0) 0) (x1 (λ x9 : (ι → (ι → ι) → ι → ι) → ι . λ x10 : ι → ι . λ x11 : ι → ι → ι . λ x12 : ι → ι . 0) 0 0 0 (λ x9 . 0) 0) (λ x9 : ι → ι . λ x10 . x6 (λ x11 . 0))) (λ x9 . x1 (λ x10 : (ι → (ι → ι) → ι → ι) → ι . λ x11 : ι → ι . λ x12 : ι → ι → ι . λ x13 : ι → ι . x0 (λ x14 . λ x15 x16 : ι → ι . λ x17 x18 . 0) 0 0 (λ x14 : ι → ι . λ x15 . 0)) (setsum 0 0) 0 (Inj1 0) (λ x10 . 0) 0) (x3 (λ x9 . setsum 0 0) (x6 (λ x9 . 0)) (λ x9 : (ι → ι) → ι . λ x10 : ι → ι . x9 (λ x11 . 0)))) (setsum (x1 (λ x9 : (ι → (ι → ι) → ι → ι) → ι . λ x10 : ι → ι . λ x11 : ι → ι → ι . λ x12 : ι → ι . x3 (λ x13 . 0) 0 (λ x13 : (ι → ι) → ι . λ x14 : ι → ι . 0)) (Inj0 0) (x3 (λ x9 . 0) 0 (λ x9 : (ι → ι) → ι . λ x10 : ι → ι . 0)) (x0 (λ x9 . λ x10 x11 : ι → ι . λ x12 x13 . 0) 0 0 (λ x9 : ι → ι . λ x10 . 0)) (λ x9 . x0 (λ x10 . λ x11 x12 : ι → ι . λ x13 x14 . 0) 0 0 (λ x10 : ι → ι . λ x11 . 0)) (x5 0)) (x2 (λ x9 : ι → (ι → ι → ι) → ι . x5 0) (setsum 0 0))) (λ x9 : ι → ι . λ x10 . x9 0)) (λ x9 : ι → ι . λ x10 . x10) = setsum (Inj1 x4) 0) ⟶ False (proof)Theorem 3165c.. : ∀ x0 : (ι → ι) → (ι → (ι → ι) → ι) → ι . ∀ x1 : ((ι → ι) → ι → ι) → (ι → ι) → (ι → (ι → ι) → ι) → ι → ι . ∀ x2 : ((ι → ι) → ι → (ι → ι → ι) → ι) → ι → ι → ι → (ι → ι) → ι . ∀ x3 : ((ι → (ι → ι → ι) → ι) → ι) → ((ι → ι) → ι) → ι . (∀ x4 : ι → ((ι → ι) → ι) → ι . ∀ x5 . ∀ x6 : ι → ι . ∀ x7 : (ι → ι) → ι → (ι → ι) → ι → ι . x3 (λ x9 : ι → (ι → ι → ι) → ι . x3 (λ x10 : ι → (ι → ι → ι) → ι . x9 (x9 (x7 (λ x11 . 0) 0 (λ x11 . 0) 0) (λ x11 x12 . x9 0 (λ x13 x14 . 0))) (λ x11 x12 . 0)) (λ x10 : ι → ι . 0)) (λ x9 : ι → ι . 0) = x3 (λ x9 : ι → (ι → ι → ι) → ι . x3 (λ x10 : ι → (ι → ι → ι) → ι . setsum (x1 (λ x11 : ι → ι . λ x12 . Inj0 0) (λ x11 . setsum 0 0) (λ x11 . λ x12 : ι → ι . Inj0 0) 0) (setsum 0 0)) (λ x10 : ι → ι . setsum (setsum (x6 0) (x9 0 (λ x11 x12 . 0))) (x1 (λ x11 : ι → ι . λ x12 . setsum 0 0) (λ x11 . setsum 0 0) (λ x11 . λ x12 : ι → ι . x2 (λ x13 : ι → ι . λ x14 . λ x15 : ι → ι → ι . 0) 0 0 0 (λ x13 . 0)) (setsum 0 0)))) (λ x9 : ι → ι . x0 (λ x10 . Inj0 0) (λ x10 . λ x11 : ι → ι . x7 (λ x12 . Inj1 0) 0 (λ x12 . x12) (x7 (λ x12 . x11 0) (x11 0) (λ x12 . x2 (λ x13 : ι → ι . λ x14 . λ x15 : ι → ι → ι . 0) 0 0 0 (λ x13 . 0)) (setsum 0 0))))) ⟶ (∀ x4 x5 x6 . ∀ x7 : (ι → (ι → ι) → ι) → ((ι → ι) → ι) → ι → ι → ι . x3 (λ x9 : ι → (ι → ι → ι) → ι . x9 0 (λ x10 x11 . Inj1 (x7 (λ x12 . λ x13 : ι → ι . x1 (λ x14 : ι → ι . λ x15 . 0) (λ x14 . 0) (λ x14 . λ x15 : ι → ι . 0) 0) (λ x12 : ι → ι . x1 (λ x13 : ι → ι . λ x14 . 0) (λ x13 . 0) (λ x13 . λ x14 : ι → ι . 0) 0) 0 (x7 (λ x12 . λ x13 : ι → ι . 0) (λ x12 : ι → ι . 0) 0 0)))) (λ x9 : ι → ι . 0) = x6) ⟶ (∀ x4 : ι → ι → (ι → ι) → ι → ι . ∀ x5 x6 . ∀ x7 : ι → ι . x2 (λ x9 : ι → ι . λ x10 . λ x11 : ι → ι → ι . setsum (Inj1 (setsum (x11 0 0) 0)) (x3 (λ x12 : ι → (ι → ι → ι) → ι . 0) (λ x12 : ι → ι . Inj1 (x1 (λ x13 : ι → ι . λ x14 . 0) (λ x13 . 0) (λ x13 . λ x14 : ι → ι . 0) 0)))) (Inj0 (x4 (x0 (λ x9 . 0) (λ x9 . λ x10 : ι → ι . x6)) 0 (λ x9 . x6) 0)) (x3 (λ x9 : ι → (ι → ι → ι) → ι . 0) (λ x9 : ι → ι . x6)) (x7 (x7 (x2 (λ x9 : ι → ι . λ x10 . λ x11 : ι → ι → ι . 0) (x1 (λ x9 : ι → ι . λ x10 . 0) (λ x9 . 0) (λ x9 . λ x10 : ι → ι . 0) 0) 0 0 (λ x9 . x0 (λ x10 . 0) (λ x10 . λ x11 : ι → ι . 0))))) (λ x9 . setsum (Inj1 x9) (Inj0 (setsum 0 (x7 0)))) = Inj0 0) ⟶ (∀ x4 : ((ι → ι) → (ι → ι) → ι → ι) → ι → ι . ∀ x5 x6 : ι → ι → ι . ∀ x7 . x2 (λ x9 : ι → ι . λ x10 . λ x11 : ι → ι → ι . 0) (x1 (λ x9 : ι → ι . λ x10 . 0) (λ x9 . x1 (λ x10 : ι → ι . λ x11 . setsum (Inj0 0) (Inj0 0)) (λ x10 . 0) (λ x10 . λ x11 : ι → ι . 0) (x1 (λ x10 : ι → ι . λ x11 . setsum 0 0) (λ x10 . x6 0 0) (λ x10 . λ x11 : ι → ι . 0) 0)) (λ x9 . λ x10 : ι → ι . setsum (x6 (x10 0) (setsum 0 0)) 0) (Inj1 (Inj1 x7))) (Inj0 0) (Inj0 (x0 (λ x9 . setsum (x5 0 0) (setsum 0 0)) (λ x9 . λ x10 : ι → ι . 0))) (λ x9 . 0) = x1 (λ x9 : ι → ι . λ x10 . setsum 0 x7) (λ x9 . x0 (λ x10 . x10) (λ x10 . λ x11 : ι → ι . 0)) (λ x9 . λ x10 : ι → ι . Inj0 (x2 (λ x11 : ι → ι . λ x12 . λ x13 : ι → ι → ι . x1 (λ x14 : ι → ι . λ x15 . 0) (λ x14 . x12) (λ x14 . λ x15 : ι → ι . Inj0 0) 0) (setsum 0 0) (setsum (x2 (λ x11 : ι → ι . λ x12 . λ x13 : ι → ι → ι . 0) 0 0 0 (λ x11 . 0)) (x10 0)) (setsum 0 (x1 (λ x11 : ι → ι . λ x12 . 0) (λ x11 . 0) (λ x11 . λ x12 : ι → ι . 0) 0)) (λ x11 . x7))) x7) ⟶ (∀ x4 : ((ι → ι) → ι) → ι . ∀ x5 : (ι → (ι → ι) → ι) → (ι → ι → ι) → ι → ι . ∀ x6 : ι → ι → ι . ∀ x7 : ι → ((ι → ι) → ι → ι) → (ι → ι) → ι . x1 (λ x9 : ι → ι . λ x10 . x3 (λ x11 : ι → (ι → ι → ι) → ι . x9 (x9 (x7 0 (λ x12 : ι → ι . λ x13 . 0) (λ x12 . 0)))) (λ x11 : ι → ι . x9 0)) (λ x9 . x5 (λ x10 . λ x11 : ι → ι . Inj1 (setsum (Inj0 0) (x3 (λ x12 : ι → (ι → ι → ι) → ι . 0) (λ x12 : ι → ι . 0)))) (λ x10 x11 . 0) (x5 (λ x10 . λ x11 : ι → ι . Inj1 (Inj0 0)) (λ x10 x11 . 0) (Inj0 0))) (λ x9 . λ x10 : ι → ι . 0) (x3 (λ x9 : ι → (ι → ι → ι) → ι . x2 (λ x10 : ι → ι . λ x11 . λ x12 : ι → ι → ι . setsum 0 (x12 0 0)) (x0 (λ x10 . x2 (λ x11 : ι → ι . λ x12 . λ x13 : ι → ι → ι . 0) 0 0 0 (λ x11 . 0)) (λ x10 . λ x11 : ι → ι . 0)) (Inj0 0) (setsum (x7 0 (λ x10 : ι → ι . λ x11 . 0) (λ x10 . 0)) (x9 0 (λ x10 x11 . 0))) (λ x10 . 0)) (λ x9 : ι → ι . x2 (λ x10 : ι → ι . λ x11 . λ x12 : ι → ι → ι . x3 (λ x13 : ι → (ι → ι → ι) → ι . setsum 0 0) (λ x13 : ι → ι . x3 (λ x14 : ι → (ι → ι → ι) → ι . 0) (λ x14 : ι → ι . 0))) (setsum (x7 0 (λ x10 : ι → ι . λ x11 . 0) (λ x10 . 0)) (x7 0 (λ x10 : ι → ι . λ x11 . 0) (λ x10 . 0))) 0 0 (λ x10 . x9 0))) = Inj1 (setsum (setsum (x6 (x3 (λ x9 : ι → (ι → ι → ι) → ι . 0) (λ x9 : ι → ι . 0)) (x6 0 0)) (Inj1 (x0 (λ x9 . 0) (λ x9 . λ x10 : ι → ι . 0)))) 0)) ⟶ (∀ x4 x5 x6 x7 . x1 (λ x9 : ι → ι . λ x10 . Inj1 (setsum x6 (x1 (λ x11 : ι → ι . λ x12 . setsum 0 0) (λ x11 . 0) (λ x11 . λ x12 : ι → ι . x3 (λ x13 : ι → (ι → ι → ι) → ι . 0) (λ x13 : ι → ι . 0)) (Inj1 0)))) (λ x9 . x5) (λ x9 . λ x10 : ι → ι . x2 (λ x11 : ι → ι . λ x12 . λ x13 : ι → ι → ι . x3 (λ x14 : ι → (ι → ι → ι) → ι . 0) (λ x14 : ι → ι . Inj1 (x1 (λ x15 : ι → ι . λ x16 . 0) (λ x15 . 0) (λ x15 . λ x16 : ι → ι . 0) 0))) (x3 (λ x11 : ι → (ι → ι → ι) → ι . setsum (x2 (λ x12 : ι → ι . λ x13 . λ x14 : ι → ι → ι . 0) 0 0 0 (λ x12 . 0)) (x2 (λ x12 : ι → ι . λ x13 . λ x14 : ι → ι → ι . 0) 0 0 0 (λ x12 . 0))) (λ x11 : ι → ι . x3 (λ x12 : ι → (ι → ι → ι) → ι . x9) (λ x12 : ι → ι . 0))) 0 0 (λ x11 . Inj0 x7)) x4 = x2 (λ x9 : ι → ι . λ x10 . λ x11 : ι → ι → ι . Inj1 x10) (x3 (λ x9 : ι → (ι → ι → ι) → ι . x7) (λ x9 : ι → ι . x0 (λ x10 . 0) (λ x10 . λ x11 : ι → ι . setsum 0 (x3 (λ x12 : ι → (ι → ι → ι) → ι . 0) (λ x12 : ι → ι . 0))))) x7 x7 (λ x9 . x7)) ⟶ (∀ x4 : (ι → ι → ι) → ι . ∀ x5 x6 . ∀ x7 : (ι → ι) → ι → (ι → ι) → ι . x0 (λ x9 . x3 (λ x10 : ι → (ι → ι → ι) → ι . x6) (λ x10 : ι → ι . Inj0 (setsum 0 (x1 (λ x11 : ι → ι . λ x12 . 0) (λ x11 . 0) (λ x11 . λ x12 : ι → ι . 0) 0)))) (λ x9 . λ x10 : ι → ι . 0) = setsum 0 (setsum x5 (x2 (λ x9 : ι → ι . λ x10 . λ x11 : ι → ι → ι . x10) (x7 (λ x9 . 0) (setsum 0 0) (λ x9 . x5)) (Inj0 (x3 (λ x9 : ι → (ι → ι → ι) → ι . 0) (λ x9 : ι → ι . 0))) (x1 (λ x9 : ι → ι . λ x10 . x10) (λ x9 . x6) (λ x9 . λ x10 : ι → ι . x9) (setsum 0 0)) (λ x9 . 0)))) ⟶ (∀ x4 : (ι → (ι → ι) → ι → ι) → ((ι → ι) → ι) → ι . ∀ x5 : ι → ι . ∀ x6 : (ι → ι → ι → ι) → ι . ∀ x7 . x0 (λ x9 . x9) (λ x9 . λ x10 : ι → ι . x10 (x0 (λ x11 . 0) (λ x11 . λ x12 : ι → ι . x0 (λ x13 . 0) (λ x13 . λ x14 : ι → ι . x14 0)))) = Inj0 (x1 (λ x9 : ι → ι . λ x10 . x1 (λ x11 : ι → ι . λ x12 . x3 (λ x13 : ι → (ι → ι → ι) → ι . 0) (λ x13 : ι → ι . setsum 0 0)) (λ x11 . x0 (λ x12 . x2 (λ x13 : ι → ι . λ x14 . λ x15 : ι → ι → ι . 0) 0 0 0 (λ x13 . 0)) (λ x12 . λ x13 : ι → ι . Inj0 0)) (λ x11 . λ x12 : ι → ι . x1 (λ x13 : ι → ι . λ x14 . 0) (λ x13 . 0) (λ x13 . λ x14 : ι → ι . setsum 0 0) (x3 (λ x13 : ι → (ι → ι → ι) → ι . 0) (λ x13 : ι → ι . 0))) (setsum (setsum 0 0) (Inj0 0))) (λ x9 . x9) (λ x9 . λ x10 : ι → ι . x3 (λ x11 : ι → (ι → ι → ι) → ι . Inj1 (x2 (λ x12 : ι → ι . λ x13 . λ x14 : ι → ι → ι . 0) 0 0 0 (λ x12 . 0))) (λ x11 : ι → ι . 0)) (setsum (x0 (λ x9 . x6 (λ x10 x11 x12 . 0)) (λ x9 . λ x10 : ι → ι . setsum 0 0)) (x5 (x5 0))))) ⟶ False (proof)Theorem 2625c.. : ∀ x0 : (ι → ι) → ι → (((ι → ι) → ι → ι) → (ι → ι) → ι) → ι . ∀ x1 : ((ι → ι → ι) → (ι → (ι → ι) → ι) → ι → (ι → ι) → ι) → ι → (((ι → ι) → ι → ι) → ι → ι → ι) → ι . ∀ x2 : (ι → ((ι → ι) → ι → ι → ι) → ι) → (((ι → ι → ι) → ι) → ((ι → ι) → ι) → (ι → ι) → ι) → ι . ∀ x3 : (ι → (ι → (ι → ι) → ι) → ι → (ι → ι) → ι) → (ι → ι) → ι → ι . (∀ x4 : ι → ι . ∀ x5 . ∀ x6 x7 : ι → ι . x3 (λ x9 . λ x10 : ι → (ι → ι) → ι . λ x11 . λ x12 : ι → ι . x10 (Inj0 0) (λ x13 . Inj1 (setsum x13 (setsum 0 0)))) (λ x9 . x7 (x7 (x2 (λ x10 . λ x11 : (ι → ι) → ι → ι → ι . x10) (λ x10 : (ι → ι → ι) → ι . λ x11 : (ι → ι) → ι . λ x12 : ι → ι . x10 (λ x13 x14 . 0))))) (x7 (x6 x5)) = x7 (x0 (λ x9 . x3 (λ x10 . λ x11 : ι → (ι → ι) → ι . λ x12 . λ x13 : ι → ι . 0) (λ x10 . setsum (x2 (λ x11 . λ x12 : (ι → ι) → ι → ι → ι . 0) (λ x11 : (ι → ι → ι) → ι . λ x12 : (ι → ι) → ι . λ x13 : ι → ι . 0)) (x6 0)) (setsum 0 x5)) (x0 (λ x9 . x5) (x2 (λ x9 . λ x10 : (ι → ι) → ι → ι → ι . x10 (λ x11 . 0) 0 0) (λ x9 : (ι → ι → ι) → ι . λ x10 : (ι → ι) → ι . λ x11 : ι → ι . x7 0)) (λ x9 : (ι → ι) → ι → ι . λ x10 : ι → ι . x7 0)) (λ x9 : (ι → ι) → ι → ι . λ x10 : ι → ι . setsum (x0 (λ x11 . x11) (x7 0) (λ x11 : (ι → ι) → ι → ι . λ x12 : ι → ι . 0)) (setsum (Inj0 0) (x7 0))))) ⟶ (∀ x4 x5 . ∀ x6 : ι → ι → ι . ∀ x7 : ι → ι . x3 (λ x9 . λ x10 : ι → (ι → ι) → ι . λ x11 . λ x12 : ι → ι . 0) (λ x9 . x7 (x6 (setsum x9 x9) (x0 (λ x10 . Inj1 0) (x6 0 0) (λ x10 : (ι → ι) → ι → ι . λ x11 : ι → ι . Inj1 0)))) (x1 (λ x9 : ι → ι → ι . λ x10 : ι → (ι → ι) → ι . λ x11 . λ x12 : ι → ι . x3 (λ x13 . λ x14 : ι → (ι → ι) → ι . λ x15 . λ x16 : ι → ι . Inj1 (setsum 0 0)) (λ x13 . x10 (Inj0 0) (λ x14 . x1 (λ x15 : ι → ι → ι . λ x16 : ι → (ι → ι) → ι . λ x17 . λ x18 : ι → ι . 0) 0 (λ x15 : (ι → ι) → ι → ι . λ x16 x17 . 0))) 0) (setsum (x3 (λ x9 . λ x10 : ι → (ι → ι) → ι . λ x11 . λ x12 : ι → ι . 0) (λ x9 . x1 (λ x10 : ι → ι → ι . λ x11 : ι → (ι → ι) → ι . λ x12 . λ x13 : ι → ι . 0) 0 (λ x10 : (ι → ι) → ι → ι . λ x11 x12 . 0)) (setsum 0 0)) (setsum x4 (setsum 0 0))) (λ x9 : (ι → ι) → ι → ι . λ x10 x11 . x2 (λ x12 . λ x13 : (ι → ι) → ι → ι → ι . 0) (λ x12 : (ι → ι → ι) → ι . λ x13 : (ι → ι) → ι . λ x14 : ι → ι . 0))) = setsum (x6 (x7 x5) (x3 (λ x9 . λ x10 : ι → (ι → ι) → ι . λ x11 . λ x12 : ι → ι . x0 (λ x13 . Inj0 0) (x3 (λ x13 . λ x14 : ι → (ι → ι) → ι . λ x15 . λ x16 : ι → ι . 0) (λ x13 . 0) 0) (λ x13 : (ι → ι) → ι → ι . λ x14 : ι → ι . x14 0)) (λ x9 . x2 (λ x10 . λ x11 : (ι → ι) → ι → ι → ι . Inj0 0) (λ x10 : (ι → ι → ι) → ι . λ x11 : (ι → ι) → ι . λ x12 : ι → ι . x12 0)) (setsum 0 0))) x4) ⟶ (∀ x4 . ∀ x5 : ι → (ι → ι → ι) → ι . ∀ x6 : (ι → ι) → ι . ∀ x7 . x2 (λ x9 . λ x10 : (ι → ι) → ι → ι → ι . x1 (λ x11 : ι → ι → ι . λ x12 : ι → (ι → ι) → ι . λ x13 . λ x14 : ι → ι . x2 (λ x15 . λ x16 : (ι → ι) → ι → ι → ι . 0) (λ x15 : (ι → ι → ι) → ι . λ x16 : (ι → ι) → ι . λ x17 : ι → ι . x15 (λ x18 x19 . 0))) (x10 (λ x11 . x7) (Inj1 (setsum 0 0)) (x2 (λ x11 . λ x12 : (ι → ι) → ι → ι → ι . 0) (λ x11 : (ι → ι → ι) → ι . λ x12 : (ι → ι) → ι . λ x13 : ι → ι . x11 (λ x14 x15 . 0)))) (λ x11 : (ι → ι) → ι → ι . λ x12 x13 . x10 (λ x14 . Inj1 0) 0 (Inj1 0))) (λ x9 : (ι → ι → ι) → ι . λ x10 : (ι → ι) → ι . λ x11 : ι → ι . 0) = x1 (λ x9 : ι → ι → ι . λ x10 : ι → (ι → ι) → ι . λ x11 . λ x12 : ι → ι . setsum 0 0) x4 (λ x9 : (ι → ι) → ι → ι . λ x10 x11 . setsum x7 x10)) ⟶ (∀ x4 : (((ι → ι) → ι → ι) → ι → ι → ι) → ((ι → ι) → ι → ι) → (ι → ι) → ι → ι . ∀ x5 : ((ι → ι) → ι → ι → ι) → (ι → ι → ι) → ι . ∀ x6 : ι → (ι → ι) → ι . ∀ x7 . x2 (λ x9 . λ x10 : (ι → ι) → ι → ι → ι . 0) (λ x9 : (ι → ι → ι) → ι . λ x10 : (ι → ι) → ι . λ x11 : ι → ι . setsum 0 (Inj1 (x11 x7))) = x5 (λ x9 : ι → ι . λ x10 x11 . setsum (Inj1 (Inj0 (x3 (λ x12 . λ x13 : ι → (ι → ι) → ι . λ x14 . λ x15 : ι → ι . 0) (λ x12 . 0) 0))) (Inj0 (Inj1 (x9 0)))) (λ x9 x10 . setsum 0 x9)) ⟶ (∀ x4 : ((ι → ι) → (ι → ι) → ι) → ι . ∀ x5 : (ι → ι) → ι . ∀ x6 : ι → ι . ∀ x7 . x1 (λ x9 : ι → ι → ι . λ x10 : ι → (ι → ι) → ι . λ x11 . λ x12 : ι → ι . setsum x11 x11) 0 (λ x9 : (ι → ι) → ι → ι . λ x10 x11 . 0) = setsum (x6 (x4 (λ x9 x10 : ι → ι . 0))) 0) ⟶ (∀ x4 x5 x6 . ∀ x7 : ι → ι . x1 (λ x9 : ι → ι → ι . λ x10 : ι → (ι → ι) → ι . λ x11 . λ x12 : ι → ι . x9 (x12 (x9 0 (setsum 0 0))) (x0 (λ x13 . x12 x11) (Inj1 (x10 0 (λ x13 . 0))) (λ x13 : (ι → ι) → ι → ι . λ x14 : ι → ι . x0 (λ x15 . x1 (λ x16 : ι → ι → ι . λ x17 : ι → (ι → ι) → ι . λ x18 . λ x19 : ι → ι . 0) 0 (λ x16 : (ι → ι) → ι → ι . λ x17 x18 . 0)) (x0 (λ x15 . 0) 0 (λ x15 : (ι → ι) → ι → ι . λ x16 : ι → ι . 0)) (λ x15 : (ι → ι) → ι → ι . λ x16 : ι → ι . x16 0)))) (setsum (x2 (λ x9 . λ x10 : (ι → ι) → ι → ι → ι . x9) (λ x9 : (ι → ι → ι) → ι . λ x10 : (ι → ι) → ι . λ x11 : ι → ι . 0)) (x0 (λ x9 . x6) (setsum (x2 (λ x9 . λ x10 : (ι → ι) → ι → ι → ι . 0) (λ x9 : (ι → ι → ι) → ι . λ x10 : (ι → ι) → ι . λ x11 : ι → ι . 0)) x5) (λ x9 : (ι → ι) → ι → ι . λ x10 : ι → ι . 0))) (λ x9 : (ι → ι) → ι → ι . λ x10 x11 . 0) = x6) ⟶ (∀ x4 x5 . ∀ x6 : (ι → ι → ι → ι) → ι . ∀ x7 : ι → ι . x0 (λ x9 . x0 (λ x10 . x3 (λ x11 . λ x12 : ι → (ι → ι) → ι . λ x13 . λ x14 : ι → ι . 0) (λ x11 . x11) (x7 (x1 (λ x11 : ι → ι → ι . λ x12 : ι → (ι → ι) → ι . λ x13 . λ x14 : ι → ι . 0) 0 (λ x11 : (ι → ι) → ι → ι . λ x12 x13 . 0)))) 0 (λ x10 : (ι → ι) → ι → ι . λ x11 : ι → ι . 0)) 0 (λ x9 : (ι → ι) → ι → ι . λ x10 : ι → ι . 0) = Inj0 0) ⟶ (∀ x4 : ((ι → ι → ι) → ι → ι) → ι . ∀ x5 . ∀ x6 x7 : (ι → ι) → ι . x0 (λ x9 . x0 (λ x10 . 0) 0 (λ x10 : (ι → ι) → ι → ι . λ x11 : ι → ι . setsum x9 (x10 (λ x12 . x12) (x2 (λ x12 . λ x13 : (ι → ι) → ι → ι → ι . 0) (λ x12 : (ι → ι → ι) → ι . λ x13 : (ι → ι) → ι . λ x14 : ι → ι . 0))))) 0 (λ x9 : (ι → ι) → ι → ι . λ x10 : ι → ι . 0) = Inj0 (Inj0 (Inj0 (x4 (λ x9 : ι → ι → ι . λ x10 . 0))))) ⟶ False (proof)Theorem b4a18.. : ∀ x0 : (ι → ι) → ι → ι → (ι → ι → ι) → (ι → ι) → ι . ∀ x1 : ((ι → ((ι → ι) → ι → ι) → ι) → ι → ι → ι) → ((ι → ι) → ι) → ι . ∀ x2 : ((((ι → ι → ι) → ι → ι) → ι → ι → ι) → ι) → (ι → ι) → ι . ∀ x3 : (ι → ((ι → ι) → ι) → ι) → ((ι → ι) → (ι → ι → ι) → ι) → ι . (∀ x4 . ∀ x5 : ((ι → ι) → (ι → ι) → ι) → ι . ∀ x6 . ∀ x7 : ι → ι → ι . x3 (λ x9 . λ x10 : (ι → ι) → ι . 0) (λ x9 : ι → ι . λ x10 : ι → ι → ι . Inj1 x6) = x4) ⟶ (∀ x4 : (ι → ι) → (ι → ι) → ι . ∀ x5 : ι → ι . ∀ x6 x7 . x3 (λ x9 . λ x10 : (ι → ι) → ι . 0) (λ x9 : ι → ι . λ x10 : ι → ι → ι . 0) = x4 (λ x9 . setsum (x0 (λ x10 . Inj0 (Inj0 0)) x6 (x1 (λ x10 : ι → ((ι → ι) → ι → ι) → ι . λ x11 x12 . 0) (λ x10 : ι → ι . x1 (λ x11 : ι → ((ι → ι) → ι → ι) → ι . λ x12 x13 . 0) (λ x11 : ι → ι . 0))) (λ x10 x11 . setsum x9 (Inj1 0)) (λ x10 . x1 (λ x11 : ι → ((ι → ι) → ι → ι) → ι . λ x12 x13 . 0) (λ x11 : ι → ι . x9))) 0) (λ x9 . setsum 0 x7)) ⟶ (∀ x4 : ((ι → ι) → ι) → ((ι → ι) → ι) → ι → ι . ∀ x5 : ι → (ι → ι → ι) → ι → ι . ∀ x6 : (ι → ι → ι) → ι . ∀ x7 . x2 (λ x9 : ((ι → ι → ι) → ι → ι) → ι → ι → ι . 0) (λ x9 . x6 (λ x10 x11 . Inj1 x7)) = Inj0 0) ⟶ (∀ x4 x5 . ∀ x6 x7 : ι → ι . x2 (λ x9 : ((ι → ι → ι) → ι → ι) → ι → ι → ι . x7 (x0 (λ x10 . x2 (λ x11 : ((ι → ι → ι) → ι → ι) → ι → ι → ι . x9 (λ x12 : ι → ι → ι . λ x13 . 0) 0 0) (λ x11 . setsum 0 0)) 0 0 (λ x10 x11 . x11) (λ x10 . setsum 0 0))) (λ x9 . setsum (x1 (λ x10 : ι → ((ι → ι) → ι → ι) → ι . λ x11 x12 . x11) (λ x10 : ι → ι . x1 (λ x11 : ι → ((ι → ι) → ι → ι) → ι . λ x12 x13 . x12) (λ x11 : ι → ι . x10 0))) 0) = setsum (x6 0) (x7 (Inj1 (setsum (x0 (λ x9 . 0) 0 0 (λ x9 x10 . 0) (λ x9 . 0)) 0)))) ⟶ (∀ x4 . ∀ x5 : ι → (ι → ι) → (ι → ι) → ι → ι . ∀ x6 : ι → ι → ι . ∀ x7 : ι → ι → (ι → ι) → ι . x1 (λ x9 : ι → ((ι → ι) → ι → ι) → ι . λ x10 x11 . x9 0 (λ x12 : ι → ι . λ x13 . x12 (x1 (λ x14 : ι → ((ι → ι) → ι → ι) → ι . λ x15 x16 . x15) (λ x14 : ι → ι . x0 (λ x15 . 0) 0 0 (λ x15 x16 . 0) (λ x15 . 0))))) (λ x9 : ι → ι . x6 0 0) = x6 (x5 0 (λ x9 . 0) (λ x9 . x5 (x7 (x2 (λ x10 : ((ι → ι → ι) → ι → ι) → ι → ι → ι . 0) (λ x10 . 0)) (x2 (λ x10 : ((ι → ι → ι) → ι → ι) → ι → ι → ι . 0) (λ x10 . 0)) (λ x10 . setsum 0 0)) (λ x10 . 0) (λ x10 . 0) (setsum x9 (x6 0 0))) 0) (x7 (Inj0 (setsum (Inj1 0) 0)) (Inj1 (x1 (λ x9 : ι → ((ι → ι) → ι → ι) → ι . λ x10 x11 . 0) (λ x9 : ι → ι . Inj0 0))) (λ x9 . setsum 0 (x6 (Inj0 0) (Inj0 0))))) ⟶ (∀ x4 x5 . ∀ x6 : ι → ι → ι → ι → ι . ∀ x7 : ι → ι → ι . x1 (λ x9 : ι → ((ι → ι) → ι → ι) → ι . λ x10 x11 . x0 (λ x12 . setsum (x0 (λ x13 . setsum 0 0) x12 (x2 (λ x13 : ((ι → ι → ι) → ι → ι) → ι → ι → ι . 0) (λ x13 . 0)) (λ x13 x14 . 0) (λ x13 . 0)) 0) 0 (x0 (λ x12 . x10) (Inj0 (x7 0 0)) 0 (λ x12 x13 . x1 (λ x14 : ι → ((ι → ι) → ι → ι) → ι . λ x15 x16 . setsum 0 0) (λ x14 : ι → ι . 0)) (λ x12 . 0)) (λ x12 x13 . setsum (x1 (λ x14 : ι → ((ι → ι) → ι → ι) → ι . λ x15 x16 . x15) (λ x14 : ι → ι . Inj1 0)) (Inj1 0)) (λ x12 . x2 (λ x13 : ((ι → ι → ι) → ι → ι) → ι → ι → ι . Inj1 x10) (λ x13 . x2 (λ x14 : ((ι → ι → ι) → ι → ι) → ι → ι → ι . x11) (λ x14 . setsum 0 0)))) (λ x9 : ι → ι . Inj1 (setsum (setsum (x1 (λ x10 : ι → ((ι → ι) → ι → ι) → ι . λ x11 x12 . 0) (λ x10 : ι → ι . 0)) (setsum 0 0)) 0)) = setsum 0 x4) ⟶ (∀ x4 : ι → ι . ∀ x5 : ι → ((ι → ι) → ι → ι) → ι . ∀ x6 : ((ι → ι → ι) → (ι → ι) → ι) → ((ι → ι) → ι → ι) → ι . ∀ x7 : ι → ι . x0 (λ x9 . x7 (Inj1 0)) 0 (x1 (λ x9 : ι → ((ι → ι) → ι → ι) → ι . λ x10 x11 . 0) (λ x9 : ι → ι . x0 (λ x10 . x9 (x6 (λ x11 : ι → ι → ι . λ x12 : ι → ι . 0) (λ x11 : ι → ι . λ x12 . 0))) (x7 (x9 0)) (setsum (setsum 0 0) 0) (λ x10 x11 . x7 x10) (λ x10 . 0))) (λ x9 x10 . x10) Inj1 = x7 (x5 (x5 0 (λ x9 : ι → ι . λ x10 . 0)) (λ x9 : ι → ι . λ x10 . Inj0 (x9 (setsum 0 0))))) ⟶ (∀ x4 x5 . ∀ x6 : ι → ((ι → ι) → ι) → ι . ∀ x7 . x0 (λ x9 . x1 (λ x10 : ι → ((ι → ι) → ι → ι) → ι . λ x11 x12 . 0) (λ x10 : ι → ι . Inj1 (x1 (λ x11 : ι → ((ι → ι) → ι → ι) → ι . λ x12 x13 . setsum 0 0) (λ x11 : ι → ι . x11 0)))) (Inj1 (Inj1 (Inj1 (setsum 0 0)))) (setsum (x1 (λ x9 : ι → ((ι → ι) → ι → ι) → ι . λ x10 x11 . setsum (setsum 0 0) x10) (λ x9 : ι → ι . x7)) (setsum 0 (x1 (λ x9 : ι → ((ι → ι) → ι → ι) → ι . λ x10 x11 . x1 (λ x12 : ι → ((ι → ι) → ι → ι) → ι . λ x13 x14 . 0) (λ x12 : ι → ι . 0)) (λ x9 : ι → ι . Inj1 0)))) (λ x9 . Inj0) (λ x9 . x5) = Inj0 x4) ⟶ False (proof)Theorem 50893.. : ∀ x0 : (((ι → ι → ι) → ((ι → ι) → ι → ι) → ι) → ι) → (((ι → ι → ι) → ι → ι → ι) → ι) → ι . ∀ x1 : (ι → (ι → (ι → ι) → ι) → ((ι → ι) → ι) → ι) → (ι → ι) → ι → ι . ∀ x2 : ((ι → (ι → ι) → ι → ι → ι) → ι → ((ι → ι) → ι → ι) → (ι → ι) → ι) → ι → ι . ∀ x3 : (((((ι → ι) → ι) → ι) → ι) → (((ι → ι) → ι) → ι → ι) → (ι → ι) → (ι → ι) → ι → ι) → (ι → ι) → (ι → ι → ι → ι) → ι . (∀ x4 : ((ι → ι → ι) → ι) → ((ι → ι) → ι) → (ι → ι) → ι → ι . ∀ x5 . ∀ x6 : (ι → ι) → ((ι → ι) → ι) → (ι → ι) → ι . ∀ x7 : (ι → ι → ι) → (ι → ι) → ι . x3 (λ x9 : (((ι → ι) → ι) → ι) → ι . λ x10 : ((ι → ι) → ι) → ι → ι . λ x11 x12 : ι → ι . λ x13 . setsum x13 0) (λ x9 . x0 (λ x10 : (ι → ι → ι) → ((ι → ι) → ι → ι) → ι . 0) (λ x10 : (ι → ι → ι) → ι → ι → ι . Inj0 (setsum (x0 (λ x11 : (ι → ι → ι) → ((ι → ι) → ι → ι) → ι . 0) (λ x11 : (ι → ι → ι) → ι → ι → ι . 0)) (Inj1 0)))) (λ x9 x10 x11 . x7 (λ x12 x13 . setsum (x2 (λ x14 : ι → (ι → ι) → ι → ι → ι . λ x15 . λ x16 : (ι → ι) → ι → ι . λ x17 : ι → ι . x3 (λ x18 : (((ι → ι) → ι) → ι) → ι . λ x19 : ((ι → ι) → ι) → ι → ι . λ x20 x21 : ι → ι . λ x22 . 0) (λ x18 . 0) (λ x18 x19 x20 . 0)) 0) 0) (λ x12 . x2 (λ x13 : ι → (ι → ι) → ι → ι → ι . λ x14 . λ x15 : (ι → ι) → ι → ι . λ x16 : ι → ι . Inj0 (x16 0)) (x1 (λ x13 . λ x14 : ι → (ι → ι) → ι . λ x15 : (ι → ι) → ι . 0) (λ x13 . setsum 0 0) (x1 (λ x13 . λ x14 : ι → (ι → ι) → ι . λ x15 : (ι → ι) → ι . 0) (λ x13 . 0) 0)))) = x0 (λ x9 : (ι → ι → ι) → ((ι → ι) → ι → ι) → ι . x0 (λ x10 : (ι → ι → ι) → ((ι → ι) → ι → ι) → ι . x0 (λ x11 : (ι → ι → ι) → ((ι → ι) → ι → ι) → ι . 0) (λ x11 : (ι → ι → ι) → ι → ι → ι . 0)) (λ x10 : (ι → ι → ι) → ι → ι → ι . 0)) (λ x9 : (ι → ι → ι) → ι → ι → ι . x1 (λ x10 . λ x11 : ι → (ι → ι) → ι . λ x12 : (ι → ι) → ι . x12 (λ x13 . setsum 0 (x2 (λ x14 : ι → (ι → ι) → ι → ι → ι . λ x15 . λ x16 : (ι → ι) → ι → ι . λ x17 : ι → ι . 0) 0))) (λ x10 . setsum (x0 (λ x11 : (ι → ι → ι) → ((ι → ι) → ι → ι) → ι . x10) (λ x11 : (ι → ι → ι) → ι → ι → ι . x2 (λ x12 : ι → (ι → ι) → ι → ι → ι . λ x13 . λ x14 : (ι → ι) → ι → ι . λ x15 : ι → ι . 0) 0)) (x1 (λ x11 . λ x12 : ι → (ι → ι) → ι . λ x13 : (ι → ι) → ι . x0 (λ x14 : (ι → ι → ι) → ((ι → ι) → ι → ι) → ι . 0) (λ x14 : (ι → ι → ι) → ι → ι → ι . 0)) (λ x11 . x1 (λ x12 . λ x13 : ι → (ι → ι) → ι . λ x14 : (ι → ι) → ι . 0) (λ x12 . 0) 0) (x3 (λ x11 : (((ι → ι) → ι) → ι) → ι . λ x12 : ((ι → ι) → ι) → ι → ι . λ x13 x14 : ι → ι . λ x15 . 0) (λ x11 . 0) (λ x11 x12 x13 . 0)))) (x1 (λ x10 . λ x11 : ι → (ι → ι) → ι . λ x12 : (ι → ι) → ι . 0) (λ x10 . Inj1 (x1 (λ x11 . λ x12 : ι → (ι → ι) → ι . λ x13 : (ι → ι) → ι . 0) (λ x11 . 0) 0)) (x1 (λ x10 . λ x11 : ι → (ι → ι) → ι . λ x12 : (ι → ι) → ι . setsum 0 0) (λ x10 . x7 (λ x11 x12 . 0) (λ x11 . 0)) 0)))) ⟶ (∀ x4 : (((ι → ι) → ι) → ι) → ι . ∀ x5 : (ι → (ι → ι) → ι) → ι . ∀ x6 x7 . x3 (λ x9 : (((ι → ι) → ι) → ι) → ι . λ x10 : ((ι → ι) → ι) → ι → ι . λ x11 x12 : ι → ι . λ x13 . 0) (λ x9 . setsum 0 0) (λ x9 x10 x11 . x9) = x5 (λ x9 . λ x10 : ι → ι . setsum (x0 (λ x11 : (ι → ι → ι) → ((ι → ι) → ι → ι) → ι . setsum (setsum 0 0) 0) (λ x11 : (ι → ι → ι) → ι → ι → ι . 0)) 0)) ⟶ (∀ x4 : ((ι → ι) → ι → ι) → (ι → ι → ι) → ι . ∀ x5 x6 . ∀ x7 : ((ι → ι → ι) → ι → ι → ι) → ((ι → ι) → ι) → ι . x2 (λ x9 : ι → (ι → ι) → ι → ι → ι . λ x10 . λ x11 : (ι → ι) → ι → ι . λ x12 : ι → ι . x3 (λ x13 : (((ι → ι) → ι) → ι) → ι . λ x14 : ((ι → ι) → ι) → ι → ι . λ x15 x16 : ι → ι . λ x17 . Inj1 (x15 (setsum 0 0))) (λ x13 . setsum x13 (x1 (λ x14 . λ x15 : ι → (ι → ι) → ι . λ x16 : (ι → ι) → ι . 0) (λ x14 . 0) (setsum 0 0))) (λ x13 x14 x15 . x2 (λ x16 : ι → (ι → ι) → ι → ι → ι . λ x17 . λ x18 : (ι → ι) → ι → ι . λ x19 : ι → ι . x16 (Inj0 0) (λ x20 . x2 (λ x21 : ι → (ι → ι) → ι → ι → ι . λ x22 . λ x23 : (ι → ι) → ι → ι . λ x24 : ι → ι . 0) 0) (x0 (λ x20 : (ι → ι → ι) → ((ι → ι) → ι → ι) → ι . 0) (λ x20 : (ι → ι → ι) → ι → ι → ι . 0)) (Inj0 0)) 0)) (setsum (x3 (λ x9 : (((ι → ι) → ι) → ι) → ι . λ x10 : ((ι → ι) → ι) → ι → ι . λ x11 x12 : ι → ι . λ x13 . x12 (x10 (λ x14 : ι → ι . 0) 0)) (λ x9 . Inj1 (setsum 0 0)) (λ x9 x10 x11 . setsum (setsum 0 0) (setsum 0 0))) (setsum 0 x5)) = x3 (λ x9 : (((ι → ι) → ι) → ι) → ι . λ x10 : ((ι → ι) → ι) → ι → ι . λ x11 x12 : ι → ι . λ x13 . x13) (λ x9 . x2 (λ x10 : ι → (ι → ι) → ι → ι → ι . λ x11 . λ x12 : (ι → ι) → ι → ι . λ x13 : ι → ι . x10 0 (λ x14 . x1 (λ x15 . λ x16 : ι → (ι → ι) → ι . λ x17 : (ι → ι) → ι . x17 (λ x18 . 0)) (λ x15 . x3 (λ x16 : (((ι → ι) → ι) → ι) → ι . λ x17 : ((ι → ι) → ι) → ι → ι . λ x18 x19 : ι → ι . λ x20 . 0) (λ x16 . 0) (λ x16 x17 x18 . 0)) x11) (x1 (λ x14 . λ x15 : ι → (ι → ι) → ι . λ x16 : (ι → ι) → ι . 0) (λ x14 . x11) (x3 (λ x14 : (((ι → ι) → ι) → ι) → ι . λ x15 : ((ι → ι) → ι) → ι → ι . λ x16 x17 : ι → ι . λ x18 . 0) (λ x14 . 0) (λ x14 x15 x16 . 0))) x11) (Inj1 0)) (λ x9 x10 x11 . setsum (setsum 0 0) (x3 (λ x12 : (((ι → ι) → ι) → ι) → ι . λ x13 : ((ι → ι) → ι) → ι → ι . λ x14 x15 : ι → ι . λ x16 . 0) (λ x12 . x11) (λ x12 x13 x14 . 0)))) ⟶ (∀ x4 : (ι → ι) → ι . ∀ x5 : (((ι → ι) → ι) → ι → ι → ι) → ι . ∀ x6 : ι → ι → (ι → ι) → ι . ∀ x7 . x2 (λ x9 : ι → (ι → ι) → ι → ι → ι . λ x10 . λ x11 : (ι → ι) → ι → ι . λ x12 : ι → ι . x10) 0 = x7) ⟶ (∀ x4 . ∀ x5 : (((ι → ι) → ι) → ι → ι) → (ι → ι) → ι . ∀ x6 . ∀ x7 : (((ι → ι) → ι → ι) → ι → ι → ι) → ι . x1 (λ x9 . λ x10 : ι → (ι → ι) → ι . λ x11 : (ι → ι) → ι . x9) (λ x9 . x3 (λ x10 : (((ι → ι) → ι) → ι) → ι . λ x11 : ((ι → ι) → ι) → ι → ι . λ x12 x13 : ι → ι . λ x14 . x1 (λ x15 . λ x16 : ι → (ι → ι) → ι . λ x17 : (ι → ι) → ι . x17 (λ x18 . Inj1 0)) (λ x15 . x13 0) (x3 (λ x15 : (((ι → ι) → ι) → ι) → ι . λ x16 : ((ι → ι) → ι) → ι → ι . λ x17 x18 : ι → ι . λ x19 . setsum 0 0) (λ x15 . x3 (λ x16 : (((ι → ι) → ι) → ι) → ι . λ x17 : ((ι → ι) → ι) → ι → ι . λ x18 x19 : ι → ι . λ x20 . 0) (λ x16 . 0) (λ x16 x17 x18 . 0)) (λ x15 x16 x17 . Inj1 0))) (λ x10 . x10) (λ x10 x11 x12 . x3 (λ x13 : (((ι → ι) → ι) → ι) → ι . λ x14 : ((ι → ι) → ι) → ι → ι . λ x15 x16 : ι → ι . λ x17 . x2 (λ x18 : ι → (ι → ι) → ι → ι → ι . λ x19 . λ x20 : (ι → ι) → ι → ι . λ x21 : ι → ι . setsum 0 0) (Inj0 0)) (λ x13 . 0) (λ x13 x14 x15 . Inj0 x13))) (Inj1 x6) = Inj0 0) ⟶ (∀ x4 : ((ι → ι) → ι) → ι . ∀ x5 : ((ι → ι) → ι → ι) → ι → ι . ∀ x6 x7 . x1 (λ x9 . λ x10 : ι → (ι → ι) → ι . λ x11 : (ι → ι) → ι . setsum 0 (x2 (λ x12 : ι → (ι → ι) → ι → ι → ι . λ x13 . λ x14 : (ι → ι) → ι → ι . λ x15 : ι → ι . 0) (x2 (λ x12 : ι → (ι → ι) → ι → ι → ι . λ x13 . λ x14 : (ι → ι) → ι → ι . λ x15 : ι → ι . x0 (λ x16 : (ι → ι → ι) → ((ι → ι) → ι → ι) → ι . 0) (λ x16 : (ι → ι → ι) → ι → ι → ι . 0)) (Inj1 0)))) (λ x9 . Inj0 (x3 (λ x10 : (((ι → ι) → ι) → ι) → ι . λ x11 : ((ι → ι) → ι) → ι → ι . λ x12 x13 : ι → ι . λ x14 . setsum (x0 (λ x15 : (ι → ι → ι) → ((ι → ι) → ι → ι) → ι . 0) (λ x15 : (ι → ι → ι) → ι → ι → ι . 0)) (x11 (λ x15 : ι → ι . 0) 0)) (λ x10 . setsum (setsum 0 0) (x0 (λ x11 : (ι → ι → ι) → ((ι → ι) → ι → ι) → ι . 0) (λ x11 : (ι → ι → ι) → ι → ι → ι . 0))) (λ x10 x11 x12 . 0))) (x5 (λ x9 : ι → ι . λ x10 . x6) (x1 (λ x9 . λ x10 : ι → (ι → ι) → ι . λ x11 : (ι → ι) → ι . Inj1 (x0 (λ x12 : (ι → ι → ι) → ((ι → ι) → ι → ι) → ι . 0) (λ x12 : (ι → ι → ι) → ι → ι → ι . 0))) (λ x9 . x2 (λ x10 : ι → (ι → ι) → ι → ι → ι . λ x11 . λ x12 : (ι → ι) → ι → ι . λ x13 : ι → ι . x1 (λ x14 . λ x15 : ι → (ι → ι) → ι . λ x16 : (ι → ι) → ι . 0) (λ x14 . 0) 0) 0) 0)) = x5 (λ x9 : ι → ι . λ x10 . Inj0 x6) (Inj0 0)) ⟶ (∀ x4 . ∀ x5 : ι → ι . ∀ x6 : ι → ((ι → ι) → ι → ι) → (ι → ι) → ι . ∀ x7 : (((ι → ι) → ι) → ι) → ι . x0 (λ x9 : (ι → ι → ι) → ((ι → ι) → ι → ι) → ι . x0 (λ x10 : (ι → ι → ι) → ((ι → ι) → ι → ι) → ι . 0) (λ x10 : (ι → ι → ι) → ι → ι → ι . Inj0 (x1 (λ x11 . λ x12 : ι → (ι → ι) → ι . λ x13 : (ι → ι) → ι . Inj0 0) (λ x11 . 0) (Inj0 0)))) (λ x9 : (ι → ι → ι) → ι → ι → ι . x0 (λ x10 : (ι → ι → ι) → ((ι → ι) → ι → ι) → ι . 0) (λ x10 : (ι → ι → ι) → ι → ι → ι . setsum (x3 (λ x11 : (((ι → ι) → ι) → ι) → ι . λ x12 : ((ι → ι) → ι) → ι → ι . λ x13 x14 : ι → ι . λ x15 . x2 (λ x16 : ι → (ι → ι) → ι → ι → ι . λ x17 . λ x18 : (ι → ι) → ι → ι . λ x19 : ι → ι . 0) 0) (λ x11 . x7 (λ x12 : (ι → ι) → ι . 0)) (λ x11 x12 x13 . setsum 0 0)) (x1 (λ x11 . λ x12 : ι → (ι → ι) → ι . λ x13 : (ι → ι) → ι . x1 (λ x14 . λ x15 : ι → (ι → ι) → ι . λ x16 : (ι → ι) → ι . 0) (λ x14 . 0) 0) (λ x11 . x11) (x1 (λ x11 . λ x12 : ι → (ι → ι) → ι . λ x13 : (ι → ι) → ι . 0) (λ x11 . 0) 0)))) = x0 (λ x9 : (ι → ι → ι) → ((ι → ι) → ι → ι) → ι . setsum (Inj1 (x6 (x1 (λ x10 . λ x11 : ι → (ι → ι) → ι . λ x12 : (ι → ι) → ι . 0) (λ x10 . 0) 0) (λ x10 : ι → ι . λ x11 . x9 (λ x12 x13 . 0) (λ x12 : ι → ι . λ x13 . 0)) (λ x10 . x6 0 (λ x11 : ι → ι . λ x12 . 0) (λ x11 . 0)))) (x3 (λ x10 : (((ι → ι) → ι) → ι) → ι . λ x11 : ((ι → ι) → ι) → ι → ι . λ x12 x13 : ι → ι . λ x14 . setsum (x13 0) (setsum 0 0)) (λ x10 . x1 (λ x11 . λ x12 : ι → (ι → ι) → ι . λ x13 : (ι → ι) → ι . Inj0 0) (λ x11 . x2 (λ x12 : ι → (ι → ι) → ι → ι → ι . λ x13 . λ x14 : (ι → ι) → ι → ι . λ x15 : ι → ι . 0) 0) (x9 (λ x11 x12 . 0) (λ x11 : ι → ι . λ x12 . 0))) (λ x10 x11 x12 . setsum (x0 (λ x13 : (ι → ι → ι) → ((ι → ι) → ι → ι) → ι . 0) (λ x13 : (ι → ι → ι) → ι → ι → ι . 0)) (setsum 0 0)))) (λ x9 : (ι → ι → ι) → ι → ι → ι . x7 (λ x10 : (ι → ι) → ι . x9 (λ x11 x12 . setsum (x9 (λ x13 x14 . 0) 0 0) 0) (x1 (λ x11 . λ x12 : ι → (ι → ι) → ι . λ x13 : (ι → ι) → ι . setsum 0 0) (λ x11 . x10 (λ x12 . 0)) 0) (x1 (λ x11 . λ x12 : ι → (ι → ι) → ι . λ x13 : (ι → ι) → ι . x2 (λ x14 : ι → (ι → ι) → ι → ι → ι . λ x15 . λ x16 : (ι → ι) → ι → ι . λ x17 : ι → ι . 0) 0) (λ x11 . 0) (x0 (λ x11 : (ι → ι → ι) → ((ι → ι) → ι → ι) → ι . 0) (λ x11 : (ι → ι → ι) → ι → ι → ι . 0)))))) ⟶ (∀ x4 : (ι → ι) → ι . ∀ x5 : ((ι → ι → ι) → ι) → ι → (ι → ι) → ι → ι . ∀ x6 : (((ι → ι) → ι → ι) → ι → ι) → ι . ∀ x7 : ι → ι . x0 (λ x9 : (ι → ι → ι) → ((ι → ι) → ι → ι) → ι . x7 0) (λ x9 : (ι → ι → ι) → ι → ι → ι . 0) = setsum (x7 (x6 (λ x9 : (ι → ι) → ι → ι . λ x10 . setsum (x7 0) 0))) (x0 (λ x9 : (ι → ι → ι) → ((ι → ι) → ι → ι) → ι . x0 (λ x10 : (ι → ι → ι) → ((ι → ι) → ι → ι) → ι . x1 (λ x11 . λ x12 : ι → (ι → ι) → ι . λ x13 : (ι → ι) → ι . setsum 0 0) (λ x11 . x1 (λ x12 . λ x13 : ι → (ι → ι) → ι . λ x14 : (ι → ι) → ι . 0) (λ x12 . 0) 0) (x9 (λ x11 x12 . 0) (λ x11 : ι → ι . λ x12 . 0))) (λ x10 : (ι → ι → ι) → ι → ι → ι . Inj1 (setsum 0 0))) (λ x9 : (ι → ι → ι) → ι → ι → ι . Inj0 (x3 (λ x10 : (((ι → ι) → ι) → ι) → ι . λ x11 : ((ι → ι) → ι) → ι → ι . λ x12 x13 : ι → ι . λ x14 . x12 0) (λ x10 . 0) (λ x10 x11 x12 . x11))))) ⟶ False (proof)Theorem 4873e.. : ∀ x0 : ((ι → ι) → ι) → ((ι → (ι → ι) → ι) → ι → (ι → ι) → ι → ι) → ι . ∀ x1 : (ι → ι) → ι → ι → ((ι → ι) → ι → ι) → (ι → ι) → ι → ι . ∀ x2 : (ι → ι → ι → ι) → (((ι → ι → ι) → ι) → ι) → ι . ∀ x3 : ((((ι → ι → ι) → ι) → ι → ι → ι) → ι) → ((ι → ι) → ι → (ι → ι) → ι → ι) → ι . (∀ x4 x5 . ∀ x6 : (ι → ι) → ι . ∀ x7 : (ι → ι → ι → ι) → ι → ι . x3 (λ x9 : ((ι → ι → ι) → ι) → ι → ι → ι . 0) (λ x9 : ι → ι . λ x10 . λ x11 : ι → ι . λ x12 . x11 (x11 (x2 (λ x13 x14 x15 . x3 (λ x16 : ((ι → ι → ι) → ι) → ι → ι → ι . 0) (λ x16 : ι → ι . λ x17 . λ x18 : ι → ι . λ x19 . 0)) (λ x13 : (ι → ι → ι) → ι . 0)))) = x4) ⟶ (∀ x4 . ∀ x5 : ((ι → ι) → ι) → ι → ι . ∀ x6 x7 . x3 (λ x9 : ((ι → ι → ι) → ι) → ι → ι → ι . x0 (λ x10 : ι → ι . 0) (λ x10 : ι → (ι → ι) → ι . λ x11 . λ x12 : ι → ι . λ x13 . x1 (λ x14 . x12 (x12 0)) (x2 (λ x14 x15 x16 . 0) (λ x14 : (ι → ι → ι) → ι . Inj1 0)) (setsum (x0 (λ x14 : ι → ι . 0) (λ x14 : ι → (ι → ι) → ι . λ x15 . λ x16 : ι → ι . λ x17 . 0)) (x3 (λ x14 : ((ι → ι → ι) → ι) → ι → ι → ι . 0) (λ x14 : ι → ι . λ x15 . λ x16 : ι → ι . λ x17 . 0))) (λ x14 : ι → ι . λ x15 . x13) (λ x14 . 0) x11)) (λ x9 : ι → ι . λ x10 . λ x11 : ι → ι . λ x12 . x9 (Inj1 (x1 (λ x13 . 0) (x0 (λ x13 : ι → ι . 0) (λ x13 : ι → (ι → ι) → ι . λ x14 . λ x15 : ι → ι . λ x16 . 0)) (setsum 0 0) (λ x13 : ι → ι . λ x14 . x12) (λ x13 . Inj1 0) (x2 (λ x13 x14 x15 . 0) (λ x13 : (ι → ι → ι) → ι . 0))))) = setsum (setsum (x3 (λ x9 : ((ι → ι → ι) → ι) → ι → ι → ι . x9 (λ x10 : ι → ι → ι . x10 0 0) (x0 (λ x10 : ι → ι . 0) (λ x10 : ι → (ι → ι) → ι . λ x11 . λ x12 : ι → ι . λ x13 . 0)) (x5 (λ x10 : ι → ι . 0) 0)) (λ x9 : ι → ι . λ x10 . λ x11 : ι → ι . λ x12 . 0)) x7) 0) ⟶ (∀ x4 : (ι → ι → ι → ι) → ι → ι . ∀ x5 : (ι → ι) → ((ι → ι) → ι → ι) → ι . ∀ x6 x7 . x2 (λ x9 x10 x11 . Inj1 (Inj1 (x2 (λ x12 x13 x14 . 0) (λ x12 : (ι → ι → ι) → ι . 0)))) (λ x9 : (ι → ι → ι) → ι . x6) = x6) ⟶ (∀ x4 x5 . ∀ x6 : ι → ι . ∀ x7 . x2 (λ x9 x10 x11 . x7) (λ x9 : (ι → ι → ι) → ι . 0) = x7) ⟶ (∀ x4 x5 x6 x7 . x1 (λ x9 . Inj0 (x1 (λ x10 . 0) (x1 (λ x10 . Inj0 0) x7 0 (λ x10 : ι → ι . λ x11 . x1 (λ x12 . 0) 0 0 (λ x12 : ι → ι . λ x13 . 0) (λ x12 . 0) 0) (λ x10 . x7) (x3 (λ x10 : ((ι → ι → ι) → ι) → ι → ι → ι . 0) (λ x10 : ι → ι . λ x11 . λ x12 : ι → ι . λ x13 . 0))) x6 (λ x10 : ι → ι . λ x11 . x3 (λ x12 : ((ι → ι → ι) → ι) → ι → ι → ι . x1 (λ x13 . 0) 0 0 (λ x13 : ι → ι . λ x14 . 0) (λ x13 . 0) 0) (λ x12 : ι → ι . λ x13 . λ x14 : ι → ι . λ x15 . Inj1 0)) (λ x10 . 0) x6)) x5 (x0 (λ x9 : ι → ι . x6) (λ x9 : ι → (ι → ι) → ι . λ x10 . λ x11 : ι → ι . λ x12 . 0)) (λ x9 : ι → ι . λ x10 . Inj1 (x2 (λ x11 x12 x13 . 0) (λ x11 : (ι → ι → ι) → ι . x0 (λ x12 : ι → ι . setsum 0 0) (λ x12 : ι → (ι → ι) → ι . λ x13 . λ x14 : ι → ι . λ x15 . setsum 0 0)))) (λ x9 . 0) x4 = setsum 0 (x2 (λ x9 x10 x11 . x11) (λ x9 : (ι → ι → ι) → ι . x3 (λ x10 : ((ι → ι → ι) → ι) → ι → ι → ι . x10 (λ x11 : ι → ι → ι . setsum 0 0) x6 (Inj1 0)) (λ x10 : ι → ι . λ x11 . λ x12 : ι → ι . λ x13 . x11)))) ⟶ (∀ x4 : ι → (ι → ι → ι) → ι . ∀ x5 x6 x7 . x1 (λ x9 . x9) (x0 (λ x9 : ι → ι . setsum (x2 (λ x10 x11 x12 . Inj0 0) (λ x10 : (ι → ι → ι) → ι . x0 (λ x11 : ι → ι . 0) (λ x11 : ι → (ι → ι) → ι . λ x12 . λ x13 : ι → ι . λ x14 . 0))) 0) (λ x9 : ι → (ι → ι) → ι . λ x10 . λ x11 : ι → ι . λ x12 . 0)) 0 (λ x9 : ι → ι . λ x10 . x1 (λ x11 . setsum (Inj0 x7) (x0 (λ x12 : ι → ι . x11) (λ x12 : ι → (ι → ι) → ι . λ x13 . λ x14 : ι → ι . λ x15 . Inj1 0))) x10 (setsum (x3 (λ x11 : ((ι → ι → ι) → ι) → ι → ι → ι . x3 (λ x12 : ((ι → ι → ι) → ι) → ι → ι → ι . 0) (λ x12 : ι → ι . λ x13 . λ x14 : ι → ι . λ x15 . 0)) (λ x11 : ι → ι . λ x12 . λ x13 : ι → ι . λ x14 . setsum 0 0)) 0) (λ x11 : ι → ι . λ x12 . Inj1 (x1 (λ x13 . setsum 0 0) (setsum 0 0) (setsum 0 0) (λ x13 : ι → ι . λ x14 . Inj0 0) (λ x13 . x10) 0)) (λ x11 . x7) 0) (λ x9 . setsum (x2 (λ x10 x11 x12 . x12) (λ x10 : (ι → ι → ι) → ι . x6)) (setsum (Inj1 x9) x5)) (Inj1 0) = x0 (λ x9 : ι → ι . setsum (x9 (x1 (λ x10 . x6) (Inj1 0) x6 (λ x10 : ι → ι . λ x11 . 0) (λ x10 . Inj1 0) (x3 (λ x10 : ((ι → ι → ι) → ι) → ι → ι → ι . 0) (λ x10 : ι → ι . λ x11 . λ x12 : ι → ι . λ x13 . 0)))) (x0 (λ x10 : ι → ι . 0) (λ x10 : ι → (ι → ι) → ι . λ x11 . λ x12 : ι → ι . λ x13 . Inj1 x11))) (λ x9 : ι → (ι → ι) → ι . λ x10 . λ x11 : ι → ι . λ x12 . setsum (Inj0 (x9 (x11 0) (λ x13 . setsum 0 0))) (x0 (λ x13 : ι → ι . Inj1 0) (λ x13 : ι → (ι → ι) → ι . λ x14 . λ x15 : ι → ι . λ x16 . setsum (x1 (λ x17 . 0) 0 0 (λ x17 : ι → ι . λ x18 . 0) (λ x17 . 0) 0) (setsum 0 0))))) ⟶ (∀ x4 . ∀ x5 : ι → ((ι → ι) → ι) → ι → ι → ι . ∀ x6 : (ι → ι) → ((ι → ι) → ι → ι) → (ι → ι) → ι → ι . ∀ x7 : ι → (ι → ι) → (ι → ι) → ι → ι . x0 (λ x9 : ι → ι . setsum (x3 (λ x10 : ((ι → ι → ι) → ι) → ι → ι → ι . setsum (x10 (λ x11 : ι → ι → ι . 0) 0 0) (x6 (λ x11 . 0) (λ x11 : ι → ι . λ x12 . 0) (λ x11 . 0) 0)) (λ x10 : ι → ι . λ x11 . λ x12 : ι → ι . λ x13 . 0)) (x2 (λ x10 x11 x12 . x10) (λ x10 : (ι → ι → ι) → ι . x1 (λ x11 . x11) (setsum 0 0) (setsum 0 0) (λ x11 : ι → ι . λ x12 . x0 (λ x13 : ι → ι . 0) (λ x13 : ι → (ι → ι) → ι . λ x14 . λ x15 : ι → ι . λ x16 . 0)) (λ x11 . 0) (x10 (λ x11 x12 . 0))))) (λ x9 : ι → (ι → ι) → ι . λ x10 . λ x11 : ι → ι . λ x12 . Inj1 (Inj1 (Inj0 (setsum 0 0)))) = x6 (λ x9 . x9) (λ x9 : ι → ι . λ x10 . x2 (λ x11 x12 x13 . x3 (λ x14 : ((ι → ι → ι) → ι) → ι → ι → ι . x11) (λ x14 : ι → ι . λ x15 . λ x16 : ι → ι . λ x17 . x1 (λ x18 . x17) (x0 (λ x18 : ι → ι . 0) (λ x18 : ι → (ι → ι) → ι . λ x19 . λ x20 : ι → ι . λ x21 . 0)) (x16 0) (λ x18 : ι → ι . λ x19 . setsum 0 0) (λ x18 . x0 (λ x19 : ι → ι . 0) (λ x19 : ι → (ι → ι) → ι . λ x20 . λ x21 : ι → ι . λ x22 . 0)) x17)) (λ x11 : (ι → ι → ι) → ι . x2 (λ x12 x13 x14 . x3 (λ x15 : ((ι → ι → ι) → ι) → ι → ι → ι . x0 (λ x16 : ι → ι . 0) (λ x16 : ι → (ι → ι) → ι . λ x17 . λ x18 : ι → ι . λ x19 . 0)) (λ x15 : ι → ι . λ x16 . λ x17 : ι → ι . λ x18 . x16)) (λ x12 : (ι → ι → ι) → ι . 0))) (λ x9 . 0) (x3 (λ x9 : ((ι → ι → ι) → ι) → ι → ι → ι . x3 (λ x10 : ((ι → ι → ι) → ι) → ι → ι → ι . x0 (λ x11 : ι → ι . x10 (λ x12 : ι → ι → ι . 0) 0 0) (λ x11 : ι → (ι → ι) → ι . λ x12 . λ x13 : ι → ι . λ x14 . x1 (λ x15 . 0) 0 0 (λ x15 : ι → ι . λ x16 . 0) (λ x15 . 0) 0)) (λ x10 : ι → ι . λ x11 . λ x12 : ι → ι . λ x13 . 0)) (λ x9 : ι → ι . λ x10 . λ x11 : ι → ι . λ x12 . x0 (λ x13 : ι → ι . x12) (λ x13 : ι → (ι → ι) → ι . λ x14 . λ x15 : ι → ι . λ x16 . 0)))) ⟶ (∀ x4 . ∀ x5 : ι → ι → ι . ∀ x6 : ι → ι → (ι → ι) → ι . ∀ x7 : (ι → ι → ι) → (ι → ι → ι) → ι . x0 (λ x9 : ι → ι . x9 0) (λ x9 : ι → (ι → ι) → ι . λ x10 . λ x11 : ι → ι . λ x12 . x3 (λ x13 : ((ι → ι → ι) → ι) → ι → ι → ι . Inj1 (x13 (λ x14 : ι → ι → ι . setsum 0 0) (x11 0) 0)) (λ x13 : ι → ι . λ x14 . λ x15 : ι → ι . λ x16 . x16)) = x3 (λ x9 : ((ι → ι → ι) → ι) → ι → ι → ι . x3 (λ x10 : ((ι → ι → ι) → ι) → ι → ι → ι . Inj0 0) (λ x10 : ι → ι . λ x11 . λ x12 : ι → ι . λ x13 . x12 (setsum (setsum 0 0) (Inj0 0)))) (λ x9 : ι → ι . λ x10 . λ x11 : ι → ι . λ x12 . x1 (λ x13 . Inj1 x10) 0 (setsum (setsum (Inj1 0) (x1 (λ x13 . 0) 0 0 (λ x13 : ι → ι . λ x14 . 0) (λ x13 . 0) 0)) 0) (λ x13 : ι → ι . λ x14 . x3 (λ x15 : ((ι → ι → ι) → ι) → ι → ι → ι . setsum (x2 (λ x16 x17 x18 . 0) (λ x16 : (ι → ι → ι) → ι . 0)) (x2 (λ x16 x17 x18 . 0) (λ x16 : (ι → ι → ι) → ι . 0))) (λ x15 : ι → ι . λ x16 . λ x17 : ι → ι . λ x18 . x3 (λ x19 : ((ι → ι → ι) → ι) → ι → ι → ι . x18) (λ x19 : ι → ι . λ x20 . λ x21 : ι → ι . λ x22 . Inj0 0))) (λ x13 . setsum 0 x10) (Inj1 0))) ⟶ False (proof)Theorem 07659.. : ∀ x0 : (((ι → ι) → ι → ι) → ι) → ((ι → ι) → ι → ι → ι → ι) → ι → ι . ∀ x1 : ((((ι → ι) → ι → ι → ι) → ι → ι → ι → ι) → ι) → (ι → ι) → ι . ∀ x2 : (ι → ι) → ι → ((ι → ι → ι) → ι) → ι . ∀ x3 : (ι → (((ι → ι) → ι) → (ι → ι) → ι) → ι) → (ι → (ι → ι) → ι) → ((ι → ι → ι) → ι → ι → ι) → ι → ι . (∀ x4 x5 x6 . ∀ x7 : ι → ((ι → ι) → ι → ι) → ι . x3 (λ x9 . λ x10 : ((ι → ι) → ι) → (ι → ι) → ι . 0) (λ x9 . λ x10 : ι → ι . 0) (λ x9 : ι → ι → ι . λ x10 x11 . 0) (Inj1 (x7 (x0 (λ x9 : (ι → ι) → ι → ι . 0) (λ x9 : ι → ι . λ x10 x11 x12 . x0 (λ x13 : (ι → ι) → ι → ι . 0) (λ x13 : ι → ι . λ x14 x15 x16 . 0) 0) 0) (λ x9 : ι → ι . λ x10 . 0))) = setsum 0 (x2 (λ x9 . setsum x5 (x3 (λ x10 . λ x11 : ((ι → ι) → ι) → (ι → ι) → ι . 0) (λ x10 . λ x11 : ι → ι . Inj0 0) (λ x10 : ι → ι → ι . λ x11 x12 . x1 (λ x13 : ((ι → ι) → ι → ι → ι) → ι → ι → ι → ι . 0) (λ x13 . 0)) (x3 (λ x10 . λ x11 : ((ι → ι) → ι) → (ι → ι) → ι . 0) (λ x10 . λ x11 : ι → ι . 0) (λ x10 : ι → ι → ι . λ x11 x12 . 0) 0))) x4 (λ x9 : ι → ι → ι . setsum 0 (x9 (x2 (λ x10 . 0) 0 (λ x10 : ι → ι → ι . 0)) (setsum 0 0))))) ⟶ (∀ x4 x5 . ∀ x6 : (((ι → ι) → ι → ι) → (ι → ι) → ι → ι) → ι . ∀ x7 . x3 (λ x9 . λ x10 : ((ι → ι) → ι) → (ι → ι) → ι . 0) (λ x9 . λ x10 : ι → ι . x2 (λ x11 . x11) 0 (λ x11 : ι → ι → ι . setsum x7 x9)) (λ x9 : ι → ι → ι . λ x10 x11 . x3 (λ x12 . λ x13 : ((ι → ι) → ι) → (ι → ι) → ι . x0 (λ x14 : (ι → ι) → ι → ι . x0 (λ x15 : (ι → ι) → ι → ι . x13 (λ x16 : ι → ι . 0) (λ x16 . 0)) (λ x15 : ι → ι . λ x16 x17 x18 . 0) (x13 (λ x15 : ι → ι . 0) (λ x15 . 0))) (λ x14 : ι → ι . λ x15 x16 x17 . x3 (λ x18 . λ x19 : ((ι → ι) → ι) → (ι → ι) → ι . x17) (λ x18 . λ x19 : ι → ι . 0) (λ x18 : ι → ι → ι . λ x19 x20 . setsum 0 0) x15) x12) (λ x12 . λ x13 : ι → ι . setsum (x0 (λ x14 : (ι → ι) → ι → ι . 0) (λ x14 : ι → ι . λ x15 x16 x17 . setsum 0 0) (setsum 0 0)) x10) (λ x12 : ι → ι → ι . λ x13 x14 . Inj1 (setsum (x1 (λ x15 : ((ι → ι) → ι → ι → ι) → ι → ι → ι → ι . 0) (λ x15 . 0)) (Inj1 0))) (setsum 0 (x9 0 x7))) (x3 (λ x9 . λ x10 : ((ι → ι) → ι) → (ι → ι) → ι . x3 (λ x11 . λ x12 : ((ι → ι) → ι) → (ι → ι) → ι . x11) (λ x11 . λ x12 : ι → ι . x9) (λ x11 : ι → ι → ι . λ x12 x13 . x1 (λ x14 : ((ι → ι) → ι → ι → ι) → ι → ι → ι → ι . 0) (λ x14 . x12)) (setsum (setsum 0 0) 0)) (λ x9 . λ x10 : ι → ι . x0 (λ x11 : (ι → ι) → ι → ι . 0) (λ x11 : ι → ι . λ x12 x13 x14 . x1 (λ x15 : ((ι → ι) → ι → ι → ι) → ι → ι → ι → ι . x12) (λ x15 . 0)) (x10 (setsum 0 0))) (λ x9 : ι → ι → ι . λ x10 x11 . Inj1 (x3 (λ x12 . λ x13 : ((ι → ι) → ι) → (ι → ι) → ι . setsum 0 0) (λ x12 . λ x13 : ι → ι . x0 (λ x14 : (ι → ι) → ι → ι . 0) (λ x14 : ι → ι . λ x15 x16 x17 . 0) 0) (λ x12 : ι → ι → ι . λ x13 x14 . 0) 0)) x7) = x2 (λ x9 . x6 (λ x10 : (ι → ι) → ι → ι . λ x11 : ι → ι . λ x12 . x9)) x5 (λ x9 : ι → ι → ι . setsum (setsum 0 (setsum x5 (setsum 0 0))) 0)) ⟶ (∀ x4 : (((ι → ι) → ι) → ι) → ι . ∀ x5 : ((ι → ι → ι) → ι) → (ι → ι → ι) → ι . ∀ x6 x7 . x2 (λ x9 . setsum (x3 (λ x10 . λ x11 : ((ι → ι) → ι) → (ι → ι) → ι . x11 (λ x12 : ι → ι . 0) (λ x12 . x3 (λ x13 . λ x14 : ((ι → ι) → ι) → (ι → ι) → ι . 0) (λ x13 . λ x14 : ι → ι . 0) (λ x13 : ι → ι → ι . λ x14 x15 . 0) 0)) (λ x10 . λ x11 : ι → ι . x9) (λ x10 : ι → ι → ι . λ x11 x12 . 0) (x3 (λ x10 . λ x11 : ((ι → ι) → ι) → (ι → ι) → ι . x10) (λ x10 . λ x11 : ι → ι . x9) (λ x10 : ι → ι → ι . λ x11 x12 . x1 (λ x13 : ((ι → ι) → ι → ι → ι) → ι → ι → ι → ι . 0) (λ x13 . 0)) (Inj1 0))) 0) (Inj0 (x5 (λ x9 : ι → ι → ι . 0) (λ x9 . x0 (λ x10 : (ι → ι) → ι → ι . 0) (λ x10 : ι → ι . λ x11 x12 x13 . x2 (λ x14 . 0) 0 (λ x14 : ι → ι → ι . 0))))) (λ x9 : ι → ι → ι . x3 (λ x10 . λ x11 : ((ι → ι) → ι) → (ι → ι) → ι . 0) (λ x10 . λ x11 : ι → ι . x3 (λ x12 . λ x13 : ((ι → ι) → ι) → (ι → ι) → ι . setsum x10 (x0 (λ x14 : (ι → ι) → ι → ι . 0) (λ x14 : ι → ι . λ x15 x16 x17 . 0) 0)) (λ x12 . λ x13 : ι → ι . x1 (λ x14 : ((ι → ι) → ι → ι → ι) → ι → ι → ι → ι . Inj1 0) (λ x14 . x11 0)) (λ x12 : ι → ι → ι . λ x13 x14 . 0) (x1 (λ x12 : ((ι → ι) → ι → ι → ι) → ι → ι → ι → ι . x3 (λ x13 . λ x14 : ((ι → ι) → ι) → (ι → ι) → ι . 0) (λ x13 . λ x14 : ι → ι . 0) (λ x13 : ι → ι → ι . λ x14 x15 . 0) 0) (λ x12 . 0))) (λ x10 : ι → ι → ι . λ x11 x12 . x11) x7) = x3 (λ x9 . λ x10 : ((ι → ι) → ι) → (ι → ι) → ι . Inj1 0) (λ x9 . λ x10 : ι → ι . setsum (setsum (x1 (λ x11 : ((ι → ι) → ι → ι → ι) → ι → ι → ι → ι . x1 (λ x12 : ((ι → ι) → ι → ι → ι) → ι → ι → ι → ι . 0) (λ x12 . 0)) (λ x11 . x3 (λ x12 . λ x13 : ((ι → ι) → ι) → (ι → ι) → ι . 0) (λ x12 . λ x13 : ι → ι . 0) (λ x12 : ι → ι → ι . λ x13 x14 . 0) 0)) (x3 (λ x11 . λ x12 : ((ι → ι) → ι) → (ι → ι) → ι . x1 (λ x13 : ((ι → ι) → ι → ι → ι) → ι → ι → ι → ι . 0) (λ x13 . 0)) (λ x11 . λ x12 : ι → ι . x3 (λ x13 . λ x14 : ((ι → ι) → ι) → (ι → ι) → ι . 0) (λ x13 . λ x14 : ι → ι . 0) (λ x13 : ι → ι → ι . λ x14 x15 . 0) 0) (λ x11 : ι → ι → ι . λ x12 x13 . Inj1 0) 0)) 0) (λ x9 : ι → ι → ι . λ x10 x11 . x9 (x1 (λ x12 : ((ι → ι) → ι → ι → ι) → ι → ι → ι → ι . x3 (λ x13 . λ x14 : ((ι → ι) → ι) → (ι → ι) → ι . x11) (λ x13 . λ x14 : ι → ι . setsum 0 0) (λ x13 : ι → ι → ι . λ x14 x15 . x1 (λ x16 : ((ι → ι) → ι → ι → ι) → ι → ι → ι → ι . 0) (λ x16 . 0)) x11) (λ x12 . setsum (Inj1 0) (setsum 0 0))) (Inj0 (setsum 0 0))) (setsum (x4 (λ x9 : (ι → ι) → ι . x3 (λ x10 . λ x11 : ((ι → ι) → ι) → (ι → ι) → ι . Inj0 0) (λ x10 . λ x11 : ι → ι . x7) (λ x10 : ι → ι → ι . λ x11 x12 . x10 0 0) 0)) (setsum x7 0))) ⟶ (∀ x4 : ((ι → ι) → (ι → ι) → ι → ι) → ι . ∀ x5 : ι → ι . ∀ x6 : ι → ((ι → ι) → ι) → ι → ι → ι . ∀ x7 . x2 (λ x9 . x2 (λ x10 . x10) (Inj1 (x1 (λ x10 : ((ι → ι) → ι → ι → ι) → ι → ι → ι → ι . 0) (λ x10 . 0))) (λ x10 : ι → ι → ι . x3 (λ x11 . λ x12 : ((ι → ι) → ι) → (ι → ι) → ι . 0) (λ x11 . λ x12 : ι → ι . x0 (λ x13 : (ι → ι) → ι → ι . setsum 0 0) (λ x13 : ι → ι . λ x14 x15 x16 . Inj1 0) (x1 (λ x13 : ((ι → ι) → ι → ι → ι) → ι → ι → ι → ι . 0) (λ x13 . 0))) (λ x11 : ι → ι → ι . λ x12 x13 . x13) x7)) 0 (λ x9 : ι → ι → ι . 0) = x2 (λ x9 . Inj1 (x2 (λ x10 . 0) 0 (λ x10 : ι → ι → ι . Inj1 (x3 (λ x11 . λ x12 : ((ι → ι) → ι) → (ι → ι) → ι . 0) (λ x11 . λ x12 : ι → ι . 0) (λ x11 : ι → ι → ι . λ x12 x13 . 0) 0)))) (Inj1 (x1 (λ x9 : ((ι → ι) → ι → ι → ι) → ι → ι → ι → ι . x6 (x6 0 (λ x10 : ι → ι . 0) 0 0) (λ x10 : ι → ι . 0) 0 (x6 0 (λ x10 : ι → ι . 0) 0 0)) (λ x9 . Inj1 0))) (λ x9 : ι → ι → ι . x9 (Inj0 0) (x5 0))) ⟶ (∀ x4 . ∀ x5 : ι → ι . ∀ x6 : (ι → ι → ι) → ι . ∀ x7 : (ι → (ι → ι) → ι) → ι . x1 (λ x9 : ((ι → ι) → ι → ι → ι) → ι → ι → ι → ι . 0) Inj1 = x7 (λ x9 . λ x10 : ι → ι . setsum 0 (x6 (λ x11 x12 . setsum 0 (Inj1 0))))) ⟶ (∀ x4 x5 x6 x7 . x1 (λ x9 : ((ι → ι) → ι → ι → ι) → ι → ι → ι → ι . setsum (x1 (λ x10 : ((ι → ι) → ι → ι → ι) → ι → ι → ι → ι . x2 (λ x11 . x2 (λ x12 . 0) 0 (λ x12 : ι → ι → ι . 0)) (Inj1 0) (λ x11 : ι → ι → ι . x11 0 0)) (λ x10 . Inj1 x6)) (x3 (λ x10 . λ x11 : ((ι → ι) → ι) → (ι → ι) → ι . x2 (λ x12 . Inj0 0) x10 (λ x12 : ι → ι → ι . x10)) (λ x10 . λ x11 : ι → ι . 0) (λ x10 : ι → ι → ι . λ x11 x12 . 0) (Inj0 (x1 (λ x10 : ((ι → ι) → ι → ι → ι) → ι → ι → ι → ι . 0) (λ x10 . 0))))) (λ x9 . 0) = x5) ⟶ (∀ x4 . ∀ x5 : ((ι → ι → ι) → (ι → ι) → ι → ι) → ι → (ι → ι) → ι . ∀ x6 : (((ι → ι) → ι → ι) → (ι → ι) → ι → ι) → ((ι → ι) → ι) → ι → ι → ι . ∀ x7 : ι → ι . x0 (λ x9 : (ι → ι) → ι → ι . Inj1 (x2 (λ x10 . x2 (λ x11 . setsum 0 0) (Inj1 0) (λ x11 : ι → ι → ι . 0)) (setsum (setsum 0 0) 0) (λ x10 : ι → ι → ι . x3 (λ x11 . λ x12 : ((ι → ι) → ι) → (ι → ι) → ι . x9 (λ x13 . 0) 0) (λ x11 . λ x12 : ι → ι . x3 (λ x13 . λ x14 : ((ι → ι) → ι) → (ι → ι) → ι . 0) (λ x13 . λ x14 : ι → ι . 0) (λ x13 : ι → ι → ι . λ x14 x15 . 0) 0) (λ x11 : ι → ι → ι . λ x12 x13 . x12) 0))) (λ x9 : ι → ι . λ x10 x11 x12 . x2 (λ x13 . x11) 0 (λ x13 : ι → ι → ι . x13 0 (Inj0 x12))) 0 = setsum (setsum (x5 (λ x9 : ι → ι → ι . λ x10 : ι → ι . λ x11 . setsum (x1 (λ x12 : ((ι → ι) → ι → ι → ι) → ι → ι → ι → ι . 0) (λ x12 . 0)) (setsum 0 0)) 0 (λ x9 . x9)) (x1 (λ x9 : ((ι → ι) → ι → ι → ι) → ι → ι → ι → ι . setsum (x6 (λ x10 : (ι → ι) → ι → ι . λ x11 : ι → ι . λ x12 . 0) (λ x10 : ι → ι . 0) 0 0) 0) (λ x9 . x1 (λ x10 : ((ι → ι) → ι → ι → ι) → ι → ι → ι → ι . Inj1 0) (λ x10 . 0)))) (setsum 0 (x5 (λ x9 : ι → ι → ι . λ x10 : ι → ι . λ x11 . setsum (Inj1 0) (setsum 0 0)) (x2 (λ x9 . x6 (λ x10 : (ι → ι) → ι → ι . λ x11 : ι → ι . λ x12 . 0) (λ x10 : ι → ι . 0) 0 0) (x0 (λ x9 : (ι → ι) → ι → ι . 0) (λ x9 : ι → ι . λ x10 x11 x12 . 0) 0) (λ x9 : ι → ι → ι . x1 (λ x10 : ((ι → ι) → ι → ι → ι) → ι → ι → ι → ι . 0) (λ x10 . 0))) (λ x9 . x1 (λ x10 : ((ι → ι) → ι → ι → ι) → ι → ι → ι → ι . x0 (λ x11 : (ι → ι) → ι → ι . 0) (λ x11 : ι → ι . λ x12 x13 x14 . 0) 0) (λ x10 . 0))))) ⟶ (∀ x4 . ∀ x5 : ι → ι . ∀ x6 . ∀ x7 : ι → ((ι → ι) → ι → ι) → (ι → ι) → ι . x0 (λ x9 : (ι → ι) → ι → ι . Inj1 (Inj0 x6)) (λ x9 : ι → ι . λ x10 x11 x12 . setsum 0 0) (x1 (λ x9 : ((ι → ι) → ι → ι → ι) → ι → ι → ι → ι . 0) (λ x9 . x9)) = Inj0 (Inj1 0)) ⟶ False (proof)Theorem bd450.. : ∀ x0 : (((ι → (ι → ι) → ι → ι) → ι) → ι) → ι → (((ι → ι) → ι) → ι) → ι . ∀ x1 : ((ι → ι) → ι → ((ι → ι) → ι → ι) → ι) → (ι → ι) → (ι → (ι → ι) → ι → ι) → ι → ι . ∀ x2 : (((ι → ι → ι) → ι) → ι) → ι → ι → ι → (ι → ι) → ι . ∀ x3 : (ι → ι → ((ι → ι) → ι → ι) → ι) → (((ι → ι → ι) → ι) → ι) → ι → ι → ι . (∀ x4 . ∀ x5 : (((ι → ι) → ι → ι) → ι) → ι → (ι → ι) → ι . ∀ x6 . ∀ x7 : ((ι → ι → ι) → ι → ι) → ι . x3 (λ x9 x10 . λ x11 : (ι → ι) → ι → ι . 0) (λ x9 : (ι → ι → ι) → ι . Inj0 (x7 (λ x10 : ι → ι → ι . λ x11 . setsum (x2 (λ x12 : (ι → ι → ι) → ι . 0) 0 0 0 (λ x12 . 0)) (x9 (λ x12 x13 . 0))))) (x3 (λ x9 x10 . λ x11 : (ι → ι) → ι → ι . x3 (λ x12 x13 . λ x14 : (ι → ι) → ι → ι . x1 (λ x15 : ι → ι . λ x16 . λ x17 : (ι → ι) → ι → ι . x14 (λ x18 . 0) 0) (λ x15 . x13) (λ x15 . λ x16 : ι → ι . λ x17 . 0) x13) (λ x12 : (ι → ι → ι) → ι . 0) (x11 (λ x12 . x0 (λ x13 : (ι → (ι → ι) → ι → ι) → ι . 0) 0 (λ x13 : (ι → ι) → ι . 0)) (Inj1 0)) (x11 (λ x12 . x10) (x0 (λ x12 : (ι → (ι → ι) → ι → ι) → ι . 0) 0 (λ x12 : (ι → ι) → ι . 0)))) (λ x9 : (ι → ι → ι) → ι . x7 (λ x10 : ι → ι → ι . λ x11 . x7 (λ x12 : ι → ι → ι . λ x13 . x2 (λ x14 : (ι → ι → ι) → ι . 0) 0 0 0 (λ x14 . 0)))) (x7 (λ x9 : ι → ι → ι . λ x10 . 0)) (x0 (λ x9 : (ι → (ι → ι) → ι → ι) → ι . Inj1 (x9 (λ x10 . λ x11 : ι → ι . λ x12 . 0))) (x0 (λ x9 : (ι → (ι → ι) → ι → ι) → ι . x3 (λ x10 x11 . λ x12 : (ι → ι) → ι → ι . 0) (λ x10 : (ι → ι → ι) → ι . 0) 0 0) (x5 (λ x9 : (ι → ι) → ι → ι . 0) 0 (λ x9 . 0)) (λ x9 : (ι → ι) → ι . Inj0 0)) (λ x9 : (ι → ι) → ι . Inj0 0))) (x2 (λ x9 : (ι → ι → ι) → ι . Inj0 (setsum (x7 (λ x10 : ι → ι → ι . λ x11 . 0)) (setsum 0 0))) (x1 (λ x9 : ι → ι . λ x10 . λ x11 : (ι → ι) → ι → ι . x11 (λ x12 . x2 (λ x13 : (ι → ι → ι) → ι . 0) 0 0 0 (λ x13 . 0)) (x1 (λ x12 : ι → ι . λ x13 . λ x14 : (ι → ι) → ι → ι . 0) (λ x12 . 0) (λ x12 . λ x13 : ι → ι . λ x14 . 0) 0)) (λ x9 . x1 (λ x10 : ι → ι . λ x11 . λ x12 : (ι → ι) → ι → ι . setsum 0 0) (λ x10 . x2 (λ x11 : (ι → ι → ι) → ι . 0) 0 0 0 (λ x11 . 0)) (λ x10 . λ x11 : ι → ι . λ x12 . x9) (x7 (λ x10 : ι → ι → ι . λ x11 . 0))) (λ x9 . λ x10 : ι → ι . λ x11 . x7 (λ x12 : ι → ι → ι . λ x13 . 0)) x4) (Inj0 x6) 0 (λ x9 . Inj0 (setsum x6 (x0 (λ x10 : (ι → (ι → ι) → ι → ι) → ι . 0) 0 (λ x10 : (ι → ι) → ι . 0))))) = x2 (λ x9 : (ι → ι → ι) → ι . setsum (x7 (λ x10 : ι → ι → ι . λ x11 . x11)) x6) (x1 (λ x9 : ι → ι . λ x10 . λ x11 : (ι → ι) → ι → ι . 0) (λ x9 . 0) (λ x9 . λ x10 : ι → ι . λ x11 . x1 (λ x12 : ι → ι . λ x13 . λ x14 : (ι → ι) → ι → ι . 0) (λ x12 . Inj1 (x1 (λ x13 : ι → ι . λ x14 . λ x15 : (ι → ι) → ι → ι . 0) (λ x13 . 0) (λ x13 . λ x14 : ι → ι . λ x15 . 0) 0)) (λ x12 . λ x13 : ι → ι . λ x14 . x1 (λ x15 : ι → ι . λ x16 . λ x17 : (ι → ι) → ι → ι . setsum 0 0) (λ x15 . Inj0 0) (λ x15 . λ x16 : ι → ι . λ x17 . setsum 0 0) (x2 (λ x15 : (ι → ι → ι) → ι . 0) 0 0 0 (λ x15 . 0))) 0) (x3 (λ x9 x10 . λ x11 : (ι → ι) → ι → ι . Inj1 (x0 (λ x12 : (ι → (ι → ι) → ι → ι) → ι . 0) 0 (λ x12 : (ι → ι) → ι . 0))) (λ x9 : (ι → ι → ι) → ι . setsum (setsum 0 0) (x9 (λ x10 x11 . 0))) 0 (x0 (λ x9 : (ι → (ι → ι) → ι → ι) → ι . 0) (x0 (λ x9 : (ι → (ι → ι) → ι → ι) → ι . 0) 0 (λ x9 : (ι → ι) → ι . 0)) (λ x9 : (ι → ι) → ι . setsum 0 0)))) (Inj0 0) (Inj0 (x2 (λ x9 : (ι → ι → ι) → ι . x0 (λ x10 : (ι → (ι → ι) → ι → ι) → ι . x2 (λ x11 : (ι → ι → ι) → ι . 0) 0 0 0 (λ x11 . 0)) 0 (λ x10 : (ι → ι) → ι . x9 (λ x11 x12 . 0))) 0 x4 (x3 (λ x9 x10 . λ x11 : (ι → ι) → ι → ι . x2 (λ x12 : (ι → ι → ι) → ι . 0) 0 0 0 (λ x12 . 0)) (λ x9 : (ι → ι → ι) → ι . x0 (λ x10 : (ι → (ι → ι) → ι → ι) → ι . 0) 0 (λ x10 : (ι → ι) → ι . 0)) (Inj1 0) 0) (λ x9 . setsum (Inj0 0) x6))) (λ x9 . setsum 0 x6)) ⟶ (∀ x4 x5 . ∀ x6 : ι → (ι → ι) → ι → ι → ι . ∀ x7 : (ι → ι) → ι . x3 (λ x9 x10 . λ x11 : (ι → ι) → ι → ι . x11 (λ x12 . setsum x9 (setsum (setsum 0 0) (Inj1 0))) 0) (λ x9 : (ι → ι → ι) → ι . 0) (x7 (λ x9 . x9)) (Inj1 (Inj0 (x7 (λ x9 . 0)))) = x7 (λ x9 . x1 (λ x10 : ι → ι . λ x11 . λ x12 : (ι → ι) → ι → ι . 0) (λ x10 . x1 (λ x11 : ι → ι . λ x12 . λ x13 : (ι → ι) → ι → ι . Inj1 (x1 (λ x14 : ι → ι . λ x15 . λ x16 : (ι → ι) → ι → ι . 0) (λ x14 . 0) (λ x14 . λ x15 : ι → ι . λ x16 . 0) 0)) (λ x11 . Inj1 (x7 (λ x12 . 0))) (λ x11 . λ x12 : ι → ι . λ x13 . 0) (Inj1 0)) (λ x10 . λ x11 : ι → ι . λ x12 . 0) (setsum (x7 (λ x10 . 0)) 0))) ⟶ (∀ x4 : (ι → ι) → ι . ∀ x5 : (ι → (ι → ι) → ι → ι) → ι . ∀ x6 : ((ι → ι → ι) → ι) → ι → ι → ι → ι . ∀ x7 : ι → ι . x2 (λ x9 : (ι → ι → ι) → ι . 0) 0 (x2 (λ x9 : (ι → ι → ι) → ι . Inj1 0) (x4 (λ x9 . x3 (λ x10 x11 . λ x12 : (ι → ι) → ι → ι . x0 (λ x13 : (ι → (ι → ι) → ι → ι) → ι . 0) 0 (λ x13 : (ι → ι) → ι . 0)) (λ x10 : (ι → ι → ι) → ι . x10 (λ x11 x12 . 0)) (x1 (λ x10 : ι → ι . λ x11 . λ x12 : (ι → ι) → ι → ι . 0) (λ x10 . 0) (λ x10 . λ x11 : ι → ι . λ x12 . 0) 0) 0)) (x2 (λ x9 : (ι → ι → ι) → ι . x7 0) 0 0 0 (λ x9 . x3 (λ x10 x11 . λ x12 : (ι → ι) → ι → ι . x3 (λ x13 x14 . λ x15 : (ι → ι) → ι → ι . 0) (λ x13 : (ι → ι → ι) → ι . 0) 0 0) (λ x10 : (ι → ι → ι) → ι . Inj1 0) (x0 (λ x10 : (ι → (ι → ι) → ι → ι) → ι . 0) 0 (λ x10 : (ι → ι) → ι . 0)) (x2 (λ x10 : (ι → ι → ι) → ι . 0) 0 0 0 (λ x10 . 0)))) (x2 (λ x9 : (ι → ι → ι) → ι . 0) 0 (x1 (λ x9 : ι → ι . λ x10 . λ x11 : (ι → ι) → ι → ι . x1 (λ x12 : ι → ι . λ x13 . λ x14 : (ι → ι) → ι → ι . 0) (λ x12 . 0) (λ x12 . λ x13 : ι → ι . λ x14 . 0) 0) (λ x9 . x0 (λ x10 : (ι → (ι → ι) → ι → ι) → ι . 0) 0 (λ x10 : (ι → ι) → ι . 0)) (λ x9 . λ x10 : ι → ι . λ x11 . x0 (λ x12 : (ι → (ι → ι) → ι → ι) → ι . 0) 0 (λ x12 : (ι → ι) → ι . 0)) 0) (x5 (λ x9 . λ x10 : ι → ι . λ x11 . x3 (λ x12 x13 . λ x14 : (ι → ι) → ι → ι . 0) (λ x12 : (ι → ι → ι) → ι . 0) 0 0)) (λ x9 . x0 (λ x10 : (ι → (ι → ι) → ι → ι) → ι . 0) (x1 (λ x10 : ι → ι . λ x11 . λ x12 : (ι → ι) → ι → ι . 0) (λ x10 . 0) (λ x10 . λ x11 : ι → ι . λ x12 . 0) 0) (λ x10 : (ι → ι) → ι . x9))) (λ x9 . x0 (λ x10 : (ι → (ι → ι) → ι → ι) → ι . 0) 0 (λ x10 : (ι → ι) → ι . 0))) (x3 (λ x9 x10 . λ x11 : (ι → ι) → ι → ι . x2 (λ x12 : (ι → ι → ι) → ι . x0 (λ x13 : (ι → (ι → ι) → ι → ι) → ι . Inj1 0) 0 (λ x13 : (ι → ι) → ι . Inj0 0)) (Inj1 (Inj1 0)) (x2 (λ x12 : (ι → ι → ι) → ι . x0 (λ x13 : (ι → (ι → ι) → ι → ι) → ι . 0) 0 (λ x13 : (ι → ι) → ι . 0)) x10 0 (x7 0) (λ x12 . x11 (λ x13 . 0) 0)) 0 (λ x12 . x0 (λ x13 : (ι → (ι → ι) → ι → ι) → ι . 0) (x0 (λ x13 : (ι → (ι → ι) → ι → ι) → ι . 0) 0 (λ x13 : (ι → ι) → ι . 0)) (λ x13 : (ι → ι) → ι . x2 (λ x14 : (ι → ι → ι) → ι . 0) 0 0 0 (λ x14 . 0)))) (λ x9 : (ι → ι → ι) → ι . x5 (λ x10 . λ x11 : ι → ι . λ x12 . Inj0 (setsum 0 0))) (Inj1 (x5 (λ x9 . λ x10 : ι → ι . λ x11 . x0 (λ x12 : (ι → (ι → ι) → ι → ι) → ι . 0) 0 (λ x12 : (ι → ι) → ι . 0)))) (x6 (λ x9 : ι → ι → ι . 0) (x1 (λ x9 : ι → ι . λ x10 . λ x11 : (ι → ι) → ι → ι . x11 (λ x12 . 0) 0) (λ x9 . x6 (λ x10 : ι → ι → ι . 0) 0 0 0) (λ x9 . λ x10 : ι → ι . λ x11 . Inj0 0) (setsum 0 0)) 0 (x0 (λ x9 : (ι → (ι → ι) → ι → ι) → ι . x3 (λ x10 x11 . λ x12 : (ι → ι) → ι → ι . 0) (λ x10 : (ι → ι → ι) → ι . 0) 0 0) (x6 (λ x9 : ι → ι → ι . 0) 0 0 0) (λ x9 : (ι → ι) → ι . setsum 0 0)))) (λ x9 . 0) = x2 (λ x9 : (ι → ι → ι) → ι . x7 0) (setsum (Inj1 (setsum (Inj0 0) 0)) (x1 (λ x9 : ι → ι . λ x10 . λ x11 : (ι → ι) → ι → ι . x0 (λ x12 : (ι → (ι → ι) → ι → ι) → ι . Inj0 0) (Inj0 0) (λ x12 : (ι → ι) → ι . x11 (λ x13 . 0) 0)) (λ x9 . 0) (λ x9 . λ x10 : ι → ι . λ x11 . x3 (λ x12 x13 . λ x14 : (ι → ι) → ι → ι . x12) (λ x12 : (ι → ι → ι) → ι . setsum 0 0) 0 (x10 0)) (x6 (λ x9 : ι → ι → ι . 0) (x1 (λ x9 : ι → ι . λ x10 . λ x11 : (ι → ι) → ι → ι . 0) (λ x9 . 0) (λ x9 . λ x10 : ι → ι . λ x11 . 0) 0) 0 (x7 0)))) (x5 (λ x9 . λ x10 : ι → ι . λ x11 . x7 (x1 (λ x12 : ι → ι . λ x13 . λ x14 : (ι → ι) → ι → ι . x1 (λ x15 : ι → ι . λ x16 . λ x17 : (ι → ι) → ι → ι . 0) (λ x15 . 0) (λ x15 . λ x16 : ι → ι . λ x17 . 0) 0) (λ x12 . x10 0) (λ x12 . λ x13 : ι → ι . λ x14 . x13 0) (x0 (λ x12 : (ι → (ι → ι) → ι → ι) → ι . 0) 0 (λ x12 : (ι → ι) → ι . 0))))) (setsum (x7 (x3 (λ x9 x10 . λ x11 : (ι → ι) → ι → ι . 0) (λ x9 : (ι → ι → ι) → ι . 0) 0 0)) (x2 (λ x9 : (ι → ι → ι) → ι . 0) 0 (x5 (λ x9 . λ x10 : ι → ι . λ x11 . x9)) (x0 (λ x9 : (ι → (ι → ι) → ι → ι) → ι . 0) (Inj1 0) (λ x9 : (ι → ι) → ι . 0)) (λ x9 . x7 (Inj1 0)))) (λ x9 . x3 (λ x10 x11 . λ x12 : (ι → ι) → ι → ι . 0) (λ x10 : (ι → ι → ι) → ι . x9) (x0 (λ x10 : (ι → (ι → ι) → ι → ι) → ι . x3 (λ x11 x12 . λ x13 : (ι → ι) → ι → ι . x13 (λ x14 . 0) 0) (λ x11 : (ι → ι → ι) → ι . x0 (λ x12 : (ι → (ι → ι) → ι → ι) → ι . 0) 0 (λ x12 : (ι → ι) → ι . 0)) (x1 (λ x11 : ι → ι . λ x12 . λ x13 : (ι → ι) → ι → ι . 0) (λ x11 . 0) (λ x11 . λ x12 : ι → ι . λ x13 . 0) 0) (Inj0 0)) 0 (λ x10 : (ι → ι) → ι . x10 (λ x11 . x1 (λ x12 : ι → ι . λ x13 . λ x14 : (ι → ι) → ι → ι . 0) (λ x12 . 0) (λ x12 . λ x13 : ι → ι . λ x14 . 0) 0))) (x1 (λ x10 : ι → ι . λ x11 . λ x12 : (ι → ι) → ι → ι . x12 (λ x13 . x10 0) (x12 (λ x13 . 0) 0)) (λ x10 . x9) (λ x10 . λ x11 : ι → ι . λ x12 . 0) (x5 (λ x10 . λ x11 : ι → ι . λ x12 . Inj1 0))))) ⟶ (∀ x4 x5 . ∀ x6 : ι → ι . ∀ x7 : ι → ι → (ι → ι) → ι . x2 (λ x9 : (ι → ι → ι) → ι . Inj0 (x3 (λ x10 x11 . λ x12 : (ι → ι) → ι → ι . x10) (λ x10 : (ι → ι → ι) → ι . x10 (λ x11 x12 . x0 (λ x13 : (ι → (ι → ι) → ι → ι) → ι . 0) 0 (λ x13 : (ι → ι) → ι . 0))) (Inj0 (Inj1 0)) x5)) (x2 (λ x9 : (ι → ι → ι) → ι . x9 (λ x10 x11 . 0)) (x6 0) (x6 (setsum x4 x5)) (Inj0 x4) (λ x9 . x3 (λ x10 x11 . λ x12 : (ι → ι) → ι → ι . x3 (λ x13 x14 . λ x15 : (ι → ι) → ι → ι . x2 (λ x16 : (ι → ι → ι) → ι . 0) 0 0 0 (λ x16 . 0)) (λ x13 : (ι → ι → ι) → ι . x1 (λ x14 : ι → ι . λ x15 . λ x16 : (ι → ι) → ι → ι . 0) (λ x14 . 0) (λ x14 . λ x15 : ι → ι . λ x16 . 0) 0) (setsum 0 0) 0) (λ x10 : (ι → ι → ι) → ι . x9) (setsum (x2 (λ x10 : (ι → ι → ι) → ι . 0) 0 0 0 (λ x10 . 0)) (x7 0 0 (λ x10 . 0))) 0)) (x0 (λ x9 : (ι → (ι → ι) → ι → ι) → ι . x7 (setsum 0 (x0 (λ x10 : (ι → (ι → ι) → ι → ι) → ι . 0) 0 (λ x10 : (ι → ι) → ι . 0))) 0 (λ x10 . x1 (λ x11 : ι → ι . λ x12 . λ x13 : (ι → ι) → ι → ι . x0 (λ x14 : (ι → (ι → ι) → ι → ι) → ι . 0) 0 (λ x14 : (ι → ι) → ι . 0)) (λ x11 . Inj0 0) (λ x11 . λ x12 : ι → ι . λ x13 . x2 (λ x14 : (ι → ι → ι) → ι . 0) 0 0 0 (λ x14 . 0)) (x0 (λ x11 : (ι → (ι → ι) → ι → ι) → ι . 0) 0 (λ x11 : (ι → ι) → ι . 0)))) x5 (λ x9 : (ι → ι) → ι . x6 (Inj0 x5))) (setsum (Inj0 0) (x2 (λ x9 : (ι → ι → ι) → ι . setsum 0 (x9 (λ x10 x11 . 0))) (x6 (setsum 0 0)) 0 (x7 x5 0 (λ x9 . setsum 0 0)) (λ x9 . x7 (Inj1 0) x5 (λ x10 . x9)))) (λ x9 . x7 (x6 0) 0 (λ x10 . x7 (x7 (setsum 0 0) 0 (λ x11 . Inj1 0)) (setsum x9 (setsum 0 0)) (λ x11 . x9))) = setsum (x3 (λ x9 x10 . λ x11 : (ι → ι) → ι → ι . x10) (λ x9 : (ι → ι → ι) → ι . x7 (setsum (Inj1 0) 0) (x3 (λ x10 x11 . λ x12 : (ι → ι) → ι → ι . x9 (λ x13 x14 . 0)) (λ x10 : (ι → ι → ι) → ι . setsum 0 0) 0 (x2 (λ x10 : (ι → ι → ι) → ι . 0) 0 0 0 (λ x10 . 0))) (λ x10 . Inj1 (setsum 0 0))) (setsum 0 (x6 0)) (x6 0)) (Inj0 x4)) ⟶ (∀ x4 x5 . ∀ x6 : ι → ι . ∀ x7 : (ι → ι) → ι . x1 (λ x9 : ι → ι . λ x10 . λ x11 : (ι → ι) → ι → ι . x10) (λ x9 . 0) (λ x9 . λ x10 : ι → ι . λ x11 . 0) (Inj1 0) = setsum (setsum (Inj0 (x6 0)) (x0 (λ x9 : (ι → (ι → ι) → ι → ι) → ι . x1 (λ x10 : ι → ι . λ x11 . λ x12 : (ι → ι) → ι → ι . Inj0 0) (λ x10 . x7 (λ x11 . 0)) (λ x10 . λ x11 : ι → ι . λ x12 . x10) 0) 0 (λ x9 : (ι → ι) → ι . x5))) (x0 (λ x9 : (ι → (ι → ι) → ι → ι) → ι . x2 (λ x10 : (ι → ι → ι) → ι . x7 (λ x11 . x1 (λ x12 : ι → ι . λ x13 . λ x14 : (ι → ι) → ι → ι . 0) (λ x12 . 0) (λ x12 . λ x13 : ι → ι . λ x14 . 0) 0)) (Inj0 0) (setsum x5 (setsum 0 0)) (x0 (λ x10 : (ι → (ι → ι) → ι → ι) → ι . x9 (λ x11 . λ x12 : ι → ι . λ x13 . 0)) (x6 0) (λ x10 : (ι → ι) → ι . 0)) (λ x10 . 0)) (x2 (λ x9 : (ι → ι → ι) → ι . 0) 0 0 (x0 (λ x9 : (ι → (ι → ι) → ι → ι) → ι . x2 (λ x10 : (ι → ι → ι) → ι . 0) 0 0 0 (λ x10 . 0)) 0 (λ x9 : (ι → ι) → ι . 0)) (λ x9 . setsum (Inj0 0) 0)) (λ x9 : (ι → ι) → ι . setsum (x7 (λ x10 . 0)) (Inj0 0)))) ⟶ (∀ x4 x5 x6 : ι → ι . ∀ x7 . x1 (λ x9 : ι → ι . λ x10 . λ x11 : (ι → ι) → ι → ι . x2 (λ x12 : (ι → ι → ι) → ι . 0) 0 (x11 (λ x12 . 0) (Inj1 (x11 (λ x12 . 0) 0))) 0 (λ x12 . x10)) (λ x9 . x6 (Inj0 0)) (λ x9 . λ x10 : ι → ι . λ x11 . 0) 0 = x2 (λ x9 : (ι → ι → ι) → ι . x0 (λ x10 : (ι → (ι → ι) → ι → ι) → ι . x3 (λ x11 x12 . λ x13 : (ι → ι) → ι → ι . 0) (λ x11 : (ι → ι → ι) → ι . Inj1 (x1 (λ x12 : ι → ι . λ x13 . λ x14 : (ι → ι) → ι → ι . 0) (λ x12 . 0) (λ x12 . λ x13 : ι → ι . λ x14 . 0) 0)) (x1 (λ x11 : ι → ι . λ x12 . λ x13 : (ι → ι) → ι → ι . Inj0 0) (λ x11 . x7) (λ x11 . λ x12 : ι → ι . λ x13 . 0) x7) 0) 0 (λ x10 : (ι → ι) → ι . x3 (λ x11 x12 . λ x13 : (ι → ι) → ι → ι . x12) (λ x11 : (ι → ι → ι) → ι . x1 (λ x12 : ι → ι . λ x13 . λ x14 : (ι → ι) → ι → ι . x13) (λ x12 . x11 (λ x13 x14 . 0)) (λ x12 . λ x13 : ι → ι . λ x14 . x14) (x9 (λ x12 x13 . 0))) (x10 (λ x11 . Inj1 0)) (setsum (x0 (λ x11 : (ι → (ι → ι) → ι → ι) → ι . 0) 0 (λ x11 : (ι → ι) → ι . 0)) (x3 (λ x11 x12 . λ x13 : (ι → ι) → ι → ι . 0) (λ x11 : (ι → ι → ι) → ι . 0) 0 0)))) (x6 0) x7 (x0 (λ x9 : (ι → (ι → ι) → ι → ι) → ι . 0) (x0 (λ x9 : (ι → (ι → ι) → ι → ι) → ι . 0) 0 (λ x9 : (ι → ι) → ι . setsum (Inj0 0) (setsum 0 0))) (λ x9 : (ι → ι) → ι . x3 (λ x10 x11 . λ x12 : (ι → ι) → ι → ι . x3 (λ x13 x14 . λ x15 : (ι → ι) → ι → ι . 0) (λ x13 : (ι → ι → ι) → ι . x1 (λ x14 : ι → ι . λ x15 . λ x16 : (ι → ι) → ι → ι . 0) (λ x14 . 0) (λ x14 . λ x15 : ι → ι . λ x16 . 0) 0) (Inj0 0) (x1 (λ x13 : ι → ι . λ x14 . λ x15 : (ι → ι) → ι → ι . 0) (λ x13 . 0) (λ x13 . λ x14 : ι → ι . λ x15 . 0) 0)) (λ x10 : (ι → ι → ι) → ι . x9 (λ x11 . x9 (λ x12 . 0))) x7 (setsum 0 (x9 (λ x10 . 0))))) (λ x9 . x5 (Inj0 (x6 0)))) ⟶ (∀ x4 : ι → ι . ∀ x5 x6 x7 . x0 (λ x9 : (ι → (ι → ι) → ι → ι) → ι . 0) 0 (λ x9 : (ι → ι) → ι . x5) = x5) ⟶ (∀ x4 : ((ι → ι → ι) → (ι → ι) → ι) → ι → ι . ∀ x5 . ∀ x6 : ι → ι → (ι → ι) → ι . ∀ x7 . x0 (λ x9 : (ι → (ι → ι) → ι → ι) → ι . setsum (x9 (λ x10 . λ x11 : ι → ι . λ x12 . 0)) (setsum (Inj0 (x1 (λ x10 : ι → ι . λ x11 . λ x12 : (ι → ι) → ι → ι . 0) (λ x10 . 0) (λ x10 . λ x11 : ι → ι . λ x12 . 0) 0)) (x9 (λ x10 . λ x11 : ι → ι . λ x12 . 0)))) 0 (λ x9 : (ι → ι) → ι . Inj0 (setsum (Inj1 0) (Inj1 x5))) = x7) ⟶ False (proof)Theorem 3677d.. : ∀ x0 : ((((ι → ι → ι) → ι → ι) → ι) → (ι → ι) → ι → ι → ι → ι) → (ι → (ι → ι) → ι → ι) → ι . ∀ x1 : (ι → ι → (ι → ι) → ι) → (ι → ι) → (ι → ι) → ι . ∀ x2 : (ι → ι → ι → ι → ι) → ι → ι . ∀ x3 : (((((ι → ι) → ι) → ι) → ι) → ι → ι) → ((ι → ι → ι → ι) → ι) → ι . (∀ x4 : ι → (ι → ι) → ι . ∀ x5 : (ι → ι) → ι → ι . ∀ x6 . ∀ x7 : ι → ι . x3 (λ x9 : (((ι → ι) → ι) → ι) → ι . λ x10 . setsum (Inj0 0) (x3 (λ x11 : (((ι → ι) → ι) → ι) → ι . λ x12 . x12) (λ x11 : ι → ι → ι → ι . x7 (x2 (λ x12 x13 x14 x15 . 0) 0)))) (λ x9 : ι → ι → ι → ι . x6) = x6) ⟶ (∀ x4 . ∀ x5 : ι → ι → ι . ∀ x6 x7 . x3 (λ x9 : (((ι → ι) → ι) → ι) → ι . λ x10 . x1 (λ x11 x12 . λ x13 : ι → ι . x0 (λ x14 : ((ι → ι → ι) → ι → ι) → ι . λ x15 : ι → ι . λ x16 x17 x18 . x17) (λ x14 . λ x15 : ι → ι . λ x16 . x13 (x15 0))) (λ x11 . x1 (λ x12 x13 . λ x14 : ι → ι . x12) (λ x12 . setsum 0 (x3 (λ x13 : (((ι → ι) → ι) → ι) → ι . λ x14 . 0) (λ x13 : ι → ι → ι → ι . 0))) (λ x12 . x9 (λ x13 : (ι → ι) → ι . x0 (λ x14 : ((ι → ι → ι) → ι → ι) → ι . λ x15 : ι → ι . λ x16 x17 x18 . 0) (λ x14 . λ x15 : ι → ι . λ x16 . 0)))) (λ x11 . x2 (λ x12 x13 x14 x15 . 0) (x0 (λ x12 : ((ι → ι → ι) → ι → ι) → ι . λ x13 : ι → ι . λ x14 x15 x16 . 0) (λ x12 . λ x13 : ι → ι . λ x14 . x1 (λ x15 x16 . λ x17 : ι → ι . 0) (λ x15 . 0) (λ x15 . 0))))) (λ x9 : ι → ι → ι → ι . 0) = Inj1 (x2 (λ x9 x10 x11 x12 . 0) (setsum (x3 (λ x9 : (((ι → ι) → ι) → ι) → ι . λ x10 . setsum 0 0) (λ x9 : ι → ι → ι → ι . x2 (λ x10 x11 x12 x13 . 0) 0)) 0))) ⟶ (∀ x4 . ∀ x5 : ((ι → ι → ι) → ι) → ι . ∀ x6 : (((ι → ι) → ι → ι) → ι → ι) → ι → ι . ∀ x7 . x2 (λ x9 x10 x11 x12 . x9) (Inj1 x7) = x5 (λ x9 : ι → ι → ι . Inj0 (setsum (x0 (λ x10 : ((ι → ι → ι) → ι → ι) → ι . λ x11 : ι → ι . λ x12 x13 x14 . x0 (λ x15 : ((ι → ι → ι) → ι → ι) → ι . λ x16 : ι → ι . λ x17 x18 x19 . 0) (λ x15 . λ x16 : ι → ι . λ x17 . 0)) (λ x10 . λ x11 : ι → ι . λ x12 . setsum 0 0)) (setsum (Inj0 0) (Inj0 0))))) ⟶ (∀ x4 : (((ι → ι) → ι) → (ι → ι) → ι → ι) → ι → ι . ∀ x5 : ((ι → ι) → ι → ι → ι) → ι . ∀ x6 . ∀ x7 : ((ι → ι) → ι → ι → ι) → ι . x2 (λ x9 x10 x11 x12 . 0) 0 = setsum (Inj0 0) 0) ⟶ (∀ x4 : ι → ι . ∀ x5 x6 x7 . x1 (λ x9 x10 . λ x11 : ι → ι . setsum 0 (Inj1 (x3 (λ x12 : (((ι → ι) → ι) → ι) → ι . λ x13 . x2 (λ x14 x15 x16 x17 . 0) 0) (λ x12 : ι → ι → ι → ι . x9)))) (λ x9 . setsum x7 (x1 (λ x10 x11 . λ x12 : ι → ι . 0) (λ x10 . x10) (λ x10 . setsum (setsum 0 0) x9))) (λ x9 . x3 (λ x10 : (((ι → ι) → ι) → ι) → ι . λ x11 . 0) (λ x10 : ι → ι → ι → ι . x6)) = x3 (λ x9 : (((ι → ι) → ι) → ι) → ι . λ x10 . Inj1 (x2 (λ x11 x12 x13 x14 . x1 (λ x15 x16 . λ x17 : ι → ι . Inj0 0) (λ x15 . x12) (λ x15 . Inj0 0)) x6)) (λ x9 : ι → ι → ι → ι . x2 (λ x10 x11 x12 x13 . Inj0 (setsum x11 (x1 (λ x14 x15 . λ x16 : ι → ι . 0) (λ x14 . 0) (λ x14 . 0)))) (x3 (λ x10 : (((ι → ι) → ι) → ι) → ι . λ x11 . 0) (λ x10 : ι → ι → ι → ι . x9 0 (x0 (λ x11 : ((ι → ι → ι) → ι → ι) → ι . λ x12 : ι → ι . λ x13 x14 x15 . 0) (λ x11 . λ x12 : ι → ι . λ x13 . 0)) (x3 (λ x11 : (((ι → ι) → ι) → ι) → ι . λ x12 . 0) (λ x11 : ι → ι → ι → ι . 0)))))) ⟶ (∀ x4 : (ι → (ι → ι) → ι → ι) → ι . ∀ x5 x6 . ∀ x7 : ι → ((ι → ι) → ι → ι) → ι → ι → ι . x1 (λ x9 x10 . λ x11 : ι → ι . 0) (setsum (Inj0 0)) (λ x9 . Inj1 (setsum (Inj0 (x3 (λ x10 : (((ι → ι) → ι) → ι) → ι . λ x11 . 0) (λ x10 : ι → ι → ι → ι . 0))) (x1 (λ x10 x11 . λ x12 : ι → ι . x11) (λ x10 . x9) (λ x10 . x9)))) = x7 (x3 (λ x9 : (((ι → ι) → ι) → ι) → ι . λ x10 . 0) (λ x9 : ι → ι → ι → ι . 0)) (λ x9 : ι → ι . λ x10 . x0 (λ x11 : ((ι → ι → ι) → ι → ι) → ι . λ x12 : ι → ι . λ x13 x14 x15 . x0 (λ x16 : ((ι → ι → ι) → ι → ι) → ι . λ x17 : ι → ι . λ x18 x19 x20 . 0) (λ x16 . λ x17 : ι → ι . λ x18 . x17 (x1 (λ x19 x20 . λ x21 : ι → ι . 0) (λ x19 . 0) (λ x19 . 0)))) (λ x11 . λ x12 : ι → ι . λ x13 . x2 (λ x14 x15 x16 x17 . x1 (λ x18 x19 . λ x20 : ι → ι . setsum 0 0) (λ x18 . Inj0 0) (λ x18 . Inj1 0)) 0)) (x4 (λ x9 . λ x10 : ι → ι . λ x11 . x2 (λ x12 x13 x14 x15 . 0) (x10 0))) (x7 (x2 (λ x9 x10 x11 x12 . Inj1 (Inj0 0)) (setsum x5 (x1 (λ x9 x10 . λ x11 : ι → ι . 0) (λ x9 . 0) (λ x9 . 0)))) (λ x9 : ι → ι . λ x10 . 0) (Inj1 0) x6)) ⟶ (∀ x4 : ι → ι . ∀ x5 . ∀ x6 : ι → ι . ∀ x7 . x0 (λ x9 : ((ι → ι → ι) → ι → ι) → ι . λ x10 : ι → ι . λ x11 x12 x13 . Inj0 (x2 (λ x14 x15 x16 x17 . x1 (λ x18 x19 . λ x20 : ι → ι . x19) (λ x18 . x15) (λ x18 . 0)) x13)) (λ x9 . λ x10 : ι → ι . setsum (x1 (λ x11 x12 . λ x13 : ι → ι . 0) (λ x11 . 0) (λ x11 . x3 (λ x12 : (((ι → ι) → ι) → ι) → ι . λ x13 . x13) (λ x12 : ι → ι → ι → ι . x0 (λ x13 : ((ι → ι → ι) → ι → ι) → ι . λ x14 : ι → ι . λ x15 x16 x17 . 0) (λ x13 . λ x14 : ι → ι . λ x15 . 0))))) = x5) ⟶ (∀ x4 x5 . ∀ x6 : ι → ι → ι → ι . ∀ x7 : ι → ι . x0 (λ x9 : ((ι → ι → ι) → ι → ι) → ι . λ x10 : ι → ι . λ x11 x12 x13 . 0) (λ x9 . λ x10 : ι → ι . λ x11 . 0) = x5) ⟶ False (proof)Theorem 4bada.. : ∀ x0 : (ι → ι → ((ι → ι) → ι) → (ι → ι) → ι → ι) → (((ι → ι → ι) → ι) → ι) → (ι → ι → ι) → ι . ∀ x1 : (ι → ι) → ι → (ι → ι) → ι . ∀ x2 : (ι → ι) → (ι → ι → ι) → ((ι → ι → ι) → ι) → ((ι → ι) → ι → ι) → (ι → ι) → ι . ∀ x3 : (ι → ι) → ι → ι → ι . (∀ x4 . ∀ x5 : (ι → (ι → ι) → ι) → ι → ι . ∀ x6 . ∀ x7 : (((ι → ι) → ι) → ι → ι → ι) → ι . x3 (λ x9 . x9) 0 0 = Inj1 0) ⟶ (∀ x4 : ι → ι . ∀ x5 : (((ι → ι) → ι → ι) → ι) → ι . ∀ x6 x7 . x3 (λ x9 . Inj1 x6) (x3 (λ x9 . x9) x6 (x3 (λ x9 . Inj1 x6) (x4 (x4 0)) (x2 (λ x9 . x0 (λ x10 x11 . λ x12 : (ι → ι) → ι . λ x13 : ι → ι . λ x14 . 0) (λ x10 : (ι → ι → ι) → ι . 0) (λ x10 x11 . 0)) (λ x9 x10 . 0) (λ x9 : ι → ι → ι . x2 (λ x10 . 0) (λ x10 x11 . 0) (λ x10 : ι → ι → ι . 0) (λ x10 : ι → ι . λ x11 . 0) (λ x10 . 0)) (λ x9 : ι → ι . λ x10 . x1 (λ x11 . 0) 0 (λ x11 . 0)) (λ x9 . x5 (λ x10 : (ι → ι) → ι → ι . 0))))) x7 = setsum (setsum (x5 (λ x9 : (ι → ι) → ι → ι . x0 (λ x10 x11 . λ x12 : (ι → ι) → ι . λ x13 : ι → ι . λ x14 . x3 (λ x15 . 0) 0 0) (λ x10 : (ι → ι → ι) → ι . 0) (λ x10 x11 . setsum 0 0))) (x0 (λ x9 x10 . λ x11 : (ι → ι) → ι . λ x12 : ι → ι . λ x13 . 0) (λ x9 : (ι → ι → ι) → ι . x2 (λ x10 . Inj1 0) (λ x10 x11 . x10) (λ x10 : ι → ι → ι . 0) (λ x10 : ι → ι . λ x11 . setsum 0 0) (λ x10 . 0)) (λ x9 x10 . x2 (λ x11 . Inj0 0) (λ x11 x12 . x11) (λ x11 : ι → ι → ι . Inj0 0) (λ x11 : ι → ι . λ x12 . x0 (λ x13 x14 . λ x15 : (ι → ι) → ι . λ x16 : ι → ι . λ x17 . 0) (λ x13 : (ι → ι → ι) → ι . 0) (λ x13 x14 . 0)) (λ x11 . x7)))) (x3 (λ x9 . Inj1 0) 0 (x1 (λ x9 . Inj1 (Inj1 0)) (x3 (λ x9 . 0) 0 x7) (λ x9 . 0)))) ⟶ (∀ x4 : ι → (ι → ι) → (ι → ι) → ι . ∀ x5 : ι → ι → ι . ∀ x6 : ι → ι → ι → ι → ι . ∀ x7 . x2 (λ x9 . x1 (λ x10 . 0) 0 (λ x10 . x0 (λ x11 x12 . λ x13 : (ι → ι) → ι . λ x14 : ι → ι . x14) (λ x11 : (ι → ι → ι) → ι . x0 (λ x12 x13 . λ x14 : (ι → ι) → ι . λ x15 : ι → ι . λ x16 . Inj1 0) (λ x12 : (ι → ι → ι) → ι . x0 (λ x13 x14 . λ x15 : (ι → ι) → ι . λ x16 : ι → ι . λ x17 . 0) (λ x13 : (ι → ι → ι) → ι . 0) (λ x13 x14 . 0)) (λ x12 x13 . x10)) (λ x11 x12 . 0))) (λ x9 x10 . x10) (λ x9 : ι → ι → ι . setsum x7 (setsum (x9 (Inj0 0) 0) (setsum (setsum 0 0) (x5 0 0)))) (λ x9 : ι → ι . λ x10 . 0) (λ x9 . x6 (x6 (x1 (λ x10 . 0) (x1 (λ x10 . 0) 0 (λ x10 . 0)) (λ x10 . x7)) (x3 (λ x10 . x6 0 0 0 0) 0 (x6 0 0 0 0)) (x0 (λ x10 x11 . λ x12 : (ι → ι) → ι . λ x13 : ι → ι . λ x14 . Inj1 0) (λ x10 : (ι → ι → ι) → ι . x9) (λ x10 x11 . 0)) (x2 (λ x10 . Inj1 0) (λ x10 x11 . Inj1 0) (λ x10 : ι → ι → ι . 0) (λ x10 : ι → ι . λ x11 . 0) (λ x10 . setsum 0 0))) 0 (setsum (setsum 0 (setsum 0 0)) (x1 (λ x10 . x6 0 0 0 0) (x6 0 0 0 0) (λ x10 . x3 (λ x11 . 0) 0 0))) (setsum (setsum x7 0) 0)) = x6 (x1 (λ x9 . 0) (x4 0 (λ x9 . 0) (λ x9 . setsum 0 0)) (λ x9 . x1 (λ x10 . x2 (λ x11 . x0 (λ x12 x13 . λ x14 : (ι → ι) → ι . λ x15 : ι → ι . λ x16 . 0) (λ x12 : (ι → ι → ι) → ι . 0) (λ x12 x13 . 0)) (λ x11 x12 . x3 (λ x13 . 0) 0 0) (λ x11 : ι → ι → ι . Inj1 0) (λ x11 : ι → ι . λ x12 . x9) (λ x11 . setsum 0 0)) 0 (λ x10 . setsum x10 0))) (x1 (λ x9 . 0) (x5 x7 (x2 (λ x9 . 0) (λ x9 x10 . setsum 0 0) (λ x9 : ι → ι → ι . x7) (λ x9 : ι → ι . λ x10 . x3 (λ x11 . 0) 0 0) (λ x9 . x0 (λ x10 x11 . λ x12 : (ι → ι) → ι . λ x13 : ι → ι . λ x14 . 0) (λ x10 : (ι → ι → ι) → ι . 0) (λ x10 x11 . 0)))) (λ x9 . 0)) (setsum (x2 (λ x9 . x9) (λ x9 x10 . 0) (λ x9 : ι → ι → ι . 0) (λ x9 : ι → ι . λ x10 . 0) (λ x9 . x7)) 0) (x4 (setsum (x3 (λ x9 . 0) (Inj1 0) (Inj0 0)) (x5 (setsum 0 0) (Inj1 0))) (λ x9 . 0) (λ x9 . 0))) ⟶ (∀ x4 : (ι → ι) → ι . ∀ x5 : (((ι → ι) → ι) → ι) → ι . ∀ x6 . ∀ x7 : (ι → ι) → ι . x2 (λ x9 . setsum x9 (x7 (λ x10 . 0))) (λ x9 x10 . x7 (λ x11 . setsum (Inj0 0) (Inj1 0))) (λ x9 : ι → ι → ι . x1 (λ x10 . 0) (x3 (λ x10 . x6) 0 (x5 (λ x10 : (ι → ι) → ι . Inj0 0))) (λ x10 . x0 (λ x11 x12 . λ x13 : (ι → ι) → ι . λ x14 : ι → ι . λ x15 . 0) (λ x11 : (ι → ι → ι) → ι . x9 (x2 (λ x12 . 0) (λ x12 x13 . 0) (λ x12 : ι → ι → ι . 0) (λ x12 : ι → ι . λ x13 . 0) (λ x12 . 0)) (setsum 0 0)) (λ x11 x12 . 0))) (λ x9 : ι → ι . λ x10 . 0) (λ x9 . 0) = x7 (λ x9 . x7 (setsum (x0 (λ x10 x11 . λ x12 : (ι → ι) → ι . λ x13 : ι → ι . λ x14 . x12 (λ x15 . 0)) (λ x10 : (ι → ι → ι) → ι . 0) (λ x10 x11 . x10))))) ⟶ (∀ x4 x5 x6 x7 . x1 (λ x9 . setsum x7 0) (Inj0 x7) (λ x9 . setsum x5 x5) = x6) ⟶ (∀ x4 : ι → ((ι → ι) → ι) → (ι → ι) → ι → ι . ∀ x5 x6 : ι → ι . ∀ x7 . x1 (λ x9 . setsum (setsum x9 (x6 (Inj0 0))) (x2 (λ x10 . setsum 0 0) (λ x10 x11 . x1 (λ x12 . 0) 0 (λ x12 . x2 (λ x13 . 0) (λ x13 x14 . 0) (λ x13 : ι → ι → ι . 0) (λ x13 : ι → ι . λ x14 . 0) (λ x13 . 0))) (λ x10 : ι → ι → ι . 0) (λ x10 : ι → ι . λ x11 . x11) Inj0)) (x3 (λ x9 . x6 (x1 (λ x10 . 0) (x1 (λ x10 . 0) 0 (λ x10 . 0)) (λ x10 . setsum 0 0))) (Inj0 (x6 (x4 0 (λ x9 : ι → ι . 0) (λ x9 . 0) 0))) x7) x6 = x6 (x2 (λ x9 . 0) (λ x9 x10 . x9) (λ x9 : ι → ι → ι . 0) (λ x9 : ι → ι . λ x10 . 0) (λ x9 . x0 (λ x10 x11 . λ x12 : (ι → ι) → ι . λ x13 : ι → ι . λ x14 . setsum (setsum 0 0) 0) (λ x10 : (ι → ι → ι) → ι . Inj0 (x0 (λ x11 x12 . λ x13 : (ι → ι) → ι . λ x14 : ι → ι . λ x15 . 0) (λ x11 : (ι → ι → ι) → ι . 0) (λ x11 x12 . 0))) (λ x10 x11 . setsum 0 (setsum 0 0))))) ⟶ (∀ x4 : (((ι → ι) → ι) → ι → ι → ι) → ((ι → ι) → ι → ι) → (ι → ι) → ι → ι . ∀ x5 x6 . ∀ x7 : (ι → ι) → ι . x0 (λ x9 x10 . λ x11 : (ι → ι) → ι . λ x12 : ι → ι . λ x13 . setsum 0 (setsum 0 (Inj1 0))) (λ x9 : (ι → ι → ι) → ι . x7 (λ x10 . x2 (λ x11 . 0) (λ x11 x12 . setsum 0 x10) (λ x11 : ι → ι → ι . Inj0 x10) (λ x11 : ι → ι . λ x12 . setsum 0 0) (λ x11 . 0))) (λ x9 x10 . setsum (setsum (x0 (λ x11 x12 . λ x13 : (ι → ι) → ι . λ x14 : ι → ι . λ x15 . x13 (λ x16 . 0)) (λ x11 : (ι → ι → ι) → ι . Inj1 0) (λ x11 x12 . 0)) (x7 (λ x11 . x2 (λ x12 . 0) (λ x12 x13 . 0) (λ x12 : ι → ι → ι . 0) (λ x12 : ι → ι . λ x13 . 0) (λ x12 . 0)))) (Inj0 0)) = x7 (λ x9 . Inj0 (x3 (λ x10 . x7 (λ x11 . x3 (λ x12 . 0) 0 0)) (setsum 0 (x7 (λ x10 . 0))) (x1 (λ x10 . x1 (λ x11 . 0) 0 (λ x11 . 0)) x9 (λ x10 . x2 (λ x11 . 0) (λ x11 x12 . 0) (λ x11 : ι → ι → ι . 0) (λ x11 : ι → ι . λ x12 . 0) (λ x11 . 0)))))) ⟶ (∀ x4 : ι → ι → ι → ι → ι . ∀ x5 . ∀ x6 : (ι → ι) → ι . ∀ x7 : ι → ι → ι . x0 (λ x9 x10 . λ x11 : (ι → ι) → ι . λ x12 : ι → ι . λ x13 . Inj0 0) (λ x9 : (ι → ι → ι) → ι . x6 (λ x10 . x10)) (λ x9 x10 . x0 (λ x11 x12 . λ x13 : (ι → ι) → ι . λ x14 : ι → ι . λ x15 . 0) (λ x11 : (ι → ι → ι) → ι . x11 (λ x12 x13 . Inj0 (x2 (λ x14 . 0) (λ x14 x15 . 0) (λ x14 : ι → ι → ι . 0) (λ x14 : ι → ι . λ x15 . 0) (λ x14 . 0)))) (λ x11 x12 . x2 (λ x13 . x11) (λ x13 x14 . setsum x13 0) (λ x13 : ι → ι → ι . 0) (λ x13 : ι → ι . λ x14 . 0) (λ x13 . 0))) = setsum (x3 (λ x9 . Inj1 (x2 (λ x10 . 0) (λ x10 x11 . 0) (λ x10 : ι → ι → ι . setsum 0 0) (λ x10 : ι → ι . λ x11 . Inj0 0) (λ x10 . x7 0 0))) (Inj0 (x0 (λ x9 x10 . λ x11 : (ι → ι) → ι . λ x12 : ι → ι . λ x13 . x11 (λ x14 . 0)) (λ x9 : (ι → ι → ι) → ι . setsum 0 0) (λ x9 x10 . setsum 0 0))) 0) x5) ⟶ False (proof)Theorem 15092.. : ∀ x0 : (ι → ι) → ι → ι . ∀ x1 : (ι → ι) → ι → ι → ((ι → ι) → ι) → ι . ∀ x2 : (ι → ι → ι) → (ι → ι) → ι . ∀ x3 : (ι → ι) → ι → ι . (∀ x4 : ι → ι . ∀ x5 : (ι → (ι → ι) → ι → ι) → ι . ∀ x6 : ι → ι → (ι → ι) → ι → ι . ∀ x7 : ι → ((ι → ι) → ι) → ι . x3 (λ x9 . x9) 0 = x7 (x6 (x1 (λ x9 . x5 (λ x10 . λ x11 : ι → ι . λ x12 . x9)) (setsum (x6 0 0 (λ x9 . 0) 0) (Inj0 0)) (x7 (x7 0 (λ x9 : ι → ι . 0)) (λ x9 : ι → ι . 0)) (λ x9 : ι → ι . x3 (λ x10 . setsum 0 0) (x5 (λ x10 . λ x11 : ι → ι . λ x12 . 0)))) (x0 (λ x9 . x5 (λ x10 . λ x11 : ι → ι . λ x12 . 0)) (x1 (λ x9 . Inj0 0) (x0 (λ x9 . 0) 0) (Inj0 0) (λ x9 : ι → ι . 0))) (λ x9 . 0) (x5 (λ x9 . λ x10 : ι → ι . λ x11 . setsum (x1 (λ x12 . 0) 0 0 (λ x12 : ι → ι . 0)) (x1 (λ x12 . 0) 0 0 (λ x12 : ι → ι . 0))))) (λ x9 : ι → ι . x0 (λ x10 . x7 0 (λ x11 : ι → ι . Inj0 0)) 0)) ⟶ (∀ x4 x5 x6 . ∀ x7 : (ι → (ι → ι) → ι → ι) → ι . x3 (λ x9 . 0) (setsum (x2 (λ x9 x10 . x2 (λ x11 x12 . Inj1 0) (λ x11 . x0 (λ x12 . 0) 0)) (λ x9 . 0)) (x1 (λ x9 . x5) x6 x6 (λ x9 : ι → ι . x3 (λ x10 . 0) (Inj0 0)))) = x6) ⟶ (∀ x4 x5 . ∀ x6 : ι → ι . ∀ x7 . x2 (λ x9 x10 . 0) (λ x9 . Inj0 x5) = Inj1 (x0 (λ x9 . x9) x5)) ⟶ (∀ x4 x5 x6 x7 . x2 (λ x9 x10 . x2 (λ x11 x12 . x10) (λ x11 . 0)) (λ x9 . 0) = x2 (λ x9 x10 . x7) (λ x9 . Inj1 x5)) ⟶ (∀ x4 : ι → ι . ∀ x5 . ∀ x6 : (ι → ι) → (ι → ι → ι) → ι . ∀ x7 . x1 (λ x9 . 0) 0 (x4 (x3 (λ x9 . 0) 0)) (λ x9 : ι → ι . setsum (x0 (λ x10 . x9 (setsum 0 0)) (x2 (λ x10 x11 . 0) (λ x10 . 0))) (x3 (λ x10 . 0) x7)) = setsum 0 (x2 (λ x9 . setsum (x1 (λ x10 . x7) 0 (setsum 0 0) (λ x10 : ι → ι . x0 (λ x11 . 0) 0))) (λ x9 . x3 (λ x10 . 0) 0))) ⟶ (∀ x4 : (((ι → ι) → ι) → ι) → ι . ∀ x5 : ι → ι . ∀ x6 x7 . x1 (λ x9 . x2 (λ x10 x11 . 0) (λ x10 . x1 (λ x11 . x9) x9 (x2 (λ x11 x12 . 0) (λ x11 . 0)) (λ x11 : ι → ι . 0))) (Inj1 (Inj0 0)) (setsum (x4 (λ x9 : (ι → ι) → ι . x2 (λ x10 x11 . setsum 0 0) (λ x10 . Inj1 0))) 0) (λ x9 : ι → ι . x7) = Inj0 0) ⟶ (∀ x4 : ι → ι . ∀ x5 : (ι → ι → ι) → ι . ∀ x6 : ι → ((ι → ι) → ι) → ι . ∀ x7 : ι → ι . x0 (λ x9 . x6 0 (λ x10 : ι → ι . x2 (λ x11 x12 . Inj0 0) (λ x11 . x11))) (x0 (λ x9 . x1 (λ x10 . x10) (x3 (λ x10 . 0) (x0 (λ x10 . 0) 0)) (x5 (λ x10 x11 . Inj1 0)) (λ x10 : ι → ι . 0)) (setsum (x2 (λ x9 x10 . 0) (λ x9 . setsum 0 0)) (setsum 0 (Inj0 0)))) = x6 (x0 (λ x9 . 0) (setsum 0 (Inj1 0))) (λ x9 : ι → ι . x9 (x3 (λ x10 . x3 (λ x11 . x0 (λ x12 . 0) 0) (setsum 0 0)) (x1 (λ x10 . setsum 0 0) (Inj1 0) (x0 (λ x10 . 0) 0) (λ x10 : ι → ι . x2 (λ x11 x12 . 0) (λ x11 . 0)))))) ⟶ (∀ x4 : ι → (ι → ι) → ι . ∀ x5 : ι → ι . ∀ x6 x7 . x0 (λ x9 . x6) x6 = Inj1 (setsum (x4 x7 (λ x9 . Inj0 (x1 (λ x10 . 0) 0 0 (λ x10 : ι → ι . 0)))) (x0 (λ x9 . 0) (x3 (λ x9 . x2 (λ x10 x11 . 0) (λ x10 . 0)) x6)))) ⟶ False (proof)Theorem 9a10f.. : ∀ x0 : ((ι → ι) → ι) → ι → ι . ∀ x1 : (((ι → (ι → ι) → ι) → ι) → (ι → ι → ι) → (ι → ι → ι) → ι → ι) → (ι → ι → ι) → ι → ι → (ι → ι) → ι . ∀ x2 : ((ι → ι) → (ι → ι → ι) → ((ι → ι) → ι) → (ι → ι) → ι → ι) → (ι → ι → (ι → ι) → ι → ι) → ι . ∀ x3 : (ι → ι → ι) → ι → ((ι → ι → ι) → (ι → ι) → ι) → ι → ι → ι . (∀ x4 : ι → ι . ∀ x5 x6 x7 . x3 (λ x9 x10 . 0) (x4 (x4 x5)) (λ x9 : ι → ι → ι . λ x10 : ι → ι . setsum x6 (Inj0 x7)) (setsum 0 (x0 (λ x9 : ι → ι . setsum 0 0) (x3 (λ x9 x10 . setsum 0 0) (setsum 0 0) (λ x9 : ι → ι → ι . λ x10 : ι → ι . x10 0) 0 0))) (x4 (x4 0)) = setsum (x1 (λ x9 : (ι → (ι → ι) → ι) → ι . λ x10 x11 : ι → ι → ι . λ x12 . x2 (λ x13 : ι → ι . λ x14 : ι → ι → ι . λ x15 : (ι → ι) → ι . λ x16 : ι → ι . λ x17 . 0) (λ x13 x14 . λ x15 : ι → ι . λ x16 . 0)) (λ x9 x10 . x1 (λ x11 : (ι → (ι → ι) → ι) → ι . λ x12 x13 : ι → ι → ι . λ x14 . 0) (λ x11 x12 . setsum 0 (x3 (λ x13 x14 . 0) 0 (λ x13 : ι → ι → ι . λ x14 : ι → ι . 0) 0 0)) 0 x9 (λ x11 . 0)) x6 0 (λ x9 . setsum (x3 (λ x10 x11 . Inj1 0) 0 (λ x10 : ι → ι → ι . λ x11 : ι → ι . x2 (λ x12 : ι → ι . λ x13 : ι → ι → ι . λ x14 : (ι → ι) → ι . λ x15 : ι → ι . λ x16 . 0) (λ x12 x13 . λ x14 : ι → ι . λ x15 . 0)) (x2 (λ x10 : ι → ι . λ x11 : ι → ι → ι . λ x12 : (ι → ι) → ι . λ x13 : ι → ι . λ x14 . 0) (λ x10 x11 . λ x12 : ι → ι . λ x13 . 0)) 0) x7)) (x1 (λ x9 : (ι → (ι → ι) → ι) → ι . λ x10 x11 : ι → ι → ι . λ x12 . x11 (setsum (setsum 0 0) 0) 0) (λ x9 x10 . 0) (Inj1 0) 0 (λ x9 . x7))) ⟶ (∀ x4 x5 . ∀ x6 : ι → ι . ∀ x7 . x3 (λ x9 x10 . x9) (x3 (λ x9 x10 . x9) (x3 (λ x9 x10 . x6 0) x5 (λ x9 : ι → ι → ι . λ x10 : ι → ι . Inj1 (x1 (λ x11 : (ι → (ι → ι) → ι) → ι . λ x12 x13 : ι → ι → ι . λ x14 . 0) (λ x11 x12 . 0) 0 0 (λ x11 . 0))) (setsum 0 0) x7) (λ x9 : ι → ι → ι . λ x10 : ι → ι . 0) x5 (setsum 0 (x3 (λ x9 x10 . x0 (λ x11 : ι → ι . 0) 0) (Inj1 0) (λ x9 : ι → ι → ι . λ x10 : ι → ι . Inj1 0) (setsum 0 0) (x1 (λ x9 : (ι → (ι → ι) → ι) → ι . λ x10 x11 : ι → ι → ι . λ x12 . 0) (λ x9 x10 . 0) 0 0 (λ x9 . 0))))) (λ x9 : ι → ι → ι . λ x10 : ι → ι . x7) 0 (setsum 0 (x0 (λ x9 : ι → ι . x0 (λ x10 : ι → ι . x2 (λ x11 : ι → ι . λ x12 : ι → ι → ι . λ x13 : (ι → ι) → ι . λ x14 : ι → ι . λ x15 . 0) (λ x11 x12 . λ x13 : ι → ι . λ x14 . 0)) (x1 (λ x10 : (ι → (ι → ι) → ι) → ι . λ x11 x12 : ι → ι → ι . λ x13 . 0) (λ x10 x11 . 0) 0 0 (λ x10 . 0))) 0)) = x7) ⟶ (∀ x4 x5 . ∀ x6 : ((ι → ι) → ι → ι) → (ι → ι) → ι → ι . ∀ x7 : ι → ι → ι . x2 (λ x9 : ι → ι . λ x10 : ι → ι → ι . λ x11 : (ι → ι) → ι . λ x12 : ι → ι . λ x13 . x0 (λ x14 : ι → ι . x3 (λ x15 x16 . setsum x13 (x0 (λ x17 : ι → ι . 0) 0)) 0 (λ x15 : ι → ι → ι . λ x16 : ι → ι . x14 0) (x14 (x3 (λ x15 x16 . 0) 0 (λ x15 : ι → ι → ι . λ x16 : ι → ι . 0) 0 0)) 0) 0) (λ x9 x10 . λ x11 : ι → ι . λ x12 . x3 (λ x13 x14 . x1 (λ x15 : (ι → (ι → ι) → ι) → ι . λ x16 x17 : ι → ι → ι . λ x18 . x0 (λ x19 : ι → ι . 0) (Inj0 0)) (λ x15 x16 . Inj0 (x3 (λ x17 x18 . 0) 0 (λ x17 : ι → ι → ι . λ x18 : ι → ι . 0) 0 0)) 0 (x0 (λ x15 : ι → ι . 0) (x0 (λ x15 : ι → ι . 0) 0)) (λ x15 . 0)) x12 (λ x13 : ι → ι → ι . λ x14 : ι → ι . Inj1 (x0 (λ x15 : ι → ι . x14 0) (setsum 0 0))) (x2 (λ x13 : ι → ι . λ x14 : ι → ι → ι . λ x15 : (ι → ι) → ι . λ x16 : ι → ι . λ x17 . setsum (Inj1 0) 0) (λ x13 x14 . λ x15 : ι → ι . λ x16 . setsum (x3 (λ x17 x18 . 0) 0 (λ x17 : ι → ι → ι . λ x18 : ι → ι . 0) 0 0) x14)) 0) = setsum (Inj0 (setsum (x1 (λ x9 : (ι → (ι → ι) → ι) → ι . λ x10 x11 : ι → ι → ι . λ x12 . x2 (λ x13 : ι → ι . λ x14 : ι → ι → ι . λ x15 : (ι → ι) → ι . λ x16 : ι → ι . λ x17 . 0) (λ x13 x14 . λ x15 : ι → ι . λ x16 . 0)) (λ x9 x10 . Inj0 0) 0 (x6 (λ x9 : ι → ι . λ x10 . 0) (λ x9 . 0) 0) (λ x9 . x0 (λ x10 : ι → ι . 0) 0)) (x6 (λ x9 : ι → ι . λ x10 . x10) (λ x9 . x6 (λ x10 : ι → ι . λ x11 . 0) (λ x10 . 0) 0) (Inj1 0)))) (x2 (λ x9 : ι → ι . λ x10 : ι → ι → ι . λ x11 : (ι → ι) → ι . λ x12 : ι → ι . λ x13 . x11 (λ x14 . x13)) (λ x9 x10 . λ x11 : ι → ι . λ x12 . x11 (Inj1 (x3 (λ x13 x14 . 0) 0 (λ x13 : ι → ι → ι . λ x14 : ι → ι . 0) 0 0))))) ⟶ (∀ x4 x5 x6 . ∀ x7 : (ι → (ι → ι) → ι → ι) → ι . x2 (λ x9 : ι → ι . λ x10 : ι → ι → ι . λ x11 : (ι → ι) → ι . λ x12 : ι → ι . λ x13 . x13) (λ x9 x10 . λ x11 : ι → ι . λ x12 . 0) = x6) ⟶ (∀ x4 . ∀ x5 : ((ι → ι → ι) → (ι → ι) → ι) → ι . ∀ x6 . ∀ x7 : (ι → ι) → ι → (ι → ι) → ι → ι . x1 (λ x9 : (ι → (ι → ι) → ι) → ι . λ x10 x11 : ι → ι → ι . λ x12 . 0) (λ x9 x10 . Inj0 (x1 (λ x11 : (ι → (ι → ι) → ι) → ι . λ x12 x13 : ι → ι → ι . λ x14 . setsum (x13 0 0) (x1 (λ x15 : (ι → (ι → ι) → ι) → ι . λ x16 x17 : ι → ι → ι . λ x18 . 0) (λ x15 x16 . 0) 0 0 (λ x15 . 0))) (λ x11 x12 . x10) x6 0 (λ x11 . x2 (λ x12 : ι → ι . λ x13 : ι → ι → ι . λ x14 : (ι → ι) → ι . λ x15 : ι → ι . λ x16 . x13 0 0) (λ x12 x13 . λ x14 : ι → ι . λ x15 . x3 (λ x16 x17 . 0) 0 (λ x16 : ι → ι → ι . λ x17 : ι → ι . 0) 0 0)))) (x1 (λ x9 : (ι → (ι → ι) → ι) → ι . λ x10 x11 : ι → ι → ι . λ x12 . x12) (λ x9 x10 . Inj1 (Inj0 (Inj1 0))) (setsum (x5 (λ x9 : ι → ι → ι . λ x10 : ι → ι . 0)) (Inj1 (x7 (λ x9 . 0) 0 (λ x9 . 0) 0))) (Inj1 (x7 (λ x9 . x9) (Inj0 0) (λ x9 . x3 (λ x10 x11 . 0) 0 (λ x10 : ι → ι → ι . λ x11 : ι → ι . 0) 0 0) 0)) (λ x9 . x1 (λ x10 : (ι → (ι → ι) → ι) → ι . λ x11 x12 : ι → ι → ι . λ x13 . x13) (λ x10 x11 . x10) 0 0 (λ x10 . 0))) (x0 (λ x9 : ι → ι . 0) (x7 (λ x9 . Inj1 (x1 (λ x10 : (ι → (ι → ι) → ι) → ι . λ x11 x12 : ι → ι → ι . λ x13 . 0) (λ x10 x11 . 0) 0 0 (λ x10 . 0))) 0 (λ x9 . Inj0 (setsum 0 0)) x6)) (λ x9 . 0) = x1 (λ x9 : (ι → (ι → ι) → ι) → ι . λ x10 x11 : ι → ι → ι . λ x12 . x11 0 (x10 0 (setsum 0 0))) (λ x9 x10 . x6) (Inj0 0) (x0 (λ x9 : ι → ι . x5 (λ x10 : ι → ι → ι . λ x11 : ι → ι . Inj0 0)) (x3 (λ x9 x10 . 0) (setsum 0 x6) (λ x9 : ι → ι → ι . λ x10 : ι → ι . x3 (λ x11 x12 . x9 0 0) (x3 (λ x11 x12 . 0) 0 (λ x11 : ι → ι → ι . λ x12 : ι → ι . 0) 0 0) (λ x11 : ι → ι → ι . λ x12 : ι → ι . x12 0) (setsum 0 0) (Inj0 0)) (x7 (λ x9 . 0) (setsum 0 0) (λ x9 . setsum 0 0) (x0 (λ x9 : ι → ι . 0) 0)) (setsum 0 (x2 (λ x9 : ι → ι . λ x10 : ι → ι → ι . λ x11 : (ι → ι) → ι . λ x12 : ι → ι . λ x13 . 0) (λ x9 x10 . λ x11 : ι → ι . λ x12 . 0))))) (λ x9 . x9)) ⟶ (∀ x4 : ι → ι → ι . ∀ x5 : (ι → ι → ι → ι) → ι . ∀ x6 . ∀ x7 : ι → ((ι → ι) → ι → ι) → (ι → ι) → ι . x1 (λ x9 : (ι → (ι → ι) → ι) → ι . λ x10 x11 : ι → ι → ι . λ x12 . setsum (Inj1 (x11 (x3 (λ x13 x14 . 0) 0 (λ x13 : ι → ι → ι . λ x14 : ι → ι . 0) 0 0) (x1 (λ x13 : (ι → (ι → ι) → ι) → ι . λ x14 x15 : ι → ι → ι . λ x16 . 0) (λ x13 x14 . 0) 0 0 (λ x13 . 0)))) (setsum (x1 (λ x13 : (ι → (ι → ι) → ι) → ι . λ x14 x15 : ι → ι → ι . λ x16 . x0 (λ x17 : ι → ι . 0) 0) (λ x13 x14 . 0) 0 (x2 (λ x13 : ι → ι . λ x14 : ι → ι → ι . λ x15 : (ι → ι) → ι . λ x16 : ι → ι . λ x17 . 0) (λ x13 x14 . λ x15 : ι → ι . λ x16 . 0)) (λ x13 . 0)) (x3 (λ x13 x14 . x13) (x1 (λ x13 : (ι → (ι → ι) → ι) → ι . λ x14 x15 : ι → ι → ι . λ x16 . 0) (λ x13 x14 . 0) 0 0 (λ x13 . 0)) (λ x13 : ι → ι → ι . λ x14 : ι → ι . 0) (setsum 0 0) (x11 0 0)))) (λ x9 x10 . setsum (x2 (λ x11 : ι → ι . λ x12 : ι → ι → ι . λ x13 : (ι → ι) → ι . λ x14 : ι → ι . λ x15 . x13 (λ x16 . 0)) (λ x11 x12 . λ x13 : ι → ι . λ x14 . 0)) 0) (x3 (λ x9 x10 . Inj1 (x0 (λ x11 : ι → ι . 0) (x1 (λ x11 : (ι → (ι → ι) → ι) → ι . λ x12 x13 : ι → ι → ι . λ x14 . 0) (λ x11 x12 . 0) 0 0 (λ x11 . 0)))) 0 (λ x9 : ι → ι → ι . λ x10 : ι → ι . Inj0 0) (setsum 0 0) (x2 (λ x9 : ι → ι . λ x10 : ι → ι → ι . λ x11 : (ι → ι) → ι . λ x12 : ι → ι . λ x13 . x1 (λ x14 : (ι → (ι → ι) → ι) → ι . λ x15 x16 : ι → ι → ι . λ x17 . Inj1 0) (λ x14 x15 . setsum 0 0) (x1 (λ x14 : (ι → (ι → ι) → ι) → ι . λ x15 x16 : ι → ι → ι . λ x17 . 0) (λ x14 x15 . 0) 0 0 (λ x14 . 0)) (x3 (λ x14 x15 . 0) 0 (λ x14 : ι → ι → ι . λ x15 : ι → ι . 0) 0 0) (λ x14 . x11 (λ x15 . 0))) (λ x9 x10 . λ x11 : ι → ι . λ x12 . 0))) (x2 (λ x9 : ι → ι . λ x10 : ι → ι → ι . λ x11 : (ι → ι) → ι . λ x12 : ι → ι . λ x13 . x11 (λ x14 . x3 (λ x15 x16 . Inj0 0) 0 (λ x15 : ι → ι → ι . λ x16 : ι → ι . x2 (λ x17 : ι → ι . λ x18 : ι → ι → ι . λ x19 : (ι → ι) → ι . λ x20 : ι → ι . λ x21 . 0) (λ x17 x18 . λ x19 : ι → ι . λ x20 . 0)) (x3 (λ x15 x16 . 0) 0 (λ x15 : ι → ι → ι . λ x16 : ι → ι . 0) 0 0) (x11 (λ x15 . 0)))) (λ x9 x10 . λ x11 : ι → ι . λ x12 . 0)) (λ x9 . x2 (λ x10 : ι → ι . λ x11 : ι → ι → ι . λ x12 : (ι → ι) → ι . λ x13 : ι → ι . λ x14 . x1 (λ x15 : (ι → (ι → ι) → ι) → ι . λ x16 x17 : ι → ι → ι . λ x18 . Inj0 (x0 (λ x19 : ι → ι . 0) 0)) (λ x15 x16 . setsum (setsum 0 0) (x2 (λ x17 : ι → ι . λ x18 : ι → ι → ι . λ x19 : (ι → ι) → ι . λ x20 : ι → ι . λ x21 . 0) (λ x17 x18 . λ x19 : ι → ι . λ x20 . 0))) (x11 (x3 (λ x15 x16 . 0) 0 (λ x15 : ι → ι → ι . λ x16 : ι → ι . 0) 0 0) 0) (x13 (Inj0 0)) (λ x15 . x0 (λ x16 : ι → ι . x14) (x1 (λ x16 : (ι → (ι → ι) → ι) → ι . λ x17 x18 : ι → ι → ι . λ x19 . 0) (λ x16 x17 . 0) 0 0 (λ x16 . 0)))) (λ x10 x11 . λ x12 : ι → ι . λ x13 . setsum x13 x13)) = x2 (λ x9 : ι → ι . λ x10 : ι → ι → ι . λ x11 : (ι → ι) → ι . λ x12 : ι → ι . Inj1) (λ x9 x10 . λ x11 : ι → ι . λ x12 . Inj1 (x11 0))) ⟶ (∀ x4 . ∀ x5 x6 x7 : ι → ι . x0 (λ x9 : ι → ι . x7 (Inj1 (setsum 0 (Inj0 0)))) (x7 0) = setsum x4 (x2 (λ x9 : ι → ι . λ x10 : ι → ι → ι . λ x11 : (ι → ι) → ι . λ x12 : ι → ι . λ x13 . x0 (λ x14 : ι → ι . 0) (x12 (x10 0 0))) (λ x9 x10 . λ x11 : ι → ι . λ x12 . x2 (λ x13 : ι → ι . λ x14 : ι → ι → ι . λ x15 : (ι → ι) → ι . λ x16 : ι → ι . λ x17 . 0) (λ x13 x14 . λ x15 : ι → ι . λ x16 . Inj1 0)))) ⟶ (∀ x4 x5 . ∀ x6 : ι → ι → ι . ∀ x7 . x0 (λ x9 : ι → ι . x9 0) (x1 (λ x9 : (ι → (ι → ι) → ι) → ι . λ x10 x11 : ι → ι → ι . λ x12 . x10 (x3 (λ x13 x14 . x2 (λ x15 : ι → ι . λ x16 : ι → ι → ι . λ x17 : (ι → ι) → ι . λ x18 : ι → ι . λ x19 . 0) (λ x15 x16 . λ x17 : ι → ι . λ x18 . 0)) (x11 0 0) (λ x13 : ι → ι → ι . λ x14 : ι → ι . x14 0) x12 (x10 0 0)) (x2 (λ x13 : ι → ι . λ x14 : ι → ι → ι . λ x15 : (ι → ι) → ι . λ x16 : ι → ι . λ x17 . x0 (λ x18 : ι → ι . 0) 0) (λ x13 x14 . λ x15 : ι → ι . λ x16 . x16))) (λ x9 x10 . x2 (λ x11 : ι → ι . λ x12 : ι → ι → ι . λ x13 : (ι → ι) → ι . λ x14 : ι → ι . λ x15 . 0) (λ x11 x12 . λ x13 : ι → ι . λ x14 . x1 (λ x15 : (ι → (ι → ι) → ι) → ι . λ x16 x17 : ι → ι → ι . λ x18 . x1 (λ x19 : (ι → (ι → ι) → ι) → ι . λ x20 x21 : ι → ι → ι . λ x22 . 0) (λ x19 x20 . 0) 0 0 (λ x19 . 0)) (λ x15 x16 . 0) x12 (x13 0) (λ x15 . 0))) 0 x4 (λ x9 . 0)) = Inj1 0) ⟶ False (proof)Theorem dc9ca.. : ∀ x0 : (((((ι → ι) → ι) → ι) → ι) → ι → ι → (ι → ι) → ι → ι) → (ι → ι) → (((ι → ι) → ι → ι) → ι → ι → ι) → ι . ∀ x1 : (ι → (ι → (ι → ι) → ι → ι) → ι → ι) → (ι → ι) → ι . ∀ x2 : (ι → ι → ι → ι) → (ι → (ι → ι → ι) → ι → ι) → ι . ∀ x3 : (ι → ι → ι) → ι → (ι → (ι → ι) → ι → ι) → ι . (∀ x4 x5 . ∀ x6 : (((ι → ι) → ι) → ι) → ι . ∀ x7 . x3 (λ x9 x10 . x3 (λ x11 x12 . setsum (x2 (λ x13 x14 x15 . 0) (λ x13 . λ x14 : ι → ι → ι . λ x15 . Inj0 0)) (setsum 0 x10)) (Inj1 (x6 (λ x11 : (ι → ι) → ι . setsum 0 0))) (λ x11 . λ x12 : ι → ι . λ x13 . setsum 0 x10)) (Inj0 (x1 (λ x9 . λ x10 : ι → (ι → ι) → ι → ι . λ x11 . setsum 0 0) (λ x9 . Inj0 (x3 (λ x10 x11 . 0) 0 (λ x10 . λ x11 : ι → ι . λ x12 . 0))))) (λ x9 . λ x10 : ι → ι . λ x11 . setsum 0 (Inj1 (x2 (λ x12 x13 x14 . x0 (λ x15 : (((ι → ι) → ι) → ι) → ι . λ x16 x17 . λ x18 : ι → ι . λ x19 . 0) (λ x15 . 0) (λ x15 : (ι → ι) → ι → ι . λ x16 x17 . 0)) (λ x12 . λ x13 : ι → ι → ι . λ x14 . x1 (λ x15 . λ x16 : ι → (ι → ι) → ι → ι . λ x17 . 0) (λ x15 . 0))))) = x3 (λ x9 x10 . setsum 0 (x1 (λ x11 . λ x12 : ι → (ι → ι) → ι → ι . λ x13 . x10) (λ x11 . x9))) (setsum (x1 (λ x9 . λ x10 : ι → (ι → ι) → ι → ι . λ x11 . 0) (λ x9 . x7)) (setsum 0 (Inj0 (x6 (λ x9 : (ι → ι) → ι . 0))))) (λ x9 . λ x10 : ι → ι . λ x11 . x11)) ⟶ (∀ x4 : ι → (ι → ι → ι) → ι . ∀ x5 : ι → ι . ∀ x6 : (ι → ι) → ι → ι . ∀ x7 : ((ι → ι) → ι → ι → ι) → ι . x3 (λ x9 x10 . x9) 0 (λ x9 . λ x10 : ι → ι . λ x11 . x1 (λ x12 . λ x13 : ι → (ι → ι) → ι → ι . λ x14 . x11) (λ x12 . setsum x12 (x2 (λ x13 x14 x15 . x12) (λ x13 . λ x14 : ι → ι → ι . λ x15 . 0)))) = x1 (λ x9 . λ x10 : ι → (ι → ι) → ι → ι . λ x11 . x3 (λ x12 x13 . x3 (λ x14 x15 . x15) x11 (λ x14 . λ x15 : ι → ι . λ x16 . Inj0 x14)) (x2 (λ x12 x13 x14 . 0) (λ x12 . λ x13 : ι → ι → ι . λ x14 . x2 (λ x15 x16 x17 . x17) (λ x15 . λ x16 : ι → ι → ι . λ x17 . x1 (λ x18 . λ x19 : ι → (ι → ι) → ι → ι . λ x20 . 0) (λ x18 . 0)))) (λ x12 . λ x13 : ι → ι . λ x14 . Inj0 0)) (λ x9 . x9)) ⟶ (∀ x4 : ι → ι → (ι → ι) → ι . ∀ x5 . ∀ x6 : ι → ι → ι . ∀ x7 : ι → (ι → ι) → ι . x2 (λ x9 x10 x11 . x7 x10 (λ x12 . Inj1 0)) (λ x9 . λ x10 : ι → ι → ι . λ x11 . x11) = x7 x5 (λ x9 . Inj1 (setsum (Inj0 (x1 (λ x10 . λ x11 : ι → (ι → ι) → ι → ι . λ x12 . 0) (λ x10 . 0))) (x1 (λ x10 . λ x11 : ι → (ι → ι) → ι → ι . λ x12 . 0) (λ x10 . 0))))) ⟶ (∀ x4 . ∀ x5 : (ι → ι) → ι . ∀ x6 : ι → ι → (ι → ι) → ι . ∀ x7 . x2 (λ x9 x10 x11 . Inj0 0) (λ x9 . λ x10 : ι → ι → ι . λ x11 . 0) = x4) ⟶ (∀ x4 . ∀ x5 : (ι → ι) → ι . ∀ x6 x7 . x1 (λ x9 . λ x10 : ι → (ι → ι) → ι → ι . λ x11 . x2 (λ x12 x13 x14 . x1 (λ x15 . λ x16 : ι → (ι → ι) → ι → ι . λ x17 . x16 (x2 (λ x18 x19 x20 . 0) (λ x18 . λ x19 : ι → ι → ι . λ x20 . 0)) (λ x18 . x17) (x16 0 (λ x18 . 0) 0)) (λ x15 . 0)) (λ x12 . λ x13 : ι → ι → ι . λ x14 . x3 (λ x15 x16 . Inj0 0) 0 (λ x15 . λ x16 : ι → ι . λ x17 . x1 (λ x18 . λ x19 : ι → (ι → ι) → ι → ι . λ x20 . x2 (λ x21 x22 x23 . 0) (λ x21 . λ x22 : ι → ι → ι . λ x23 . 0)) (λ x18 . Inj1 0)))) (λ x9 . x9) = x2 (λ x9 x10 x11 . x7) (λ x9 . λ x10 : ι → ι → ι . λ x11 . x7)) ⟶ (∀ x4 : ι → ι . ∀ x5 x6 x7 . x1 (λ x9 . λ x10 : ι → (ι → ι) → ι → ι . λ x11 . x2 (λ x12 x13 x14 . x11) (λ x12 . λ x13 : ι → ι → ι . λ x14 . 0)) (λ x9 . x0 (λ x10 : (((ι → ι) → ι) → ι) → ι . λ x11 x12 . λ x13 : ι → ι . λ x14 . x2 (λ x15 x16 x17 . Inj1 0) (λ x15 . λ x16 : ι → ι → ι . λ x17 . setsum (x3 (λ x18 x19 . 0) 0 (λ x18 . λ x19 : ι → ι . λ x20 . 0)) (x3 (λ x18 x19 . 0) 0 (λ x18 . λ x19 : ι → ι . λ x20 . 0)))) (λ x10 . setsum (x1 (λ x11 . λ x12 : ι → (ι → ι) → ι → ι . λ x13 . x0 (λ x14 : (((ι → ι) → ι) → ι) → ι . λ x15 x16 . λ x17 : ι → ι . λ x18 . 0) (λ x14 . 0) (λ x14 : (ι → ι) → ι → ι . λ x15 x16 . 0)) (λ x11 . x1 (λ x12 . λ x13 : ι → (ι → ι) → ι → ι . λ x14 . 0) (λ x12 . 0))) (x0 (λ x11 : (((ι → ι) → ι) → ι) → ι . λ x12 x13 . λ x14 : ι → ι . λ x15 . Inj1 0) (λ x11 . x9) (λ x11 : (ι → ι) → ι → ι . λ x12 x13 . setsum 0 0))) (λ x10 : (ι → ι) → ι → ι . λ x11 x12 . x10 (λ x13 . setsum (x1 (λ x14 . λ x15 : ι → (ι → ι) → ι → ι . λ x16 . 0) (λ x14 . 0)) (x3 (λ x14 x15 . 0) 0 (λ x14 . λ x15 : ι → ι . λ x16 . 0))) (setsum (x2 (λ x13 x14 x15 . 0) (λ x13 . λ x14 : ι → ι → ι . λ x15 . 0)) (x3 (λ x13 x14 . 0) 0 (λ x13 . λ x14 : ι → ι . λ x15 . 0))))) = Inj0 x5) ⟶ (∀ x4 : (ι → ι) → (ι → ι → ι) → (ι → ι) → ι . ∀ x5 : (((ι → ι) → ι → ι) → (ι → ι) → ι → ι) → ι . ∀ x6 : ι → ι . ∀ x7 : (((ι → ι) → ι → ι) → (ι → ι) → ι) → ι . x0 (λ x9 : (((ι → ι) → ι) → ι) → ι . λ x10 x11 . λ x12 : ι → ι . λ x13 . Inj0 (Inj1 x13)) (λ x9 . 0) (λ x9 : (ι → ι) → ι → ι . λ x10 x11 . x9 (λ x12 . x1 (λ x13 . λ x14 : ι → (ι → ι) → ι → ι . λ x15 . 0) (λ x13 . x13)) 0) = x5 (λ x9 : (ι → ι) → ι → ι . λ x10 : ι → ι . λ x11 . setsum (Inj1 (x0 (λ x12 : (((ι → ι) → ι) → ι) → ι . λ x13 x14 . λ x15 : ι → ι . λ x16 . x1 (λ x17 . λ x18 : ι → (ι → ι) → ι → ι . λ x19 . 0) (λ x17 . 0)) (λ x12 . x2 (λ x13 x14 x15 . 0) (λ x13 . λ x14 : ι → ι → ι . λ x15 . 0)) (λ x12 : (ι → ι) → ι → ι . λ x13 x14 . setsum 0 0))) (setsum (setsum 0 (x9 (λ x12 . 0) 0)) (setsum (x7 (λ x12 : (ι → ι) → ι → ι . λ x13 : ι → ι . 0)) (setsum 0 0))))) ⟶ (∀ x4 x5 . ∀ x6 : (ι → ι) → ι . ∀ x7 . x0 (λ x9 : (((ι → ι) → ι) → ι) → ι . λ x10 x11 . λ x12 : ι → ι . λ x13 . x2 (λ x14 x15 x16 . x3 (λ x17 x18 . x3 (λ x19 x20 . 0) x17 (λ x19 . λ x20 : ι → ι . λ x21 . x19)) (x3 (λ x17 x18 . Inj0 0) (setsum 0 0) (λ x17 . λ x18 : ι → ι . λ x19 . x18 0)) (λ x17 . λ x18 : ι → ι . Inj1)) (λ x14 . λ x15 : ι → ι → ι . λ x16 . x1 (λ x17 . λ x18 : ι → (ι → ι) → ι → ι . λ x19 . Inj0 (x2 (λ x20 x21 x22 . 0) (λ x20 . λ x21 : ι → ι → ι . λ x22 . 0))) (λ x17 . 0))) (λ x9 . 0) (λ x9 : (ι → ι) → ι → ι . λ x10 x11 . x9 (λ x12 . x0 (λ x13 : (((ι → ι) → ι) → ι) → ι . λ x14 x15 . λ x16 : ι → ι . λ x17 . x3 (λ x18 x19 . Inj0 0) (x1 (λ x18 . λ x19 : ι → (ι → ι) → ι → ι . λ x20 . 0) (λ x18 . 0)) (λ x18 . λ x19 : ι → ι . λ x20 . Inj1 0)) (λ x13 . 0) (λ x13 : (ι → ι) → ι → ι . λ x14 x15 . x1 (λ x16 . λ x17 : ι → (ι → ι) → ι → ι . λ x18 . setsum 0 0) (λ x16 . x3 (λ x17 x18 . 0) 0 (λ x17 . λ x18 : ι → ι . λ x19 . 0)))) x7) = Inj1 (x3 (λ x9 x10 . 0) 0 (λ x9 . λ x10 : ι → ι . λ x11 . x11))) ⟶ False (proof)Theorem 2bfdd.. : ∀ x0 : (ι → ι → ι) → (ι → ι → (ι → ι) → ι → ι) → (((ι → ι) → ι) → (ι → ι) → ι → ι) → ι . ∀ x1 : (ι → ι → ι) → (((ι → ι → ι) → ι) → ι) → ι . ∀ x2 : (ι → ι) → (((ι → ι → ι) → ι → ι → ι) → (ι → ι) → (ι → ι) → ι → ι) → ι . ∀ x3 : (ι → ι) → ι → ι . (∀ x4 x5 x6 x7 . x3 (λ x9 . setsum (x2 (λ x10 . 0) (λ x10 : (ι → ι → ι) → ι → ι → ι . λ x11 x12 : ι → ι . λ x13 . 0)) x6) (x2 (λ x9 . 0) (λ x9 : (ι → ι → ι) → ι → ι → ι . λ x10 x11 : ι → ι . λ x12 . x2 (λ x13 . x1 (λ x14 x15 . x0 (λ x16 x17 . 0) (λ x16 x17 . λ x18 : ι → ι . λ x19 . 0) (λ x16 : (ι → ι) → ι . λ x17 : ι → ι . λ x18 . 0)) (λ x14 : (ι → ι → ι) → ι . 0)) (λ x13 : (ι → ι → ι) → ι → ι → ι . λ x14 x15 : ι → ι . λ x16 . x14 (x15 0)))) = Inj1 (setsum x5 0)) ⟶ (∀ x4 x5 x6 x7 . x3 (λ x9 . Inj1 (x2 (λ x10 . Inj0 (x0 (λ x11 x12 . 0) (λ x11 x12 . λ x13 : ι → ι . λ x14 . 0) (λ x11 : (ι → ι) → ι . λ x12 : ι → ι . λ x13 . 0))) (λ x10 : (ι → ι → ι) → ι → ι → ι . λ x11 x12 : ι → ι . λ x13 . 0))) (setsum (x1 (λ x9 . x3 (λ x10 . x7)) (λ x9 : (ι → ι → ι) → ι . x0 (λ x10 x11 . setsum 0 0) (λ x10 x11 . λ x12 : ι → ι . λ x13 . Inj1 0) (λ x10 : (ι → ι) → ι . λ x11 : ι → ι . λ x12 . 0))) x5) = x6) ⟶ (∀ x4 x5 : (ι → ι) → ι . ∀ x6 : (((ι → ι) → ι → ι) → ι) → ι . ∀ x7 . x2 (λ x9 . x3 (λ x10 . 0) (Inj1 0)) (λ x9 : (ι → ι → ι) → ι → ι → ι . λ x10 x11 : ι → ι . λ x12 . x3 (λ x13 . 0) (setsum (Inj0 (x3 (λ x13 . 0) 0)) 0)) = x3 (λ x9 . x0 (λ x10 x11 . setsum 0 0) (λ x10 x11 . λ x12 : ι → ι . λ x13 . x2 (λ x14 . 0) (λ x14 : (ι → ι → ι) → ι → ι → ι . λ x15 x16 : ι → ι . λ x17 . 0)) (λ x10 : (ι → ι) → ι . λ x11 : ι → ι . λ x12 . Inj0 (x2 (λ x13 . 0) (λ x13 : (ι → ι → ι) → ι → ι → ι . λ x14 x15 : ι → ι . λ x16 . x13 (λ x17 x18 . 0) 0 0)))) (x2 (λ x9 . x9) (λ x9 : (ι → ι → ι) → ι → ι → ι . λ x10 x11 : ι → ι . λ x12 . x10 (x0 (λ x13 x14 . x11 0) (λ x13 x14 . λ x15 : ι → ι . λ x16 . 0) (λ x13 : (ι → ι) → ι . λ x14 : ι → ι . λ x15 . x2 (λ x16 . 0) (λ x16 : (ι → ι → ι) → ι → ι → ι . λ x17 x18 : ι → ι . λ x19 . 0)))))) ⟶ (∀ x4 . ∀ x5 : ι → ((ι → ι) → ι → ι) → (ι → ι) → ι → ι . ∀ x6 : (ι → (ι → ι) → ι) → ι → ι → ι → ι . ∀ x7 : (ι → ι) → ι → ι → ι . x2 (λ x9 . setsum (x0 (λ x10 x11 . x1 (λ x12 x13 . x13) (λ x12 : (ι → ι → ι) → ι . x11)) (λ x10 x11 . λ x12 : ι → ι . λ x13 . x13) (λ x10 : (ι → ι) → ι . λ x11 : ι → ι . λ x12 . 0)) (x5 (x6 (λ x10 . λ x11 : ι → ι . x0 (λ x12 x13 . 0) (λ x12 x13 . λ x14 : ι → ι . λ x15 . 0) (λ x12 : (ι → ι) → ι . λ x13 : ι → ι . λ x14 . 0)) (x0 (λ x10 x11 . 0) (λ x10 x11 . λ x12 : ι → ι . λ x13 . 0) (λ x10 : (ι → ι) → ι . λ x11 : ι → ι . λ x12 . 0)) (setsum 0 0) (x6 (λ x10 . λ x11 : ι → ι . 0) 0 0 0)) (λ x10 : ι → ι . λ x11 . Inj1 (x2 (λ x12 . 0) (λ x12 : (ι → ι → ι) → ι → ι → ι . λ x13 x14 : ι → ι . λ x15 . 0))) (λ x10 . 0) (setsum x9 0))) (λ x9 : (ι → ι → ι) → ι → ι → ι . λ x10 x11 : ι → ι . λ x12 . 0) = x4) ⟶ (∀ x4 x5 x6 . ∀ x7 : (((ι → ι) → ι → ι) → ι) → ι . x1 (λ x9 x10 . setsum (Inj0 x6) (x2 (λ x11 . x0 (λ x12 x13 . Inj1 0) (λ x12 x13 . λ x14 : ι → ι . λ x15 . x12) (λ x12 : (ι → ι) → ι . λ x13 : ι → ι . λ x14 . 0)) (λ x11 : (ι → ι → ι) → ι → ι → ι . λ x12 x13 : ι → ι . λ x14 . x1 (λ x15 x16 . setsum 0 0) (λ x15 : (ι → ι → ι) → ι . 0)))) (λ x9 : (ι → ι → ι) → ι . 0) = setsum (Inj1 (x7 (λ x9 : (ι → ι) → ι → ι . 0))) (x3 (λ x9 . 0) 0)) ⟶ (∀ x4 : (ι → ι) → ι . ∀ x5 x6 x7 . x1 (λ x9 x10 . x6) (λ x9 : (ι → ι → ι) → ι . Inj1 (x9 (λ x10 x11 . x9 (λ x12 x13 . Inj0 0)))) = Inj1 (x2 (λ x9 . setsum 0 (x0 (λ x10 x11 . 0) (λ x10 x11 . λ x12 : ι → ι . λ x13 . 0) (λ x10 : (ι → ι) → ι . λ x11 : ι → ι . λ x12 . x3 (λ x13 . 0) 0))) (λ x9 : (ι → ι → ι) → ι → ι → ι . λ x10 x11 : ι → ι . λ x12 . x10 (x0 (λ x13 x14 . x2 (λ x15 . 0) (λ x15 : (ι → ι → ι) → ι → ι → ι . λ x16 x17 : ι → ι . λ x18 . 0)) (λ x13 x14 . λ x15 : ι → ι . λ x16 . 0) (λ x13 : (ι → ι) → ι . λ x14 : ι → ι . λ x15 . x2 (λ x16 . 0) (λ x16 : (ι → ι → ι) → ι → ι → ι . λ x17 x18 : ι → ι . λ x19 . 0)))))) ⟶ (∀ x4 x5 x6 . ∀ x7 : (ι → ι) → ι → ι → ι → ι . x0 (λ x9 x10 . 0) (λ x9 x10 . λ x11 : ι → ι . λ x12 . Inj0 (setsum (setsum x12 (x1 (λ x13 x14 . 0) (λ x13 : (ι → ι → ι) → ι . 0))) (setsum 0 (x0 (λ x13 x14 . 0) (λ x13 x14 . λ x15 : ι → ι . λ x16 . 0) (λ x13 : (ι → ι) → ι . λ x14 : ι → ι . λ x15 . 0))))) (λ x9 : (ι → ι) → ι . λ x10 : ι → ι . λ x11 . 0) = setsum (x3 (λ x9 . x5) 0) (x0 (λ x9 x10 . x3 (λ x11 . Inj1 (Inj0 0)) (x0 (λ x11 x12 . x2 (λ x13 . 0) (λ x13 : (ι → ι → ι) → ι → ι → ι . λ x14 x15 : ι → ι . λ x16 . 0)) (λ x11 x12 . λ x13 : ι → ι . λ x14 . x14) (λ x11 : (ι → ι) → ι . λ x12 : ι → ι . λ x13 . x10))) (λ x9 x10 . λ x11 : ι → ι . λ x12 . 0) (λ x9 : (ι → ι) → ι . λ x10 : ι → ι . λ x11 . Inj1 (x2 (λ x12 . Inj0 0) (λ x12 : (ι → ι → ι) → ι → ι → ι . λ x13 x14 : ι → ι . λ x15 . setsum 0 0))))) ⟶ (∀ x4 . ∀ x5 : ι → (ι → ι → ι) → (ι → ι) → ι → ι . ∀ x6 . ∀ x7 : ι → ι . x0 (λ x9 x10 . x1 (λ x11 x12 . x1 (λ x13 x14 . Inj1 x11) (λ x13 : (ι → ι → ι) → ι . Inj0 (x1 (λ x14 x15 . 0) (λ x14 : (ι → ι → ι) → ι . 0)))) (λ x11 : (ι → ι → ι) → ι . x10)) (λ x9 x10 . λ x11 : ι → ι . λ x12 . Inj0 0) (λ x9 : (ι → ι) → ι . λ x10 : ι → ι . λ x11 . x2 (λ x12 . 0) (λ x12 : (ι → ι → ι) → ι → ι → ι . λ x13 x14 : ι → ι . λ x15 . 0)) = x1 (λ x9 x10 . x0 (λ x11 x12 . 0) (λ x11 x12 . λ x13 : ι → ι . λ x14 . 0) (λ x11 : (ι → ι) → ι . λ x12 : ι → ι . λ x13 . x2 (λ x14 . x3 (λ x15 . x2 (λ x16 . 0) (λ x16 : (ι → ι → ι) → ι → ι → ι . λ x17 x18 : ι → ι . λ x19 . 0)) x13) (λ x14 : (ι → ι → ι) → ι → ι → ι . λ x15 x16 : ι → ι . λ x17 . x1 (λ x18 x19 . 0) (λ x18 : (ι → ι → ι) → ι . x1 (λ x19 x20 . 0) (λ x19 : (ι → ι → ι) → ι . 0))))) (λ x9 : (ι → ι → ι) → ι . x0 (λ x10 x11 . x1 (λ x12 x13 . x0 (λ x14 x15 . x0 (λ x16 x17 . 0) (λ x16 x17 . λ x18 : ι → ι . λ x19 . 0) (λ x16 : (ι → ι) → ι . λ x17 : ι → ι . λ x18 . 0)) (λ x14 x15 . λ x16 : ι → ι . λ x17 . 0) (λ x14 : (ι → ι) → ι . λ x15 : ι → ι . λ x16 . x3 (λ x17 . 0) 0)) (λ x12 : (ι → ι → ι) → ι . 0)) (λ x10 x11 . λ x12 : ι → ι . λ x13 . x12 (x12 (x12 0))) (λ x10 : (ι → ι) → ι . λ x11 : ι → ι . λ x12 . 0))) ⟶ False (proof)Theorem ab27c.. : ∀ x0 : ((((ι → ι → ι) → ι → ι) → ι) → ι) → ι → ι . ∀ x1 : (((ι → (ι → ι) → ι) → ι) → ι → ι) → ((((ι → ι) → ι) → (ι → ι) → ι) → ι → ι) → ι . ∀ x2 : (ι → ι → ι) → ((ι → ι → ι) → ((ι → ι) → ι) → ι) → ι → ι → (ι → ι) → ι . ∀ x3 : ((ι → ι) → ι) → ι → ((ι → ι → ι) → ι) → ι . (∀ x4 : ι → ι . ∀ x5 x6 . ∀ x7 : ι → ι . x3 (λ x9 : ι → ι . x1 (λ x10 : (ι → (ι → ι) → ι) → ι . λ x11 . Inj1 0) (λ x10 : ((ι → ι) → ι) → (ι → ι) → ι . λ x11 . setsum (Inj1 0) (x10 (λ x12 : ι → ι . x2 (λ x13 x14 . 0) (λ x13 : ι → ι → ι . λ x14 : (ι → ι) → ι . 0) 0 0 (λ x13 . 0)) (λ x12 . x11)))) (x2 (λ x9 x10 . setsum x6 (setsum (x0 (λ x11 : ((ι → ι → ι) → ι → ι) → ι . 0) 0) 0)) (λ x9 : ι → ι → ι . λ x10 : (ι → ι) → ι . 0) (setsum 0 (x3 (λ x9 : ι → ι . x2 (λ x10 x11 . 0) (λ x10 : ι → ι → ι . λ x11 : (ι → ι) → ι . 0) 0 0 (λ x10 . 0)) (x1 (λ x9 : (ι → (ι → ι) → ι) → ι . λ x10 . 0) (λ x9 : ((ι → ι) → ι) → (ι → ι) → ι . λ x10 . 0)) (λ x9 : ι → ι → ι . 0))) (Inj1 (x7 x6)) (λ x9 . setsum (Inj1 (x1 (λ x10 : (ι → (ι → ι) → ι) → ι . λ x11 . 0) (λ x10 : ((ι → ι) → ι) → (ι → ι) → ι . λ x11 . 0))) (x3 (λ x10 : ι → ι . x1 (λ x11 : (ι → (ι → ι) → ι) → ι . λ x12 . 0) (λ x11 : ((ι → ι) → ι) → (ι → ι) → ι . λ x12 . 0)) (setsum 0 0) (λ x10 : ι → ι → ι . x7 0)))) (λ x9 : ι → ι → ι . 0) = x2 (λ x9 x10 . Inj0 (setsum (x2 (λ x11 x12 . setsum 0 0) (λ x11 : ι → ι → ι . λ x12 : (ι → ι) → ι . x9) (Inj1 0) 0 (λ x11 . 0)) (setsum 0 (Inj1 0)))) (λ x9 : ι → ι → ι . λ x10 : (ι → ι) → ι . Inj0 (Inj1 (x1 (λ x11 : (ι → (ι → ι) → ι) → ι . λ x12 . x12) (λ x11 : ((ι → ι) → ι) → (ι → ι) → ι . λ x12 . x3 (λ x13 : ι → ι . 0) 0 (λ x13 : ι → ι → ι . 0))))) (Inj0 (x0 (λ x9 : ((ι → ι → ι) → ι → ι) → ι . 0) (setsum (x4 0) (setsum 0 0)))) (setsum (x1 (λ x9 : (ι → (ι → ι) → ι) → ι . λ x10 . setsum (x9 (λ x11 . λ x12 : ι → ι . 0)) (x1 (λ x11 : (ι → (ι → ι) → ι) → ι . λ x12 . 0) (λ x11 : ((ι → ι) → ι) → (ι → ι) → ι . λ x12 . 0))) (λ x9 : ((ι → ι) → ι) → (ι → ι) → ι . λ x10 . x6)) (x3 (λ x9 : ι → ι . 0) 0 (λ x9 : ι → ι → ι . x3 (λ x10 : ι → ι . 0) (x2 (λ x10 x11 . 0) (λ x10 : ι → ι → ι . λ x11 : (ι → ι) → ι . 0) 0 0 (λ x10 . 0)) (λ x10 : ι → ι → ι . x0 (λ x11 : ((ι → ι → ι) → ι → ι) → ι . 0) 0)))) (λ x9 . setsum (x7 x5) (x1 (λ x10 : (ι → (ι → ι) → ι) → ι . λ x11 . x11) (λ x10 : ((ι → ι) → ι) → (ι → ι) → ι . λ x11 . Inj0 0)))) ⟶ (∀ x4 : ι → (ι → ι) → ι → ι → ι . ∀ x5 . ∀ x6 : ((ι → ι → ι) → ι → ι → ι) → ι . ∀ x7 . x3 (λ x9 : ι → ι . 0) (x0 (λ x9 : ((ι → ι → ι) → ι → ι) → ι . x9 (λ x10 : ι → ι → ι . λ x11 . setsum x7 (x9 (λ x12 : ι → ι → ι . λ x13 . 0)))) (setsum (setsum (x0 (λ x9 : ((ι → ι → ι) → ι → ι) → ι . 0) 0) (x0 (λ x9 : ((ι → ι → ι) → ι → ι) → ι . 0) 0)) (x0 (λ x9 : ((ι → ι → ι) → ι → ι) → ι . x5) (x0 (λ x9 : ((ι → ι → ι) → ι → ι) → ι . 0) 0)))) (λ x9 : ι → ι → ι . x0 (λ x10 : ((ι → ι → ι) → ι → ι) → ι . x0 (λ x11 : ((ι → ι → ι) → ι → ι) → ι . x1 (λ x12 : (ι → (ι → ι) → ι) → ι . λ x13 . x0 (λ x14 : ((ι → ι → ι) → ι → ι) → ι . 0) 0) (λ x12 : ((ι → ι) → ι) → (ι → ι) → ι . λ x13 . Inj0 0)) (Inj1 (x1 (λ x11 : (ι → (ι → ι) → ι) → ι . λ x12 . 0) (λ x11 : ((ι → ι) → ι) → (ι → ι) → ι . λ x12 . 0)))) 0) = Inj1 0) ⟶ (∀ x4 . ∀ x5 x6 : ι → ι → ι . ∀ x7 : ι → ι . x2 (λ x9 x10 . x6 x9 x9) (λ x9 : ι → ι → ι . λ x10 : (ι → ι) → ι . x9 (x10 (λ x11 . Inj1 (x3 (λ x12 : ι → ι . 0) 0 (λ x12 : ι → ι → ι . 0)))) 0) 0 (setsum 0 0) (λ x9 . x0 (λ x10 : ((ι → ι → ι) → ι → ι) → ι . setsum (x6 0 0) (x10 (λ x11 : ι → ι → ι . λ x12 . Inj1 0))) (x6 (x6 (x7 0) 0) 0)) = x6 (setsum 0 (setsum (Inj0 (Inj1 0)) (Inj1 (x0 (λ x9 : ((ι → ι → ι) → ι → ι) → ι . 0) 0)))) x4) ⟶ (∀ x4 x5 x6 . ∀ x7 : (ι → ι) → ι → (ι → ι) → ι → ι . x2 (λ x9 x10 . 0) (λ x9 : ι → ι → ι . λ x10 : (ι → ι) → ι . x0 (λ x11 : ((ι → ι → ι) → ι → ι) → ι . x9 (x9 (x0 (λ x12 : ((ι → ι → ι) → ι → ι) → ι . 0) 0) (x7 (λ x12 . 0) 0 (λ x12 . 0) 0)) (x0 (λ x12 : ((ι → ι → ι) → ι → ι) → ι . x3 (λ x13 : ι → ι . 0) 0 (λ x13 : ι → ι → ι . 0)) 0)) 0) x6 (setsum (Inj0 0) (Inj0 (x2 (λ x9 x10 . x10) (λ x9 : ι → ι → ι . λ x10 : (ι → ι) → ι . Inj0 0) x5 x5 (λ x9 . 0)))) (λ x9 . 0) = x6) ⟶ (∀ x4 . ∀ x5 : ((ι → ι → ι) → ι → ι) → ((ι → ι) → ι → ι) → ι . ∀ x6 : ι → ((ι → ι) → ι → ι) → (ι → ι) → ι . ∀ x7 : ((ι → ι) → (ι → ι) → ι → ι) → ι → ι . x1 (λ x9 : (ι → (ι → ι) → ι) → ι . λ x10 . setsum (Inj0 0) (x0 (λ x11 : ((ι → ι → ι) → ι → ι) → ι . 0) (x6 (setsum 0 0) (λ x11 : ι → ι . λ x12 . x2 (λ x13 x14 . 0) (λ x13 : ι → ι → ι . λ x14 : (ι → ι) → ι . 0) 0 0 (λ x13 . 0)) (λ x11 . 0)))) (λ x9 : ((ι → ι) → ι) → (ι → ι) → ι . λ x10 . 0) = x6 (setsum (Inj0 0) x4) (λ x9 : ι → ι . λ x10 . Inj1 (x6 (x0 (λ x11 : ((ι → ι → ι) → ι → ι) → ι . x1 (λ x12 : (ι → (ι → ι) → ι) → ι . λ x13 . 0) (λ x12 : ((ι → ι) → ι) → (ι → ι) → ι . λ x13 . 0)) 0) (λ x11 : ι → ι . λ x12 . x12) (λ x11 . 0))) (λ x9 . 0)) ⟶ (∀ x4 : ι → ((ι → ι) → ι → ι) → ι → ι . ∀ x5 x6 . ∀ x7 : ι → ι . x1 (λ x9 : (ι → (ι → ι) → ι) → ι . λ x10 . Inj0 0) (λ x9 : ((ι → ι) → ι) → (ι → ι) → ι . Inj1) = x7 (x1 (λ x9 : (ι → (ι → ι) → ι) → ι . λ x10 . Inj1 (x9 (λ x11 . λ x12 : ι → ι . 0))) (λ x9 : ((ι → ι) → ι) → (ι → ι) → ι . λ x10 . x2 (λ x11 x12 . 0) (λ x11 : ι → ι → ι . λ x12 : (ι → ι) → ι . x1 (λ x13 : (ι → (ι → ι) → ι) → ι . λ x14 . x12 (λ x15 . 0)) (λ x13 : ((ι → ι) → ι) → (ι → ι) → ι . λ x14 . x11 0 0)) 0 x6 (λ x11 . Inj1 0)))) ⟶ (∀ x4 . ∀ x5 : ι → ι → (ι → ι) → ι . ∀ x6 : ι → ι → ι → ι → ι . ∀ x7 : (ι → (ι → ι) → ι → ι) → ι . x0 (λ x9 : ((ι → ι → ι) → ι → ι) → ι . setsum (x0 (λ x10 : ((ι → ι → ι) → ι → ι) → ι . x1 (λ x11 : (ι → (ι → ι) → ι) → ι . λ x12 . x2 (λ x13 x14 . 0) (λ x13 : ι → ι → ι . λ x14 : (ι → ι) → ι . 0) 0 0 (λ x13 . 0)) (λ x11 : ((ι → ι) → ι) → (ι → ι) → ι . λ x12 . x0 (λ x13 : ((ι → ι → ι) → ι → ι) → ι . 0) 0)) 0) (setsum (setsum 0 (x3 (λ x10 : ι → ι . 0) 0 (λ x10 : ι → ι → ι . 0))) 0)) 0 = Inj1 0) ⟶ (∀ x4 : ι → ι . ∀ x5 . ∀ x6 : (ι → ι) → ι → ι . ∀ x7 : ι → ι . x0 (λ x9 : ((ι → ι → ι) → ι → ι) → ι . x9 (λ x10 : ι → ι → ι . λ x11 . Inj0 (x10 (x0 (λ x12 : ((ι → ι → ι) → ι → ι) → ι . 0) 0) 0))) (x3 (λ x9 : ι → ι . x2 (λ x10 x11 . x3 (λ x12 : ι → ι . x3 (λ x13 : ι → ι . 0) 0 (λ x13 : ι → ι → ι . 0)) (Inj1 0) (λ x12 : ι → ι → ι . 0)) (λ x10 : ι → ι → ι . λ x11 : (ι → ι) → ι . 0) (Inj0 (x0 (λ x10 : ((ι → ι → ι) → ι → ι) → ι . 0) 0)) 0 (setsum (x7 0))) 0 (λ x9 : ι → ι → ι . x2 (λ x10 x11 . 0) (λ x10 : ι → ι → ι . λ x11 : (ι → ι) → ι . setsum (x10 0 0) (x2 (λ x12 x13 . 0) (λ x12 : ι → ι → ι . λ x13 : (ι → ι) → ι . 0) 0 0 (λ x12 . 0))) x5 (Inj1 0) (λ x10 . Inj0 0))) = x3 (λ x9 : ι → ι . x7 (x7 (x9 (x7 0)))) (x6 (λ x9 . x2 (λ x10 x11 . x11) (λ x10 : ι → ι → ι . λ x11 : (ι → ι) → ι . 0) (setsum (x7 0) (x2 (λ x10 x11 . 0) (λ x10 : ι → ι → ι . λ x11 : (ι → ι) → ι . 0) 0 0 (λ x10 . 0))) 0 (λ x10 . x2 (λ x11 x12 . Inj0 0) (λ x11 : ι → ι → ι . λ x12 : (ι → ι) → ι . Inj1 0) (Inj0 0) 0 (λ x11 . setsum 0 0))) (x2 (λ x9 x10 . x10) (λ x9 : ι → ι → ι . λ x10 : (ι → ι) → ι . x7 (x1 (λ x11 : (ι → (ι → ι) → ι) → ι . λ x12 . 0) (λ x11 : ((ι → ι) → ι) → (ι → ι) → ι . λ x12 . 0))) (Inj0 0) (x0 (λ x9 : ((ι → ι → ι) → ι → ι) → ι . x2 (λ x10 x11 . 0) (λ x10 : ι → ι → ι . λ x11 : (ι → ι) → ι . 0) 0 0 (λ x10 . 0)) (x0 (λ x9 : ((ι → ι → ι) → ι → ι) → ι . 0) 0)) (λ x9 . Inj1 (setsum 0 0)))) (λ x9 : ι → ι → ι . Inj1 (setsum (x3 (λ x10 : ι → ι . setsum 0 0) (setsum 0 0) (λ x10 : ι → ι → ι . x3 (λ x11 : ι → ι . 0) 0 (λ x11 : ι → ι → ι . 0))) 0))) ⟶ False (proof)Theorem f8888.. : ∀ x0 : (ι → ι → ι) → ι → ι → (ι → ι) → ι . ∀ x1 : (ι → (ι → ι → ι → ι) → ι → ι → ι → ι) → (ι → ι) → ι . ∀ x2 : ((ι → ι) → ι → ι) → (ι → (ι → ι → ι) → ι) → ι . ∀ x3 : ((ι → ((ι → ι) → ι → ι) → ι) → ι) → ι → ι . (∀ x4 x5 x6 . ∀ x7 : ((ι → ι → ι) → (ι → ι) → ι) → ι . x3 (λ x9 : ι → ((ι → ι) → ι → ι) → ι . setsum (x1 (λ x10 . λ x11 : ι → ι → ι → ι . λ x12 x13 x14 . setsum x12 (setsum 0 0)) (λ x10 . x6)) (x7 (λ x10 : ι → ι → ι . λ x11 : ι → ι . setsum (x11 0) (x3 (λ x12 : ι → ((ι → ι) → ι → ι) → ι . 0) 0)))) x4 = setsum (Inj0 0) (setsum (x7 (λ x9 : ι → ι → ι . λ x10 : ι → ι . x7 (λ x11 : ι → ι → ι . λ x12 : ι → ι . Inj0 0))) 0)) ⟶ (∀ x4 x5 . ∀ x6 : (ι → ι) → ι . ∀ x7 : (ι → ι → ι) → ((ι → ι) → ι → ι) → ι . x3 (λ x9 : ι → ((ι → ι) → ι → ι) → ι . x9 (x7 (λ x10 x11 . setsum 0 0) (λ x10 : ι → ι . λ x11 . x1 (λ x12 . λ x13 : ι → ι → ι → ι . λ x14 x15 x16 . 0) (λ x12 . x11))) (λ x10 : ι → ι . x3 (λ x11 : ι → ((ι → ι) → ι → ι) → ι . x11 (Inj0 0) (λ x12 : ι → ι . λ x13 . x1 (λ x14 . λ x15 : ι → ι → ι → ι . λ x16 x17 x18 . 0) (λ x14 . 0))))) (setsum (x0 (λ x9 x10 . x7 (λ x11 x12 . 0) (λ x11 : ι → ι . λ x12 . setsum 0 0)) (setsum (setsum 0 0) 0) 0 (λ x9 . setsum 0 0)) (x3 (λ x9 : ι → ((ι → ι) → ι → ι) → ι . x6 (λ x10 . 0)) (x7 (λ x9 x10 . setsum 0 0) (λ x9 : ι → ι . λ x10 . x1 (λ x11 . λ x12 : ι → ι → ι → ι . λ x13 x14 x15 . 0) (λ x11 . 0))))) = setsum (x0 (λ x9 x10 . Inj0 (setsum x10 0)) (x3 (λ x9 : ι → ((ι → ι) → ι → ι) → ι . x9 0 (λ x10 : ι → ι . λ x11 . 0)) 0) (Inj1 (x2 (λ x9 : ι → ι . λ x10 . x6 (λ x11 . 0)) (λ x9 . λ x10 : ι → ι → ι . x10 0 0))) (λ x9 . x7 (λ x10 x11 . x10) (λ x10 : ι → ι . setsum (Inj1 0)))) 0) ⟶ (∀ x4 . ∀ x5 : ι → ι → ι → ι . ∀ x6 : ι → ι . ∀ x7 . x2 (λ x9 : ι → ι . λ x10 . x9 0) (λ x9 . λ x10 : ι → ι → ι . x9) = x4) ⟶ (∀ x4 . ∀ x5 : ι → ι → ι → ι . ∀ x6 : ι → ι → ι → ι → ι . ∀ x7 : ((ι → ι) → ι → ι) → ι . x2 (λ x9 : ι → ι . λ x10 . x1 (λ x11 . λ x12 : ι → ι → ι → ι . λ x13 x14 x15 . 0) (λ x11 . 0)) (λ x9 . λ x10 : ι → ι → ι . x6 (x1 (λ x11 . λ x12 : ι → ι → ι → ι . λ x13 x14 x15 . x12 0 0 x14) (λ x11 . x9)) (x2 (λ x11 : ι → ι . λ x12 . Inj1 0) (λ x11 . λ x12 : ι → ι → ι . setsum x9 (x2 (λ x13 : ι → ι . λ x14 . 0) (λ x13 . λ x14 : ι → ι → ι . 0)))) 0 (Inj0 (Inj0 (x3 (λ x11 : ι → ((ι → ι) → ι → ι) → ι . 0) 0)))) = x6 (x6 0 0 (x1 (λ x9 . λ x10 : ι → ι → ι → ι . λ x11 x12 x13 . Inj0 (setsum 0 0)) (λ x9 . 0)) (x1 (λ x9 . λ x10 : ι → ι → ι → ι . λ x11 x12 x13 . x1 (λ x14 . λ x15 : ι → ι → ι → ι . λ x16 x17 x18 . 0) (λ x14 . x2 (λ x15 : ι → ι . λ x16 . 0) (λ x15 . λ x16 : ι → ι → ι . 0))) (λ x9 . 0))) (x5 (x3 (λ x9 : ι → ((ι → ι) → ι → ι) → ι . x6 0 (x7 (λ x10 : ι → ι . λ x11 . 0)) (Inj0 0) (x5 0 0 0)) 0) x4 0) (Inj1 0) (x3 (λ x9 : ι → ((ι → ι) → ι → ι) → ι . 0) (x6 (x1 (λ x9 . λ x10 : ι → ι → ι → ι . λ x11 x12 x13 . setsum 0 0) (λ x9 . x5 0 0 0)) (setsum (x3 (λ x9 : ι → ((ι → ι) → ι → ι) → ι . 0) 0) (x7 (λ x9 : ι → ι . λ x10 . 0))) (setsum (x6 0 0 0 0) (x5 0 0 0)) 0))) ⟶ (∀ x4 : (ι → (ι → ι) → ι) → ((ι → ι) → ι → ι) → ι . ∀ x5 . ∀ x6 : ι → ι . ∀ x7 . x1 (λ x9 . λ x10 : ι → ι → ι → ι . λ x11 x12 x13 . setsum (x3 (λ x14 : ι → ((ι → ι) → ι → ι) → ι . x3 (λ x15 : ι → ((ι → ι) → ι → ι) → ι . x0 (λ x16 x17 . 0) 0 0 (λ x16 . 0)) 0) (setsum (setsum 0 0) x12)) (x0 (λ x14 x15 . x3 (λ x16 : ι → ((ι → ι) → ι → ι) → ι . x15) (Inj0 0)) 0 0 (λ x14 . x2 (λ x15 : ι → ι . λ x16 . x3 (λ x17 : ι → ((ι → ι) → ι → ι) → ι . 0) 0) (λ x15 . λ x16 : ι → ι → ι . x3 (λ x17 : ι → ((ι → ι) → ι → ι) → ι . 0) 0)))) (λ x9 . 0) = Inj0 (x4 (λ x9 . λ x10 : ι → ι . Inj1 0) (λ x9 : ι → ι . λ x10 . x6 0))) ⟶ (∀ x4 : ι → ι . ∀ x5 : (ι → ι) → ι → ι . ∀ x6 : ι → ((ι → ι) → ι → ι) → ι . ∀ x7 . x1 (λ x9 . λ x10 : ι → ι → ι → ι . λ x11 x12 x13 . Inj0 (Inj1 (x3 (λ x14 : ι → ((ι → ι) → ι → ι) → ι . x11) (x0 (λ x14 x15 . 0) 0 0 (λ x14 . 0))))) (λ x9 . x1 (λ x10 . λ x11 : ι → ι → ι → ι . λ x12 x13 x14 . setsum (x11 0 0 (Inj1 0)) x12) (setsum (Inj1 (x1 (λ x10 . λ x11 : ι → ι → ι → ι . λ x12 x13 x14 . 0) (λ x10 . 0))))) = setsum 0 0) ⟶ (∀ x4 . ∀ x5 : (((ι → ι) → ι → ι) → (ι → ι) → ι) → ι . ∀ x6 : (ι → ι) → (ι → ι → ι) → ι . ∀ x7 . x0 (λ x9 x10 . x10) (Inj1 (x2 (λ x9 : ι → ι . λ x10 . 0) (λ x9 . λ x10 : ι → ι → ι . Inj1 (x2 (λ x11 : ι → ι . λ x12 . 0) (λ x11 . λ x12 : ι → ι → ι . 0))))) (x0 (λ x9 x10 . 0) (Inj1 (setsum 0 (x0 (λ x9 x10 . 0) 0 0 (λ x9 . 0)))) x4 (λ x9 . x3 (λ x10 : ι → ((ι → ι) → ι → ι) → ι . 0) (x0 (λ x10 x11 . 0) (x0 (λ x10 x11 . 0) 0 0 (λ x10 . 0)) (setsum 0 0) (λ x10 . x1 (λ x11 . λ x12 : ι → ι → ι → ι . λ x13 x14 x15 . 0) (λ x11 . 0))))) (λ x9 . x9) = Inj0 (x0 (λ x9 x10 . x7) (setsum (setsum (x0 (λ x9 x10 . 0) 0 0 (λ x9 . 0)) (x1 (λ x9 . λ x10 : ι → ι → ι → ι . λ x11 x12 x13 . 0) (λ x9 . 0))) 0) (setsum (setsum (x5 (λ x9 : (ι → ι) → ι → ι . λ x10 : ι → ι . 0)) 0) (setsum x4 0)) (λ x9 . x6 (λ x10 . 0) (λ x10 x11 . x10)))) ⟶ (∀ x4 x5 x6 x7 . x0 (λ x9 x10 . x10) 0 (x0 (λ x9 x10 . x9) x5 (Inj0 x7) (λ x9 . x7)) (λ x9 . x7) = Inj0 (x2 (λ x9 : ι → ι . λ x10 . x3 (λ x11 : ι → ((ι → ι) → ι → ι) → ι . x10) x7) (λ x9 . λ x10 : ι → ι → ι . 0))) ⟶ False (proof)Theorem cd8e8.. : ∀ x0 : (ι → (ι → ι) → ι) → ι → ι → (ι → ι) → ι . ∀ x1 : (ι → ι) → ((ι → ι → ι) → ι) → ι . ∀ x2 : (ι → ι → (ι → ι → ι) → (ι → ι) → ι) → (ι → ι) → ((ι → ι) → ι) → ι . ∀ x3 : (ι → ι) → ((ι → ι) → (ι → ι → ι) → ι) → ι → ι . (∀ x4 : (ι → ι) → ι → ι → ι → ι . ∀ x5 : (ι → ι → ι) → ι . ∀ x6 : (ι → ι → ι → ι) → ι . ∀ x7 : ((ι → ι → ι) → ι) → ι . x3 (λ x9 . 0) (λ x9 : ι → ι . λ x10 : ι → ι → ι . 0) (x7 (λ x9 : ι → ι → ι . setsum (x9 0 (x7 (λ x10 : ι → ι → ι . 0))) (x7 (λ x10 : ι → ι → ι . x2 (λ x11 x12 . λ x13 : ι → ι → ι . λ x14 : ι → ι . 0) (λ x11 . 0) (λ x11 : ι → ι . 0))))) = x7 (λ x9 : ι → ι → ι . setsum (Inj0 (x7 (λ x10 : ι → ι → ι . setsum 0 0))) (x3 (λ x10 . x7 (λ x11 : ι → ι → ι . 0)) (λ x10 : ι → ι . λ x11 : ι → ι → ι . 0) (x9 (Inj0 0) (setsum 0 0))))) ⟶ (∀ x4 . ∀ x5 : ι → ι . ∀ x6 x7 . x3 (λ x9 . x7) (λ x9 : ι → ι . λ x10 : ι → ι → ι . x9 x6) x7 = x7) ⟶ (∀ x4 : (((ι → ι) → ι → ι) → (ι → ι) → ι → ι) → ι . ∀ x5 x6 x7 . x2 (λ x9 x10 . λ x11 : ι → ι → ι . λ x12 : ι → ι . 0) (λ x9 . x3 (λ x10 . 0) (λ x10 : ι → ι . λ x11 : ι → ι → ι . x9) x9) (λ x9 : ι → ι . setsum (x0 (λ x10 . λ x11 : ι → ι . x3 (λ x12 . x0 (λ x13 . λ x14 : ι → ι . 0) 0 0 (λ x13 . 0)) (λ x12 : ι → ι . λ x13 : ι → ι → ι . setsum 0 0) (Inj0 0)) (x0 (λ x10 . λ x11 : ι → ι . x3 (λ x12 . 0) (λ x12 : ι → ι . λ x13 : ι → ι → ι . 0) 0) 0 (Inj1 0) (λ x10 . Inj1 0)) (Inj1 (setsum 0 0)) (λ x10 . x10)) 0) = setsum x5 0) ⟶ (∀ x4 . ∀ x5 : ι → ι → ι → ι → ι . ∀ x6 : (((ι → ι) → ι → ι) → ι → ι) → ι . ∀ x7 . x2 (λ x9 x10 . λ x11 : ι → ι → ι . λ x12 : ι → ι . 0) (λ x9 . x1 (λ x10 . x10) (λ x10 : ι → ι → ι . x10 0 (x10 (x1 (λ x11 . 0) (λ x11 : ι → ι → ι . 0)) x7))) (λ x9 : ι → ι . x9 (x1 (λ x10 . 0) (λ x10 : ι → ι → ι . x6 (λ x11 : (ι → ι) → ι → ι . λ x12 . x1 (λ x13 . 0) (λ x13 : ι → ι → ι . 0))))) = setsum (x2 (λ x9 x10 . λ x11 : ι → ι → ι . λ x12 : ι → ι . setsum 0 (setsum (x11 0 0) x9)) (λ x9 . x6 (λ x10 : (ι → ι) → ι → ι . λ x11 . setsum (x10 (λ x12 . 0) 0) 0)) (λ x9 : ι → ι . x7)) (x1 (λ x9 . setsum x7 0) (λ x9 : ι → ι → ι . x9 (x9 (Inj1 0) 0) (x1 (λ x10 . x7) (λ x10 : ι → ι → ι . x10 0 0))))) ⟶ (∀ x4 : ι → ι . ∀ x5 . ∀ x6 : ((ι → ι) → ι) → ι → (ι → ι) → ι → ι . ∀ x7 . x1 (λ x9 . setsum 0 (Inj0 (x6 (λ x10 : ι → ι . x6 (λ x11 : ι → ι . 0) 0 (λ x11 . 0) 0) (Inj1 0) (λ x10 . x10) x7))) (λ x9 : ι → ι → ι . 0) = x4 (x6 (λ x9 : ι → ι . x9 (setsum 0 0)) x5 (λ x9 . x2 (λ x10 x11 . λ x12 : ι → ι → ι . λ x13 : ι → ι . 0) (λ x10 . x2 (λ x11 x12 . λ x13 : ι → ι → ι . λ x14 : ι → ι . 0) (λ x11 . x2 (λ x12 x13 . λ x14 : ι → ι → ι . λ x15 : ι → ι . 0) (λ x12 . 0) (λ x12 : ι → ι . 0)) (λ x11 : ι → ι . setsum 0 0)) (λ x10 : ι → ι . x0 (λ x11 . λ x12 : ι → ι . x0 (λ x13 . λ x14 : ι → ι . 0) 0 0 (λ x13 . 0)) 0 (x2 (λ x11 x12 . λ x13 : ι → ι → ι . λ x14 : ι → ι . 0) (λ x11 . 0) (λ x11 : ι → ι . 0)) (λ x11 . x9))) (x4 (Inj1 (setsum 0 0))))) ⟶ (∀ x4 : ((ι → ι → ι) → (ι → ι) → ι → ι) → (ι → ι) → ι . ∀ x5 : (ι → ι → ι → ι) → ((ι → ι) → ι) → ι → ι . ∀ x6 : ι → ι . ∀ x7 : (((ι → ι) → ι → ι) → ι) → ι . x1 (λ x9 . Inj0 0) (λ x9 : ι → ι → ι . Inj0 (Inj0 (x5 (λ x10 x11 x12 . x11) (λ x10 : ι → ι . x10 0) (Inj0 0)))) = Inj1 (Inj1 (x2 (λ x9 x10 . λ x11 : ι → ι → ι . λ x12 : ι → ι . x9) (λ x9 . Inj1 (x3 (λ x10 . 0) (λ x10 : ι → ι . λ x11 : ι → ι → ι . 0) 0)) (λ x9 : ι → ι . x6 (setsum 0 0))))) ⟶ (∀ x4 . ∀ x5 : ((ι → ι) → ι) → ι . ∀ x6 x7 . x0 (λ x9 . λ x10 : ι → ι . x9) 0 0 (λ x9 . x6) = x6) ⟶ (∀ x4 : ι → ι . ∀ x5 : ((ι → ι → ι) → ι) → ((ι → ι) → ι) → ι → ι . ∀ x6 x7 . x0 (λ x9 . λ x10 : ι → ι . setsum (x2 (λ x11 x12 . λ x13 : ι → ι → ι . λ x14 : ι → ι . 0) x10 (λ x11 : ι → ι . x1 (λ x12 . x12) (λ x12 : ι → ι → ι . x2 (λ x13 x14 . λ x15 : ι → ι → ι . λ x16 : ι → ι . 0) (λ x13 . 0) (λ x13 : ι → ι . 0)))) 0) (Inj0 (x1 (λ x9 . x6) (λ x9 : ι → ι → ι . x0 (λ x10 . λ x11 : ι → ι . x7) (x3 (λ x10 . 0) (λ x10 : ι → ι . λ x11 : ι → ι → ι . 0) 0) (Inj0 0) (λ x10 . 0)))) 0 (λ x9 . setsum x9 x6) = setsum (x4 (x3 (λ x9 . 0) (λ x9 : ι → ι . λ x10 : ι → ι → ι . 0) (setsum 0 (x3 (λ x9 . 0) (λ x9 : ι → ι . λ x10 : ι → ι → ι . 0) 0)))) (x3 (λ x9 . 0) (λ x9 : ι → ι . λ x10 : ι → ι → ι . x1 (λ x11 . x1 (λ x12 . x11) (λ x12 : ι → ι → ι . x11)) (λ x11 : ι → ι → ι . x2 (λ x12 x13 . λ x14 : ι → ι → ι . λ x15 : ι → ι . x0 (λ x16 . λ x17 : ι → ι . 0) 0 0 (λ x16 . 0)) (λ x12 . x12) (λ x12 : ι → ι . 0))) 0)) ⟶ False (proof)Theorem cd23f.. : ∀ x0 : (ι → ι) → ι → (((ι → ι) → ι → ι) → ι) → (ι → ι → ι) → ι . ∀ x1 : ((((ι → ι) → ι) → ι) → ι) → (ι → ι) → ι . ∀ x2 : ((((ι → ι) → ι → ι → ι) → ι → ι) → ι → ι) → ι → ι . ∀ x3 : (ι → ι) → ι → ι . (∀ x4 : (ι → (ι → ι) → ι) → ((ι → ι) → ι) → ι . ∀ x5 x6 . ∀ x7 : (((ι → ι) → ι → ι) → ι) → ι . x3 (λ x9 . x1 (λ x10 : ((ι → ι) → ι) → ι . 0) (λ x10 . x0 (λ x11 . x2 (λ x12 : ((ι → ι) → ι → ι → ι) → ι → ι . λ x13 . Inj1 0) (setsum 0 0)) x10 (λ x11 : (ι → ι) → ι → ι . 0) (λ x11 x12 . 0))) (Inj1 (setsum 0 (x0 (λ x9 . x2 (λ x10 : ((ι → ι) → ι → ι → ι) → ι → ι . λ x11 . 0) 0) x6 (λ x9 : (ι → ι) → ι → ι . 0) (λ x9 x10 . 0)))) = Inj0 (setsum (setsum (x2 (λ x9 : ((ι → ι) → ι → ι → ι) → ι → ι . λ x10 . x2 (λ x11 : ((ι → ι) → ι → ι → ι) → ι → ι . λ x12 . 0) 0) (Inj1 0)) x6) (x3 (λ x9 . x2 (λ x10 : ((ι → ι) → ι → ι → ι) → ι → ι . λ x11 . 0) x6) (x2 (λ x9 : ((ι → ι) → ι → ι → ι) → ι → ι . λ x10 . 0) (setsum 0 0))))) ⟶ (∀ x4 . ∀ x5 : (((ι → ι) → ι) → (ι → ι) → ι → ι) → ι → ι . ∀ x6 : (ι → ι → ι → ι) → ι → ι . ∀ x7 : (ι → (ι → ι) → ι → ι) → (ι → ι) → ι → ι . x3 (λ x9 . Inj0 (x2 (λ x10 : ((ι → ι) → ι → ι → ι) → ι → ι . λ x11 . x1 (λ x12 : ((ι → ι) → ι) → ι . 0) (λ x12 . x0 (λ x13 . 0) 0 (λ x13 : (ι → ι) → ι → ι . 0) (λ x13 x14 . 0))) x9)) 0 = x5 (λ x9 : (ι → ι) → ι . λ x10 : ι → ι . λ x11 . setsum 0 0) x4) ⟶ (∀ x4 : ((ι → ι) → (ι → ι) → ι → ι) → (ι → ι → ι) → ι . ∀ x5 : (((ι → ι) → ι → ι) → (ι → ι) → ι → ι) → ι . ∀ x6 : (((ι → ι) → ι) → ι) → (ι → ι) → ι . ∀ x7 . x2 (λ x9 : ((ι → ι) → ι → ι → ι) → ι → ι . λ x10 . 0) (Inj0 (x6 (λ x9 : (ι → ι) → ι . setsum (Inj1 0) x7) (λ x9 . x9))) = x6 (λ x9 : (ι → ι) → ι . setsum 0 0) (λ x9 . 0)) ⟶ (∀ x4 . ∀ x5 : ι → ι . ∀ x6 x7 . x2 (λ x9 : ((ι → ι) → ι → ι → ι) → ι → ι . λ x10 . 0) 0 = Inj1 0) ⟶ (∀ x4 : ι → ((ι → ι) → ι → ι) → ι → ι . ∀ x5 x6 . ∀ x7 : (((ι → ι) → ι → ι) → ι → ι → ι) → ι . x1 (λ x9 : ((ι → ι) → ι) → ι . 0) (λ x9 . 0) = setsum (x0 (λ x9 . Inj0 0) (setsum 0 x6) (λ x9 : (ι → ι) → ι → ι . x7 (λ x10 : (ι → ι) → ι → ι . λ x11 x12 . x12)) (λ x9 x10 . Inj1 (x7 (λ x11 : (ι → ι) → ι → ι . λ x12 x13 . x0 (λ x14 . 0) 0 (λ x14 : (ι → ι) → ι → ι . 0) (λ x14 x15 . 0))))) (x2 (λ x9 : ((ι → ι) → ι → ι → ι) → ι → ι . λ x10 . x10) 0)) ⟶ (∀ x4 : (ι → (ι → ι) → ι → ι) → (ι → ι → ι) → ι . ∀ x5 : (((ι → ι) → ι) → ι) → ((ι → ι) → ι) → ι . ∀ x6 . ∀ x7 : ι → ι → ι . x1 (λ x9 : ((ι → ι) → ι) → ι . Inj0 (Inj1 0)) (λ x9 . x3 (λ x10 . x0 (λ x11 . 0) (Inj0 (x0 (λ x11 . 0) 0 (λ x11 : (ι → ι) → ι → ι . 0) (λ x11 x12 . 0))) (λ x11 : (ι → ι) → ι → ι . Inj1 0) (λ x11 x12 . x2 (λ x13 : ((ι → ι) → ι → ι → ι) → ι → ι . λ x14 . x13 (λ x15 : ι → ι . λ x16 x17 . 0) 0) x9)) (setsum (Inj0 x9) (setsum (setsum 0 0) (Inj0 0)))) = setsum (x1 (λ x9 : ((ι → ι) → ι) → ι . setsum (Inj0 0) 0) (λ x9 . x7 (x0 (λ x10 . x7 0 0) (setsum 0 0) (λ x10 : (ι → ι) → ι → ι . x0 (λ x11 . 0) 0 (λ x11 : (ι → ι) → ι → ι . 0) (λ x11 x12 . 0)) (λ x10 x11 . Inj1 0)) (setsum (setsum 0 0) (Inj0 0)))) (x1 (λ x9 : ((ι → ι) → ι) → ι . 0) (λ x9 . 0))) ⟶ (∀ x4 : ι → ι → ι . ∀ x5 . ∀ x6 : ι → (ι → ι → ι) → ι . ∀ x7 : ι → ((ι → ι) → ι) → (ι → ι) → ι . x0 (x2 (λ x9 : ((ι → ι) → ι → ι → ι) → ι → ι . λ x10 . x3 (λ x11 . x9 (λ x12 : ι → ι . λ x13 x14 . setsum 0 0) 0) (Inj1 0))) 0 (λ x9 : (ι → ι) → ι → ι . x5) (λ x9 x10 . setsum (x0 (λ x11 . setsum (x1 (λ x12 : ((ι → ι) → ι) → ι . 0) (λ x12 . 0)) (x0 (λ x12 . 0) 0 (λ x12 : (ι → ι) → ι → ι . 0) (λ x12 x13 . 0))) (x1 (λ x11 : ((ι → ι) → ι) → ι . x11 (λ x12 : ι → ι . 0)) (λ x11 . Inj1 0)) (λ x11 : (ι → ι) → ι → ι . setsum 0 (x7 0 (λ x12 : ι → ι . 0) (λ x12 . 0))) (λ x11 x12 . 0)) (x2 (λ x11 : ((ι → ι) → ι → ι → ι) → ι → ι . λ x12 . x12) (Inj1 (setsum 0 0)))) = Inj0 (Inj1 (x4 (x0 (λ x9 . x7 0 (λ x10 : ι → ι . 0) (λ x10 . 0)) 0 (λ x9 : (ι → ι) → ι → ι . Inj1 0) (λ x9 x10 . x9)) (Inj0 x5)))) ⟶ (∀ x4 : ι → ((ι → ι) → ι) → ι . ∀ x5 . ∀ x6 : (ι → ι → ι → ι) → ι . ∀ x7 . x0 (λ x9 . setsum x7 0) (x3 (λ x9 . 0) x7) (λ x9 : (ι → ι) → ι → ι . x7) (λ x9 x10 . 0) = x3 (λ x9 . x1 (λ x10 : ((ι → ι) → ι) → ι . x10 (λ x11 : ι → ι . 0)) (λ x10 . x9)) (setsum (x2 (λ x9 : ((ι → ι) → ι → ι → ι) → ι → ι . λ x10 . setsum 0 (x2 (λ x11 : ((ι → ι) → ι → ι → ι) → ι → ι . λ x12 . 0) 0)) (Inj0 (setsum 0 0))) (setsum x5 (setsum (Inj0 0) 0)))) ⟶ False (proof)Theorem 8c027.. : ∀ x0 : ((ι → ι → ι) → ι) → ι → ι . ∀ x1 : (ι → (ι → ι) → ι) → ι → ι . ∀ x2 : (ι → ι) → ι → ι . ∀ x3 : (ι → ι) → ((ι → ι) → ((ι → ι) → ι → ι) → ι) → ι . (∀ x4 x5 . ∀ x6 : (((ι → ι) → ι) → ι) → ι . ∀ x7 : ι → ι . x3 (λ x9 . 0) (λ x9 : ι → ι . λ x10 : (ι → ι) → ι → ι . Inj1 0) = x4) ⟶ (∀ x4 x5 . ∀ x6 : ι → ι → ι . ∀ x7 : ι → ι . x3 x7 (λ x9 : ι → ι . λ x10 : (ι → ι) → ι → ι . x10 (λ x11 . x0 (λ x12 : ι → ι → ι . 0) (x3 (λ x12 . x3 (λ x13 . 0) (λ x13 : ι → ι . λ x14 : (ι → ι) → ι → ι . 0)) (λ x12 : ι → ι . λ x13 : (ι → ι) → ι → ι . x13 (λ x14 . 0) 0))) (setsum (Inj0 (x1 (λ x11 . λ x12 : ι → ι . 0) 0)) (x3 (λ x11 . setsum 0 0) (λ x11 : ι → ι . λ x12 : (ι → ι) → ι → ι . x1 (λ x13 . λ x14 : ι → ι . 0) 0)))) = x7 x4) ⟶ (∀ x4 x5 . ∀ x6 : (ι → ι → ι → ι) → ι . ∀ x7 . x2 (λ x9 . setsum 0 0) x5 = x5) ⟶ (∀ x4 . ∀ x5 : ι → (ι → ι) → ι . ∀ x6 : ((ι → ι) → ι) → ι → ι . ∀ x7 : (ι → ι) → ι → (ι → ι) → ι → ι . x2 (λ x9 . setsum (x2 (λ x10 . x1 (λ x11 . λ x12 : ι → ι . 0) x9) (x2 (λ x10 . 0) 0)) (setsum (Inj0 x9) x9)) 0 = Inj1 x4) ⟶ (∀ x4 : ι → ι . ∀ x5 : ((ι → ι → ι) → ι) → ι . ∀ x6 x7 . x1 (λ x9 . λ x10 : ι → ι . 0) (setsum (setsum 0 0) (x4 x7)) = setsum 0 (x3 (λ x9 . 0) (λ x9 : ι → ι . λ x10 : (ι → ι) → ι → ι . x7))) ⟶ (∀ x4 x5 . ∀ x6 : (ι → ι → ι) → ((ι → ι) → ι → ι) → ι → ι → ι . ∀ x7 : ι → ((ι → ι) → ι) → ι → ι . x1 (λ x9 . λ x10 : ι → ι . 0) (x7 (x3 (λ x9 . 0) (λ x9 : ι → ι . λ x10 : (ι → ι) → ι → ι . x0 (λ x11 : ι → ι → ι . 0) (x9 0))) (λ x9 : ι → ι . setsum (Inj1 (x7 0 (λ x10 : ι → ι . 0) 0)) (x1 (λ x10 . λ x11 : ι → ι . x3 (λ x12 . 0) (λ x12 : ι → ι . λ x13 : (ι → ι) → ι → ι . 0)) x5)) x5) = setsum x4 0) ⟶ (∀ x4 : (((ι → ι) → ι) → (ι → ι) → ι → ι) → ((ι → ι) → ι → ι) → ι . ∀ x5 . ∀ x6 : ((ι → ι) → ι → ι → ι) → ι → ι → ι . ∀ x7 : ι → ι → ι → ι → ι . x0 (λ x9 : ι → ι → ι . x3 (λ x10 . x1 (λ x11 . λ x12 : ι → ι . x0 (λ x13 : ι → ι → ι . 0) (Inj1 0)) 0) (λ x10 : ι → ι . λ x11 : (ι → ι) → ι → ι . setsum (x7 (x3 (λ x12 . 0) (λ x12 : ι → ι . λ x13 : (ι → ι) → ι → ι . 0)) (x10 0) (x10 0) (x2 (λ x12 . 0) 0)) (Inj0 (Inj0 0)))) 0 = Inj1 (x7 0 0 (Inj0 0) 0)) ⟶ (∀ x4 : (ι → ι) → ι → (ι → ι) → ι . ∀ x5 x6 x7 . x0 (λ x9 : ι → ι → ι . x3 (λ x10 . x9 (x2 (λ x11 . 0) (x0 (λ x11 : ι → ι → ι . 0) 0)) (Inj0 x10)) (λ x10 : ι → ι . λ x11 : (ι → ι) → ι → ι . x2 (λ x12 . x2 (λ x13 . Inj1 0) 0) 0)) (x1 (λ x9 . λ x10 : ι → ι . x1 (λ x11 . λ x12 : ι → ι . 0) (x1 (λ x11 . λ x12 : ι → ι . x9) 0)) x7) = setsum (x4 (λ x9 . 0) x5 (λ x9 . 0)) x7) ⟶ False (proof)Theorem 381ed.. : ∀ x0 : ((ι → ι) → (((ι → ι) → ι) → ι) → ι → (ι → ι) → ι → ι) → ι → ι . ∀ x1 x2 : (ι → ι) → ι → ι . ∀ x3 : (ι → ι) → (ι → ι) → ι . (∀ x4 x5 . ∀ x6 : (((ι → ι) → ι → ι) → (ι → ι) → ι) → ι . ∀ x7 . x3 (λ x9 . x2 (λ x10 . x7) 0) (λ x9 . x7) = x2 (λ x9 . x5) (setsum (setsum (Inj0 0) 0) x4)) ⟶ (∀ x4 : (((ι → ι) → ι → ι) → ι → ι) → ι → ι . ∀ x5 : (ι → ι) → ι → ι . ∀ x6 : ι → ι . ∀ x7 : (ι → (ι → ι) → ι) → ι . x3 (λ x9 . x0 (λ x10 : ι → ι . λ x11 : ((ι → ι) → ι) → ι . λ x12 . λ x13 : ι → ι . λ x14 . x3 (λ x15 . x15) (λ x15 . Inj1 (x1 (λ x16 . 0) 0))) 0) (λ x9 . x7 (λ x10 . λ x11 : ι → ι . 0)) = x7 (λ x9 . λ x10 : ι → ι . Inj0 (x6 x9))) ⟶ (∀ x4 . ∀ x5 : ι → ι . ∀ x6 . ∀ x7 : ι → (ι → ι) → ι . x2 (λ x9 . x9) (setsum x6 (x0 (λ x9 : ι → ι . λ x10 : ((ι → ι) → ι) → ι . λ x11 . λ x12 : ι → ι . λ x13 . setsum 0 0) 0)) = x5 x4) ⟶ (∀ x4 : ι → (ι → ι) → ι . ∀ x5 x6 . ∀ x7 : (ι → ι → ι → ι) → ι → ι . x2 (λ x9 . 0) (Inj1 (x2 (λ x9 . x7 (λ x10 x11 x12 . setsum 0 0) (Inj1 0)) (x2 (λ x9 . x9) (Inj0 0)))) = x7 (λ x9 x10 . x0 (λ x11 : ι → ι . λ x12 : ((ι → ι) → ι) → ι . λ x13 . λ x14 : ι → ι . λ x15 . Inj1 (Inj0 x15))) 0) ⟶ (∀ x4 x5 x6 . ∀ x7 : (ι → ι → ι → ι) → ι → ι . x1 (λ x9 . x5) 0 = Inj1 x6) ⟶ (∀ x4 : ι → ι → ι . ∀ x5 x6 . ∀ x7 : ι → ((ι → ι) → ι → ι) → ι . x1 (λ x9 . x3 (λ x10 . 0) (λ x10 . x9)) (x0 (λ x9 : ι → ι . λ x10 : ((ι → ι) → ι) → ι . λ x11 . λ x12 : ι → ι . λ x13 . 0) (x4 (setsum (x4 0 0) 0) (Inj1 x6))) = x0 (λ x9 : ι → ι . λ x10 : ((ι → ι) → ι) → ι . λ x11 . λ x12 : ι → ι . λ x13 . x12 (x3 (λ x14 . x0 (λ x15 : ι → ι . λ x16 : ((ι → ι) → ι) → ι . λ x17 . λ x18 : ι → ι . λ x19 . Inj0 0) (x12 0)) (λ x14 . 0))) (x3 (λ x9 . x9) (λ x9 . x9))) ⟶ (∀ x4 . ∀ x5 : (((ι → ι) → ι → ι) → (ι → ι) → ι → ι) → ι . ∀ x6 x7 . x0 (λ x9 : ι → ι . λ x10 : ((ι → ι) → ι) → ι . λ x11 . λ x12 : ι → ι . λ x13 . x13) 0 = Inj0 x6) ⟶ (∀ x4 : (((ι → ι) → ι) → ι) → ι . ∀ x5 . ∀ x6 : (((ι → ι) → ι) → ι) → ι . ∀ x7 . x0 (λ x9 : ι → ι . λ x10 : ((ι → ι) → ι) → ι . λ x11 . λ x12 : ι → ι . λ x13 . 0) (setsum (setsum x5 (x4 (λ x9 : (ι → ι) → ι . x6 (λ x10 : (ι → ι) → ι . 0)))) (Inj0 0)) = x5) ⟶ False (proof)Theorem f02bb.. : ∀ x0 : (ι → ι → (ι → ι → ι) → ι → ι) → ((ι → ι) → ι) → (ι → ι) → ι . ∀ x1 : ((ι → ((ι → ι) → ι → ι) → ι → ι) → ι) → ι → ((ι → ι) → ι → ι → ι) → ι . ∀ x2 : (ι → ι → ι) → ι → ι → ((ι → ι) → ι → ι) → ι . ∀ x3 : (ι → ι) → (ι → ι) → ι . (∀ x4 . ∀ x5 : (ι → ι → ι → ι) → ι . ∀ x6 x7 . x3 (λ x9 . 0) (λ x9 . setsum (Inj1 0) (Inj1 0)) = x4) ⟶ (∀ x4 . ∀ x5 : ((ι → ι) → (ι → ι) → ι → ι) → (ι → ι → ι) → ι . ∀ x6 : ι → ι . ∀ x7 . x3 (λ x9 . x3 (λ x10 . x10) (λ x10 . 0)) (λ x9 . 0) = x3 (λ x9 . setsum 0 0) (λ x9 . Inj0 x7)) ⟶ (∀ x4 x5 . ∀ x6 : ι → ι → ι → ι . ∀ x7 . x2 (λ x9 x10 . x0 (λ x11 x12 . λ x13 : ι → ι → ι . λ x14 . x11) (λ x11 : ι → ι . x11 (Inj1 0)) (λ x11 . 0)) (Inj0 0) x4 (λ x9 : ι → ι . λ x10 . 0) = x0 (λ x9 x10 . λ x11 : ι → ι → ι . λ x12 . Inj1 (x0 (λ x13 x14 . λ x15 : ι → ι → ι . λ x16 . setsum 0 (x1 (λ x17 : ι → ((ι → ι) → ι → ι) → ι → ι . 0) 0 (λ x17 : ι → ι . λ x18 x19 . 0))) (λ x13 : ι → ι . x11 (x1 (λ x14 : ι → ((ι → ι) → ι → ι) → ι → ι . 0) 0 (λ x14 : ι → ι . λ x15 x16 . 0)) (Inj0 0)) (λ x13 . Inj0 x12))) (λ x9 : ι → ι . x6 (setsum (x6 (x1 (λ x10 : ι → ((ι → ι) → ι → ι) → ι → ι . 0) 0 (λ x10 : ι → ι . λ x11 x12 . 0)) (Inj1 0) x5) (x1 (λ x10 : ι → ((ι → ι) → ι → ι) → ι → ι . 0) 0 (λ x10 : ι → ι . λ x11 x12 . x12))) 0 (x9 (Inj1 (Inj1 0)))) (λ x9 . Inj0 (x2 (λ x10 x11 . x1 (λ x12 : ι → ((ι → ι) → ι → ι) → ι → ι . 0) (x2 (λ x12 x13 . 0) 0 0 (λ x12 : ι → ι . λ x13 . 0)) (λ x12 : ι → ι . λ x13 x14 . setsum 0 0)) x7 0 (λ x10 : ι → ι . λ x11 . x11)))) ⟶ (∀ x4 x5 x6 . ∀ x7 : (ι → ι → ι) → (ι → ι → ι) → (ι → ι) → ι . x2 (λ x9 . Inj1) x6 0 (λ x9 : ι → ι . Inj1) = setsum 0 x5) ⟶ (∀ x4 x5 . ∀ x6 : (ι → ι) → ι . ∀ x7 . x1 (λ x9 : ι → ((ι → ι) → ι → ι) → ι → ι . setsum (Inj1 (setsum x5 0)) x7) 0 (λ x9 : ι → ι . λ x10 x11 . x9 0) = x4) ⟶ (∀ x4 . ∀ x5 : ((ι → ι) → ι) → ((ι → ι) → ι → ι) → ι . ∀ x6 . ∀ x7 : (((ι → ι) → ι → ι) → ι) → ι → ι → ι . x1 (λ x9 : ι → ((ι → ι) → ι → ι) → ι → ι . Inj0 0) (x2 (λ x9 x10 . setsum (x2 (λ x11 x12 . x10) (x2 (λ x11 x12 . 0) 0 0 (λ x11 : ι → ι . λ x12 . 0)) (x7 (λ x11 : (ι → ι) → ι → ι . 0) 0 0) (λ x11 : ι → ι . λ x12 . x0 (λ x13 x14 . λ x15 : ι → ι → ι . λ x16 . 0) (λ x13 : ι → ι . 0) (λ x13 . 0))) (Inj1 (Inj0 0))) (x5 (λ x9 : ι → ι . 0) (λ x9 : ι → ι . λ x10 . x7 (λ x11 : (ι → ι) → ι → ι . Inj1 0) (x1 (λ x11 : ι → ((ι → ι) → ι → ι) → ι → ι . 0) 0 (λ x11 : ι → ι . λ x12 x13 . 0)) 0)) x6 (λ x9 : ι → ι . λ x10 . 0)) (λ x9 : ι → ι . λ x10 x11 . x9 0) = setsum (Inj1 (x5 (λ x9 : ι → ι . x2 (λ x10 x11 . x11) (x0 (λ x10 x11 . λ x12 : ι → ι → ι . λ x13 . 0) (λ x10 : ι → ι . 0) (λ x10 . 0)) (x5 (λ x10 : ι → ι . 0) (λ x10 : ι → ι . λ x11 . 0)) (λ x10 : ι → ι . λ x11 . setsum 0 0)) (λ x9 : ι → ι . λ x10 . x1 (λ x11 : ι → ((ι → ι) → ι → ι) → ι → ι . x10) (x3 (λ x11 . 0) (λ x11 . 0)) (λ x11 : ι → ι . λ x12 x13 . Inj0 0)))) 0) ⟶ (∀ x4 : (ι → (ι → ι) → ι) → ι . ∀ x5 x6 . ∀ x7 : ((ι → ι → ι) → (ι → ι) → ι → ι) → ι . x0 (λ x9 x10 . λ x11 : ι → ι → ι . λ x12 . setsum 0 (x2 (λ x13 x14 . x14) x12 0 (λ x13 : ι → ι . λ x14 . Inj1 0))) (λ x9 : ι → ι . Inj0 x5) (λ x9 . 0) = Inj1 (x7 (λ x9 : ι → ι → ι . λ x10 : ι → ι . λ x11 . Inj1 (setsum x11 x11)))) ⟶ (∀ x4 : ι → ι → ι . ∀ x5 : (ι → (ι → ι) → ι → ι) → ι . ∀ x6 . ∀ x7 : ι → ((ι → ι) → ι) → ι . x0 (λ x9 x10 . λ x11 : ι → ι → ι . λ x12 . x11 (Inj1 (x2 (λ x13 x14 . setsum 0 0) (x3 (λ x13 . 0) (λ x13 . 0)) 0 (λ x13 : ι → ι . λ x14 . x2 (λ x15 x16 . 0) 0 0 (λ x15 : ι → ι . λ x16 . 0)))) (x2 (λ x13 x14 . x2 (λ x15 x16 . x0 (λ x17 x18 . λ x19 : ι → ι → ι . λ x20 . 0) (λ x17 : ι → ι . 0) (λ x17 . 0)) 0 0 (λ x15 : ι → ι . λ x16 . Inj1 0)) 0 (Inj0 (x1 (λ x13 : ι → ((ι → ι) → ι → ι) → ι → ι . 0) 0 (λ x13 : ι → ι . λ x14 x15 . 0))) (λ x13 : ι → ι . λ x14 . setsum x12 (setsum 0 0)))) (λ x9 : ι → ι . setsum (x2 (λ x10 x11 . x2 (λ x12 x13 . Inj0 0) x10 (x9 0) (λ x12 : ι → ι . λ x13 . Inj0 0)) x6 (Inj0 (x1 (λ x10 : ι → ((ι → ι) → ι → ι) → ι → ι . 0) 0 (λ x10 : ι → ι . λ x11 x12 . 0))) (λ x10 : ι → ι . λ x11 . x9 (Inj0 0))) (x9 (setsum (x3 (λ x10 . 0) (λ x10 . 0)) (setsum 0 0)))) (λ x9 . Inj0 (x7 0 (λ x10 : ι → ι . x6))) = setsum (Inj0 (x5 (λ x9 . λ x10 : ι → ι . λ x11 . x7 (x2 (λ x12 x13 . 0) 0 0 (λ x12 : ι → ι . λ x13 . 0)) (λ x12 : ι → ι . x0 (λ x13 x14 . λ x15 : ι → ι → ι . λ x16 . 0) (λ x13 : ι → ι . 0) (λ x13 . 0))))) (setsum (x3 (λ x9 . 0) (λ x9 . setsum x6 (Inj1 0))) 0)) ⟶ False (proof)Theorem 1cbc7.. : ∀ x0 : (((ι → (ι → ι) → ι) → ((ι → ι) → ι → ι) → ι) → ι) → ι → ι → ι → ι → ι . ∀ x1 : (ι → ι → ι) → (((ι → ι) → ι) → ι → ι → ι) → ι . ∀ x2 : (ι → (((ι → ι) → ι → ι) → ι) → ι → (ι → ι) → ι → ι) → (ι → ι) → (((ι → ι) → ι → ι) → (ι → ι) → ι → ι) → ι . ∀ x3 : ((ι → ι) → ι → ι) → ((ι → (ι → ι) → ι → ι) → ι) → ι . (∀ x4 . ∀ x5 : ι → ι . ∀ x6 : ι → ι → ι → ι . ∀ x7 : (ι → ι) → ι . x3 (λ x9 : ι → ι . λ x10 . setsum (x2 (λ x11 . λ x12 : ((ι → ι) → ι → ι) → ι . λ x13 . λ x14 : ι → ι . λ x15 . 0) (λ x11 . Inj1 (Inj0 0)) (λ x11 : (ι → ι) → ι → ι . λ x12 : ι → ι . λ x13 . 0)) 0) (λ x9 : ι → (ι → ι) → ι → ι . 0) = Inj0 0) ⟶ (∀ x4 x5 . ∀ x6 : ι → ι → ι → ι → ι . ∀ x7 . x3 (λ x9 : ι → ι . λ x10 . x3 (λ x11 : ι → ι . λ x12 . setsum (x2 (λ x13 . λ x14 : ((ι → ι) → ι → ι) → ι . λ x15 . λ x16 : ι → ι . λ x17 . x2 (λ x18 . λ x19 : ((ι → ι) → ι → ι) → ι . λ x20 . λ x21 : ι → ι . λ x22 . 0) (λ x18 . 0) (λ x18 : (ι → ι) → ι → ι . λ x19 : ι → ι . λ x20 . 0)) (λ x13 . Inj1 0) (λ x13 : (ι → ι) → ι → ι . λ x14 : ι → ι . λ x15 . setsum 0 0)) (x0 (λ x13 : (ι → (ι → ι) → ι) → ((ι → ι) → ι → ι) → ι . x2 (λ x14 . λ x15 : ((ι → ι) → ι → ι) → ι . λ x16 . λ x17 : ι → ι . λ x18 . 0) (λ x14 . 0) (λ x14 : (ι → ι) → ι → ι . λ x15 : ι → ι . λ x16 . 0)) (setsum 0 0) (x2 (λ x13 . λ x14 : ((ι → ι) → ι → ι) → ι . λ x15 . λ x16 : ι → ι . λ x17 . 0) (λ x13 . 0) (λ x13 : (ι → ι) → ι → ι . λ x14 : ι → ι . λ x15 . 0)) 0 0)) (λ x11 : ι → (ι → ι) → ι → ι . x9 (x0 (λ x12 : (ι → (ι → ι) → ι) → ((ι → ι) → ι → ι) → ι . 0) (x1 (λ x12 x13 . 0) (λ x12 : (ι → ι) → ι . λ x13 x14 . 0)) (x3 (λ x12 : ι → ι . λ x13 . 0) (λ x12 : ι → (ι → ι) → ι → ι . 0)) (x2 (λ x12 . λ x13 : ((ι → ι) → ι → ι) → ι . λ x14 . λ x15 : ι → ι . λ x16 . 0) (λ x12 . 0) (λ x12 : (ι → ι) → ι → ι . λ x13 : ι → ι . λ x14 . 0)) (Inj1 0)))) (λ x9 : ι → (ι → ι) → ι → ι . 0) = setsum (Inj0 (Inj0 (setsum 0 x7))) (x2 (λ x9 . λ x10 : ((ι → ι) → ι → ι) → ι . λ x11 . λ x12 : ι → ι . λ x13 . setsum (setsum x11 (setsum 0 0)) (x1 (λ x14 x15 . x15) (λ x14 : (ι → ι) → ι . λ x15 x16 . x14 (λ x17 . 0)))) (λ x9 . Inj0 (Inj0 x7)) (λ x9 : (ι → ι) → ι → ι . λ x10 : ι → ι . λ x11 . x1 (λ x12 x13 . setsum (Inj1 0) (x0 (λ x14 : (ι → (ι → ι) → ι) → ((ι → ι) → ι → ι) → ι . 0) 0 0 0 0)) (λ x12 : (ι → ι) → ι . λ x13 x14 . x14)))) ⟶ (∀ x4 . ∀ x5 : (((ι → ι) → ι) → (ι → ι) → ι) → ι . ∀ x6 : ι → ι . ∀ x7 : ((ι → ι) → ι) → ι . x2 (λ x9 . λ x10 : ((ι → ι) → ι → ι) → ι . λ x11 . λ x12 : ι → ι . λ x13 . x2 (λ x14 . λ x15 : ((ι → ι) → ι → ι) → ι . λ x16 . λ x17 : ι → ι . λ x18 . 0) (x0 (λ x14 : (ι → (ι → ι) → ι) → ((ι → ι) → ι → ι) → ι . setsum 0 0) x11 x11 (setsum (setsum 0 0) 0)) (λ x14 : (ι → ι) → ι → ι . λ x15 : ι → ι . λ x16 . x15 (x14 (λ x17 . 0) 0))) (λ x9 . x6 (Inj0 0)) (λ x9 : (ι → ι) → ι → ι . λ x10 : ι → ι . λ x11 . x10 (setsum 0 (x7 (λ x12 : ι → ι . Inj1 0)))) = x2 (λ x9 . λ x10 : ((ι → ι) → ι → ι) → ι . λ x11 . λ x12 : ι → ι . λ x13 . Inj1 0) (λ x9 . setsum (x0 (λ x10 : (ι → (ι → ι) → ι) → ((ι → ι) → ι → ι) → ι . setsum 0 (x3 (λ x11 : ι → ι . λ x12 . 0) (λ x11 : ι → (ι → ι) → ι → ι . 0))) 0 0 (x3 (λ x10 : ι → ι . λ x11 . x7 (λ x12 : ι → ι . 0)) (λ x10 : ι → (ι → ι) → ι → ι . x6 0)) (x6 0)) (x2 (λ x10 . λ x11 : ((ι → ι) → ι → ι) → ι . λ x12 . λ x13 : ι → ι . λ x14 . 0) (x0 (λ x10 : (ι → (ι → ι) → ι) → ((ι → ι) → ι → ι) → ι . x0 (λ x11 : (ι → (ι → ι) → ι) → ((ι → ι) → ι → ι) → ι . 0) 0 0 0 0) (x6 0) (setsum 0 0) (x6 0)) (λ x10 : (ι → ι) → ι → ι . λ x11 : ι → ι . x11))) (λ x9 : (ι → ι) → ι → ι . λ x10 : ι → ι . Inj1)) ⟶ (∀ x4 x5 : ι → ι . ∀ x6 . ∀ x7 : (((ι → ι) → ι) → ι) → ι . x2 (λ x9 . λ x10 : ((ι → ι) → ι → ι) → ι . λ x11 . λ x12 : ι → ι . λ x13 . 0) (λ x9 . setsum 0 x6) (λ x9 : (ι → ι) → ι → ι . λ x10 : ι → ι . λ x11 . setsum 0 (setsum (x3 (λ x12 : ι → ι . λ x13 . 0) (λ x12 : ι → (ι → ι) → ι → ι . 0)) 0)) = setsum (x0 (λ x9 : (ι → (ι → ι) → ι) → ((ι → ι) → ι → ι) → ι . x5 (x5 (x1 (λ x10 x11 . 0) (λ x10 : (ι → ι) → ι . λ x11 x12 . 0)))) 0 (Inj0 (x4 x6)) (x1 (λ x9 x10 . 0) (λ x9 : (ι → ι) → ι . λ x10 x11 . x2 (λ x12 . λ x13 : ((ι → ι) → ι → ι) → ι . λ x14 . λ x15 : ι → ι . λ x16 . x15 0) (λ x12 . x1 (λ x13 x14 . 0) (λ x13 : (ι → ι) → ι . λ x14 x15 . 0)) (λ x12 : (ι → ι) → ι → ι . λ x13 : ι → ι . λ x14 . x14))) (x5 0)) (Inj1 (x7 (λ x9 : (ι → ι) → ι . x1 (λ x10 x11 . x3 (λ x12 : ι → ι . λ x13 . 0) (λ x12 : ι → (ι → ι) → ι → ι . 0)) (λ x10 : (ι → ι) → ι . λ x11 x12 . x0 (λ x13 : (ι → (ι → ι) → ι) → ((ι → ι) → ι → ι) → ι . 0) 0 0 0 0))))) ⟶ (∀ x4 : ι → (ι → ι → ι) → ι . ∀ x5 : ι → (ι → ι → ι) → (ι → ι) → ι → ι . ∀ x6 x7 . x1 (λ x9 x10 . x10) (λ x9 : (ι → ι) → ι . λ x10 x11 . 0) = x5 (x1 (λ x9 x10 . x0 (λ x11 : (ι → (ι → ι) → ι) → ((ι → ι) → ι → ι) → ι . x9) (Inj1 (Inj1 0)) (x1 (λ x11 x12 . x9) (λ x11 : (ι → ι) → ι . λ x12 x13 . Inj1 0)) (setsum (x0 (λ x11 : (ι → (ι → ι) → ι) → ((ι → ι) → ι → ι) → ι . 0) 0 0 0 0) x7) (Inj1 0)) (λ x9 : (ι → ι) → ι . λ x10 x11 . Inj0 x7)) (λ x9 x10 . Inj0 (x0 (λ x11 : (ι → (ι → ι) → ι) → ((ι → ι) → ι → ι) → ι . 0) (x3 (λ x11 : ι → ι . λ x12 . x2 (λ x13 . λ x14 : ((ι → ι) → ι → ι) → ι . λ x15 . λ x16 : ι → ι . λ x17 . 0) (λ x13 . 0) (λ x13 : (ι → ι) → ι → ι . λ x14 : ι → ι . λ x15 . 0)) (λ x11 : ι → (ι → ι) → ι → ι . 0)) (x1 (λ x11 x12 . x11) (λ x11 : (ι → ι) → ι . λ x12 x13 . 0)) 0 (Inj1 0))) (λ x9 . Inj1 (setsum (Inj1 (x5 0 (λ x10 x11 . 0) (λ x10 . 0) 0)) x6)) (x4 (x2 (λ x9 . λ x10 : ((ι → ι) → ι → ι) → ι . λ x11 . λ x12 : ι → ι . λ x13 . x13) (λ x9 . x2 (λ x10 . λ x11 : ((ι → ι) → ι → ι) → ι . λ x12 . λ x13 : ι → ι . λ x14 . x1 (λ x15 x16 . 0) (λ x15 : (ι → ι) → ι . λ x16 x17 . 0)) (λ x10 . x1 (λ x11 x12 . 0) (λ x11 : (ι → ι) → ι . λ x12 x13 . 0)) (λ x10 : (ι → ι) → ι → ι . λ x11 : ι → ι . λ x12 . 0)) (λ x9 : (ι → ι) → ι → ι . λ x10 : ι → ι . λ x11 . x1 (λ x12 x13 . x13) (λ x12 : (ι → ι) → ι . λ x13 x14 . setsum 0 0))) (λ x9 x10 . x10))) ⟶ (∀ x4 . ∀ x5 : (ι → ι) → ι . ∀ x6 : ι → ((ι → ι) → ι) → ι . ∀ x7 : (ι → ι → ι) → (ι → ι) → ι . x1 (λ x9 x10 . x6 (x7 (λ x11 x12 . 0) (λ x11 . x9)) (λ x11 : ι → ι . Inj0 (setsum x10 (x3 (λ x12 : ι → ι . λ x13 . 0) (λ x12 : ι → (ι → ι) → ι → ι . 0))))) (λ x9 : (ι → ι) → ι . λ x10 x11 . setsum (x9 (λ x12 . x9 (λ x13 . x1 (λ x14 x15 . 0) (λ x14 : (ι → ι) → ι . λ x15 x16 . 0)))) (x2 (λ x12 . λ x13 : ((ι → ι) → ι → ι) → ι . λ x14 . λ x15 : ι → ι . λ x16 . 0) (λ x12 . x3 (λ x13 : ι → ι . λ x14 . x13 0) (λ x13 : ι → (ι → ι) → ι → ι . x0 (λ x14 : (ι → (ι → ι) → ι) → ((ι → ι) → ι → ι) → ι . 0) 0 0 0 0)) (λ x12 : (ι → ι) → ι → ι . λ x13 : ι → ι . λ x14 . x1 (λ x15 x16 . setsum 0 0) (λ x15 : (ι → ι) → ι . λ x16 x17 . x17)))) = x6 (setsum (x2 (λ x9 . λ x10 : ((ι → ι) → ι → ι) → ι . λ x11 . λ x12 : ι → ι . λ x13 . x3 (λ x14 : ι → ι . λ x15 . Inj1 0) (λ x14 : ι → (ι → ι) → ι → ι . x1 (λ x15 x16 . 0) (λ x15 : (ι → ι) → ι . λ x16 x17 . 0))) (λ x9 . Inj1 0) (λ x9 : (ι → ι) → ι → ι . λ x10 : ι → ι . λ x11 . x3 (λ x12 : ι → ι . λ x13 . x2 (λ x14 . λ x15 : ((ι → ι) → ι → ι) → ι . λ x16 . λ x17 : ι → ι . λ x18 . 0) (λ x14 . 0) (λ x14 : (ι → ι) → ι → ι . λ x15 : ι → ι . λ x16 . 0)) (λ x12 : ι → (ι → ι) → ι → ι . setsum 0 0))) (Inj1 (setsum (setsum 0 0) (x5 (λ x9 . 0))))) (λ x9 : ι → ι . setsum (x2 (λ x10 . λ x11 : ((ι → ι) → ι → ι) → ι . λ x12 . λ x13 : ι → ι . λ x14 . x1 (λ x15 x16 . Inj0 0) (λ x15 : (ι → ι) → ι . λ x16 x17 . setsum 0 0)) (λ x10 . 0) (λ x10 : (ι → ι) → ι → ι . λ x11 : ι → ι . λ x12 . x2 (λ x13 . λ x14 : ((ι → ι) → ι → ι) → ι . λ x15 . λ x16 : ι → ι . λ x17 . x16 0) (λ x13 . x1 (λ x14 x15 . 0) (λ x14 : (ι → ι) → ι . λ x15 x16 . 0)) (λ x13 : (ι → ι) → ι → ι . λ x14 : ι → ι . λ x15 . 0))) 0)) ⟶ (∀ x4 x5 x6 x7 . x0 (λ x9 : (ι → (ι → ι) → ι) → ((ι → ι) → ι → ι) → ι . 0) 0 0 0 x5 = Inj0 x7) ⟶ (∀ x4 : (ι → (ι → ι) → ι → ι) → (ι → ι) → (ι → ι) → ι → ι . ∀ x5 : (((ι → ι) → ι) → ι) → ι . ∀ x6 : ((ι → ι → ι) → ι → ι) → ι . ∀ x7 . x0 (λ x9 : (ι → (ι → ι) → ι) → ((ι → ι) → ι → ι) → ι . x2 (λ x10 . λ x11 : ((ι → ι) → ι → ι) → ι . λ x12 . λ x13 : ι → ι . λ x14 . x13 (x13 (x3 (λ x15 : ι → ι . λ x16 . 0) (λ x15 : ι → (ι → ι) → ι → ι . 0)))) (λ x10 . setsum 0 0) (λ x10 : (ι → ι) → ι → ι . λ x11 : ι → ι . λ x12 . x3 (λ x13 : ι → ι . λ x14 . setsum x14 x14) (λ x13 : ι → (ι → ι) → ι → ι . x11 (setsum 0 0)))) 0 0 (x2 (λ x9 . λ x10 : ((ι → ι) → ι → ι) → ι . λ x11 . λ x12 : ι → ι . λ x13 . Inj1 0) (λ x9 . setsum (Inj0 (Inj0 0)) (x5 (λ x10 : (ι → ι) → ι . setsum 0 0))) (λ x9 : (ι → ι) → ι → ι . λ x10 : ι → ι . λ x11 . x0 (λ x12 : (ι → (ι → ι) → ι) → ((ι → ι) → ι → ι) → ι . x2 (λ x13 . λ x14 : ((ι → ι) → ι → ι) → ι . λ x15 . λ x16 : ι → ι . λ x17 . Inj0 0) (λ x13 . Inj0 0) (λ x13 : (ι → ι) → ι → ι . λ x14 : ι → ι . λ x15 . 0)) 0 (x2 (λ x12 . λ x13 : ((ι → ι) → ι → ι) → ι . λ x14 . λ x15 : ι → ι . λ x16 . x1 (λ x17 x18 . 0) (λ x17 : (ι → ι) → ι . λ x18 x19 . 0)) (λ x12 . x10 0) (λ x12 : (ι → ι) → ι → ι . λ x13 : ι → ι . λ x14 . Inj1 0)) (x3 (λ x12 : ι → ι . λ x13 . 0) (λ x12 : ι → (ι → ι) → ι → ι . x10 0)) (x10 (setsum 0 0)))) (setsum (Inj1 (x5 (λ x9 : (ι → ι) → ι . x1 (λ x10 x11 . 0) (λ x10 : (ι → ι) → ι . λ x11 x12 . 0)))) (x1 (λ x9 x10 . setsum (x2 (λ x11 . λ x12 : ((ι → ι) → ι → ι) → ι . λ x13 . λ x14 : ι → ι . λ x15 . 0) (λ x11 . 0) (λ x11 : (ι → ι) → ι → ι . λ x12 : ι → ι . λ x13 . 0)) (x1 (λ x11 x12 . 0) (λ x11 : (ι → ι) → ι . λ x12 x13 . 0))) (λ x9 : (ι → ι) → ι . λ x10 x11 . x1 (λ x12 x13 . x0 (λ x14 : (ι → (ι → ι) → ι) → ((ι → ι) → ι → ι) → ι . 0) 0 0 0 0) (λ x12 : (ι → ι) → ι . λ x13 x14 . 0)))) = Inj0 (Inj0 (Inj0 0))) ⟶ False (proof)Theorem aefa3.. : ∀ x0 : (ι → ι) → (ι → ι) → ι . ∀ x1 x2 : (ι → ι) → ι → ι . ∀ x3 : (((((ι → ι) → ι) → (ι → ι) → ι → ι) → ((ι → ι) → ι → ι) → ι) → ι) → ι → ι . (∀ x4 : ι → ι → ι . ∀ x5 : (ι → ι → ι → ι) → (ι → ι) → ι → ι → ι . ∀ x6 : ι → ι → ι . ∀ x7 . x3 (λ x9 : (((ι → ι) → ι) → (ι → ι) → ι → ι) → ((ι → ι) → ι → ι) → ι . x9 (λ x10 : (ι → ι) → ι . λ x11 : ι → ι . λ x12 . 0) (λ x10 : ι → ι . λ x11 . 0)) 0 = x5 (λ x9 x10 x11 . 0) (λ x9 . x3 (λ x10 : (((ι → ι) → ι) → (ι → ι) → ι → ι) → ((ι → ι) → ι → ι) → ι . Inj1 (setsum 0 (Inj0 0))) (x6 (x1 (λ x10 . x3 (λ x11 : (((ι → ι) → ι) → (ι → ι) → ι → ι) → ((ι → ι) → ι → ι) → ι . 0) 0) (x1 (λ x10 . 0) 0)) (setsum (x3 (λ x10 : (((ι → ι) → ι) → (ι → ι) → ι → ι) → ((ι → ι) → ι → ι) → ι . 0) 0) 0))) 0 (x3 (λ x9 : (((ι → ι) → ι) → (ι → ι) → ι → ι) → ((ι → ι) → ι → ι) → ι . 0) 0)) ⟶ (∀ x4 x5 : ι → ι . ∀ x6 : ((ι → ι → ι) → (ι → ι) → ι → ι) → (ι → ι) → ι . ∀ x7 . x3 (λ x9 : (((ι → ι) → ι) → (ι → ι) → ι → ι) → ((ι → ι) → ι → ι) → ι . x1 (λ x10 . 0) (x1 (λ x10 . Inj0 0) x7)) (x5 (x6 (λ x9 : ι → ι → ι . λ x10 : ι → ι . λ x11 . x7) (setsum 0))) = setsum (x4 (Inj0 (setsum (x6 (λ x9 : ι → ι → ι . λ x10 : ι → ι . λ x11 . 0) (λ x9 . 0)) (x1 (λ x9 . 0) 0)))) (Inj1 (Inj0 (x4 (x6 (λ x9 : ι → ι → ι . λ x10 : ι → ι . λ x11 . 0) (λ x9 . 0)))))) ⟶ (∀ x4 x5 x6 . ∀ x7 : ι → (ι → ι → ι) → ι . x2 (λ x9 . setsum (x0 (λ x10 . x3 (λ x11 : (((ι → ι) → ι) → (ι → ι) → ι → ι) → ((ι → ι) → ι → ι) → ι . x11 (λ x12 : (ι → ι) → ι . λ x13 : ι → ι . λ x14 . 0) (λ x12 : ι → ι . λ x13 . 0)) (Inj1 0)) (λ x10 . Inj1 0)) (x1 (λ x10 . x10) x9)) x4 = Inj1 (x3 (λ x9 : (((ι → ι) → ι) → (ι → ι) → ι → ι) → ((ι → ι) → ι → ι) → ι . 0) (setsum (x3 (λ x9 : (((ι → ι) → ι) → (ι → ι) → ι → ι) → ((ι → ι) → ι → ι) → ι . 0) (x1 (λ x9 . 0) 0)) x5))) ⟶ (∀ x4 x5 x6 x7 . x2 (λ x9 . x2 (λ x10 . x7) (Inj0 (x1 (λ x10 . setsum 0 0) x9))) (setsum 0 0) = Inj1 x6) ⟶ (∀ x4 . ∀ x5 : (((ι → ι) → ι) → ι) → ι . ∀ x6 . ∀ x7 : (ι → ι) → ι . x1 (λ x9 . x2 (λ x10 . x9) (Inj0 (x7 (λ x10 . setsum 0 0)))) 0 = x2 (λ x9 . x2 (λ x10 . x9) 0) x4) ⟶ (∀ x4 x5 . ∀ x6 : (((ι → ι) → ι) → (ι → ι) → ι → ι) → ((ι → ι) → ι) → (ι → ι) → ι . ∀ x7 : ι → ι . x1 (λ x9 . x0 (λ x10 . x6 (λ x11 : (ι → ι) → ι . λ x12 : ι → ι . λ x13 . x10) (λ x11 : ι → ι . x7 0) (λ x11 . setsum 0 (x3 (λ x12 : (((ι → ι) → ι) → (ι → ι) → ι → ι) → ((ι → ι) → ι → ι) → ι . 0) 0))) (λ x10 . x2 (λ x11 . x7 0) (x2 (λ x11 . x11) (x0 (λ x11 . 0) (λ x11 . 0))))) 0 = setsum 0 0) ⟶ (∀ x4 . ∀ x5 : ι → ι → ι . ∀ x6 x7 . x0 (λ x9 . Inj1 (x3 (λ x10 : (((ι → ι) → ι) → (ι → ι) → ι → ι) → ((ι → ι) → ι → ι) → ι . x6) 0)) (λ x9 . setsum x6 (x2 (λ x10 . setsum 0 x9) 0)) = Inj1 0) ⟶ (∀ x4 . ∀ x5 : ι → (ι → ι → ι) → ι → ι → ι . ∀ x6 : (ι → ι) → ι . ∀ x7 : ((ι → ι) → (ι → ι) → ι → ι) → ι . x0 (λ x9 . x9) (λ x9 . x7 (λ x10 x11 : ι → ι . λ x12 . setsum x12 (x2 (λ x13 . x3 (λ x14 : (((ι → ι) → ι) → (ι → ι) → ι → ι) → ((ι → ι) → ι → ι) → ι . 0) 0) (Inj0 0)))) = x7 (λ x9 x10 : ι → ι . λ x11 . x10 (x3 (λ x12 : (((ι → ι) → ι) → (ι → ι) → ι → ι) → ((ι → ι) → ι → ι) → ι . 0) (Inj0 (x7 (λ x12 x13 : ι → ι . λ x14 . 0)))))) ⟶ False (proof)Theorem 22432.. : ∀ x0 : (((ι → ι) → ι) → ι) → ((ι → ι) → ι) → (((ι → ι) → ι) → ι) → ι . ∀ x1 : (ι → ι) → (ι → ι) → ι → ι → (ι → ι) → ι . ∀ x2 : ((ι → (ι → ι) → ι) → (ι → ι) → ((ι → ι) → ι → ι) → ι) → ι → (ι → (ι → ι) → ι → ι) → ((ι → ι) → ι → ι) → ι → ι . ∀ x3 : (((((ι → ι) → ι → ι) → ι) → ((ι → ι) → ι → ι) → ι) → ι) → (ι → ι → ι → ι → ι) → ι → ι . (∀ x4 . ∀ x5 : (ι → ι) → ι . ∀ x6 : ι → (ι → ι) → ι . ∀ x7 : ((ι → ι) → ι → ι → ι) → (ι → ι → ι) → ι → ι . x3 (λ x9 : (((ι → ι) → ι → ι) → ι) → ((ι → ι) → ι → ι) → ι . setsum 0 (setsum 0 0)) (λ x9 x10 x11 x12 . x0 (λ x13 : (ι → ι) → ι . x13 (λ x14 . 0)) (λ x13 : ι → ι . 0) (λ x13 : (ι → ι) → ι . x12)) (x3 (λ x9 : (((ι → ι) → ι → ι) → ι) → ((ι → ι) → ι → ι) → ι . 0) (λ x9 x10 x11 x12 . x9) 0) = setsum (x5 (λ x9 . 0)) x4) ⟶ (∀ x4 . ∀ x5 : (ι → ι) → ι → (ι → ι) → ι . ∀ x6 : ι → ι . ∀ x7 . x3 (λ x9 : (((ι → ι) → ι → ι) → ι) → ((ι → ι) → ι → ι) → ι . 0) (λ x9 x10 x11 x12 . x10) (setsum (Inj1 (x5 (λ x9 . x1 (λ x10 . 0) (λ x10 . 0) 0 0 (λ x10 . 0)) (x1 (λ x9 . 0) (λ x9 . 0) 0 0 (λ x9 . 0)) (λ x9 . 0))) (setsum (x6 (Inj1 0)) (x0 (λ x9 : (ι → ι) → ι . setsum 0 0) (λ x9 : ι → ι . 0) (λ x9 : (ι → ι) → ι . setsum 0 0)))) = setsum (setsum x4 (x6 (Inj0 (x5 (λ x9 . 0) 0 (λ x9 . 0))))) (Inj0 0)) ⟶ (∀ x4 . ∀ x5 x6 : ι → ι . ∀ x7 . x2 (λ x9 : ι → (ι → ι) → ι . λ x10 : ι → ι . λ x11 : (ι → ι) → ι → ι . Inj1 (setsum (x9 (x9 0 (λ x12 . 0)) (λ x12 . x9 0 (λ x13 . 0))) (Inj1 (x2 (λ x12 : ι → (ι → ι) → ι . λ x13 : ι → ι . λ x14 : (ι → ι) → ι → ι . 0) 0 (λ x12 . λ x13 : ι → ι . λ x14 . 0) (λ x12 : ι → ι . λ x13 . 0) 0)))) 0 (λ x9 . λ x10 : ι → ι . λ x11 . 0) (λ x9 : ι → ι . λ x10 . x2 (λ x11 : ι → (ι → ι) → ι . λ x12 : ι → ι . λ x13 : (ι → ι) → ι → ι . 0) (Inj1 0) (λ x11 . λ x12 : ι → ι . λ x13 . setsum x11 (x12 x11)) (λ x11 : ι → ι . λ x12 . x2 (λ x13 : ι → (ι → ι) → ι . λ x14 : ι → ι . λ x15 : (ι → ι) → ι → ι . Inj1 (Inj1 0)) (x11 (setsum 0 0)) (λ x13 . λ x14 : ι → ι . λ x15 . x2 (λ x16 : ι → (ι → ι) → ι . λ x17 : ι → ι . λ x18 : (ι → ι) → ι → ι . x0 (λ x19 : (ι → ι) → ι . 0) (λ x19 : ι → ι . 0) (λ x19 : (ι → ι) → ι . 0)) (Inj0 0) (λ x16 . λ x17 : ι → ι . λ x18 . setsum 0 0) (λ x16 : ι → ι . λ x17 . x16 0) 0) (λ x13 : ι → ι . λ x14 . x12) 0) (Inj0 0)) x7 = Inj1 0) ⟶ (∀ x4 : ((ι → ι → ι) → ι) → ι . ∀ x5 x6 x7 . x2 (λ x9 : ι → (ι → ι) → ι . λ x10 : ι → ι . λ x11 : (ι → ι) → ι → ι . 0) (x4 (λ x9 : ι → ι → ι . x1 (λ x10 . x7) (λ x10 . x0 (λ x11 : (ι → ι) → ι . 0) (λ x11 : ι → ι . Inj1 0) (λ x11 : (ι → ι) → ι . setsum 0 0)) (setsum 0 0) (x1 (λ x10 . x7) (λ x10 . x0 (λ x11 : (ι → ι) → ι . 0) (λ x11 : ι → ι . 0) (λ x11 : (ι → ι) → ι . 0)) (x3 (λ x10 : (((ι → ι) → ι → ι) → ι) → ((ι → ι) → ι → ι) → ι . 0) (λ x10 x11 x12 x13 . 0) 0) (Inj0 0) (λ x10 . 0)) (λ x10 . x10))) (λ x9 . λ x10 : ι → ι . λ x11 . setsum 0 (x0 (λ x12 : (ι → ι) → ι . x12 (λ x13 . 0)) (λ x12 : ι → ι . setsum (setsum 0 0) (x12 0)) (λ x12 : (ι → ι) → ι . Inj1 x11))) (λ x9 : ι → ι . λ x10 . x3 (λ x11 : (((ι → ι) → ι → ι) → ι) → ((ι → ι) → ι → ι) → ι . Inj1 0) (λ x11 x12 x13 x14 . x14) (Inj0 x6)) (Inj0 (setsum x7 x5)) = setsum (Inj0 0) x6) ⟶ (∀ x4 : ι → ι . ∀ x5 : (ι → ι) → ι . ∀ x6 x7 : ι → ι . x1 (λ x9 . Inj1 0) (λ x9 . x0 (λ x10 : (ι → ι) → ι . 0) (λ x10 : ι → ι . setsum (x6 0) (x3 (λ x11 : (((ι → ι) → ι → ι) → ι) → ((ι → ι) → ι → ι) → ι . x7 0) (λ x11 x12 x13 x14 . 0) (Inj0 0))) (λ x10 : (ι → ι) → ι . x9)) (x6 0) 0 (λ x9 . x2 (λ x10 : ι → (ι → ι) → ι . λ x11 : ι → ι . λ x12 : (ι → ι) → ι → ι . x1 (λ x13 . x1 (λ x14 . x14) (λ x14 . x2 (λ x15 : ι → (ι → ι) → ι . λ x16 : ι → ι . λ x17 : (ι → ι) → ι → ι . 0) 0 (λ x15 . λ x16 : ι → ι . λ x17 . 0) (λ x15 : ι → ι . λ x16 . 0) 0) x13 (setsum 0 0) (λ x14 . x1 (λ x15 . 0) (λ x15 . 0) 0 0 (λ x15 . 0))) (λ x13 . x2 (λ x14 : ι → (ι → ι) → ι . λ x15 : ι → ι . λ x16 : (ι → ι) → ι → ι . 0) (x0 (λ x14 : (ι → ι) → ι . 0) (λ x14 : ι → ι . 0) (λ x14 : (ι → ι) → ι . 0)) (λ x14 . λ x15 : ι → ι . λ x16 . Inj0 0) (λ x14 : ι → ι . λ x15 . x12 (λ x16 . 0) 0) 0) (x0 (λ x13 : (ι → ι) → ι . x1 (λ x14 . 0) (λ x14 . 0) 0 0 (λ x14 . 0)) (λ x13 : ι → ι . x12 (λ x14 . 0) 0) (λ x13 : (ι → ι) → ι . x1 (λ x14 . 0) (λ x14 . 0) 0 0 (λ x14 . 0))) (setsum 0 0) (λ x13 . 0)) x9 (λ x10 . λ x11 : ι → ι . λ x12 . x9) (λ x10 : ι → ι . λ x11 . x2 (λ x12 : ι → (ι → ι) → ι . λ x13 : ι → ι . λ x14 : (ι → ι) → ι → ι . x0 (λ x15 : (ι → ι) → ι . x2 (λ x16 : ι → (ι → ι) → ι . λ x17 : ι → ι . λ x18 : (ι → ι) → ι → ι . 0) 0 (λ x16 . λ x17 : ι → ι . λ x18 . 0) (λ x16 : ι → ι . λ x17 . 0) 0) (λ x15 : ι → ι . x2 (λ x16 : ι → (ι → ι) → ι . λ x17 : ι → ι . λ x18 : (ι → ι) → ι → ι . 0) 0 (λ x16 . λ x17 : ι → ι . λ x18 . 0) (λ x16 : ι → ι . λ x17 . 0) 0) (λ x15 : (ι → ι) → ι . 0)) 0 (λ x12 . λ x13 : ι → ι . λ x14 . setsum x14 (setsum 0 0)) (λ x12 : ι → ι . λ x13 . Inj1 (setsum 0 0)) (x10 0)) x9) = x6 (x1 (λ x9 . x0 (λ x10 : (ι → ι) → ι . x0 (λ x11 : (ι → ι) → ι . x1 (λ x12 . 0) (λ x12 . 0) 0 0 (λ x12 . 0)) (λ x11 : ι → ι . 0) (λ x11 : (ι → ι) → ι . Inj1 0)) (λ x10 : ι → ι . Inj1 (x7 0)) (λ x10 : (ι → ι) → ι . x10 (λ x11 . x2 (λ x12 : ι → (ι → ι) → ι . λ x13 : ι → ι . λ x14 : (ι → ι) → ι → ι . 0) 0 (λ x12 . λ x13 : ι → ι . λ x14 . 0) (λ x12 : ι → ι . λ x13 . 0) 0))) (λ x9 . x0 (λ x10 : (ι → ι) → ι . Inj1 0) (λ x10 : ι → ι . x7 (setsum 0 0)) (λ x10 : (ι → ι) → ι . 0)) (x5 (λ x9 . x3 (λ x10 : (((ι → ι) → ι → ι) → ι) → ((ι → ι) → ι → ι) → ι . 0) (λ x10 x11 x12 x13 . 0) (x5 (λ x10 . 0)))) (x4 0) (λ x9 . x5 (λ x10 . x9)))) ⟶ (∀ x4 : ι → ι . ∀ x5 . ∀ x6 : ι → ι . ∀ x7 : (ι → ι) → ι . x1 (λ x9 . setsum (x2 (λ x10 : ι → (ι → ι) → ι . λ x11 : ι → ι . λ x12 : (ι → ι) → ι → ι . x12 (λ x13 . x12 (λ x14 . 0) 0) (Inj0 0)) 0 (λ x10 . λ x11 : ι → ι . λ x12 . 0) (λ x10 : ι → ι . λ x11 . 0) (x6 (setsum 0 0))) 0) (λ x9 . x9) (x2 (λ x9 : ι → (ι → ι) → ι . λ x10 : ι → ι . λ x11 : (ι → ι) → ι → ι . 0) (x2 (λ x9 : ι → (ι → ι) → ι . λ x10 : ι → ι . λ x11 : (ι → ι) → ι → ι . x11 (λ x12 . x0 (λ x13 : (ι → ι) → ι . 0) (λ x13 : ι → ι . 0) (λ x13 : (ι → ι) → ι . 0)) (x7 (λ x12 . 0))) (x7 (λ x9 . x0 (λ x10 : (ι → ι) → ι . 0) (λ x10 : ι → ι . 0) (λ x10 : (ι → ι) → ι . 0))) (λ x9 . λ x10 : ι → ι . λ x11 . 0) (λ x9 : ι → ι . λ x10 . x9 (x9 0)) (x3 (λ x9 : (((ι → ι) → ι → ι) → ι) → ((ι → ι) → ι → ι) → ι . Inj1 0) (λ x9 x10 x11 x12 . 0) (x7 (λ x9 . 0)))) (λ x9 . λ x10 : ι → ι . λ x11 . 0) (λ x9 : ι → ι . λ x10 . 0) x5) (setsum 0 x5) (λ x9 . x7 (λ x10 . x10)) = x7 (λ x9 . x7 (λ x10 . setsum 0 (x3 (λ x11 : (((ι → ι) → ι → ι) → ι) → ((ι → ι) → ι → ι) → ι . 0) (λ x11 x12 x13 x14 . 0) (x3 (λ x11 : (((ι → ι) → ι → ι) → ι) → ((ι → ι) → ι → ι) → ι . 0) (λ x11 x12 x13 x14 . 0) 0))))) ⟶ (∀ x4 : (((ι → ι) → ι) → ι) → ι → ι . ∀ x5 : ι → (ι → ι → ι) → (ι → ι) → ι → ι . ∀ x6 . ∀ x7 : ι → ι → ι . x0 (λ x9 : (ι → ι) → ι . 0) (λ x9 : ι → ι . 0) (λ x9 : (ι → ι) → ι . Inj0 (x3 (λ x10 : (((ι → ι) → ι → ι) → ι) → ((ι → ι) → ι → ι) → ι . x0 (λ x11 : (ι → ι) → ι . 0) (λ x11 : ι → ι . x10 (λ x12 : (ι → ι) → ι → ι . 0) (λ x12 : ι → ι . λ x13 . 0)) (λ x11 : (ι → ι) → ι . Inj0 0)) (λ x10 x11 x12 x13 . x0 (λ x14 : (ι → ι) → ι . x12) (λ x14 : ι → ι . 0) (λ x14 : (ι → ι) → ι . x13)) (x1 (λ x10 . x9 (λ x11 . 0)) (λ x10 . 0) (x0 (λ x10 : (ι → ι) → ι . 0) (λ x10 : ι → ι . 0) (λ x10 : (ι → ι) → ι . 0)) 0 (λ x10 . x0 (λ x11 : (ι → ι) → ι . 0) (λ x11 : ι → ι . 0) (λ x11 : (ι → ι) → ι . 0))))) = x4 (λ x9 : (ι → ι) → ι . 0) (x5 (x4 (λ x9 : (ι → ι) → ι . x1 (λ x10 . 0) (λ x10 . x10) (setsum 0 0) (x9 (λ x10 . 0)) (λ x10 . Inj0 0)) (Inj1 (x0 (λ x9 : (ι → ι) → ι . 0) (λ x9 : ι → ι . 0) (λ x9 : (ι → ι) → ι . 0)))) (λ x9 x10 . x10) (setsum 0) (x4 (λ x9 : (ι → ι) → ι . Inj1 (Inj1 0)) (setsum (x5 0 (λ x9 x10 . 0) (λ x9 . 0) 0) 0)))) ⟶ (∀ x4 . ∀ x5 : ι → ι . ∀ x6 . ∀ x7 : ι → ι → ι . x0 (λ x9 : (ι → ι) → ι . x2 (λ x10 : ι → (ι → ι) → ι . λ x11 : ι → ι . λ x12 : (ι → ι) → ι → ι . 0) 0 (λ x10 . λ x11 : ι → ι . λ x12 . 0) (λ x10 : ι → ι . λ x11 . x3 (λ x12 : (((ι → ι) → ι → ι) → ι) → ((ι → ι) → ι → ι) → ι . x11) (λ x12 x13 x14 x15 . setsum x14 x14) (x10 (x2 (λ x12 : ι → (ι → ι) → ι . λ x13 : ι → ι . λ x14 : (ι → ι) → ι → ι . 0) 0 (λ x12 . λ x13 : ι → ι . λ x14 . 0) (λ x12 : ι → ι . λ x13 . 0) 0))) 0) (λ x9 : ι → ι . x5 (setsum (x7 0 0) 0)) (λ x9 : (ι → ι) → ι . 0) = x5 (x1 (λ x9 . 0) (λ x9 . 0) (x0 (λ x9 : (ι → ι) → ι . 0) (λ x9 : ι → ι . x1 (λ x10 . 0) (λ x10 . x10) (Inj0 0) (Inj0 0) (λ x10 . x10)) (λ x9 : (ι → ι) → ι . x3 (λ x10 : (((ι → ι) → ι → ι) → ι) → ((ι → ι) → ι → ι) → ι . x9 (λ x11 . 0)) (λ x10 x11 x12 x13 . 0) (x1 (λ x10 . 0) (λ x10 . 0) 0 0 (λ x10 . 0)))) (x3 (λ x9 : (((ι → ι) → ι → ι) → ι) → ((ι → ι) → ι → ι) → ι . 0) (λ x9 x10 x11 x12 . x9) (setsum (x1 (λ x9 . 0) (λ x9 . 0) 0 0 (λ x9 . 0)) (x5 0))) (λ x9 . 0))) ⟶ False (proof)Theorem a9210.. : ∀ x0 : (ι → ι → ι) → (ι → ι → ι → ι) → ι . ∀ x1 : (ι → ι) → ι → ι → ι . ∀ x2 : (ι → ι → ι) → ι → ι . ∀ x3 : (((ι → (ι → ι) → ι → ι) → ι) → ι) → ι → ι . (∀ x4 . ∀ x5 : (ι → ι) → ι → ι . ∀ x6 : ι → ι . ∀ x7 . x3 (λ x9 : (ι → (ι → ι) → ι → ι) → ι . x7) x4 = x7) ⟶ (∀ x4 : ι → ι . ∀ x5 x6 x7 . x3 (λ x9 : (ι → (ι → ι) → ι → ι) → ι . x0 (λ x10 x11 . x1 (λ x12 . x3 (λ x13 : (ι → (ι → ι) → ι → ι) → ι . 0) (setsum 0 0)) 0 (x9 (λ x12 . λ x13 : ι → ι . λ x14 . x13 0))) (λ x10 x11 x12 . x12)) (setsum 0 0) = setsum x7 (x1 (λ x9 . x0 (λ x10 x11 . x3 (λ x12 : (ι → (ι → ι) → ι → ι) → ι . 0) x7) (λ x10 x11 x12 . x10)) (x1 (λ x9 . x6) x5 (setsum (Inj1 0) x7)) (setsum x7 (x1 (λ x9 . 0) (x4 0) x7)))) ⟶ (∀ x4 : ι → ι → ι → ι . ∀ x5 x6 . ∀ x7 : (((ι → ι) → ι) → ι → ι) → ι . x2 (λ x9 x10 . x2 (λ x11 x12 . setsum (Inj0 0) 0) 0) 0 = x2 (λ x9 x10 . Inj1 0) (setsum x6 (x4 x6 0 (x3 (λ x9 : (ι → (ι → ι) → ι → ι) → ι . 0) x6)))) ⟶ (∀ x4 . ∀ x5 : ι → ι → (ι → ι) → ι → ι . ∀ x6 . ∀ x7 : ι → ι . x2 (λ x9 x10 . x3 (λ x11 : (ι → (ι → ι) → ι → ι) → ι . 0) (x0 (λ x11 x12 . x0 (λ x13 x14 . x1 (λ x15 . 0) 0 0) (λ x13 x14 x15 . Inj1 0)) (λ x11 x12 x13 . setsum x10 x12))) (Inj0 0) = setsum 0 (setsum 0 0)) ⟶ (∀ x4 : ι → ι → (ι → ι) → ι . ∀ x5 x6 . ∀ x7 : (ι → ι) → ((ι → ι) → ι) → ι → ι → ι . x1 (λ x9 . x3 (λ x10 : (ι → (ι → ι) → ι → ι) → ι . 0) (Inj1 (x3 (λ x10 : (ι → (ι → ι) → ι → ι) → ι . x6) 0))) (x1 (λ x9 . Inj0 (setsum (Inj0 0) (x2 (λ x10 x11 . 0) 0))) x5 (Inj0 (Inj1 0))) (x0 (λ x9 x10 . 0) (λ x9 x10 x11 . x9)) = setsum x6 (setsum (x0 (λ x9 x10 . Inj0 (setsum 0 0)) (λ x9 x10 x11 . x7 (λ x12 . x10) (λ x12 : ι → ι . x9) x9 (x1 (λ x12 . 0) 0 0))) (x0 (λ x9 x10 . x3 (λ x11 : (ι → (ι → ι) → ι → ι) → ι . x2 (λ x12 x13 . 0) 0) (setsum 0 0)) (λ x9 x10 x11 . 0)))) ⟶ (∀ x4 . ∀ x5 : (ι → ι → ι → ι) → ι . ∀ x6 . ∀ x7 : (ι → ι) → ι → ι . x1 (λ x9 . 0) (x3 (λ x9 : (ι → (ι → ι) → ι → ι) → ι . 0) (setsum (x2 (λ x9 x10 . x9) 0) 0)) 0 = x3 (λ x9 : (ι → (ι → ι) → ι → ι) → ι . setsum (Inj0 (setsum x6 x6)) (setsum (x5 (λ x10 x11 x12 . x0 (λ x13 x14 . 0) (λ x13 x14 x15 . 0))) (setsum (x5 (λ x10 x11 x12 . 0)) 0))) (x0 (λ x9 x10 . x0 (λ x11 x12 . setsum (x1 (λ x13 . 0) 0 0) 0) (λ x11 x12 x13 . x12)) (λ x9 x10 x11 . setsum x9 (Inj1 (x2 (λ x12 x13 . 0) 0))))) ⟶ (∀ x4 . ∀ x5 : ((ι → ι) → ι) → ι . ∀ x6 x7 . x0 (λ x9 x10 . x3 (λ x11 : (ι → (ι → ι) → ι → ι) → ι . 0) x9) (λ x9 x10 x11 . setsum 0 (Inj1 0)) = setsum 0 (Inj0 (x1 (x3 (λ x9 : (ι → (ι → ι) → ι → ι) → ι . x3 (λ x10 : (ι → (ι → ι) → ι → ι) → ι . 0) 0)) (x2 (λ x9 x10 . 0) x7) (x0 (λ x9 x10 . x1 (λ x11 . 0) 0 0) (λ x9 x10 x11 . x3 (λ x12 : (ι → (ι → ι) → ι → ι) → ι . 0) 0))))) ⟶ (∀ x4 : (ι → ι) → ι . ∀ x5 : ι → ι . ∀ x6 . ∀ x7 : ι → ι → ι . x0 (λ x9 x10 . setsum x6 x9) (λ x9 x10 x11 . 0) = x7 (setsum (setsum (x0 (λ x9 x10 . x2 (λ x11 x12 . 0) 0) (λ x9 x10 x11 . 0)) (x3 (λ x9 : (ι → (ι → ι) → ι → ι) → ι . x2 (λ x10 x11 . 0) 0) (x0 (λ x9 x10 . 0) (λ x9 x10 x11 . 0)))) (x5 (x2 (λ x9 x10 . x6) (x3 (λ x9 : (ι → (ι → ι) → ι → ι) → ι . 0) 0)))) (x7 (Inj1 (setsum 0 0)) (x0 (λ x9 x10 . 0) (λ x9 x10 x11 . 0)))) ⟶ False (proof)Theorem b4f37.. : ∀ x0 : (ι → ι) → ι → ι . ∀ x1 : (ι → ι) → (ι → ι → ι → ι → ι) → ((ι → ι → ι) → (ι → ι) → ι → ι) → ι → (ι → ι) → ι . ∀ x2 : (ι → ι → ι) → ι → ι → ι → ι . ∀ x3 : ((ι → ι → ι) → ι) → (((ι → ι → ι) → ι → ι) → ι → (ι → ι) → ι → ι) → ι . (∀ x4 : (ι → (ι → ι) → ι) → ι . ∀ x5 : ι → ι . ∀ x6 : (ι → ι) → ι . ∀ x7 . x3 (λ x9 : ι → ι → ι . x2 (λ x10 x11 . setsum 0 (x3 (λ x12 : ι → ι → ι . x12 0 0) (λ x12 : (ι → ι → ι) → ι → ι . λ x13 . λ x14 : ι → ι . λ x15 . 0))) (Inj1 (Inj0 x7)) 0 (x5 (Inj1 (x5 0)))) (λ x9 : (ι → ι → ι) → ι → ι . λ x10 . λ x11 : ι → ι . λ x12 . Inj1 (x3 (λ x13 : ι → ι → ι . x12) (λ x13 : (ι → ι → ι) → ι → ι . λ x14 . λ x15 : ι → ι . λ x16 . x14))) = Inj0 (Inj0 (x2 (λ x9 x10 . x2 (λ x11 x12 . x1 (λ x13 . 0) (λ x13 x14 x15 x16 . 0) (λ x13 : ι → ι → ι . λ x14 : ι → ι . λ x15 . 0) 0 (λ x13 . 0)) 0 (x6 (λ x11 . 0)) 0) (setsum (x0 (λ x9 . 0) 0) (Inj1 0)) (setsum (setsum 0 0) x7) 0))) ⟶ (∀ x4 : ι → ι → ι . ∀ x5 : (ι → ι → ι → ι) → (ι → ι) → ι → ι → ι . ∀ x6 . ∀ x7 : (((ι → ι) → ι → ι) → ι → ι) → ι → ι → ι → ι . x3 (λ x9 : ι → ι → ι . 0) (λ x9 : (ι → ι → ι) → ι → ι . λ x10 . λ x11 : ι → ι . λ x12 . 0) = setsum 0 (x7 (λ x9 : (ι → ι) → ι → ι . λ x10 . Inj0 (setsum (x9 (λ x11 . 0) 0) x6)) (x0 (λ x9 . 0) (x3 (λ x9 : ι → ι → ι . x2 (λ x10 x11 . 0) 0 0 0) (λ x9 : (ι → ι → ι) → ι → ι . λ x10 . λ x11 : ι → ι . λ x12 . x0 (λ x13 . 0) 0))) (x4 0 (setsum 0 (setsum 0 0))) (Inj1 (x4 (x5 (λ x9 x10 x11 . 0) (λ x9 . 0) 0 0) (Inj0 0))))) ⟶ (∀ x4 . ∀ x5 : (ι → ι → ι → ι) → ι . ∀ x6 . ∀ x7 : ((ι → ι → ι) → ι → ι → ι) → ι → ι → ι → ι . x2 (λ x9 x10 . 0) (x2 (λ x9 x10 . x0 (λ x11 . 0) x9) x6 (setsum 0 (x5 (λ x9 x10 x11 . 0))) (setsum x4 (Inj1 (setsum 0 0)))) (x3 (λ x9 : ι → ι → ι . x9 (x9 0 (x5 (λ x10 x11 x12 . 0))) (x2 (λ x10 x11 . setsum 0 0) 0 (Inj0 0) (Inj0 0))) (λ x9 : (ι → ι → ι) → ι → ι . λ x10 . λ x11 : ι → ι . λ x12 . x12)) 0 = setsum (setsum 0 (setsum (x0 (λ x9 . x3 (λ x10 : ι → ι → ι . 0) (λ x10 : (ι → ι → ι) → ι → ι . λ x11 . λ x12 : ι → ι . λ x13 . 0)) x6) 0)) 0) ⟶ (∀ x4 x5 . ∀ x6 : ι → ι . ∀ x7 . x2 (λ x9 x10 . x1 Inj0 (λ x11 x12 x13 x14 . setsum x11 x13) (λ x11 : ι → ι → ι . λ x12 : ι → ι . λ x13 . x0 (λ x14 . 0) 0) (setsum (x2 (λ x11 x12 . 0) (x6 0) (setsum 0 0) x9) (setsum 0 (x2 (λ x11 x12 . 0) 0 0 0))) (λ x11 . setsum x10 (Inj0 (x0 (λ x12 . 0) 0)))) (Inj1 (Inj0 0)) (setsum (setsum (x6 (x3 (λ x9 : ι → ι → ι . 0) (λ x9 : (ι → ι → ι) → ι → ι . λ x10 . λ x11 : ι → ι . λ x12 . 0))) 0) (setsum (setsum (setsum 0 0) (setsum 0 0)) (Inj0 (x2 (λ x9 x10 . 0) 0 0 0)))) (Inj0 (Inj0 (x2 (λ x9 x10 . 0) (x6 0) (setsum 0 0) 0))) = setsum (setsum (x2 (λ x9 x10 . 0) (x6 x4) (setsum (x2 (λ x9 x10 . 0) 0 0 0) (Inj0 0)) (setsum (x3 (λ x9 : ι → ι → ι . 0) (λ x9 : (ι → ι → ι) → ι → ι . λ x10 . λ x11 : ι → ι . λ x12 . 0)) x7)) x4) (x6 x4)) ⟶ (∀ x4 : ι → ((ι → ι) → ι) → (ι → ι) → ι → ι . ∀ x5 : (ι → ι) → ι → ι . ∀ x6 x7 . x1 (λ x9 . x7) (λ x9 x10 x11 x12 . x2 (λ x13 x14 . 0) (x3 (λ x13 : ι → ι → ι . 0) (λ x13 : (ι → ι → ι) → ι → ι . λ x14 . λ x15 : ι → ι . λ x16 . Inj1 (x1 (λ x17 . 0) (λ x17 x18 x19 x20 . 0) (λ x17 : ι → ι → ι . λ x18 : ι → ι . λ x19 . 0) 0 (λ x17 . 0)))) (Inj1 (x0 (λ x13 . x2 (λ x14 x15 . 0) 0 0 0) (x1 (λ x13 . 0) (λ x13 x14 x15 x16 . 0) (λ x13 : ι → ι → ι . λ x14 : ι → ι . λ x15 . 0) 0 (λ x13 . 0)))) x10) (λ x9 : ι → ι → ι . λ x10 : ι → ι . λ x11 . x9 (Inj0 (x2 (λ x12 x13 . Inj1 0) (x0 (λ x12 . 0) 0) 0 0)) (x0 (λ x12 . setsum (x9 0 0) (x9 0 0)) (x1 (λ x12 . setsum 0 0) (λ x12 x13 x14 x15 . 0) (λ x12 : ι → ι → ι . λ x13 : ι → ι . λ x14 . Inj0 0) 0 (λ x12 . 0)))) 0 (λ x9 . x6) = Inj1 (setsum 0 (Inj1 (Inj0 (setsum 0 0))))) ⟶ (∀ x4 : (ι → ι) → ι . ∀ x5 : ((ι → ι) → (ι → ι) → ι) → ι . ∀ x6 : ι → ι → ι . ∀ x7 : ι → ι . x1 (λ x9 . 0) (λ x9 x10 x11 x12 . 0) (λ x9 : ι → ι → ι . λ x10 : ι → ι . λ x11 . 0) (setsum (Inj1 (x6 (x7 0) (x6 0 0))) 0) (λ x9 . setsum (x3 (λ x10 : ι → ι → ι . x3 (λ x11 : ι → ι → ι . x10 0 0) (λ x11 : (ι → ι → ι) → ι → ι . λ x12 . λ x13 : ι → ι . λ x14 . 0)) (λ x10 : (ι → ι → ι) → ι → ι . λ x11 . λ x12 : ι → ι . λ x13 . Inj1 0)) (x3 (λ x10 : ι → ι → ι . 0) (λ x10 : (ι → ι → ι) → ι → ι . λ x11 . λ x12 : ι → ι . λ x13 . 0))) = x4 (λ x9 . x7 0)) ⟶ (∀ x4 : ι → ι → ι . ∀ x5 : (ι → (ι → ι) → ι) → ι → ι . ∀ x6 x7 . x0 (λ x9 . x6) (x4 0 (setsum 0 (x2 (λ x9 x10 . 0) (x2 (λ x9 x10 . 0) 0 0 0) (x1 (λ x9 . 0) (λ x9 x10 x11 x12 . 0) (λ x9 : ι → ι → ι . λ x10 : ι → ι . λ x11 . 0) 0 (λ x9 . 0)) x6))) = x4 (x5 (λ x9 . λ x10 : ι → ι . x0 (λ x11 . Inj1 x9) x9) (Inj1 (x0 (λ x9 . x5 (λ x10 . λ x11 : ι → ι . 0) 0) (x2 (λ x9 x10 . 0) 0 0 0)))) (setsum x7 (x4 0 0))) ⟶ (∀ x4 : (ι → ι) → ι . ∀ x5 : ι → ι → (ι → ι) → ι → ι . ∀ x6 x7 . x0 (λ x9 . x3 (λ x10 : ι → ι → ι . setsum (setsum (Inj0 0) (Inj0 0)) (x0 (λ x11 . x0 (λ x12 . 0) 0) (x0 (λ x11 . 0) 0))) (λ x10 : (ι → ι → ι) → ι → ι . λ x11 . λ x12 : ι → ι . λ x13 . Inj0 (x0 (λ x14 . x13) 0))) (setsum (setsum (x0 (λ x9 . x1 (λ x10 . 0) (λ x10 x11 x12 x13 . 0) (λ x10 : ι → ι → ι . λ x11 : ι → ι . λ x12 . 0) 0 (λ x10 . 0)) 0) (x3 (λ x9 : ι → ι → ι . x5 0 0 (λ x10 . 0) 0) (λ x9 : (ι → ι → ι) → ι → ι . λ x10 . λ x11 : ι → ι . λ x12 . setsum 0 0))) (x2 (λ x9 x10 . x0 (λ x11 . x3 (λ x12 : ι → ι → ι . 0) (λ x12 : (ι → ι → ι) → ι → ι . λ x13 . λ x14 : ι → ι . λ x15 . 0)) 0) 0 (Inj1 (x0 (λ x9 . 0) 0)) (Inj1 0))) = Inj0 0) ⟶ False (proof)Theorem 36f64.. : ∀ x0 : (((ι → (ι → ι) → ι) → ι → ι) → ι) → ι → ι . ∀ x1 : (ι → ι → ι) → (ι → ((ι → ι) → ι) → (ι → ι) → ι) → ι . ∀ x2 : (((ι → ι) → ι) → ι) → (((ι → ι) → ι → ι → ι) → ι) → (((ι → ι) → ι) → ι) → ι → ι → ι . ∀ x3 : (ι → ι) → ((ι → ι) → ι) → ι . (∀ x4 : ι → ι . ∀ x5 . ∀ x6 : ι → (ι → ι → ι) → ι . ∀ x7 . x3 (λ x9 . x7) (λ x9 : ι → ι . 0) = x7) ⟶ (∀ x4 : ι → ι → ι → ι → ι . ∀ x5 . ∀ x6 : ι → ι . ∀ x7 . x3 Inj0 (λ x9 : ι → ι . 0) = x7) ⟶ (∀ x4 : ι → ι . ∀ x5 . ∀ x6 : (ι → ι) → ι → ι . ∀ x7 : (ι → ι) → (ι → ι) → ι . x2 (λ x9 : (ι → ι) → ι . setsum 0 0) (λ x9 : (ι → ι) → ι → ι → ι . x9 (λ x10 . x10) 0 x5) (λ x9 : (ι → ι) → ι . x2 (λ x10 : (ι → ι) → ι . 0) (λ x10 : (ι → ι) → ι → ι → ι . x9 (x0 (λ x11 : (ι → (ι → ι) → ι) → ι → ι . setsum 0 0))) (λ x10 : (ι → ι) → ι . x6 (λ x11 . 0) (x1 (λ x11 x12 . x1 (λ x13 x14 . 0) (λ x13 . λ x14 : (ι → ι) → ι . λ x15 : ι → ι . 0)) (λ x11 . λ x12 : (ι → ι) → ι . λ x13 : ι → ι . x11))) (setsum x5 (setsum (x6 (λ x10 . 0) 0) (x2 (λ x10 : (ι → ι) → ι . 0) (λ x10 : (ι → ι) → ι → ι → ι . 0) (λ x10 : (ι → ι) → ι . 0) 0 0))) (setsum (Inj0 (x1 (λ x10 x11 . 0) (λ x10 . λ x11 : (ι → ι) → ι . λ x12 : ι → ι . 0))) (x9 (λ x10 . 0)))) x5 (setsum (setsum 0 0) (x7 (λ x9 . x7 (λ x10 . x6 (λ x11 . 0) 0) (λ x10 . x0 (λ x11 : (ι → (ι → ι) → ι) → ι → ι . 0) 0)) (λ x9 . x7 (λ x10 . x9) (λ x10 . x3 (λ x11 . 0) (λ x11 : ι → ι . 0))))) = Inj0 (x2 (λ x9 : (ι → ι) → ι . Inj0 (Inj1 (x1 (λ x10 x11 . 0) (λ x10 . λ x11 : (ι → ι) → ι . λ x12 : ι → ι . 0)))) (λ x9 : (ι → ι) → ι → ι → ι . x5) (λ x9 : (ι → ι) → ι . x9 (λ x10 . x2 (λ x11 : (ι → ι) → ι . x7 (λ x12 . 0) (λ x12 . 0)) (λ x11 : (ι → ι) → ι → ι → ι . x10) (λ x11 : (ι → ι) → ι . setsum 0 0) 0 (x9 (λ x11 . 0)))) (x1 (λ x9 x10 . 0) (λ x9 . λ x10 : (ι → ι) → ι . λ x11 : ι → ι . 0)) 0)) ⟶ (∀ x4 : ι → ι . ∀ x5 : (((ι → ι) → ι → ι) → ι) → ι → (ι → ι) → ι → ι . ∀ x6 . ∀ x7 : ι → (ι → ι) → ι → ι . x2 (λ x9 : (ι → ι) → ι . x2 (λ x10 : (ι → ι) → ι . setsum (x10 (λ x11 . setsum 0 0)) (x10 (λ x11 . x2 (λ x12 : (ι → ι) → ι . 0) (λ x12 : (ι → ι) → ι → ι → ι . 0) (λ x12 : (ι → ι) → ι . 0) 0 0))) (λ x10 : (ι → ι) → ι → ι → ι . Inj1 (x2 (λ x11 : (ι → ι) → ι . x9 (λ x12 . 0)) (λ x11 : (ι → ι) → ι → ι → ι . 0) (λ x11 : (ι → ι) → ι . Inj0 0) (setsum 0 0) (x10 (λ x11 . 0) 0 0))) (λ x10 : (ι → ι) → ι . x10 (λ x11 . x7 (x1 (λ x12 x13 . 0) (λ x12 . λ x13 : (ι → ι) → ι . λ x14 : ι → ι . 0)) (λ x12 . x12) 0)) (x3 (λ x10 . setsum (Inj1 0) 0) (λ x10 : ι → ι . Inj1 0)) (Inj0 0)) (λ x9 : (ι → ι) → ι → ι → ι . x3 (λ x10 . x2 (λ x11 : (ι → ι) → ι . x9 (λ x12 . x0 (λ x13 : (ι → (ι → ι) → ι) → ι → ι . 0) 0) (x1 (λ x12 x13 . 0) (λ x12 . λ x13 : (ι → ι) → ι . λ x14 : ι → ι . 0)) (Inj1 0)) (λ x11 : (ι → ι) → ι → ι → ι . x9 (λ x12 . 0) 0 (setsum 0 0)) (λ x11 : (ι → ι) → ι . x0 (λ x12 : (ι → (ι → ι) → ι) → ι → ι . setsum 0 0) (setsum 0 0)) (x0 (λ x11 : (ι → (ι → ι) → ι) → ι → ι . 0) (x1 (λ x11 x12 . 0) (λ x11 . λ x12 : (ι → ι) → ι . λ x13 : ι → ι . 0))) 0) (λ x10 : ι → ι . x10 (Inj1 (x7 0 (λ x11 . 0) 0)))) (λ x9 : (ι → ι) → ι . 0) (Inj0 (x2 (λ x9 : (ι → ι) → ι . 0) (λ x9 : (ι → ι) → ι → ι → ι . 0) (λ x9 : (ι → ι) → ι . x5 (λ x10 : (ι → ι) → ι → ι . x2 (λ x11 : (ι → ι) → ι . 0) (λ x11 : (ι → ι) → ι → ι → ι . 0) (λ x11 : (ι → ι) → ι . 0) 0 0) (x3 (λ x10 . 0) (λ x10 : ι → ι . 0)) (λ x10 . 0) (x5 (λ x10 : (ι → ι) → ι → ι . 0) 0 (λ x10 . 0) 0)) x6 (x7 (x7 0 (λ x9 . 0) 0) (λ x9 . x5 (λ x10 : (ι → ι) → ι → ι . 0) 0 (λ x10 . 0) 0) (x4 0)))) (Inj1 (setsum (x1 (λ x9 x10 . x1 (λ x11 x12 . 0) (λ x11 . λ x12 : (ι → ι) → ι . λ x13 : ι → ι . 0)) (λ x9 . λ x10 : (ι → ι) → ι . λ x11 : ι → ι . x7 0 (λ x12 . 0) 0)) x6)) = x2 (λ x9 : (ι → ι) → ι . x0 (λ x10 : (ι → (ι → ι) → ι) → ι → ι . x10 (λ x11 . λ x12 : ι → ι . x0 (λ x13 : (ι → (ι → ι) → ι) → ι → ι . x0 (λ x14 : (ι → (ι → ι) → ι) → ι → ι . 0) 0) (setsum 0 0)) (Inj0 (x7 0 (λ x11 . 0) 0))) (setsum (x7 (x9 (λ x10 . 0)) (λ x10 . 0) (setsum 0 0)) (x2 (λ x10 : (ι → ι) → ι . 0) (λ x10 : (ι → ι) → ι → ι → ι . x3 (λ x11 . 0) (λ x11 : ι → ι . 0)) (λ x10 : (ι → ι) → ι . Inj0 0) (x2 (λ x10 : (ι → ι) → ι . 0) (λ x10 : (ι → ι) → ι → ι → ι . 0) (λ x10 : (ι → ι) → ι . 0) 0 0) (x7 0 (λ x10 . 0) 0)))) (λ x9 : (ι → ι) → ι → ι → ι . setsum (setsum (Inj1 (x2 (λ x10 : (ι → ι) → ι . 0) (λ x10 : (ι → ι) → ι → ι → ι . 0) (λ x10 : (ι → ι) → ι . 0) 0 0)) (x5 (λ x10 : (ι → ι) → ι → ι . x0 (λ x11 : (ι → (ι → ι) → ι) → ι → ι . 0) 0) 0 (λ x10 . 0) (x1 (λ x10 x11 . 0) (λ x10 . λ x11 : (ι → ι) → ι . λ x12 : ι → ι . 0)))) (x3 (λ x10 . 0) (λ x10 : ι → ι . x0 (λ x11 : (ι → (ι → ι) → ι) → ι → ι . x0 (λ x12 : (ι → (ι → ι) → ι) → ι → ι . 0) 0) (x10 0)))) (λ x9 : (ι → ι) → ι . x1 (λ x10 x11 . 0) (λ x10 . λ x11 : (ι → ι) → ι . λ x12 : ι → ι . x9 (λ x13 . x13))) (x1 (λ x9 x10 . x9) (λ x9 . λ x10 : (ι → ι) → ι . λ x11 : ι → ι . 0)) (setsum (x4 (x5 (λ x9 : (ι → ι) → ι → ι . setsum 0 0) (Inj1 0) (λ x9 . 0) 0)) x6)) ⟶ (∀ x4 x5 x6 . ∀ x7 : ι → ι . x1 (λ x9 x10 . 0) (λ x9 . λ x10 : (ι → ι) → ι . λ x11 : ι → ι . Inj1 x9) = setsum (setsum (x0 (λ x9 : (ι → (ι → ι) → ι) → ι → ι . x1 (λ x10 x11 . 0) (λ x10 . λ x11 : (ι → ι) → ι . λ x12 : ι → ι . setsum 0 0)) (Inj0 (x3 (λ x9 . 0) (λ x9 : ι → ι . 0)))) x6) (x2 (λ x9 : (ι → ι) → ι . 0) (λ x9 : (ι → ι) → ι → ι → ι . 0) (λ x9 : (ι → ι) → ι . x9 x7) (x7 (x2 (λ x9 : (ι → ι) → ι . 0) (λ x9 : (ι → ι) → ι → ι → ι . 0) (λ x9 : (ι → ι) → ι . 0) (x3 (λ x9 . 0) (λ x9 : ι → ι . 0)) 0)) x6)) ⟶ (∀ x4 : ((ι → ι) → (ι → ι) → ι) → ι . ∀ x5 . ∀ x6 : (((ι → ι) → ι → ι) → ι) → ι . ∀ x7 : ι → ι . x1 (λ x9 x10 . 0) (λ x9 . λ x10 : (ι → ι) → ι . λ x11 : ι → ι . 0) = x6 (λ x9 : (ι → ι) → ι → ι . 0)) ⟶ (∀ x4 . ∀ x5 : (ι → ι) → ι → (ι → ι) → ι → ι . ∀ x6 : (((ι → ι) → ι → ι) → (ι → ι) → ι) → (ι → ι → ι) → ι → ι → ι . ∀ x7 : ι → ι → ι → ι → ι . x0 (λ x9 : (ι → (ι → ι) → ι) → ι → ι . 0) (x1 (λ x9 x10 . x0 (λ x11 : (ι → (ι → ι) → ι) → ι → ι . x2 (λ x12 : (ι → ι) → ι . 0) (λ x12 : (ι → ι) → ι → ι → ι . x11 (λ x13 . λ x14 : ι → ι . 0) 0) (λ x12 : (ι → ι) → ι . 0) (setsum 0 0) (x1 (λ x12 x13 . 0) (λ x12 . λ x13 : (ι → ι) → ι . λ x14 : ι → ι . 0))) (setsum 0 (x1 (λ x11 x12 . 0) (λ x11 . λ x12 : (ι → ι) → ι . λ x13 : ι → ι . 0)))) (λ x9 . λ x10 : (ι → ι) → ι . λ x11 : ι → ι . x2 (λ x12 : (ι → ι) → ι . x3 (λ x13 . setsum 0 0) (λ x13 : ι → ι . Inj0 0)) (λ x12 : (ι → ι) → ι → ι → ι . setsum (x11 0) (Inj1 0)) (λ x12 : (ι → ι) → ι . setsum (Inj0 0) (x3 (λ x13 . 0) (λ x13 : ι → ι . 0))) (setsum (x10 (λ x12 . 0)) (setsum 0 0)) (Inj1 x9))) = x1 (λ x9 x10 . setsum 0 (x3 (λ x11 . setsum (setsum 0 0) 0) (λ x11 : ι → ι . 0))) (λ x9 . λ x10 : (ι → ι) → ι . λ x11 : ι → ι . x7 (x11 0) (x2 (λ x12 : (ι → ι) → ι . x2 (λ x13 : (ι → ι) → ι . 0) (λ x13 : (ι → ι) → ι → ι → ι . 0) (λ x13 : (ι → ι) → ι . 0) (x12 (λ x13 . 0)) (x3 (λ x13 . 0) (λ x13 : ι → ι . 0))) (λ x12 : (ι → ι) → ι → ι → ι . setsum (x10 (λ x13 . 0)) (setsum 0 0)) (λ x12 : (ι → ι) → ι . x1 (λ x13 x14 . 0) (λ x13 . λ x14 : (ι → ι) → ι . λ x15 : ι → ι . x2 (λ x16 : (ι → ι) → ι . 0) (λ x16 : (ι → ι) → ι → ι → ι . 0) (λ x16 : (ι → ι) → ι . 0) 0 0)) 0 0) 0 (x11 (setsum (x11 0) (Inj0 0))))) ⟶ (∀ x4 x5 . ∀ x6 : (ι → (ι → ι) → ι → ι) → ι . ∀ x7 . x0 (λ x9 : (ι → (ι → ι) → ι) → ι → ι . x9 (λ x10 . λ x11 : ι → ι . x2 (λ x12 : (ι → ι) → ι . x9 (λ x13 . λ x14 : ι → ι . x13) (x2 (λ x13 : (ι → ι) → ι . 0) (λ x13 : (ι → ι) → ι → ι → ι . 0) (λ x13 : (ι → ι) → ι . 0) 0 0)) (λ x12 : (ι → ι) → ι → ι → ι . setsum (x12 (λ x13 . 0) 0 0) (setsum 0 0)) (λ x12 : (ι → ι) → ι . 0) (setsum x7 (x9 (λ x12 . λ x13 : ι → ι . 0) 0)) x7) (x0 (λ x10 : (ι → (ι → ι) → ι) → ι → ι . setsum (x1 (λ x11 x12 . 0) (λ x11 . λ x12 : (ι → ι) → ι . λ x13 : ι → ι . 0)) (x1 (λ x11 x12 . 0) (λ x11 . λ x12 : (ι → ι) → ι . λ x13 : ι → ι . 0))) (setsum 0 0))) (setsum (x1 (λ x9 x10 . 0) (λ x9 . λ x10 : (ι → ι) → ι . λ x11 : ι → ι . setsum (Inj0 0) (x10 (λ x12 . 0)))) (Inj0 x5)) = x6 (λ x9 . λ x10 : ι → ι . λ x11 . 0)) ⟶ False (proof)Theorem 2836d.. : ∀ x0 : ((ι → ι) → (((ι → ι) → ι → ι) → (ι → ι) → ι) → ι → ι) → (ι → ι → ι) → (ι → ι) → ι . ∀ x1 : (((ι → (ι → ι) → ι → ι) → ι) → ι) → ι → ι → ι . ∀ x2 : ((((ι → ι) → ι → ι) → ((ι → ι) → ι) → ι) → (ι → ι → ι) → ι → ι → ι) → ι → ((ι → ι) → (ι → ι) → ι) → ι → ι . ∀ x3 : (((ι → ι) → ι) → ((ι → ι → ι) → ι) → (ι → ι → ι) → ι) → ι → ι . (∀ x4 : ι → (ι → ι) → (ι → ι) → ι → ι . ∀ x5 : (((ι → ι) → ι → ι) → (ι → ι) → ι → ι) → ι . ∀ x6 : ι → ι . ∀ x7 : ι → ι → ι . x3 (λ x9 : (ι → ι) → ι . λ x10 : (ι → ι → ι) → ι . λ x11 : ι → ι → ι . x2 (λ x12 : ((ι → ι) → ι → ι) → ((ι → ι) → ι) → ι . λ x13 : ι → ι → ι . λ x14 x15 . Inj1 0) (x2 (λ x12 : ((ι → ι) → ι → ι) → ((ι → ι) → ι) → ι . λ x13 : ι → ι → ι . λ x14 x15 . x13 (x2 (λ x16 : ((ι → ι) → ι → ι) → ((ι → ι) → ι) → ι . λ x17 : ι → ι → ι . λ x18 x19 . 0) 0 (λ x16 x17 : ι → ι . 0) 0) (x1 (λ x16 : (ι → (ι → ι) → ι → ι) → ι . 0) 0 0)) (x9 (λ x12 . setsum 0 0)) (λ x12 x13 : ι → ι . Inj0 (setsum 0 0)) 0) (λ x12 x13 : ι → ι . x3 (λ x14 : (ι → ι) → ι . λ x15 : (ι → ι → ι) → ι . λ x16 : ι → ι → ι . Inj0 (setsum 0 0)) (x0 (λ x14 : ι → ι . λ x15 : ((ι → ι) → ι → ι) → (ι → ι) → ι . λ x16 . x15 (λ x17 : ι → ι . λ x18 . 0) (λ x17 . 0)) (λ x14 x15 . x1 (λ x16 : (ι → (ι → ι) → ι → ι) → ι . 0) 0 0) (λ x14 . 0))) (x11 (setsum 0 (Inj0 0)) 0)) (x7 (Inj1 (setsum 0 0)) 0) = x2 (λ x9 : ((ι → ι) → ι → ι) → ((ι → ι) → ι) → ι . λ x10 : ι → ι → ι . λ x11 x12 . x11) (x7 (setsum (x3 (λ x9 : (ι → ι) → ι . λ x10 : (ι → ι → ι) → ι . λ x11 : ι → ι → ι . 0) (x7 0 0)) 0) (x3 (λ x9 : (ι → ι) → ι . λ x10 : (ι → ι → ι) → ι . λ x11 : ι → ι → ι . setsum (x7 0 0) (x7 0 0)) (setsum (Inj1 0) 0))) (λ x9 x10 : ι → ι . x2 (λ x11 : ((ι → ι) → ι → ι) → ((ι → ι) → ι) → ι . λ x12 : ι → ι → ι . λ x13 x14 . x1 (λ x15 : (ι → (ι → ι) → ι → ι) → ι . 0) 0 x13) (setsum 0 0) (λ x11 x12 : ι → ι . x1 (λ x13 : (ι → (ι → ι) → ι → ι) → ι . 0) (x12 0) (x10 (x2 (λ x13 : ((ι → ι) → ι → ι) → ((ι → ι) → ι) → ι . λ x14 : ι → ι → ι . λ x15 x16 . 0) 0 (λ x13 x14 : ι → ι . 0) 0))) (x7 0 0)) (Inj1 0)) ⟶ (∀ x4 x5 . ∀ x6 x7 : ι → ι . x3 (λ x9 : (ι → ι) → ι . λ x10 : (ι → ι → ι) → ι . λ x11 : ι → ι → ι . x10 (λ x12 . Inj0)) (x0 (λ x9 : ι → ι . λ x10 : ((ι → ι) → ι → ι) → (ι → ι) → ι . λ x11 . x2 (λ x12 : ((ι → ι) → ι → ι) → ((ι → ι) → ι) → ι . λ x13 : ι → ι → ι . λ x14 x15 . setsum 0 0) x11 (λ x12 x13 : ι → ι . 0) (x3 (λ x12 : (ι → ι) → ι . λ x13 : (ι → ι → ι) → ι . λ x14 : ι → ι → ι . Inj1 0) 0)) (λ x9 x10 . Inj0 (x1 (λ x11 : (ι → (ι → ι) → ι → ι) → ι . x11 (λ x12 . λ x13 : ι → ι . λ x14 . 0)) (setsum 0 0) 0)) (λ x9 . setsum 0 (x2 (λ x10 : ((ι → ι) → ι → ι) → ((ι → ι) → ι) → ι . λ x11 : ι → ι → ι . λ x12 x13 . x0 (λ x14 : ι → ι . λ x15 : ((ι → ι) → ι → ι) → (ι → ι) → ι . λ x16 . 0) (λ x14 x15 . 0) (λ x14 . 0)) (x7 0) (λ x10 x11 : ι → ι . x9) (x2 (λ x10 : ((ι → ι) → ι → ι) → ((ι → ι) → ι) → ι . λ x11 : ι → ι → ι . λ x12 x13 . 0) 0 (λ x10 x11 : ι → ι . 0) 0)))) = Inj1 0) ⟶ (∀ x4 . ∀ x5 : (((ι → ι) → ι) → (ι → ι) → ι) → ι → ι → ι → ι . ∀ x6 . ∀ x7 : ι → (ι → ι → ι) → ι . x2 (λ x9 : ((ι → ι) → ι → ι) → ((ι → ι) → ι) → ι . λ x10 : ι → ι → ι . λ x11 x12 . x1 (λ x13 : (ι → (ι → ι) → ι → ι) → ι . 0) x11 (x2 (λ x13 : ((ι → ι) → ι → ι) → ((ι → ι) → ι) → ι . λ x14 : ι → ι → ι . λ x15 x16 . setsum (Inj1 0) (setsum 0 0)) (setsum (Inj1 0) (x0 (λ x13 : ι → ι . λ x14 : ((ι → ι) → ι → ι) → (ι → ι) → ι . λ x15 . 0) (λ x13 x14 . 0) (λ x13 . 0))) (λ x13 x14 : ι → ι . setsum 0 (x1 (λ x15 : (ι → (ι → ι) → ι → ι) → ι . 0) 0 0)) 0)) (x0 (λ x9 : ι → ι . λ x10 : ((ι → ι) → ι → ι) → (ι → ι) → ι . λ x11 . 0) (λ x9 x10 . Inj1 (setsum 0 0)) (λ x9 . Inj0 (setsum (x5 (λ x10 : (ι → ι) → ι . λ x11 : ι → ι . 0) 0 0 0) (setsum 0 0)))) (λ x9 x10 : ι → ι . x0 (λ x11 : ι → ι . λ x12 : ((ι → ι) → ι → ι) → (ι → ι) → ι . λ x13 . x1 (λ x14 : (ι → (ι → ι) → ι → ι) → ι . Inj0 0) (x10 (x0 (λ x14 : ι → ι . λ x15 : ((ι → ι) → ι → ι) → (ι → ι) → ι . λ x16 . 0) (λ x14 x15 . 0) (λ x14 . 0))) (Inj0 0)) (λ x11 x12 . x0 (λ x13 : ι → ι . λ x14 : ((ι → ι) → ι → ι) → (ι → ι) → ι . λ x15 . Inj0 (setsum 0 0)) (λ x13 x14 . x14) (λ x13 . x11)) (λ x11 . 0)) 0 = setsum (x5 (λ x9 : (ι → ι) → ι . λ x10 : ι → ι . 0) (setsum 0 (x3 (λ x9 : (ι → ι) → ι . λ x10 : (ι → ι → ι) → ι . λ x11 : ι → ι → ι . x1 (λ x12 : (ι → (ι → ι) → ι → ι) → ι . 0) 0 0) 0)) (x0 (λ x9 : ι → ι . λ x10 : ((ι → ι) → ι → ι) → (ι → ι) → ι . λ x11 . 0) (λ x9 x10 . x10) (λ x9 . x2 (λ x10 : ((ι → ι) → ι → ι) → ((ι → ι) → ι) → ι . λ x11 : ι → ι → ι . λ x12 x13 . x1 (λ x14 : (ι → (ι → ι) → ι → ι) → ι . 0) 0 0) 0 (λ x10 x11 : ι → ι . x0 (λ x12 : ι → ι . λ x13 : ((ι → ι) → ι → ι) → (ι → ι) → ι . λ x14 . 0) (λ x12 x13 . 0) (λ x12 . 0)) 0)) 0) 0) ⟶ (∀ x4 . ∀ x5 : (ι → ι) → ι . ∀ x6 : ι → ι . ∀ x7 . x2 (λ x9 : ((ι → ι) → ι → ι) → ((ι → ι) → ι) → ι . λ x10 : ι → ι → ι . λ x11 x12 . x1 (λ x13 : (ι → (ι → ι) → ι → ι) → ι . Inj1 0) (x10 0 0) (setsum (setsum 0 x12) x11)) 0 (λ x9 x10 : ι → ι . x10 0) (Inj0 x4) = x1 (λ x9 : (ι → (ι → ι) → ι → ι) → ι . x7) x7 (x6 (x2 (λ x9 : ((ι → ι) → ι → ι) → ((ι → ι) → ι) → ι . λ x10 : ι → ι → ι . λ x11 x12 . x2 (λ x13 : ((ι → ι) → ι → ι) → ((ι → ι) → ι) → ι . λ x14 : ι → ι → ι . λ x15 x16 . 0) (x9 (λ x13 : ι → ι . λ x14 . 0) (λ x13 : ι → ι . 0)) (λ x13 x14 : ι → ι . x0 (λ x15 : ι → ι . λ x16 : ((ι → ι) → ι → ι) → (ι → ι) → ι . λ x17 . 0) (λ x15 x16 . 0) (λ x15 . 0)) (x2 (λ x13 : ((ι → ι) → ι → ι) → ((ι → ι) → ι) → ι . λ x14 : ι → ι → ι . λ x15 x16 . 0) 0 (λ x13 x14 : ι → ι . 0) 0)) x4 (λ x9 x10 : ι → ι . x1 (λ x11 : (ι → (ι → ι) → ι → ι) → ι . x3 (λ x12 : (ι → ι) → ι . λ x13 : (ι → ι → ι) → ι . λ x14 : ι → ι → ι . 0) 0) 0 (x9 0)) x7))) ⟶ (∀ x4 . ∀ x5 : ι → ι → (ι → ι) → ι → ι . ∀ x6 x7 . x1 (λ x9 : (ι → (ι → ι) → ι → ι) → ι . x9 (λ x10 . λ x11 : ι → ι . λ x12 . x10)) 0 (setsum x7 (x0 (λ x9 : ι → ι . λ x10 : ((ι → ι) → ι → ι) → (ι → ι) → ι . λ x11 . x9 (x0 (λ x12 : ι → ι . λ x13 : ((ι → ι) → ι → ι) → (ι → ι) → ι . λ x14 . 0) (λ x12 x13 . 0) (λ x12 . 0))) (λ x9 x10 . Inj0 (Inj1 0)) (λ x9 . Inj0 0))) = setsum (setsum 0 x6) x7) ⟶ (∀ x4 . ∀ x5 : ι → ι . ∀ x6 : ι → ι → ι . ∀ x7 : ((ι → ι → ι) → ι) → ι . x1 (λ x9 : (ι → (ι → ι) → ι → ι) → ι . x6 (x1 (λ x10 : (ι → (ι → ι) → ι → ι) → ι . x3 (λ x11 : (ι → ι) → ι . λ x12 : (ι → ι → ι) → ι . λ x13 : ι → ι → ι . setsum 0 0) 0) (setsum 0 (x0 (λ x10 : ι → ι . λ x11 : ((ι → ι) → ι → ι) → (ι → ι) → ι . λ x12 . 0) (λ x10 x11 . 0) (λ x10 . 0))) (x6 (x9 (λ x10 . λ x11 : ι → ι . λ x12 . 0)) 0)) (Inj1 (x6 (x1 (λ x10 : (ι → (ι → ι) → ι → ι) → ι . 0) 0 0) (Inj1 0)))) (x7 (λ x9 : ι → ι → ι . Inj0 (x9 0 (x0 (λ x10 : ι → ι . λ x11 : ((ι → ι) → ι → ι) → (ι → ι) → ι . λ x12 . 0) (λ x10 x11 . 0) (λ x10 . 0))))) (x5 (x3 (λ x9 : (ι → ι) → ι . λ x10 : (ι → ι → ι) → ι . λ x11 : ι → ι → ι . x10 (λ x12 x13 . x2 (λ x14 : ((ι → ι) → ι → ι) → ((ι → ι) → ι) → ι . λ x15 : ι → ι → ι . λ x16 x17 . 0) 0 (λ x14 x15 : ι → ι . 0) 0)) (x1 (λ x9 : (ι → (ι → ι) → ι → ι) → ι . 0) 0 (x1 (λ x9 : (ι → (ι → ι) → ι → ι) → ι . 0) 0 0)))) = x5 (x6 (x7 (λ x9 : ι → ι → ι . x0 (λ x10 : ι → ι . λ x11 : ((ι → ι) → ι → ι) → (ι → ι) → ι . λ x12 . 0) (λ x10 x11 . 0) (λ x10 . setsum 0 0))) (x5 (x1 (λ x9 : (ι → (ι → ι) → ι → ι) → ι . 0) (setsum 0 0) (x6 0 0))))) ⟶ (∀ x4 : ι → ι . ∀ x5 x6 . ∀ x7 : ((ι → ι → ι) → ι) → ((ι → ι) → ι) → ι . x0 (λ x9 : ι → ι . λ x10 : ((ι → ι) → ι → ι) → (ι → ι) → ι . λ x11 . x11) (λ x9 x10 . x10) (λ x9 . x9) = x7 (λ x9 : ι → ι → ι . x0 (λ x10 : ι → ι . λ x11 : ((ι → ι) → ι → ι) → (ι → ι) → ι . λ x12 . 0) (λ x10 x11 . x2 (λ x12 : ((ι → ι) → ι → ι) → ((ι → ι) → ι) → ι . λ x13 : ι → ι → ι . λ x14 x15 . x0 (λ x16 : ι → ι . λ x17 : ((ι → ι) → ι → ι) → (ι → ι) → ι . λ x18 . setsum 0 0) (λ x16 x17 . Inj1 0) (λ x16 . x15)) (Inj0 0) (λ x12 x13 : ι → ι . x3 (λ x14 : (ι → ι) → ι . λ x15 : (ι → ι → ι) → ι . λ x16 : ι → ι → ι . x1 (λ x17 : (ι → (ι → ι) → ι → ι) → ι . 0) 0 0) (setsum 0 0)) 0) (λ x10 . 0)) (λ x9 : ι → ι . 0)) ⟶ (∀ x4 . ∀ x5 : ((ι → ι) → ι → ι) → ι . ∀ x6 x7 . x0 (λ x9 : ι → ι . λ x10 : ((ι → ι) → ι → ι) → (ι → ι) → ι . λ x11 . x3 (λ x12 : (ι → ι) → ι . λ x13 : (ι → ι → ι) → ι . λ x14 : ι → ι → ι . x1 (λ x15 : (ι → (ι → ι) → ι → ι) → ι . 0) (x0 (λ x15 : ι → ι . λ x16 : ((ι → ι) → ι → ι) → (ι → ι) → ι . λ x17 . Inj1 0) (λ x15 x16 . x3 (λ x17 : (ι → ι) → ι . λ x18 : (ι → ι → ι) → ι . λ x19 : ι → ι → ι . 0) 0) (λ x15 . x13 (λ x16 x17 . 0))) (x0 (λ x15 : ι → ι . λ x16 : ((ι → ι) → ι → ι) → (ι → ι) → ι . λ x17 . 0) (λ x15 x16 . setsum 0 0) (λ x15 . 0))) 0) (λ x9 x10 . 0) (λ x9 . x0 (λ x10 : ι → ι . λ x11 : ((ι → ι) → ι → ι) → (ι → ι) → ι . λ x12 . 0) (λ x10 x11 . x9) (λ x10 . x6)) = setsum (x3 (λ x9 : (ι → ι) → ι . λ x10 : (ι → ι → ι) → ι . λ x11 : ι → ι → ι . x10 (λ x12 x13 . x0 (λ x14 : ι → ι . λ x15 : ((ι → ι) → ι → ι) → (ι → ι) → ι . λ x16 . x1 (λ x17 : (ι → (ι → ι) → ι → ι) → ι . 0) 0 0) (λ x14 x15 . Inj1 0) (λ x14 . setsum 0 0))) x7) 0) ⟶ False (proof)Theorem 0eb92.. : ∀ x0 : (ι → ι) → ι → (ι → ι) → ι → ι . ∀ x1 : (ι → ι → ι) → ι → (((ι → ι) → ι) → ι) → (ι → ι) → ι . ∀ x2 : (ι → ι) → (ι → ((ι → ι) → ι → ι) → ι) → ι . ∀ x3 : ((((ι → ι) → ι) → ((ι → ι) → ι → ι) → ι) → ι) → ι → ι → ι → ι . (∀ x4 x5 . ∀ x6 : ι → ι → (ι → ι) → ι . ∀ x7 . x3 (λ x9 : ((ι → ι) → ι) → ((ι → ι) → ι → ι) → ι . x5) x4 (x2 (λ x9 . Inj0 0) (λ x9 . λ x10 : (ι → ι) → ι → ι . 0)) 0 = Inj1 (x1 (λ x9 x10 . x9) (Inj0 0) (λ x9 : (ι → ι) → ι . x3 (λ x10 : ((ι → ι) → ι) → ((ι → ι) → ι → ι) → ι . setsum (x9 (λ x11 . 0)) (x0 (λ x11 . 0) 0 (λ x11 . 0) 0)) (Inj0 (Inj0 0)) (x2 (λ x10 . x3 (λ x11 : ((ι → ι) → ι) → ((ι → ι) → ι → ι) → ι . 0) 0 0 0) (λ x10 . λ x11 : (ι → ι) → ι → ι . Inj1 0)) x7) (λ x9 . x2 (λ x10 . 0) (λ x10 . λ x11 : (ι → ι) → ι → ι . x7)))) ⟶ (∀ x4 . ∀ x5 : ι → ι . ∀ x6 x7 . x3 (λ x9 : ((ι → ι) → ι) → ((ι → ι) → ι → ι) → ι . x1 (λ x10 x11 . x10) (Inj1 (x2 (λ x10 . 0) (λ x10 . λ x11 : (ι → ι) → ι → ι . setsum 0 0))) (λ x10 : (ι → ι) → ι . x9 (λ x11 : ι → ι . 0) (λ x11 : ι → ι . λ x12 . setsum x12 x12)) (λ x10 . Inj1 0)) x7 0 0 = Inj1 0) ⟶ (∀ x4 x5 . ∀ x6 x7 : ι → ι . x2 (λ x9 . x9) (λ x9 . λ x10 : (ι → ι) → ι → ι . setsum 0 (x1 (λ x11 x12 . x1 (λ x13 x14 . Inj0 0) (x3 (λ x13 : ((ι → ι) → ι) → ((ι → ι) → ι → ι) → ι . 0) 0 0 0) (λ x13 : (ι → ι) → ι . x3 (λ x14 : ((ι → ι) → ι) → ((ι → ι) → ι → ι) → ι . 0) 0 0 0) (λ x13 . x1 (λ x14 x15 . 0) 0 (λ x14 : (ι → ι) → ι . 0) (λ x14 . 0))) 0 (λ x11 : (ι → ι) → ι . 0) (λ x11 . x11))) = x6 (setsum (x1 (λ x9 . x3 (λ x10 : ((ι → ι) → ι) → ((ι → ι) → ι → ι) → ι . x3 (λ x11 : ((ι → ι) → ι) → ((ι → ι) → ι → ι) → ι . 0) 0 0 0) (Inj0 0) (x0 (λ x10 . 0) 0 (λ x10 . 0) 0)) (x3 (λ x9 : ((ι → ι) → ι) → ((ι → ι) → ι → ι) → ι . Inj1 0) (x2 (λ x9 . 0) (λ x9 . λ x10 : (ι → ι) → ι → ι . 0)) (Inj0 0) x4) (λ x9 : (ι → ι) → ι . setsum (Inj0 0) (x2 (λ x10 . 0) (λ x10 . λ x11 : (ι → ι) → ι → ι . 0))) (λ x9 . Inj0 x5)) 0)) ⟶ (∀ x4 . ∀ x5 : (((ι → ι) → ι → ι) → ι → ι) → ι → (ι → ι) → ι . ∀ x6 : ((ι → ι → ι) → ι) → ι . ∀ x7 : (ι → (ι → ι) → ι) → ((ι → ι) → ι) → ι . x2 (λ x9 . x6 (λ x10 : ι → ι → ι . Inj1 (x0 (λ x11 . x2 (λ x12 . 0) (λ x12 . λ x13 : (ι → ι) → ι → ι . 0)) (setsum 0 0) (λ x11 . 0) (Inj1 0)))) (λ x9 . λ x10 : (ι → ι) → ι → ι . x1 (λ x11 x12 . x9) (x1 (λ x11 x12 . x2 (λ x13 . x2 (λ x14 . 0) (λ x14 . λ x15 : (ι → ι) → ι → ι . 0)) (λ x13 . λ x14 : (ι → ι) → ι → ι . x11)) 0 (λ x11 : (ι → ι) → ι . 0) (λ x11 . setsum (x0 (λ x12 . 0) 0 (λ x12 . 0) 0) (x0 (λ x12 . 0) 0 (λ x12 . 0) 0))) (λ x11 : (ι → ι) → ι . Inj1 (Inj0 0)) (λ x11 . 0)) = x6 (λ x9 : ι → ι → ι . setsum 0 (x0 (λ x10 . x10) 0 (λ x10 . x9 x10 (x7 (λ x11 . λ x12 : ι → ι . 0) (λ x11 : ι → ι . 0))) (Inj1 (Inj1 0))))) ⟶ (∀ x4 . ∀ x5 : ι → ι . ∀ x6 : (ι → ι) → ι . ∀ x7 : ι → (ι → ι → ι) → ι . x1 (λ x9 x10 . x10) x4 (λ x9 : (ι → ι) → ι . 0) (λ x9 . x7 (Inj0 (x2 (λ x10 . 0) (λ x10 . λ x11 : (ι → ι) → ι → ι . x0 (λ x12 . 0) 0 (λ x12 . 0) 0))) (λ x10 x11 . x11)) = x4) ⟶ (∀ x4 x5 x6 . ∀ x7 : ι → ι . x1 (λ x9 x10 . x1 (λ x11 x12 . Inj1 (x1 (λ x13 x14 . x11) (x1 (λ x13 x14 . 0) 0 (λ x13 : (ι → ι) → ι . 0) (λ x13 . 0)) (λ x13 : (ι → ι) → ι . 0) (λ x13 . 0))) 0 (λ x11 : (ι → ι) → ι . setsum (setsum (x0 (λ x12 . 0) 0 (λ x12 . 0) 0) 0) (x2 (λ x12 . setsum 0 0) (λ x12 . λ x13 : (ι → ι) → ι → ι . 0))) (λ x11 . x9)) x4 (λ x9 : (ι → ι) → ι . x5) (λ x9 . x9) = x4) ⟶ (∀ x4 . ∀ x5 : (ι → (ι → ι) → ι) → (ι → ι → ι) → (ι → ι) → ι . ∀ x6 : ι → (ι → ι) → ι . ∀ x7 . x0 (λ x9 . x9) (x1 (λ x9 x10 . 0) (Inj0 (x3 (λ x9 : ((ι → ι) → ι) → ((ι → ι) → ι → ι) → ι . 0) (setsum 0 0) 0 (setsum 0 0))) (λ x9 : (ι → ι) → ι . 0) (λ x9 . Inj1 (x5 (λ x10 . λ x11 : ι → ι . x11 0) (λ x10 x11 . Inj0 0) (λ x10 . Inj1 0)))) (λ x9 . x0 (λ x10 . x3 (λ x11 : ((ι → ι) → ι) → ((ι → ι) → ι → ι) → ι . 0) 0 (x0 (λ x11 . x7) (x2 (λ x11 . 0) (λ x11 . λ x12 : (ι → ι) → ι → ι . 0)) (λ x11 . x10) x10) x9) x7 (λ x10 . x1 (λ x11 x12 . x9) (x3 (λ x11 : ((ι → ι) → ι) → ((ι → ι) → ι → ι) → ι . x3 (λ x12 : ((ι → ι) → ι) → ((ι → ι) → ι → ι) → ι . 0) 0 0 0) (x0 (λ x11 . 0) 0 (λ x11 . 0) 0) (x3 (λ x11 : ((ι → ι) → ι) → ((ι → ι) → ι → ι) → ι . 0) 0 0 0) (Inj0 0)) (λ x11 : (ι → ι) → ι . Inj0 (x2 (λ x12 . 0) (λ x12 . λ x13 : (ι → ι) → ι → ι . 0))) (λ x11 . x3 (λ x12 : ((ι → ι) → ι) → ((ι → ι) → ι → ι) → ι . setsum 0 0) 0 x10 0)) 0) (x0 (λ x9 . x0 (λ x10 . 0) (x5 (λ x10 . λ x11 : ι → ι . setsum 0 0) (λ x10 x11 . x10) (λ x10 . x6 0 (λ x11 . 0))) (λ x10 . x0 (λ x11 . Inj0 0) x7 (λ x11 . x0 (λ x12 . 0) 0 (λ x12 . 0) 0) 0) (x2 (λ x10 . x10) (λ x10 . λ x11 : (ι → ι) → ι → ι . 0))) 0 (x3 (λ x9 : ((ι → ι) → ι) → ((ι → ι) → ι → ι) → ι . 0) (x2 (λ x9 . x3 (λ x10 : ((ι → ι) → ι) → ((ι → ι) → ι → ι) → ι . 0) 0 0 0) (λ x9 . λ x10 : (ι → ι) → ι → ι . setsum 0 0)) 0) (Inj0 0)) = setsum (Inj1 (x1 (λ x9 x10 . x3 (λ x11 : ((ι → ι) → ι) → ((ι → ι) → ι → ι) → ι . x0 (λ x12 . 0) 0 (λ x12 . 0) 0) x9 (setsum 0 0) (x0 (λ x11 . 0) 0 (λ x11 . 0) 0)) (x6 x4 (λ x9 . x5 (λ x10 . λ x11 : ι → ι . 0) (λ x10 x11 . 0) (λ x10 . 0))) (λ x9 : (ι → ι) → ι . Inj1 (x9 (λ x10 . 0))) Inj1)) (x5 (λ x9 . λ x10 : ι → ι . x2 (λ x11 . x10 (x10 0)) (λ x11 . λ x12 : (ι → ι) → ι → ι . 0)) (λ x9 x10 . Inj1 (x0 (λ x11 . x2 (λ x12 . 0) (λ x12 . λ x13 : (ι → ι) → ι → ι . 0)) (x3 (λ x11 : ((ι → ι) → ι) → ((ι → ι) → ι → ι) → ι . 0) 0 0 0) (λ x11 . x10) x9)) (λ x9 . x7))) ⟶ (∀ x4 : ι → ι . ∀ x5 x6 x7 . x0 (λ x9 . x1 (λ x10 x11 . x0 (λ x12 . 0) (setsum 0 (x1 (λ x12 x13 . 0) 0 (λ x12 : (ι → ι) → ι . 0) (λ x12 . 0))) (λ x12 . x3 (λ x13 : ((ι → ι) → ι) → ((ι → ι) → ι → ι) → ι . setsum 0 0) 0 (x2 (λ x13 . 0) (λ x13 . λ x14 : (ι → ι) → ι → ι . 0)) x9) (x1 (λ x12 x13 . 0) x9 (λ x12 : (ι → ι) → ι . x11) (λ x12 . x9))) x7 (λ x10 : (ι → ι) → ι . x7) (λ x10 . 0)) x5 (λ x9 . setsum (x3 (λ x10 : ((ι → ι) → ι) → ((ι → ι) → ι → ι) → ι . x2 (λ x11 . 0) (λ x11 . λ x12 : (ι → ι) → ι → ι . x10 (λ x13 : ι → ι . 0) (λ x13 : ι → ι . λ x14 . 0))) 0 (setsum 0 0) 0) x6) x7 = x5) ⟶ False (proof)Theorem b1ccf.. : ∀ x0 : (((((ι → ι) → ι) → (ι → ι) → ι → ι) → (ι → ι → ι) → ι → ι → ι) → ι → ((ι → ι) → ι) → ι) → ((ι → ι → ι) → ι) → (ι → (ι → ι) → ι → ι) → ι . ∀ x1 : (ι → ι → ι) → (((ι → ι) → ι → ι → ι) → ι → ι) → ι . ∀ x2 : (((ι → ι) → ι) → ι → ι → ι → ι → ι) → ι → ι . ∀ x3 : (((ι → ι → ι → ι) → ι → ι → ι → ι) → ι → ι) → ι → ι . (∀ x4 : ι → ι . ∀ x5 : (ι → ι → ι → ι) → ι . ∀ x6 : ι → ι . ∀ x7 . x3 (λ x9 : (ι → ι → ι → ι) → ι → ι → ι → ι . λ x10 . setsum x10 (x0 (λ x11 : (((ι → ι) → ι) → (ι → ι) → ι → ι) → (ι → ι → ι) → ι → ι → ι . λ x12 . λ x13 : (ι → ι) → ι . Inj1 (x1 (λ x14 x15 . 0) (λ x14 : (ι → ι) → ι → ι → ι . λ x15 . 0))) (λ x11 : ι → ι → ι . 0) (λ x11 . λ x12 : ι → ι . x2 (λ x13 : (ι → ι) → ι . λ x14 x15 x16 x17 . setsum 0 0)))) (x5 (λ x9 x10 x11 . x10)) = x5 (λ x9 x10 x11 . Inj1 x7)) ⟶ (∀ x4 : (ι → (ι → ι) → ι → ι) → ι . ∀ x5 : (((ι → ι) → ι) → (ι → ι) → ι → ι) → ι . ∀ x6 . ∀ x7 : (((ι → ι) → ι) → ι → ι) → (ι → ι → ι) → (ι → ι) → ι . x3 (λ x9 : (ι → ι → ι → ι) → ι → ι → ι → ι . λ x10 . Inj1 0) 0 = x5 (λ x9 : (ι → ι) → ι . λ x10 : ι → ι . λ x11 . x11)) ⟶ (∀ x4 . ∀ x5 : ι → ι → (ι → ι) → ι → ι . ∀ x6 : ι → ι . ∀ x7 . x2 (λ x9 : (ι → ι) → ι . λ x10 x11 x12 x13 . setsum (Inj1 (Inj0 (Inj1 0))) (Inj1 x12)) (setsum (x1 (λ x9 x10 . 0) (λ x9 : (ι → ι) → ι → ι → ι . λ x10 . Inj1 0)) (Inj1 0)) = Inj1 (x1 (λ x9 x10 . x6 x9) (λ x9 : (ι → ι) → ι → ι → ι . λ x10 . setsum (Inj0 (setsum 0 0)) 0))) ⟶ (∀ x4 : ι → ι → ι . ∀ x5 : ((ι → ι → ι) → ι) → ι . ∀ x6 : (((ι → ι) → ι) → ι) → ι → ι . ∀ x7 : ι → ι . x2 (λ x9 : (ι → ι) → ι . λ x10 x11 x12 x13 . x0 (λ x14 : (((ι → ι) → ι) → (ι → ι) → ι → ι) → (ι → ι → ι) → ι → ι → ι . λ x15 . λ x16 : (ι → ι) → ι . setsum (x2 (λ x17 : (ι → ι) → ι . λ x18 x19 x20 x21 . 0) (setsum 0 0)) (x16 (λ x17 . x17))) (λ x14 : ι → ι → ι . setsum x11 (x1 (λ x15 x16 . 0) (λ x15 : (ι → ι) → ι → ι → ι . λ x16 . setsum 0 0))) (λ x14 . λ x15 : ι → ι . λ x16 . Inj0 x14)) (x4 (x0 (λ x9 : (((ι → ι) → ι) → (ι → ι) → ι → ι) → (ι → ι → ι) → ι → ι → ι . λ x10 . λ x11 : (ι → ι) → ι . 0) (λ x9 : ι → ι → ι . x6 (λ x10 : (ι → ι) → ι . x6 (λ x11 : (ι → ι) → ι . 0) 0) (x1 (λ x10 x11 . 0) (λ x10 : (ι → ι) → ι → ι → ι . λ x11 . 0))) (λ x9 . λ x10 : ι → ι . λ x11 . x2 (λ x12 : (ι → ι) → ι . λ x13 x14 x15 x16 . x3 (λ x17 : (ι → ι → ι → ι) → ι → ι → ι → ι . λ x18 . 0) 0) 0)) (Inj0 0)) = Inj0 (x7 (x5 (λ x9 : ι → ι → ι . x3 (λ x10 : (ι → ι → ι → ι) → ι → ι → ι → ι . λ x11 . x10 (λ x12 x13 x14 . 0) 0 0 0) (Inj0 0))))) ⟶ (∀ x4 x5 x6 x7 . x1 (λ x9 x10 . x6) (λ x9 : (ι → ι) → ι → ι → ι . λ x10 . Inj1 0) = setsum (x0 (λ x9 : (((ι → ι) → ι) → (ι → ι) → ι → ι) → (ι → ι → ι) → ι → ι → ι . λ x10 . λ x11 : (ι → ι) → ι . Inj0 (x11 (λ x12 . setsum 0 0))) (λ x9 : ι → ι → ι . Inj1 (x9 (x0 (λ x10 : (((ι → ι) → ι) → (ι → ι) → ι → ι) → (ι → ι → ι) → ι → ι → ι . λ x11 . λ x12 : (ι → ι) → ι . 0) (λ x10 : ι → ι → ι . 0) (λ x10 . λ x11 : ι → ι . λ x12 . 0)) (x3 (λ x10 : (ι → ι → ι → ι) → ι → ι → ι → ι . λ x11 . 0) 0))) (λ x9 . λ x10 : ι → ι . λ x11 . setsum x11 (Inj0 (x1 (λ x12 x13 . 0) (λ x12 : (ι → ι) → ι → ι → ι . λ x13 . 0))))) x6) ⟶ (∀ x4 : (ι → ι) → ι . ∀ x5 . ∀ x6 : (((ι → ι) → ι) → (ι → ι) → ι → ι) → ι . ∀ x7 . x1 (λ x9 x10 . x7) (λ x9 : (ι → ι) → ι → ι → ι . λ x10 . Inj1 (x6 (λ x11 : (ι → ι) → ι . λ x12 : ι → ι . λ x13 . x0 (λ x14 : (((ι → ι) → ι) → (ι → ι) → ι → ι) → (ι → ι → ι) → ι → ι → ι . λ x15 . λ x16 : (ι → ι) → ι . x15) (λ x14 : ι → ι → ι . Inj1 0) (λ x14 . λ x15 : ι → ι . λ x16 . x13)))) = x7) ⟶ (∀ x4 . ∀ x5 : ι → ((ι → ι) → ι) → ι . ∀ x6 : (ι → ι) → ((ι → ι) → ι → ι) → (ι → ι) → ι → ι . ∀ x7 : ((ι → ι → ι) → ι) → ι . x0 (λ x9 : (((ι → ι) → ι) → (ι → ι) → ι → ι) → (ι → ι → ι) → ι → ι → ι . λ x10 . λ x11 : (ι → ι) → ι . x1 (λ x12 x13 . 0) (λ x12 : (ι → ι) → ι → ι → ι . λ x13 . x0 (λ x14 : (((ι → ι) → ι) → (ι → ι) → ι → ι) → (ι → ι → ι) → ι → ι → ι . λ x15 . λ x16 : (ι → ι) → ι . x3 (λ x17 : (ι → ι → ι → ι) → ι → ι → ι → ι . λ x18 . Inj1 0) (Inj0 0)) (λ x14 : ι → ι → ι . 0) (λ x14 . λ x15 : ι → ι . λ x16 . 0))) (λ x9 : ι → ι → ι . 0) (λ x9 . λ x10 : ι → ι . λ x11 . 0) = x1 (λ x9 x10 . x7 (λ x11 : ι → ι → ι . x9)) (λ x9 : (ι → ι) → ι → ι → ι . λ x10 . setsum 0 0)) ⟶ (∀ x4 : (ι → (ι → ι) → ι → ι) → ι → ι . ∀ x5 . ∀ x6 : (((ι → ι) → ι → ι) → ι → ι) → ι . ∀ x7 : ι → ι . x0 (λ x9 : (((ι → ι) → ι) → (ι → ι) → ι → ι) → (ι → ι → ι) → ι → ι → ι . λ x10 . λ x11 : (ι → ι) → ι . x3 (λ x12 : (ι → ι → ι → ι) → ι → ι → ι → ι . λ x13 . 0) (x9 (λ x12 : (ι → ι) → ι . λ x13 : ι → ι . λ x14 . Inj1 0) (λ x12 x13 . Inj0 (Inj0 0)) (x2 (λ x12 : (ι → ι) → ι . λ x13 x14 x15 x16 . x0 (λ x17 : (((ι → ι) → ι) → (ι → ι) → ι → ι) → (ι → ι → ι) → ι → ι → ι . λ x18 . λ x19 : (ι → ι) → ι . 0) (λ x17 : ι → ι → ι . 0) (λ x17 . λ x18 : ι → ι . λ x19 . 0)) x10) 0)) (λ x9 : ι → ι → ι . x9 (x6 (λ x10 : (ι → ι) → ι → ι . λ x11 . Inj0 (x2 (λ x12 : (ι → ι) → ι . λ x13 x14 x15 x16 . 0) 0))) 0) (λ x9 . λ x10 : ι → ι . λ x11 . x9) = setsum (x3 (λ x9 : (ι → ι → ι → ι) → ι → ι → ι → ι . λ x10 . x2 (λ x11 : (ι → ι) → ι . λ x12 x13 x14 x15 . x13) (x1 (λ x11 x12 . x3 (λ x13 : (ι → ι → ι → ι) → ι → ι → ι → ι . λ x14 . 0) 0) (λ x11 : (ι → ι) → ι → ι → ι . λ x12 . x9 (λ x13 x14 x15 . 0) 0 0 0))) (x4 (λ x9 . λ x10 : ι → ι . λ x11 . x3 (λ x12 : (ι → ι → ι → ι) → ι → ι → ι → ι . λ x13 . setsum 0 0) 0) (x4 (λ x9 . λ x10 : ι → ι . λ x11 . x2 (λ x12 : (ι → ι) → ι . λ x13 x14 x15 x16 . 0) 0) (x0 (λ x9 : (((ι → ι) → ι) → (ι → ι) → ι → ι) → (ι → ι → ι) → ι → ι → ι . λ x10 . λ x11 : (ι → ι) → ι . 0) (λ x9 : ι → ι → ι . 0) (λ x9 . λ x10 : ι → ι . λ x11 . 0))))) (x1 (λ x9 x10 . 0) (λ x9 : (ι → ι) → ι → ι → ι . λ x10 . 0))) ⟶ False (proof)Theorem 822fd.. : ∀ x0 : (((((ι → ι) → ι → ι) → ι → ι) → ι) → ι) → (ι → ι) → ι → ι . ∀ x1 : (((((ι → ι) → ι → ι) → ι) → ι → ι) → ι → ι → (ι → ι) → ι) → ι → (ι → (ι → ι) → ι) → ι . ∀ x2 : (ι → ι → ι) → (((ι → ι → ι) → (ι → ι) → ι → ι) → ι) → (ι → ι) → ι → (ι → ι) → ι . ∀ x3 : (ι → ι) → ((ι → ι) → ι → ι → ι → ι) → ι . (∀ x4 x5 x6 x7 . x3 (λ x9 . x7) (λ x9 : ι → ι . λ x10 x11 x12 . x3 (λ x13 . x3 (λ x14 . setsum x13 (setsum 0 0)) (λ x14 : ι → ι . λ x15 x16 x17 . x14 x15)) (λ x13 : ι → ι . λ x14 x15 x16 . x16)) = x3 (λ x9 . x6) (λ x9 : ι → ι . λ x10 x11 x12 . x12)) ⟶ (∀ x4 . ∀ x5 : ι → (ι → ι) → ι → ι . ∀ x6 : ι → ι → ι → ι → ι . ∀ x7 . x3 (λ x9 . x2 (λ x10 x11 . x2 (λ x12 x13 . setsum 0 0) (λ x12 : (ι → ι → ι) → (ι → ι) → ι → ι . Inj0 0) (setsum (setsum 0 0)) (setsum (Inj1 0) x11) (λ x12 . Inj1 x10)) (λ x10 : (ι → ι → ι) → (ι → ι) → ι → ι . 0) (λ x10 . 0) (x6 (Inj1 0) 0 (x5 0 (λ x10 . setsum 0 0) (x3 (λ x10 . 0) (λ x10 : ι → ι . λ x11 x12 x13 . 0))) (setsum 0 0)) (λ x10 . x1 (λ x11 : (((ι → ι) → ι → ι) → ι) → ι → ι . λ x12 x13 . λ x14 : ι → ι . x12) (x1 (λ x11 : (((ι → ι) → ι → ι) → ι) → ι → ι . λ x12 x13 . λ x14 : ι → ι . 0) (x6 0 0 0 0) (λ x11 . λ x12 : ι → ι . Inj1 0)) (λ x11 . λ x12 : ι → ι . x10))) (λ x9 : ι → ι . λ x10 x11 x12 . x1 (λ x13 : (((ι → ι) → ι → ι) → ι) → ι → ι . λ x14 x15 . λ x16 : ι → ι . 0) x11 (λ x13 . λ x14 : ι → ι . x14 0)) = Inj1 (setsum (x6 (Inj0 (Inj1 0)) 0 0 x7) x7)) ⟶ (∀ x4 x5 x6 . ∀ x7 : ι → ((ι → ι) → ι → ι) → (ι → ι) → ι . x2 (λ x9 x10 . x0 (λ x11 : (((ι → ι) → ι → ι) → ι → ι) → ι . x2 (λ x12 x13 . x1 (λ x14 : (((ι → ι) → ι → ι) → ι) → ι → ι . λ x15 x16 . λ x17 : ι → ι . Inj1 0) 0 (λ x14 . λ x15 : ι → ι . 0)) (λ x12 : (ι → ι → ι) → (ι → ι) → ι → ι . x11 (λ x13 : (ι → ι) → ι → ι . λ x14 . setsum 0 0)) (λ x12 . x1 (λ x13 : (((ι → ι) → ι → ι) → ι) → ι → ι . λ x14 x15 . λ x16 : ι → ι . 0) (setsum 0 0) (λ x13 . λ x14 : ι → ι . x12)) 0 (λ x12 . Inj0 0)) (λ x11 . x7 (x7 0 (λ x12 : ι → ι . λ x13 . x0 (λ x14 : (((ι → ι) → ι → ι) → ι → ι) → ι . 0) (λ x14 . 0) 0) (λ x12 . x1 (λ x13 : (((ι → ι) → ι → ι) → ι) → ι → ι . λ x14 x15 . λ x16 : ι → ι . 0) 0 (λ x13 . λ x14 : ι → ι . 0))) (λ x12 : ι → ι . setsum x10) (λ x12 . 0)) 0) (λ x9 : (ι → ι → ι) → (ι → ι) → ι → ι . x0 (λ x10 : (((ι → ι) → ι → ι) → ι → ι) → ι . x6) (λ x10 . 0) (setsum (x1 (λ x10 : (((ι → ι) → ι → ι) → ι) → ι → ι . λ x11 x12 . λ x13 : ι → ι . 0) 0 (λ x10 . λ x11 : ι → ι . x3 (λ x12 . 0) (λ x12 : ι → ι . λ x13 x14 x15 . 0))) (x3 (λ x10 . x6) (λ x10 : ι → ι . λ x11 x12 x13 . Inj0 0)))) (λ x9 . setsum (setsum (x0 (λ x10 : (((ι → ι) → ι → ι) → ι → ι) → ι . x10 (λ x11 : (ι → ι) → ι → ι . λ x12 . 0)) (λ x10 . x1 (λ x11 : (((ι → ι) → ι → ι) → ι) → ι → ι . λ x12 x13 . λ x14 : ι → ι . 0) 0 (λ x11 . λ x12 : ι → ι . 0)) (setsum 0 0)) (Inj1 0)) (setsum x6 0)) 0 (λ x9 . x1 (λ x10 : (((ι → ι) → ι → ι) → ι) → ι → ι . λ x11 x12 . λ x13 : ι → ι . 0) 0 (λ x10 . λ x11 : ι → ι . 0)) = setsum (setsum 0 (x1 (λ x9 : (((ι → ι) → ι → ι) → ι) → ι → ι . λ x10 x11 . λ x12 : ι → ι . x0 (λ x13 : (((ι → ι) → ι → ι) → ι → ι) → ι . 0) (λ x13 . x11) 0) (x2 (λ x9 x10 . setsum 0 0) (λ x9 : (ι → ι → ι) → (ι → ι) → ι → ι . setsum 0 0) (λ x9 . Inj1 0) 0 (λ x9 . Inj1 0)) (λ x9 . λ x10 : ι → ι . x7 (x2 (λ x11 x12 . 0) (λ x11 : (ι → ι → ι) → (ι → ι) → ι → ι . 0) (λ x11 . 0) 0 (λ x11 . 0)) (λ x11 : ι → ι . λ x12 . x10 0) (λ x11 . 0)))) (x3 (λ x9 . x0 (λ x10 : (((ι → ι) → ι → ι) → ι → ι) → ι . 0) (λ x10 . x9) (Inj0 0)) (λ x9 : ι → ι . λ x10 x11 x12 . 0))) ⟶ (∀ x4 . ∀ x5 : ι → ι → ι → ι → ι . ∀ x6 . ∀ x7 : (ι → (ι → ι) → ι) → ι → ι → ι → ι . x2 (λ x9 x10 . Inj0 0) (λ x9 : (ι → ι → ι) → (ι → ι) → ι → ι . x3 (λ x10 . 0) (λ x10 : ι → ι . λ x11 x12 x13 . 0)) (λ x9 . setsum (Inj0 (Inj0 (x1 (λ x10 : (((ι → ι) → ι → ι) → ι) → ι → ι . λ x11 x12 . λ x13 : ι → ι . 0) 0 (λ x10 . λ x11 : ι → ι . 0)))) x6) (x2 (λ x9 x10 . setsum (x0 (λ x11 : (((ι → ι) → ι → ι) → ι → ι) → ι . 0) (λ x11 . x2 (λ x12 x13 . 0) (λ x12 : (ι → ι → ι) → (ι → ι) → ι → ι . 0) (λ x12 . 0) 0 (λ x12 . 0)) (x3 (λ x11 . 0) (λ x11 : ι → ι . λ x12 x13 x14 . 0))) (setsum (setsum 0 0) (setsum 0 0))) (λ x9 : (ι → ι → ι) → (ι → ι) → ι → ι . 0) (λ x9 . 0) 0 (λ x9 . x1 (λ x10 : (((ι → ι) → ι → ι) → ι) → ι → ι . λ x11 x12 . λ x13 : ι → ι . x2 (λ x14 x15 . x12) (λ x14 : (ι → ι → ι) → (ι → ι) → ι → ι . setsum 0 0) (λ x14 . setsum 0 0) x11 (λ x14 . x3 (λ x15 . 0) (λ x15 : ι → ι . λ x16 x17 x18 . 0))) (x0 (λ x10 : (((ι → ι) → ι → ι) → ι → ι) → ι . x10 (λ x11 : (ι → ι) → ι → ι . λ x12 . 0)) (λ x10 . 0) (x7 (λ x10 . λ x11 : ι → ι . 0) 0 0 0)) (λ x10 . λ x11 : ι → ι . setsum (x1 (λ x12 : (((ι → ι) → ι → ι) → ι) → ι → ι . λ x13 x14 . λ x15 : ι → ι . 0) 0 (λ x12 . λ x13 : ι → ι . 0)) x9))) (λ x9 . x5 (Inj0 (x2 (λ x10 x11 . 0) (λ x10 : (ι → ι → ι) → (ι → ι) → ι → ι . x7 (λ x11 . λ x12 : ι → ι . 0) 0 0 0) (λ x10 . setsum 0 0) (setsum 0 0) (λ x10 . x2 (λ x11 x12 . 0) (λ x11 : (ι → ι → ι) → (ι → ι) → ι → ι . 0) (λ x11 . 0) 0 (λ x11 . 0)))) (setsum (x1 (λ x10 : (((ι → ι) → ι → ι) → ι) → ι → ι . λ x11 x12 . λ x13 : ι → ι . x10 (λ x14 : (ι → ι) → ι → ι . 0) 0) (x3 (λ x10 . 0) (λ x10 : ι → ι . λ x11 x12 x13 . 0)) (λ x10 . λ x11 : ι → ι . x7 (λ x12 . λ x13 : ι → ι . 0) 0 0 0)) (setsum x6 (x7 (λ x10 . λ x11 : ι → ι . 0) 0 0 0))) 0 (x5 (setsum x9 0) (x1 (λ x10 : (((ι → ι) → ι → ι) → ι) → ι → ι . λ x11 x12 . λ x13 : ι → ι . x11) (Inj0 0) (λ x10 . λ x11 : ι → ι . x11 0)) 0 0)) = x2 (λ x9 x10 . Inj0 (x7 (λ x11 . λ x12 : ι → ι . x12 x11) (x0 (λ x11 : (((ι → ι) → ι → ι) → ι → ι) → ι . 0) (λ x11 . 0) 0) 0 (setsum x10 x9))) (λ x9 : (ι → ι → ι) → (ι → ι) → ι → ι . x7 (λ x10 . λ x11 : ι → ι . x3 (λ x12 . x10) (λ x12 : ι → ι . λ x13 x14 x15 . 0)) 0 (x7 (λ x10 . λ x11 : ι → ι . x1 (λ x12 : (((ι → ι) → ι → ι) → ι) → ι → ι . λ x13 x14 . λ x15 : ι → ι . 0) x10 (λ x12 . λ x13 : ι → ι . x3 (λ x14 . 0) (λ x14 : ι → ι . λ x15 x16 x17 . 0))) (Inj0 (x3 (λ x10 . 0) (λ x10 : ι → ι . λ x11 x12 x13 . 0))) (Inj0 0) 0) (x0 (λ x10 : (((ι → ι) → ι → ι) → ι → ι) → ι . setsum 0 (x2 (λ x11 x12 . 0) (λ x11 : (ι → ι → ι) → (ι → ι) → ι → ι . 0) (λ x11 . 0) 0 (λ x11 . 0))) (λ x10 . 0) (Inj1 (Inj0 0)))) (λ x9 . x2 (λ x10 x11 . 0) (λ x10 : (ι → ι → ι) → (ι → ι) → ι → ι . 0) (λ x10 . 0) (x1 (λ x10 : (((ι → ι) → ι → ι) → ι) → ι → ι . λ x11 x12 . λ x13 : ι → ι . 0) (x5 0 0 (x3 (λ x10 . 0) (λ x10 : ι → ι . λ x11 x12 x13 . 0)) (setsum 0 0)) (λ x10 . λ x11 : ι → ι . setsum 0 (Inj0 0))) (λ x10 . x1 (λ x11 : (((ι → ι) → ι → ι) → ι) → ι → ι . λ x12 x13 . λ x14 : ι → ι . x12) 0 (λ x11 . λ x12 : ι → ι . x3 (λ x13 . x12 0) (λ x13 : ι → ι . λ x14 x15 x16 . 0)))) x6 (λ x9 . Inj1 (setsum x6 (Inj1 (Inj0 0))))) ⟶ (∀ x4 : ((ι → ι) → ι) → ι . ∀ x5 : (((ι → ι) → ι) → ι → ι) → ι . ∀ x6 : ι → ι . ∀ x7 : (ι → ι) → ι . x1 (λ x9 : (((ι → ι) → ι → ι) → ι) → ι → ι . λ x10 x11 . λ x12 : ι → ι . Inj0 (x3 (λ x13 . setsum x13 (x3 (λ x14 . 0) (λ x14 : ι → ι . λ x15 x16 x17 . 0))) (λ x13 : ι → ι . λ x14 x15 x16 . x1 (λ x17 : (((ι → ι) → ι → ι) → ι) → ι → ι . λ x18 x19 . λ x20 : ι → ι . setsum 0 0) (setsum 0 0) (λ x17 . λ x18 : ι → ι . x3 (λ x19 . 0) (λ x19 : ι → ι . λ x20 x21 x22 . 0))))) (x0 (λ x9 : (((ι → ι) → ι → ι) → ι → ι) → ι . 0) (λ x9 . setsum (x5 (λ x10 : (ι → ι) → ι . λ x11 . Inj0 0)) (x2 (λ x10 x11 . x1 (λ x12 : (((ι → ι) → ι → ι) → ι) → ι → ι . λ x13 x14 . λ x15 : ι → ι . 0) 0 (λ x12 . λ x13 : ι → ι . 0)) (λ x10 : (ι → ι → ι) → (ι → ι) → ι → ι . x1 (λ x11 : (((ι → ι) → ι → ι) → ι) → ι → ι . λ x12 x13 . λ x14 : ι → ι . 0) 0 (λ x11 . λ x12 : ι → ι . 0)) (λ x10 . x9) 0 (λ x10 . x1 (λ x11 : (((ι → ι) → ι → ι) → ι) → ι → ι . λ x12 x13 . λ x14 : ι → ι . 0) 0 (λ x11 . λ x12 : ι → ι . 0)))) (x1 (λ x9 : (((ι → ι) → ι → ι) → ι) → ι → ι . λ x10 x11 . λ x12 : ι → ι . Inj0 (x12 0)) 0 (λ x9 . λ x10 : ι → ι . x3 (λ x11 . x11) (λ x11 : ι → ι . λ x12 x13 x14 . Inj1 0)))) (λ x9 . λ x10 : ι → ι . 0) = x0 (λ x9 : (((ι → ι) → ι → ι) → ι → ι) → ι . x1 (λ x10 : (((ι → ι) → ι → ι) → ι) → ι → ι . λ x11 x12 . λ x13 : ι → ι . x0 (λ x14 : (((ι → ι) → ι → ι) → ι → ι) → ι . 0) (λ x14 . x3 (λ x15 . x1 (λ x16 : (((ι → ι) → ι → ι) → ι) → ι → ι . λ x17 x18 . λ x19 : ι → ι . 0) 0 (λ x16 . λ x17 : ι → ι . 0)) (λ x15 : ι → ι . λ x16 x17 x18 . setsum 0 0)) 0) (x2 (λ x10 x11 . setsum (x2 (λ x12 x13 . 0) (λ x12 : (ι → ι → ι) → (ι → ι) → ι → ι . 0) (λ x12 . 0) 0 (λ x12 . 0)) (Inj1 0)) (λ x10 : (ι → ι → ι) → (ι → ι) → ι → ι . x10 (λ x11 x12 . 0) (λ x11 . x11) 0) (λ x10 . x3 (λ x11 . x1 (λ x12 : (((ι → ι) → ι → ι) → ι) → ι → ι . λ x13 x14 . λ x15 : ι → ι . 0) 0 (λ x12 . λ x13 : ι → ι . 0)) (λ x11 : ι → ι . λ x12 x13 x14 . 0)) (x7 (λ x10 . x1 (λ x11 : (((ι → ι) → ι → ι) → ι) → ι → ι . λ x12 x13 . λ x14 : ι → ι . 0) 0 (λ x11 . λ x12 : ι → ι . 0))) (λ x10 . 0)) (λ x10 . λ x11 : ι → ι . x7 (λ x12 . x10))) (λ x9 . x6 (x7 (λ x10 . x0 (λ x11 : (((ι → ι) → ι → ι) → ι → ι) → ι . setsum 0 0) (λ x11 . Inj1 0) (x6 0)))) (x1 (λ x9 : (((ι → ι) → ι → ι) → ι) → ι → ι . λ x10 x11 . λ x12 : ι → ι . 0) 0 (λ x9 . λ x10 : ι → ι . 0))) ⟶ (∀ x4 : ((ι → ι → ι) → ι) → ι . ∀ x5 . ∀ x6 : (ι → (ι → ι) → ι → ι) → ι . ∀ x7 . x1 (λ x9 : (((ι → ι) → ι → ι) → ι) → ι → ι . λ x10 x11 . λ x12 : ι → ι . setsum (x9 (λ x13 : (ι → ι) → ι → ι . x3 (λ x14 . 0) (λ x14 : ι → ι . λ x15 x16 x17 . x2 (λ x18 x19 . 0) (λ x18 : (ι → ι → ι) → (ι → ι) → ι → ι . 0) (λ x18 . 0) 0 (λ x18 . 0))) x10) 0) 0 (λ x9 . λ x10 : ι → ι . 0) = x4 (λ x9 : ι → ι → ι . x6 (λ x10 . λ x11 : ι → ι . λ x12 . Inj1 (x1 (λ x13 : (((ι → ι) → ι → ι) → ι) → ι → ι . λ x14 x15 . λ x16 : ι → ι . setsum 0 0) 0 (λ x13 . λ x14 : ι → ι . setsum 0 0))))) ⟶ (∀ x4 . ∀ x5 : (ι → ι) → ι . ∀ x6 . ∀ x7 : ι → ι → ι . x0 (λ x9 : (((ι → ι) → ι → ι) → ι → ι) → ι . x5 (λ x10 . x1 (λ x11 : (((ι → ι) → ι → ι) → ι) → ι → ι . λ x12 x13 . λ x14 : ι → ι . 0) 0 (λ x11 . λ x12 : ι → ι . setsum (setsum 0 0) (x2 (λ x13 x14 . 0) (λ x13 : (ι → ι → ι) → (ι → ι) → ι → ι . 0) (λ x13 . 0) 0 (λ x13 . 0))))) (λ x9 . Inj1 0) (x5 (λ x9 . x2 (λ x10 x11 . x9) (λ x10 : (ι → ι → ι) → (ι → ι) → ι → ι . x10 (λ x11 x12 . Inj1 0) (λ x11 . x10 (λ x12 x13 . 0) (λ x12 . 0) 0) (Inj0 0)) (λ x10 . x1 (λ x11 : (((ι → ι) → ι → ι) → ι) → ι → ι . λ x12 x13 . λ x14 : ι → ι . x1 (λ x15 : (((ι → ι) → ι → ι) → ι) → ι → ι . λ x16 x17 . λ x18 : ι → ι . 0) 0 (λ x15 . λ x16 : ι → ι . 0)) (x3 (λ x11 . 0) (λ x11 : ι → ι . λ x12 x13 x14 . 0)) (λ x11 . λ x12 : ι → ι . Inj1 0)) (x0 (λ x10 : (((ι → ι) → ι → ι) → ι → ι) → ι . x10 (λ x11 : (ι → ι) → ι → ι . λ x12 . 0)) (λ x10 . x2 (λ x11 x12 . 0) (λ x11 : (ι → ι → ι) → (ι → ι) → ι → ι . 0) (λ x11 . 0) 0 (λ x11 . 0)) 0) (λ x10 . setsum (x3 (λ x11 . 0) (λ x11 : ι → ι . λ x12 x13 x14 . 0)) (x7 0 0)))) = setsum (setsum (x2 (λ x9 x10 . x7 (x2 (λ x11 x12 . 0) (λ x11 : (ι → ι → ι) → (ι → ι) → ι → ι . 0) (λ x11 . 0) 0 (λ x11 . 0)) (x7 0 0)) (λ x9 : (ι → ι → ι) → (ι → ι) → ι → ι . setsum 0 (Inj1 0)) (λ x9 . 0) (x1 (λ x9 : (((ι → ι) → ι → ι) → ι) → ι → ι . λ x10 x11 . λ x12 : ι → ι . x1 (λ x13 : (((ι → ι) → ι → ι) → ι) → ι → ι . λ x14 x15 . λ x16 : ι → ι . 0) 0 (λ x13 . λ x14 : ι → ι . 0)) (x7 0 0) (λ x9 . λ x10 : ι → ι . setsum 0 0)) (λ x9 . 0)) 0) (Inj1 (x5 (λ x9 . 0)))) ⟶ (∀ x4 : (ι → ι) → ((ι → ι) → ι → ι) → ι → ι . ∀ x5 x6 . ∀ x7 : ι → ((ι → ι) → ι) → ι → ι . x0 (λ x9 : (((ι → ι) → ι → ι) → ι → ι) → ι . setsum 0 x6) (λ x9 . 0) (setsum 0 (x7 (x3 (λ x9 . setsum 0 0) (λ x9 : ι → ι . λ x10 x11 x12 . Inj1 0)) (λ x9 : ι → ι . 0) 0)) = Inj0 0) ⟶ False (proof)Theorem 99962.. : ∀ x0 : ((ι → (ι → ι → ι) → ι) → (ι → ι → ι → ι) → ι) → (ι → ι → ι → ι → ι) → (ι → ι → ι) → ι . ∀ x1 : (ι → ι → ι) → (((ι → ι → ι) → ι) → ι) → ι → (ι → ι) → ι → ι → ι . ∀ x2 : ((ι → ((ι → ι) → ι) → ι → ι) → ((ι → ι → ι) → ι) → ι) → ((ι → ι) → ι) → ι . ∀ x3 : ((((ι → ι) → ι) → ι → (ι → ι) → ι → ι) → ι) → ((ι → ι) → ι) → ι → ι → ι → ι . (∀ x4 . ∀ x5 : ((ι → ι → ι) → ι) → ι → ι . ∀ x6 . ∀ x7 : ι → ι . x3 (λ x9 : ((ι → ι) → ι) → ι → (ι → ι) → ι → ι . 0) (λ x9 : ι → ι . 0) 0 x6 (x1 (λ x9 x10 . setsum 0 (x3 (λ x11 : ((ι → ι) → ι) → ι → (ι → ι) → ι → ι . setsum 0 0) (λ x11 : ι → ι . x9) (x0 (λ x11 : ι → (ι → ι → ι) → ι . λ x12 : ι → ι → ι → ι . 0) (λ x11 x12 x13 x14 . 0) (λ x11 x12 . 0)) (x0 (λ x11 : ι → (ι → ι → ι) → ι . λ x12 : ι → ι → ι → ι . 0) (λ x11 x12 x13 x14 . 0) (λ x11 x12 . 0)) (x1 (λ x11 x12 . 0) (λ x11 : (ι → ι → ι) → ι . 0) 0 (λ x11 . 0) 0 0))) (λ x9 : (ι → ι → ι) → ι . x3 (λ x10 : ((ι → ι) → ι) → ι → (ι → ι) → ι → ι . Inj1 (Inj0 0)) (λ x10 : ι → ι . x1 (λ x11 x12 . 0) (λ x11 : (ι → ι → ι) → ι . x1 (λ x12 x13 . 0) (λ x12 : (ι → ι → ι) → ι . 0) 0 (λ x12 . 0) 0 0) (x10 0) (λ x11 . 0) (x3 (λ x11 : ((ι → ι) → ι) → ι → (ι → ι) → ι → ι . 0) (λ x11 : ι → ι . 0) 0 0 0) (x10 0)) (x0 (λ x10 : ι → (ι → ι → ι) → ι . λ x11 : ι → ι → ι → ι . x1 (λ x12 x13 . 0) (λ x12 : (ι → ι → ι) → ι . 0) 0 (λ x12 . 0) 0 0) (λ x10 x11 x12 x13 . x10) (λ x10 x11 . Inj1 0)) (x7 0) (x2 (λ x10 : ι → ((ι → ι) → ι) → ι → ι . λ x11 : (ι → ι → ι) → ι . 0) (λ x10 : ι → ι . x0 (λ x11 : ι → (ι → ι → ι) → ι . λ x12 : ι → ι → ι → ι . 0) (λ x11 x12 x13 x14 . 0) (λ x11 x12 . 0)))) (x1 (λ x9 x10 . 0) (λ x9 : (ι → ι → ι) → ι . x5 (λ x10 : ι → ι → ι . 0) (x0 (λ x10 : ι → (ι → ι → ι) → ι . λ x11 : ι → ι → ι → ι . 0) (λ x10 x11 x12 x13 . 0) (λ x10 x11 . 0))) (x0 (λ x9 : ι → (ι → ι → ι) → ι . λ x10 : ι → ι → ι → ι . x6) (λ x9 x10 x11 x12 . setsum 0 0) (λ x9 x10 . Inj0 0)) (λ x9 . 0) (Inj0 (x3 (λ x9 : ((ι → ι) → ι) → ι → (ι → ι) → ι → ι . 0) (λ x9 : ι → ι . 0) 0 0 0)) (x1 (λ x9 x10 . 0) (λ x9 : (ι → ι → ι) → ι . x7 0) (x2 (λ x9 : ι → ((ι → ι) → ι) → ι → ι . λ x10 : (ι → ι → ι) → ι . 0) (λ x9 : ι → ι . 0)) (λ x9 . x2 (λ x10 : ι → ((ι → ι) → ι) → ι → ι . λ x11 : (ι → ι → ι) → ι . 0) (λ x10 : ι → ι . 0)) (x3 (λ x9 : ((ι → ι) → ι) → ι → (ι → ι) → ι → ι . 0) (λ x9 : ι → ι . 0) 0 0 0) (x0 (λ x9 : ι → (ι → ι → ι) → ι . λ x10 : ι → ι → ι → ι . 0) (λ x9 x10 x11 x12 . 0) (λ x9 x10 . 0)))) (λ x9 . Inj1 0) (x2 (λ x9 : ι → ((ι → ι) → ι) → ι → ι . λ x10 : (ι → ι → ι) → ι . 0) (λ x9 : ι → ι . x0 (λ x10 : ι → (ι → ι → ι) → ι . λ x11 : ι → ι → ι → ι . x9 0) (λ x10 x11 x12 x13 . x2 (λ x14 : ι → ((ι → ι) → ι) → ι → ι . λ x15 : (ι → ι → ι) → ι . 0) (λ x14 : ι → ι . 0)) (λ x10 x11 . Inj0 0))) (x5 (λ x9 : ι → ι → ι . setsum (x9 0 0) (x5 (λ x10 : ι → ι → ι . 0) 0)) 0)) = x6) ⟶ (∀ x4 x5 x6 x7 . x3 (λ x9 : ((ι → ι) → ι) → ι → (ι → ι) → ι → ι . setsum 0 (x1 (λ x10 x11 . x0 (λ x12 : ι → (ι → ι → ι) → ι . λ x13 : ι → ι → ι → ι . x2 (λ x14 : ι → ((ι → ι) → ι) → ι → ι . λ x15 : (ι → ι → ι) → ι . 0) (λ x14 : ι → ι . 0)) (λ x12 x13 x14 x15 . x0 (λ x16 : ι → (ι → ι → ι) → ι . λ x17 : ι → ι → ι → ι . 0) (λ x16 x17 x18 x19 . 0) (λ x16 x17 . 0)) (λ x12 x13 . x3 (λ x14 : ((ι → ι) → ι) → ι → (ι → ι) → ι → ι . 0) (λ x14 : ι → ι . 0) 0 0 0)) (λ x10 : (ι → ι → ι) → ι . x10 (λ x11 x12 . setsum 0 0)) (setsum (x3 (λ x10 : ((ι → ι) → ι) → ι → (ι → ι) → ι → ι . 0) (λ x10 : ι → ι . 0) 0 0 0) 0) (λ x10 . x0 (λ x11 : ι → (ι → ι → ι) → ι . λ x12 : ι → ι → ι → ι . x11 0 (λ x13 x14 . 0)) (λ x11 x12 x13 x14 . 0) (λ x11 x12 . 0)) (setsum (x9 (λ x10 : ι → ι . 0) 0 (λ x10 . 0) 0) (setsum 0 0)) (Inj0 x7))) (λ x9 : ι → ι . x0 (λ x10 : ι → (ι → ι → ι) → ι . λ x11 : ι → ι → ι → ι . 0) (λ x10 x11 x12 x13 . x1 (λ x14 x15 . x13) (λ x14 : (ι → ι → ι) → ι . x11) 0 (λ x14 . x2 (λ x15 : ι → ((ι → ι) → ι) → ι → ι . λ x16 : (ι → ι → ι) → ι . x0 (λ x17 : ι → (ι → ι → ι) → ι . λ x18 : ι → ι → ι → ι . 0) (λ x17 x18 x19 x20 . 0) (λ x17 x18 . 0)) (λ x15 : ι → ι . 0)) (x3 (λ x14 : ((ι → ι) → ι) → ι → (ι → ι) → ι → ι . x3 (λ x15 : ((ι → ι) → ι) → ι → (ι → ι) → ι → ι . 0) (λ x15 : ι → ι . 0) 0 0 0) (λ x14 : ι → ι . Inj1 0) 0 0 (Inj0 0)) (setsum x12 (x3 (λ x14 : ((ι → ι) → ι) → ι → (ι → ι) → ι → ι . 0) (λ x14 : ι → ι . 0) 0 0 0))) (λ x10 x11 . Inj0 x10)) 0 (Inj1 (x1 (λ x9 x10 . Inj1 (Inj1 0)) (λ x9 : (ι → ι → ι) → ι . x0 (λ x10 : ι → (ι → ι → ι) → ι . λ x11 : ι → ι → ι → ι . x3 (λ x12 : ((ι → ι) → ι) → ι → (ι → ι) → ι → ι . 0) (λ x12 : ι → ι . 0) 0 0 0) (λ x10 x11 x12 x13 . Inj1 0) (λ x10 x11 . 0)) (setsum (x3 (λ x9 : ((ι → ι) → ι) → ι → (ι → ι) → ι → ι . 0) (λ x9 : ι → ι . 0) 0 0 0) 0) (λ x9 . x0 (λ x10 : ι → (ι → ι → ι) → ι . λ x11 : ι → ι → ι → ι . x7) (λ x10 x11 x12 x13 . 0) (λ x10 x11 . 0)) (setsum (x3 (λ x9 : ((ι → ι) → ι) → ι → (ι → ι) → ι → ι . 0) (λ x9 : ι → ι . 0) 0 0 0) 0) (x0 (λ x9 : ι → (ι → ι → ι) → ι . λ x10 : ι → ι → ι → ι . x2 (λ x11 : ι → ((ι → ι) → ι) → ι → ι . λ x12 : (ι → ι → ι) → ι . 0) (λ x11 : ι → ι . 0)) (λ x9 x10 x11 x12 . Inj0 0) (λ x9 x10 . x6)))) (Inj0 x7) = x0 (λ x9 : ι → (ι → ι → ι) → ι . λ x10 : ι → ι → ι → ι . Inj0 (Inj0 0)) (λ x9 x10 x11 x12 . x1 (λ x13 x14 . x13) (λ x13 : (ι → ι → ι) → ι . 0) 0 (λ x13 . x2 (λ x14 : ι → ((ι → ι) → ι) → ι → ι . λ x15 : (ι → ι → ι) → ι . x0 (λ x16 : ι → (ι → ι → ι) → ι . λ x17 : ι → ι → ι → ι . setsum 0 0) (λ x16 x17 x18 x19 . x19) (λ x16 x17 . x1 (λ x18 x19 . 0) (λ x18 : (ι → ι → ι) → ι . 0) 0 (λ x18 . 0) 0 0)) (λ x14 : ι → ι . x3 (λ x15 : ((ι → ι) → ι) → ι → (ι → ι) → ι → ι . x1 (λ x16 x17 . 0) (λ x16 : (ι → ι → ι) → ι . 0) 0 (λ x16 . 0) 0 0) (λ x15 : ι → ι . x0 (λ x16 : ι → (ι → ι → ι) → ι . λ x17 : ι → ι → ι → ι . 0) (λ x16 x17 x18 x19 . 0) (λ x16 x17 . 0)) (Inj1 0) 0 (setsum 0 0))) (Inj1 0) 0) (λ x9 x10 . setsum 0 (x3 (λ x11 : ((ι → ι) → ι) → ι → (ι → ι) → ι → ι . setsum 0 0) (λ x11 : ι → ι . x10) (Inj1 (Inj1 0)) x6 (x1 (λ x11 x12 . x11) (λ x11 : (ι → ι → ι) → ι . x10) x10 (λ x11 . setsum 0 0) (x1 (λ x11 x12 . 0) (λ x11 : (ι → ι → ι) → ι . 0) 0 (λ x11 . 0) 0 0) x7)))) ⟶ (∀ x4 : ((ι → ι → ι) → (ι → ι) → ι → ι) → ι . ∀ x5 . ∀ x6 : ι → ι . ∀ x7 . x2 (λ x9 : ι → ((ι → ι) → ι) → ι → ι . λ x10 : (ι → ι → ι) → ι . x10 (λ x11 x12 . 0)) (λ x9 : ι → ι . 0) = x5) ⟶ (∀ x4 : ι → ((ι → ι) → ι → ι) → ι . ∀ x5 : ι → ι → ι → ι → ι . ∀ x6 : (ι → (ι → ι) → ι → ι) → ((ι → ι) → ι) → ι . ∀ x7 . x2 (λ x9 : ι → ((ι → ι) → ι) → ι → ι . λ x10 : (ι → ι → ι) → ι . 0) (λ x9 : ι → ι . 0) = Inj0 (x5 (x6 (λ x9 . λ x10 : ι → ι . λ x11 . setsum 0 0) (λ x9 : ι → ι . x6 (λ x10 . λ x11 : ι → ι . λ x12 . Inj0 0) (λ x10 : ι → ι . Inj0 0))) 0 0 (x4 0 (λ x9 : ι → ι . λ x10 . setsum (x0 (λ x11 : ι → (ι → ι → ι) → ι . λ x12 : ι → ι → ι → ι . 0) (λ x11 x12 x13 x14 . 0) (λ x11 x12 . 0)) (x3 (λ x11 : ((ι → ι) → ι) → ι → (ι → ι) → ι → ι . 0) (λ x11 : ι → ι . 0) 0 0 0))))) ⟶ (∀ x4 x5 . ∀ x6 : (ι → (ι → ι) → ι) → ι → ι → ι . ∀ x7 . x1 (λ x9 x10 . x9) (λ x9 : (ι → ι → ι) → ι . Inj0 (x6 (λ x10 . λ x11 : ι → ι . x10) 0 (x3 (λ x10 : ((ι → ι) → ι) → ι → (ι → ι) → ι → ι . 0) (λ x10 : ι → ι . x9 (λ x11 x12 . 0)) x5 (Inj1 0) (setsum 0 0)))) (setsum (setsum (setsum (Inj0 0) (Inj0 0)) (setsum (setsum 0 0) (setsum 0 0))) x4) (λ x9 . setsum (x1 (λ x10 x11 . x10) (λ x10 : (ι → ι → ι) → ι . x10 (λ x11 x12 . 0)) (x1 (λ x10 x11 . x7) (λ x10 : (ι → ι → ι) → ι . 0) (x3 (λ x10 : ((ι → ι) → ι) → ι → (ι → ι) → ι → ι . 0) (λ x10 : ι → ι . 0) 0 0 0) (λ x10 . Inj0 0) 0 (Inj0 0)) (λ x10 . x7) (x0 (λ x10 : ι → (ι → ι → ι) → ι . λ x11 : ι → ι → ι → ι . Inj1 0) (λ x10 x11 x12 x13 . 0) (λ x10 x11 . x1 (λ x12 x13 . 0) (λ x12 : (ι → ι → ι) → ι . 0) 0 (λ x12 . 0) 0 0)) x7) (Inj1 x5)) (x6 (λ x9 . λ x10 : ι → ι . x9) (setsum (Inj0 (x3 (λ x9 : ((ι → ι) → ι) → ι → (ι → ι) → ι → ι . 0) (λ x9 : ι → ι . 0) 0 0 0)) 0) (x1 (λ x9 x10 . x0 (λ x11 : ι → (ι → ι → ι) → ι . λ x12 : ι → ι → ι → ι . setsum 0 0) (λ x11 x12 x13 x14 . x12) (λ x11 x12 . setsum 0 0)) (λ x9 : (ι → ι → ι) → ι . x0 (λ x10 : ι → (ι → ι → ι) → ι . λ x11 : ι → ι → ι → ι . setsum 0 0) (λ x10 x11 x12 x13 . setsum 0 0) (λ x10 x11 . setsum 0 0)) (setsum 0 (x1 (λ x9 x10 . 0) (λ x9 : (ι → ι → ι) → ι . 0) 0 (λ x9 . 0) 0 0)) (λ x9 . Inj0 (x1 (λ x10 x11 . 0) (λ x10 : (ι → ι → ι) → ι . 0) 0 (λ x10 . 0) 0 0)) (x2 (λ x9 : ι → ((ι → ι) → ι) → ι → ι . λ x10 : (ι → ι → ι) → ι . Inj1 0) (λ x9 : ι → ι . x9 0)) (Inj0 (Inj0 0)))) x4 = x4) ⟶ (∀ x4 . ∀ x5 : ι → (ι → ι) → (ι → ι) → ι → ι . ∀ x6 x7 . x1 (λ x9 x10 . x9) (λ x9 : (ι → ι → ι) → ι . x7) 0 (λ x9 . x5 (x5 x9 (λ x10 . x3 (λ x11 : ((ι → ι) → ι) → ι → (ι → ι) → ι → ι . 0) (λ x11 : ι → ι . Inj1 0) (setsum 0 0) (x0 (λ x11 : ι → (ι → ι → ι) → ι . λ x12 : ι → ι → ι → ι . 0) (λ x11 x12 x13 x14 . 0) (λ x11 x12 . 0)) (setsum 0 0)) Inj1 0) (λ x10 . 0) (λ x10 . x6) 0) x7 (x1 (λ x9 x10 . x7) (λ x9 : (ι → ι → ι) → ι . Inj1 x6) x7 (λ x9 . x5 0 (λ x10 . setsum 0 x6) (λ x10 . x9) (Inj1 (x3 (λ x10 : ((ι → ι) → ι) → ι → (ι → ι) → ι → ι . 0) (λ x10 : ι → ι . 0) 0 0 0))) (Inj1 (x3 (λ x9 : ((ι → ι) → ι) → ι → (ι → ι) → ι → ι . setsum 0 0) (λ x9 : ι → ι . x1 (λ x10 x11 . 0) (λ x10 : (ι → ι → ι) → ι . 0) 0 (λ x10 . 0) 0 0) (setsum 0 0) (x0 (λ x9 : ι → (ι → ι → ι) → ι . λ x10 : ι → ι → ι → ι . 0) (λ x9 x10 x11 x12 . 0) (λ x9 x10 . 0)) (setsum 0 0))) (setsum (x0 (λ x9 : ι → (ι → ι → ι) → ι . λ x10 : ι → ι → ι → ι . x2 (λ x11 : ι → ((ι → ι) → ι) → ι → ι . λ x12 : (ι → ι → ι) → ι . 0) (λ x11 : ι → ι . 0)) (λ x9 x10 x11 x12 . 0) (λ x9 x10 . 0)) (x0 (λ x9 : ι → (ι → ι → ι) → ι . λ x10 : ι → ι → ι → ι . 0) (λ x9 x10 x11 x12 . x1 (λ x13 x14 . 0) (λ x13 : (ι → ι → ι) → ι . 0) 0 (λ x13 . 0) 0 0) (λ x9 x10 . x3 (λ x11 : ((ι → ι) → ι) → ι → (ι → ι) → ι → ι . 0) (λ x11 : ι → ι . 0) 0 0 0)))) = Inj0 x6) ⟶ (∀ x4 . ∀ x5 : ι → ι . ∀ x6 : ((ι → ι) → ι → ι) → ι . ∀ x7 : ι → ((ι → ι) → ι) → ι . x0 (λ x9 : ι → (ι → ι → ι) → ι . λ x10 : ι → ι → ι → ι . Inj0 (x3 (λ x11 : ((ι → ι) → ι) → ι → (ι → ι) → ι → ι . x11 (λ x12 : ι → ι . setsum 0 0) (x2 (λ x12 : ι → ((ι → ι) → ι) → ι → ι . λ x13 : (ι → ι → ι) → ι . 0) (λ x12 : ι → ι . 0)) (λ x12 . x10 0 0 0) (setsum 0 0)) (λ x11 : ι → ι . x0 (λ x12 : ι → (ι → ι → ι) → ι . λ x13 : ι → ι → ι → ι . setsum 0 0) (λ x12 x13 x14 x15 . x13) (λ x12 x13 . setsum 0 0)) (x10 (x1 (λ x11 x12 . 0) (λ x11 : (ι → ι → ι) → ι . 0) 0 (λ x11 . 0) 0 0) 0 0) (x3 (λ x11 : ((ι → ι) → ι) → ι → (ι → ι) → ι → ι . 0) (λ x11 : ι → ι . 0) (setsum 0 0) (x6 (λ x11 : ι → ι . λ x12 . 0)) (x1 (λ x11 x12 . 0) (λ x11 : (ι → ι → ι) → ι . 0) 0 (λ x11 . 0) 0 0)) 0)) (λ x9 x10 x11 x12 . 0) (λ x9 x10 . Inj1 (Inj1 x9)) = setsum (setsum (x0 (λ x9 : ι → (ι → ι → ι) → ι . λ x10 : ι → ι → ι → ι . Inj1 (x10 0 0 0)) (λ x9 x10 x11 x12 . x10) (λ x9 x10 . x0 (λ x11 : ι → (ι → ι → ι) → ι . λ x12 : ι → ι → ι → ι . 0) (λ x11 x12 x13 x14 . x3 (λ x15 : ((ι → ι) → ι) → ι → (ι → ι) → ι → ι . 0) (λ x15 : ι → ι . 0) 0 0 0) (λ x11 x12 . setsum 0 0))) (x6 (λ x9 : ι → ι . λ x10 . x0 (λ x11 : ι → (ι → ι → ι) → ι . λ x12 : ι → ι → ι → ι . x2 (λ x13 : ι → ((ι → ι) → ι) → ι → ι . λ x14 : (ι → ι → ι) → ι . 0) (λ x13 : ι → ι . 0)) (λ x11 x12 x13 x14 . x0 (λ x15 : ι → (ι → ι → ι) → ι . λ x16 : ι → ι → ι → ι . 0) (λ x15 x16 x17 x18 . 0) (λ x15 x16 . 0)) (λ x11 x12 . setsum 0 0)))) (x7 0 (λ x9 : ι → ι . 0))) ⟶ (∀ x4 : (ι → (ι → ι) → ι → ι) → ((ι → ι) → ι) → ι → ι → ι . ∀ x5 : (ι → ι) → ι → ι . ∀ x6 x7 . x0 (λ x9 : ι → (ι → ι → ι) → ι . λ x10 : ι → ι → ι → ι . x2 (λ x11 : ι → ((ι → ι) → ι) → ι → ι . λ x12 : (ι → ι → ι) → ι . x10 (x12 (λ x13 x14 . x3 (λ x15 : ((ι → ι) → ι) → ι → (ι → ι) → ι → ι . 0) (λ x15 : ι → ι . 0) 0 0 0)) (x2 (λ x13 : ι → ((ι → ι) → ι) → ι → ι . λ x14 : (ι → ι → ι) → ι . x11 0 (λ x15 : ι → ι . 0) 0) (λ x13 : ι → ι . x12 (λ x14 x15 . 0))) 0) (λ x11 : ι → ι . 0)) (λ x9 x10 x11 x12 . x12) (λ x9 x10 . x1 (λ x11 . x1 (λ x12 x13 . 0) (λ x12 : (ι → ι → ι) → ι . setsum (x12 (λ x13 x14 . 0)) x11) (x1 (λ x12 x13 . setsum 0 0) (λ x12 : (ι → ι → ι) → ι . x3 (λ x13 : ((ι → ι) → ι) → ι → (ι → ι) → ι → ι . 0) (λ x13 : ι → ι . 0) 0 0 0) x9 (λ x12 . x3 (λ x13 : ((ι → ι) → ι) → ι → (ι → ι) → ι → ι . 0) (λ x13 : ι → ι . 0) 0 0 0) (x3 (λ x12 : ((ι → ι) → ι) → ι → (ι → ι) → ι → ι . 0) (λ x12 : ι → ι . 0) 0 0 0) x10) (λ x12 . 0) x11) (λ x11 : (ι → ι → ι) → ι . 0) (x1 (λ x11 x12 . x12) (λ x11 : (ι → ι → ι) → ι . x9) 0 (λ x11 . 0) x7 0) (λ x11 . 0) (x3 (λ x11 : ((ι → ι) → ι) → ι → (ι → ι) → ι → ι . x9) (λ x11 : ι → ι . x0 (λ x12 : ι → (ι → ι → ι) → ι . λ x13 : ι → ι → ι → ι . x3 (λ x14 : ((ι → ι) → ι) → ι → (ι → ι) → ι → ι . 0) (λ x14 : ι → ι . 0) 0 0 0) (λ x12 x13 x14 x15 . x12) (λ x12 x13 . x10)) (setsum x6 (x1 (λ x11 x12 . 0) (λ x11 : (ι → ι → ι) → ι . 0) 0 (λ x11 . 0) 0 0)) (x1 (λ x11 x12 . 0) (λ x11 : (ι → ι → ι) → ι . x11 (λ x12 x13 . 0)) 0 (λ x11 . x3 (λ x12 : ((ι → ι) → ι) → ι → (ι → ι) → ι → ι . 0) (λ x12 : ι → ι . 0) 0 0 0) x9 x6) 0) 0) = setsum (x2 (λ x9 : ι → ((ι → ι) → ι) → ι → ι . λ x10 : (ι → ι → ι) → ι . Inj0 0) (λ x9 : ι → ι . Inj0 0)) (x2 (λ x9 : ι → ((ι → ι) → ι) → ι → ι . λ x10 : (ι → ι → ι) → ι . x9 (setsum 0 x7) (λ x11 : ι → ι . 0) (x2 (λ x11 : ι → ((ι → ι) → ι) → ι → ι . λ x12 : (ι → ι → ι) → ι . x10 (λ x13 x14 . 0)) (λ x11 : ι → ι . 0))) (λ x9 : ι → ι . x2 (λ x10 : ι → ((ι → ι) → ι) → ι → ι . λ x11 : (ι → ι → ι) → ι . x0 (λ x12 : ι → (ι → ι → ι) → ι . λ x13 : ι → ι → ι → ι . 0) (λ x12 x13 x14 x15 . x12) (λ x12 x13 . x1 (λ x14 x15 . 0) (λ x14 : (ι → ι → ι) → ι . 0) 0 (λ x14 . 0) 0 0)) (λ x10 : ι → ι . x2 (λ x11 : ι → ((ι → ι) → ι) → ι → ι . λ x12 : (ι → ι → ι) → ι . x0 (λ x13 : ι → (ι → ι → ι) → ι . λ x14 : ι → ι → ι → ι . 0) (λ x13 x14 x15 x16 . 0) (λ x13 x14 . 0)) (λ x11 : ι → ι . x7))))) ⟶ False (proof)Theorem e2151.. : ∀ x0 : (ι → ι) → (ι → ι → (ι → ι) → ι → ι) → ((ι → ι → ι) → (ι → ι) → ι → ι) → ι . ∀ x1 : (((((ι → ι) → ι → ι) → ι) → ((ι → ι) → ι → ι) → ι) → (((ι → ι) → ι → ι) → (ι → ι) → ι) → ι) → ι → ι → ι → ι . ∀ x2 : (ι → ι) → (ι → ι) → ι . ∀ x3 : (((((ι → ι) → ι → ι) → ι → ι → ι) → ((ι → ι) → ι → ι) → (ι → ι) → ι) → ι) → ι → ι . (∀ x4 . ∀ x5 : ι → ι . ∀ x6 : ι → ((ι → ι) → ι) → ι . ∀ x7 : ((ι → ι → ι) → ι → ι) → ι . x3 (λ x9 : (((ι → ι) → ι → ι) → ι → ι → ι) → ((ι → ι) → ι → ι) → (ι → ι) → ι . 0) 0 = x6 (setsum 0 0) (λ x9 : ι → ι . Inj0 (x6 (setsum (Inj0 0) (x5 0)) (λ x10 : ι → ι . setsum (x9 0) (x3 (λ x11 : (((ι → ι) → ι → ι) → ι → ι → ι) → ((ι → ι) → ι → ι) → (ι → ι) → ι . 0) 0))))) ⟶ (∀ x4 . ∀ x5 : (ι → ι → ι) → ι . ∀ x6 x7 . x3 (λ x9 : (((ι → ι) → ι → ι) → ι → ι → ι) → ((ι → ι) → ι → ι) → (ι → ι) → ι . 0) (x1 (λ x9 : (((ι → ι) → ι → ι) → ι) → ((ι → ι) → ι → ι) → ι . λ x10 : ((ι → ι) → ι → ι) → (ι → ι) → ι . Inj1 (x2 (λ x11 . setsum 0 0) (λ x11 . 0))) (x2 (λ x9 . 0) (λ x9 . x7)) (Inj1 0) (Inj1 (x0 (λ x9 . Inj1 0) (λ x9 x10 . λ x11 : ι → ι . λ x12 . x2 (λ x13 . 0) (λ x13 . 0)) (λ x9 : ι → ι → ι . λ x10 : ι → ι . λ x11 . x1 (λ x12 : (((ι → ι) → ι → ι) → ι) → ((ι → ι) → ι → ι) → ι . λ x13 : ((ι → ι) → ι → ι) → (ι → ι) → ι . 0) 0 0 0)))) = Inj0 (x0 (λ x9 . x3 (λ x10 : (((ι → ι) → ι → ι) → ι → ι → ι) → ((ι → ι) → ι → ι) → (ι → ι) → ι . 0) 0) (λ x9 x10 . λ x11 : ι → ι . λ x12 . x0 (λ x13 . x2 (λ x14 . 0) (λ x14 . 0)) (λ x13 x14 . λ x15 : ι → ι . x1 (λ x16 : (((ι → ι) → ι → ι) → ι) → ((ι → ι) → ι → ι) → ι . λ x17 : ((ι → ι) → ι → ι) → (ι → ι) → ι . setsum 0 0) 0 (x15 0)) (λ x13 : ι → ι → ι . λ x14 : ι → ι . λ x15 . 0)) (λ x9 : ι → ι → ι . λ x10 : ι → ι . λ x11 . x9 0 (Inj1 x11)))) ⟶ (∀ x4 : ι → ι . ∀ x5 : ((ι → ι → ι) → ι) → ι → (ι → ι) → ι . ∀ x6 : ι → (ι → ι → ι) → ι . ∀ x7 . x2 (λ x9 . 0) (λ x9 . x2 (λ x10 . x0 (λ x11 . 0) (λ x11 x12 . λ x13 : ι → ι . λ x14 . x3 (λ x15 : (((ι → ι) → ι → ι) → ι → ι → ι) → ((ι → ι) → ι → ι) → (ι → ι) → ι . Inj0 0) (x13 0)) (λ x11 : ι → ι → ι . λ x12 : ι → ι . λ x13 . 0)) (λ x10 . x0 (λ x11 . x7) (λ x11 x12 . λ x13 : ι → ι . λ x14 . 0) (λ x11 : ι → ι → ι . λ x12 : ι → ι . Inj1))) = Inj1 0) ⟶ (∀ x4 : ((ι → ι) → ι) → ι . ∀ x5 . ∀ x6 : ((ι → ι) → ι) → ι . ∀ x7 : (ι → ι) → ι → ι . x2 (λ x9 . Inj0 (x3 (λ x10 : (((ι → ι) → ι → ι) → ι → ι → ι) → ((ι → ι) → ι → ι) → (ι → ι) → ι . x2 (λ x11 . x2 (λ x12 . 0) (λ x12 . 0)) (λ x11 . 0)) x5)) (λ x9 . x6 (λ x10 : ι → ι . x2 (λ x11 . x3 (λ x12 : (((ι → ι) → ι → ι) → ι → ι → ι) → ((ι → ι) → ι → ι) → (ι → ι) → ι . setsum 0 0) 0) (λ x11 . 0))) = setsum (setsum 0 0) 0) ⟶ (∀ x4 . ∀ x5 : (ι → ι) → ι → ι . ∀ x6 x7 . x1 (λ x9 : (((ι → ι) → ι → ι) → ι) → ((ι → ι) → ι → ι) → ι . λ x10 : ((ι → ι) → ι → ι) → (ι → ι) → ι . 0) x7 0 0 = x7) ⟶ (∀ x4 x5 x6 : ι → ι . ∀ x7 . x1 (λ x9 : (((ι → ι) → ι → ι) → ι) → ((ι → ι) → ι → ι) → ι . λ x10 : ((ι → ι) → ι → ι) → (ι → ι) → ι . Inj1 0) (x6 0) (x1 (λ x9 : (((ι → ι) → ι → ι) → ι) → ((ι → ι) → ι → ι) → ι . λ x10 : ((ι → ι) → ι → ι) → (ι → ι) → ι . x7) (Inj0 (x4 (x6 0))) (setsum (Inj1 (x3 (λ x9 : (((ι → ι) → ι → ι) → ι → ι → ι) → ((ι → ι) → ι → ι) → (ι → ι) → ι . 0) 0)) (x6 0)) 0) (x6 (x0 (λ x9 . Inj1 (x5 0)) (λ x9 x10 . λ x11 : ι → ι . λ x12 . x2 (λ x13 . Inj0 0) (λ x13 . Inj1 0)) (λ x9 : ι → ι → ι . λ x10 : ι → ι . λ x11 . 0))) = setsum (x0 (λ x9 . Inj0 0) (λ x9 x10 . λ x11 : ι → ι . λ x12 . x12) (λ x9 : ι → ι → ι . λ x10 : ι → ι . λ x11 . 0)) 0) ⟶ (∀ x4 . ∀ x5 x6 : ι → ι . ∀ x7 . x0 (λ x9 . setsum (Inj0 0) (x0 (λ x10 . Inj0 (x3 (λ x11 : (((ι → ι) → ι → ι) → ι → ι → ι) → ((ι → ι) → ι → ι) → (ι → ι) → ι . 0) 0)) (λ x10 x11 . λ x12 : ι → ι . λ x13 . x3 (λ x14 : (((ι → ι) → ι → ι) → ι → ι → ι) → ((ι → ι) → ι → ι) → (ι → ι) → ι . x2 (λ x15 . 0) (λ x15 . 0)) x10) (λ x10 : ι → ι → ι . λ x11 : ι → ι . λ x12 . x3 (λ x13 : (((ι → ι) → ι → ι) → ι → ι → ι) → ((ι → ι) → ι → ι) → (ι → ι) → ι . x12) 0))) (λ x9 x10 . λ x11 : ι → ι . λ x12 . x2 (λ x13 . x10) (λ x13 . x10)) (λ x9 : ι → ι → ι . λ x10 : ι → ι . λ x11 . x1 (λ x12 : (((ι → ι) → ι → ι) → ι) → ((ι → ι) → ι → ι) → ι . λ x13 : ((ι → ι) → ι → ι) → (ι → ι) → ι . 0) (x9 (Inj1 0) x7) x7 (x0 (λ x12 . x11) (λ x12 x13 . λ x14 : ι → ι . λ x15 . Inj0 0) (λ x12 : ι → ι → ι . λ x13 : ι → ι . λ x14 . setsum 0 (Inj1 0)))) = setsum (setsum (x0 (λ x9 . 0) (λ x9 x10 . λ x11 : ι → ι . x11) (λ x9 : ι → ι → ι . λ x10 : ι → ι . λ x11 . setsum x11 (Inj1 0))) (Inj0 (setsum 0 (setsum 0 0)))) (setsum 0 0)) ⟶ (∀ x4 : (ι → ι) → ι . ∀ x5 : ((ι → ι → ι) → (ι → ι) → ι → ι) → ι → (ι → ι) → ι . ∀ x6 : ι → (ι → ι) → (ι → ι) → ι → ι . ∀ x7 : (ι → ι) → ι → ι . x0 (λ x9 . 0) (λ x9 x10 . λ x11 : ι → ι . λ x12 . 0) (λ x9 : ι → ι → ι . λ x10 : ι → ι . λ x11 . setsum (x2 (λ x12 . Inj0 0) (λ x12 . x11)) (x2 (λ x12 . x2 (λ x13 . Inj1 0) (λ x13 . Inj1 0)) (λ x12 . 0))) = x7 (λ x9 . Inj1 (x3 (λ x10 : (((ι → ι) → ι → ι) → ι → ι → ι) → ((ι → ι) → ι → ι) → (ι → ι) → ι . x2 (λ x11 . 0) (λ x11 . x0 (λ x12 . 0) (λ x12 x13 . λ x14 : ι → ι . λ x15 . 0) (λ x12 : ι → ι → ι . λ x13 : ι → ι . λ x14 . 0))) (Inj0 0))) (Inj0 0)) ⟶ False (proof)Theorem 89179.. : ∀ x0 : (ι → ι) → (ι → ι) → ι → ι → ι . ∀ x1 : (ι → (ι → ι → ι → ι) → (ι → ι) → (ι → ι) → ι → ι) → ι → (ι → ι → ι) → ι → ι . ∀ x2 : ((ι → ι) → (((ι → ι) → ι → ι) → ι) → ι) → (ι → ι) → (ι → ι) → ι . ∀ x3 : ((((ι → ι → ι) → (ι → ι) → ι → ι) → ((ι → ι) → ι → ι) → ι) → (ι → ι) → ((ι → ι) → ι) → ι) → ((((ι → ι) → ι) → ι → ι) → ((ι → ι) → ι → ι) → ι) → ι . (∀ x4 . ∀ x5 : (ι → ι → ι → ι) → (ι → ι → ι) → ι . ∀ x6 . ∀ x7 : (ι → ι) → ι . x3 (λ x9 : ((ι → ι → ι) → (ι → ι) → ι → ι) → ((ι → ι) → ι → ι) → ι . λ x10 : ι → ι . λ x11 : (ι → ι) → ι . setsum (Inj1 0) 0) (λ x9 : ((ι → ι) → ι) → ι → ι . λ x10 : (ι → ι) → ι → ι . setsum 0 (x3 (λ x11 : ((ι → ι → ι) → (ι → ι) → ι → ι) → ((ι → ι) → ι → ι) → ι . λ x12 : ι → ι . λ x13 : (ι → ι) → ι . x3 (λ x14 : ((ι → ι → ι) → (ι → ι) → ι → ι) → ((ι → ι) → ι → ι) → ι . λ x15 : ι → ι . λ x16 : (ι → ι) → ι . x1 (λ x17 . λ x18 : ι → ι → ι → ι . λ x19 x20 : ι → ι . λ x21 . 0) 0 (λ x17 x18 . 0) 0) (λ x14 : ((ι → ι) → ι) → ι → ι . λ x15 : (ι → ι) → ι → ι . x3 (λ x16 : ((ι → ι → ι) → (ι → ι) → ι → ι) → ((ι → ι) → ι → ι) → ι . λ x17 : ι → ι . λ x18 : (ι → ι) → ι . 0) (λ x16 : ((ι → ι) → ι) → ι → ι . λ x17 : (ι → ι) → ι → ι . 0))) (λ x11 : ((ι → ι) → ι) → ι → ι . λ x12 : (ι → ι) → ι → ι . x11 (λ x13 : ι → ι . Inj0 0) (Inj0 0)))) = x5 (λ x9 x10 x11 . setsum (setsum (x3 (λ x12 : ((ι → ι → ι) → (ι → ι) → ι → ι) → ((ι → ι) → ι → ι) → ι . λ x13 : ι → ι . λ x14 : (ι → ι) → ι . Inj1 0) (λ x12 : ((ι → ι) → ι) → ι → ι . λ x13 : (ι → ι) → ι → ι . Inj1 0)) (Inj0 x9)) (x1 (λ x12 . λ x13 : ι → ι → ι → ι . λ x14 x15 : ι → ι . λ x16 . x15 (x14 0)) (x7 (λ x12 . x9)) (λ x12 x13 . 0) (x1 (λ x12 . λ x13 : ι → ι → ι → ι . λ x14 x15 : ι → ι . λ x16 . Inj0 0) (x7 (λ x12 . 0)) (λ x12 x13 . x2 (λ x14 : ι → ι . λ x15 : ((ι → ι) → ι → ι) → ι . 0) (λ x14 . 0) (λ x14 . 0)) 0))) (λ x9 x10 . 0)) ⟶ (∀ x4 : ι → ι → (ι → ι) → ι . ∀ x5 x6 x7 . x3 (λ x9 : ((ι → ι → ι) → (ι → ι) → ι → ι) → ((ι → ι) → ι → ι) → ι . λ x10 : ι → ι . λ x11 : (ι → ι) → ι . x1 (λ x12 . λ x13 : ι → ι → ι → ι . λ x14 x15 : ι → ι . λ x16 . x1 (λ x17 . λ x18 : ι → ι → ι → ι . λ x19 x20 : ι → ι . λ x21 . x21) 0 (λ x17 x18 . x3 (λ x19 : ((ι → ι → ι) → (ι → ι) → ι → ι) → ((ι → ι) → ι → ι) → ι . λ x20 : ι → ι . λ x21 : (ι → ι) → ι . Inj0 0) (λ x19 : ((ι → ι) → ι) → ι → ι . λ x20 : (ι → ι) → ι → ι . x3 (λ x21 : ((ι → ι → ι) → (ι → ι) → ι → ι) → ((ι → ι) → ι → ι) → ι . λ x22 : ι → ι . λ x23 : (ι → ι) → ι . 0) (λ x21 : ((ι → ι) → ι) → ι → ι . λ x22 : (ι → ι) → ι → ι . 0))) (x0 (λ x17 . x14 0) (λ x17 . 0) (setsum 0 0) (x0 (λ x17 . 0) (λ x17 . 0) 0 0))) (Inj0 (Inj0 (x3 (λ x12 : ((ι → ι → ι) → (ι → ι) → ι → ι) → ((ι → ι) → ι → ι) → ι . λ x13 : ι → ι . λ x14 : (ι → ι) → ι . 0) (λ x12 : ((ι → ι) → ι) → ι → ι . λ x13 : (ι → ι) → ι → ι . 0)))) (λ x12 x13 . setsum x12 (x1 (λ x14 . λ x15 : ι → ι → ι → ι . λ x16 x17 : ι → ι . λ x18 . Inj1 0) (Inj0 0) (λ x14 x15 . 0) (x3 (λ x14 : ((ι → ι → ι) → (ι → ι) → ι → ι) → ((ι → ι) → ι → ι) → ι . λ x15 : ι → ι . λ x16 : (ι → ι) → ι . 0) (λ x14 : ((ι → ι) → ι) → ι → ι . λ x15 : (ι → ι) → ι → ι . 0)))) 0) (λ x9 : ((ι → ι) → ι) → ι → ι . λ x10 : (ι → ι) → ι → ι . 0) = setsum x5 0) ⟶ (∀ x4 : ι → ι → ι . ∀ x5 : (((ι → ι) → ι → ι) → ι) → ι → ι . ∀ x6 x7 . x2 (λ x9 : ι → ι . λ x10 : ((ι → ι) → ι → ι) → ι . Inj1 (x1 (λ x11 . λ x12 : ι → ι → ι → ι . λ x13 x14 : ι → ι . λ x15 . x2 (λ x16 : ι → ι . λ x17 : ((ι → ι) → ι → ι) → ι . x1 (λ x18 . λ x19 : ι → ι → ι → ι . λ x20 x21 : ι → ι . λ x22 . 0) 0 (λ x18 x19 . 0) 0) (λ x16 . x16) (λ x16 . x3 (λ x17 : ((ι → ι → ι) → (ι → ι) → ι → ι) → ((ι → ι) → ι → ι) → ι . λ x18 : ι → ι . λ x19 : (ι → ι) → ι . 0) (λ x17 : ((ι → ι) → ι) → ι → ι . λ x18 : (ι → ι) → ι → ι . 0))) x6 (λ x11 x12 . setsum (x2 (λ x13 : ι → ι . λ x14 : ((ι → ι) → ι → ι) → ι . 0) (λ x13 . 0) (λ x13 . 0)) 0) (x2 (λ x11 : ι → ι . λ x12 : ((ι → ι) → ι → ι) → ι . 0) (λ x11 . x3 (λ x12 : ((ι → ι → ι) → (ι → ι) → ι → ι) → ((ι → ι) → ι → ι) → ι . λ x13 : ι → ι . λ x14 : (ι → ι) → ι . 0) (λ x12 : ((ι → ι) → ι) → ι → ι . λ x13 : (ι → ι) → ι → ι . 0)) (λ x11 . 0)))) (λ x9 . x6) (λ x9 . 0) = x6) ⟶ (∀ x4 x5 x6 x7 . x2 (λ x9 : ι → ι . λ x10 : ((ι → ι) → ι → ι) → ι . Inj0 (x1 (λ x11 . λ x12 : ι → ι → ι → ι . λ x13 x14 : ι → ι . λ x15 . x1 (λ x16 . λ x17 : ι → ι → ι → ι . λ x18 x19 : ι → ι . λ x20 . x18 0) (x1 (λ x16 . λ x17 : ι → ι → ι → ι . λ x18 x19 : ι → ι . λ x20 . 0) 0 (λ x16 x17 . 0) 0) (λ x16 x17 . x14 0) (x1 (λ x16 . λ x17 : ι → ι → ι → ι . λ x18 x19 : ι → ι . λ x20 . 0) 0 (λ x16 x17 . 0) 0)) (setsum 0 (x0 (λ x11 . 0) (λ x11 . 0) 0 0)) (λ x11 x12 . setsum (Inj1 0) (setsum 0 0)) 0)) (λ x9 . 0) (λ x9 . x5) = x5) ⟶ (∀ x4 x5 . ∀ x6 : ι → ι . ∀ x7 . x1 (λ x9 . λ x10 : ι → ι → ι → ι . λ x11 x12 : ι → ι . λ x13 . Inj0 (x10 (setsum (x10 0 0 0) (Inj0 0)) (x12 (x3 (λ x14 : ((ι → ι → ι) → (ι → ι) → ι → ι) → ((ι → ι) → ι → ι) → ι . λ x15 : ι → ι . λ x16 : (ι → ι) → ι . 0) (λ x14 : ((ι → ι) → ι) → ι → ι . λ x15 : (ι → ι) → ι → ι . 0))) 0)) (Inj0 0) (λ x9 x10 . x2 (λ x11 : ι → ι . λ x12 : ((ι → ι) → ι → ι) → ι . x2 (λ x13 : ι → ι . λ x14 : ((ι → ι) → ι → ι) → ι . x3 (λ x15 : ((ι → ι → ι) → (ι → ι) → ι → ι) → ((ι → ι) → ι → ι) → ι . λ x16 : ι → ι . λ x17 : (ι → ι) → ι . Inj1 0) (λ x15 : ((ι → ι) → ι) → ι → ι . λ x16 : (ι → ι) → ι → ι . setsum 0 0)) (λ x13 . setsum 0 (Inj1 0)) (λ x13 . x1 (λ x14 . λ x15 : ι → ι → ι → ι . λ x16 x17 : ι → ι . λ x18 . x3 (λ x19 : ((ι → ι → ι) → (ι → ι) → ι → ι) → ((ι → ι) → ι → ι) → ι . λ x20 : ι → ι . λ x21 : (ι → ι) → ι . 0) (λ x19 : ((ι → ι) → ι) → ι → ι . λ x20 : (ι → ι) → ι → ι . 0)) 0 (λ x14 x15 . x1 (λ x16 . λ x17 : ι → ι → ι → ι . λ x18 x19 : ι → ι . λ x20 . 0) 0 (λ x16 x17 . 0) 0) (Inj0 0))) (λ x11 . Inj1 x10) (λ x11 . 0)) (setsum x5 (x1 (λ x9 . λ x10 : ι → ι → ι → ι . λ x11 x12 : ι → ι . λ x13 . 0) (x1 (λ x9 . λ x10 : ι → ι → ι → ι . λ x11 x12 : ι → ι . λ x13 . x11 0) x4 (λ x9 x10 . x10) x7) (λ x9 x10 . x10) 0)) = Inj0 (x6 (Inj0 0))) ⟶ (∀ x4 x5 x6 . ∀ x7 : ι → ((ι → ι) → ι) → ι . x1 (λ x9 . λ x10 : ι → ι → ι → ι . λ x11 x12 : ι → ι . λ x13 . x3 (λ x14 : ((ι → ι → ι) → (ι → ι) → ι → ι) → ((ι → ι) → ι → ι) → ι . λ x15 : ι → ι . λ x16 : (ι → ι) → ι . x0 (λ x17 . x15 (x16 (λ x18 . 0))) (λ x17 . setsum (x3 (λ x18 : ((ι → ι → ι) → (ι → ι) → ι → ι) → ((ι → ι) → ι → ι) → ι . λ x19 : ι → ι . λ x20 : (ι → ι) → ι . 0) (λ x18 : ((ι → ι) → ι) → ι → ι . λ x19 : (ι → ι) → ι → ι . 0)) 0) 0 (x2 (λ x17 : ι → ι . λ x18 : ((ι → ι) → ι → ι) → ι . x17 0) (λ x17 . Inj0 0) (λ x17 . x16 (λ x18 . 0)))) (λ x14 : ((ι → ι) → ι) → ι → ι . λ x15 : (ι → ι) → ι → ι . setsum (x12 0) (Inj1 (x12 0)))) (setsum 0 0) (λ x9 x10 . x6) (setsum (Inj1 (x1 (λ x9 . λ x10 : ι → ι → ι → ι . λ x11 x12 : ι → ι . λ x13 . 0) x5 (λ x9 x10 . setsum 0 0) (x1 (λ x9 . λ x10 : ι → ι → ι → ι . λ x11 x12 : ι → ι . λ x13 . 0) 0 (λ x9 x10 . 0) 0))) (x1 (λ x9 . λ x10 : ι → ι → ι → ι . λ x11 x12 : ι → ι . λ x13 . x11 (x12 0)) (x0 (λ x9 . 0) (λ x9 . 0) (setsum 0 0) (x2 (λ x9 : ι → ι . λ x10 : ((ι → ι) → ι → ι) → ι . 0) (λ x9 . 0) (λ x9 . 0))) (λ x9 x10 . 0) (Inj0 0))) = x6) ⟶ (∀ x4 . ∀ x5 : (((ι → ι) → ι) → ι → ι) → ι → (ι → ι) → ι → ι . ∀ x6 : (((ι → ι) → ι) → ι) → ι . ∀ x7 : ι → ((ι → ι) → ι) → (ι → ι) → ι → ι . x0 (λ x9 . Inj1 0) (setsum 0) 0 (Inj0 (x5 (λ x9 : (ι → ι) → ι . λ x10 . 0) 0 (λ x9 . 0) (x3 (λ x9 : ((ι → ι → ι) → (ι → ι) → ι → ι) → ((ι → ι) → ι → ι) → ι . λ x10 : ι → ι . λ x11 : (ι → ι) → ι . 0) (λ x9 : ((ι → ι) → ι) → ι → ι . λ x10 : (ι → ι) → ι → ι . 0)))) = setsum (setsum 0 (setsum (Inj0 (setsum 0 0)) (x0 (λ x9 . x5 (λ x10 : (ι → ι) → ι . λ x11 . 0) 0 (λ x10 . 0) 0) (λ x9 . setsum 0 0) (setsum 0 0) (Inj0 0)))) (x0 (λ x9 . Inj1 (x5 (λ x10 : (ι → ι) → ι . λ x11 . x2 (λ x12 : ι → ι . λ x13 : ((ι → ι) → ι → ι) → ι . 0) (λ x12 . 0) (λ x12 . 0)) (x2 (λ x10 : ι → ι . λ x11 : ((ι → ι) → ι → ι) → ι . 0) (λ x10 . 0) (λ x10 . 0)) (λ x10 . 0) (setsum 0 0))) (λ x9 . x0 (λ x10 . x6 (λ x11 : (ι → ι) → ι . x3 (λ x12 : ((ι → ι → ι) → (ι → ι) → ι → ι) → ((ι → ι) → ι → ι) → ι . λ x13 : ι → ι . λ x14 : (ι → ι) → ι . 0) (λ x12 : ((ι → ι) → ι) → ι → ι . λ x13 : (ι → ι) → ι → ι . 0))) (λ x10 . setsum (x1 (λ x11 . λ x12 : ι → ι → ι → ι . λ x13 x14 : ι → ι . λ x15 . 0) 0 (λ x11 x12 . 0) 0) x9) 0 (Inj0 (setsum 0 0))) x4 0)) ⟶ (∀ x4 . ∀ x5 : ι → ((ι → ι) → ι → ι) → (ι → ι) → ι . ∀ x6 . ∀ x7 : (ι → ι → ι) → ι → ι . x0 (λ x9 . x1 (λ x10 . λ x11 : ι → ι → ι → ι . λ x12 x13 : ι → ι . λ x14 . 0) (x5 (Inj0 x9) (λ x10 : ι → ι . λ x11 . x9) (λ x10 . x0 (λ x11 . x7 (λ x12 x13 . 0) 0) (λ x11 . 0) x10 (x7 (λ x11 x12 . 0) 0))) (λ x10 x11 . x11) (x7 (λ x10 x11 . x7 (λ x12 x13 . x13) x9) (x7 (λ x10 x11 . Inj1 0) (x0 (λ x10 . 0) (λ x10 . 0) 0 0)))) (λ x9 . x7 (λ x10 x11 . x3 (λ x12 : ((ι → ι → ι) → (ι → ι) → ι → ι) → ((ι → ι) → ι → ι) → ι . λ x13 : ι → ι . λ x14 : (ι → ι) → ι . x12 (λ x15 : ι → ι → ι . λ x16 : ι → ι . λ x17 . x0 (λ x18 . 0) (λ x18 . 0) 0 0) (λ x15 : ι → ι . λ x16 . Inj1 0)) (λ x12 : ((ι → ι) → ι) → ι → ι . λ x13 : (ι → ι) → ι → ι . x12 (λ x14 : ι → ι . x12 (λ x15 : ι → ι . 0) 0) (Inj0 0))) (x7 (λ x10 x11 . x9) (x3 (λ x10 : ((ι → ι → ι) → (ι → ι) → ι → ι) → ((ι → ι) → ι → ι) → ι . λ x11 : ι → ι . λ x12 : (ι → ι) → ι . x9) (λ x10 : ((ι → ι) → ι) → ι → ι . λ x11 : (ι → ι) → ι → ι . Inj1 0)))) x4 x6 = setsum (x7 (λ x9 x10 . 0) x4) 0) ⟶ False (proof)Theorem 71531.. : ∀ x0 : (ι → ι) → ι → ι . ∀ x1 : ((((ι → ι → ι) → ι) → ((ι → ι) → ι) → ι) → ι) → ι → ((ι → ι → ι) → ι) → ι . ∀ x2 : (ι → (((ι → ι) → ι → ι) → ι → ι) → ι) → (ι → ((ι → ι) → ι) → ι) → ι . ∀ x3 : ((ι → ι → ι) → ι) → ((((ι → ι) → ι → ι) → ι → ι → ι) → ι → ι) → (((ι → ι) → ι) → ι) → ι → ι . (∀ x4 : ι → ι → ι → ι . ∀ x5 : ι → ι → ι → ι → ι . ∀ x6 . ∀ x7 : ι → ι → ι . x3 (λ x9 : ι → ι → ι . 0) (λ x9 : ((ι → ι) → ι → ι) → ι → ι → ι . λ x10 . x6) (λ x9 : (ι → ι) → ι . setsum x6 0) (x2 (λ x9 . λ x10 : ((ι → ι) → ι → ι) → ι → ι . x3 (λ x11 : ι → ι → ι . 0) (λ x11 : ((ι → ι) → ι → ι) → ι → ι → ι . λ x12 . 0) (λ x11 : (ι → ι) → ι . 0) 0) (λ x9 . λ x10 : (ι → ι) → ι . setsum (x7 0 x9) x6)) = x6) ⟶ (∀ x4 : ι → ((ι → ι) → ι) → ι . ∀ x5 : ι → ι . ∀ x6 . ∀ x7 : ι → ((ι → ι) → ι) → ι → ι . x3 (λ x9 : ι → ι → ι . x3 (λ x10 : ι → ι → ι . 0) (λ x10 : ((ι → ι) → ι → ι) → ι → ι → ι . λ x11 . x0 (λ x12 . x9 0 (Inj0 0)) 0) (λ x10 : (ι → ι) → ι . x2 (λ x11 . λ x12 : ((ι → ι) → ι → ι) → ι → ι . Inj0 (x0 (λ x13 . 0) 0)) (λ x11 . λ x12 : (ι → ι) → ι . Inj0 0)) 0) (λ x9 : ((ι → ι) → ι → ι) → ι → ι → ι . λ x10 . 0) (λ x9 : (ι → ι) → ι . 0) (x3 (λ x9 : ι → ι → ι . Inj0 (x3 (λ x10 : ι → ι → ι . Inj0 0) (λ x10 : ((ι → ι) → ι → ι) → ι → ι → ι . λ x11 . Inj0 0) (λ x10 : (ι → ι) → ι . x1 (λ x11 : ((ι → ι → ι) → ι) → ((ι → ι) → ι) → ι . 0) 0 (λ x11 : ι → ι → ι . 0)) (Inj0 0))) (λ x9 : ((ι → ι) → ι → ι) → ι → ι → ι . λ x10 . Inj1 (x3 (λ x11 : ι → ι → ι . 0) (λ x11 : ((ι → ι) → ι → ι) → ι → ι → ι . λ x12 . setsum 0 0) (λ x11 : (ι → ι) → ι . x2 (λ x12 . λ x13 : ((ι → ι) → ι → ι) → ι → ι . 0) (λ x12 . λ x13 : (ι → ι) → ι . 0)) (Inj0 0))) (λ x9 : (ι → ι) → ι . 0) (Inj1 (x2 (λ x9 . λ x10 : ((ι → ι) → ι → ι) → ι → ι . x10 (λ x11 : ι → ι . λ x12 . 0) 0) (λ x9 . λ x10 : (ι → ι) → ι . setsum 0 0)))) = setsum (x2 (λ x9 . λ x10 : ((ι → ι) → ι → ι) → ι → ι . 0) (λ x9 . λ x10 : (ι → ι) → ι . x10 (λ x11 . 0))) (x2 (λ x9 . λ x10 : ((ι → ι) → ι → ι) → ι → ι . x6) (λ x9 . λ x10 : (ι → ι) → ι . Inj1 (Inj0 0)))) ⟶ (∀ x4 x5 x6 . ∀ x7 : ι → ι . x2 (λ x9 . λ x10 : ((ι → ι) → ι → ι) → ι → ι . 0) (λ x9 . λ x10 : (ι → ι) → ι . x6) = x6) ⟶ (∀ x4 : ι → ι → ι → ι . ∀ x5 x6 x7 . x2 (λ x9 . λ x10 : ((ι → ι) → ι → ι) → ι → ι . Inj0 (x3 (λ x11 : ι → ι → ι . setsum (x3 (λ x12 : ι → ι → ι . 0) (λ x12 : ((ι → ι) → ι → ι) → ι → ι → ι . λ x13 . 0) (λ x12 : (ι → ι) → ι . 0) 0) x7) (λ x11 : ((ι → ι) → ι → ι) → ι → ι → ι . λ x12 . x11 (λ x13 : ι → ι . λ x14 . x11 (λ x15 : ι → ι . λ x16 . 0) 0 0) 0 (Inj0 0)) (λ x11 : (ι → ι) → ι . x9) (Inj1 (Inj0 0)))) (λ x9 . λ x10 : (ι → ι) → ι . setsum 0 (setsum x9 0)) = x6) ⟶ (∀ x4 : ι → (ι → ι → ι) → ι . ∀ x5 x6 x7 . x1 (λ x9 : ((ι → ι → ι) → ι) → ((ι → ι) → ι) → ι . x2 (λ x10 . λ x11 : ((ι → ι) → ι → ι) → ι → ι . x7) (λ x10 . λ x11 : (ι → ι) → ι . x10)) 0 (λ x9 : ι → ι → ι . setsum 0 (x0 (x3 (λ x10 : ι → ι → ι . x1 (λ x11 : ((ι → ι → ι) → ι) → ((ι → ι) → ι) → ι . 0) 0 (λ x11 : ι → ι → ι . 0)) (λ x10 : ((ι → ι) → ι → ι) → ι → ι → ι . λ x11 . x11) (λ x10 : (ι → ι) → ι . x9 0 0)) 0)) = setsum (x2 (λ x9 . λ x10 : ((ι → ι) → ι → ι) → ι → ι . 0) (λ x9 . λ x10 : (ι → ι) → ι . x3 (λ x11 : ι → ι → ι . x2 (λ x12 . λ x13 : ((ι → ι) → ι → ι) → ι → ι . 0) (λ x12 . λ x13 : (ι → ι) → ι . x2 (λ x14 . λ x15 : ((ι → ι) → ι → ι) → ι → ι . 0) (λ x14 . λ x15 : (ι → ι) → ι . 0))) (λ x11 : ((ι → ι) → ι → ι) → ι → ι → ι . λ x12 . x2 (λ x13 . λ x14 : ((ι → ι) → ι → ι) → ι → ι . Inj1 0) (λ x13 . λ x14 : (ι → ι) → ι . Inj1 0)) (λ x11 : (ι → ι) → ι . 0) (x2 (λ x11 . λ x12 : ((ι → ι) → ι → ι) → ι → ι . 0) (λ x11 . λ x12 : (ι → ι) → ι . Inj0 0)))) 0) ⟶ (∀ x4 x5 . ∀ x6 : (ι → ι) → ι . ∀ x7 . x1 (λ x9 : ((ι → ι → ι) → ι) → ((ι → ι) → ι) → ι . x2 (λ x10 . λ x11 : ((ι → ι) → ι → ι) → ι → ι . x2 (λ x12 . λ x13 : ((ι → ι) → ι → ι) → ι → ι . 0) (λ x12 . λ x13 : (ι → ι) → ι . setsum x12 (setsum 0 0))) (λ x10 . λ x11 : (ι → ι) → ι . setsum (x2 (λ x12 . λ x13 : ((ι → ι) → ι → ι) → ι → ι . setsum 0 0) (λ x12 . λ x13 : (ι → ι) → ι . x0 (λ x14 . 0) 0)) 0)) x5 (λ x9 : ι → ι → ι . Inj0 (Inj1 (Inj0 0))) = setsum 0 (Inj1 x5)) ⟶ (∀ x4 x5 x6 x7 . x0 (λ x9 . 0) x7 = setsum (setsum 0 0) (setsum (x2 (λ x9 . λ x10 : ((ι → ι) → ι → ι) → ι → ι . setsum (Inj0 0) (setsum 0 0)) (λ x9 . λ x10 : (ι → ι) → ι . 0)) x5)) ⟶ (∀ x4 . ∀ x5 : (ι → ι → ι → ι) → ((ι → ι) → ι → ι) → ι . ∀ x6 x7 . x0 (λ x9 . x1 (λ x10 : ((ι → ι → ι) → ι) → ((ι → ι) → ι) → ι . 0) x6 (λ x10 : ι → ι → ι . setsum 0 x9)) (setsum (x1 (λ x9 : ((ι → ι → ι) → ι) → ((ι → ι) → ι) → ι . x6) (x3 (λ x9 : ι → ι → ι . Inj1 0) (λ x9 : ((ι → ι) → ι → ι) → ι → ι → ι . λ x10 . setsum 0 0) (λ x9 : (ι → ι) → ι . x3 (λ x10 : ι → ι → ι . 0) (λ x10 : ((ι → ι) → ι → ι) → ι → ι → ι . λ x11 . 0) (λ x10 : (ι → ι) → ι . 0) 0) (setsum 0 0)) (λ x9 : ι → ι → ι . 0)) 0) = x1 (λ x9 : ((ι → ι → ι) → ι) → ((ι → ι) → ι) → ι . setsum (x3 (λ x10 : ι → ι → ι . 0) (λ x10 : ((ι → ι) → ι → ι) → ι → ι → ι . λ x11 . 0) (λ x10 : (ι → ι) → ι . setsum (x2 (λ x11 . λ x12 : ((ι → ι) → ι → ι) → ι → ι . 0) (λ x11 . λ x12 : (ι → ι) → ι . 0)) 0) (x5 (λ x10 x11 x12 . x11) (λ x10 : ι → ι . λ x11 . 0))) (Inj1 (Inj0 0))) (Inj1 0) (λ x9 : ι → ι → ι . Inj0 (setsum x7 (x0 (λ x10 . x6) (Inj0 0))))) ⟶ False (proof)Theorem 43419.. : ∀ x0 : (ι → ι → ι) → ι → ι . ∀ x1 : (ι → ι → ι) → (ι → ι → (ι → ι) → ι → ι) → ι . ∀ x2 : (ι → ι) → (ι → ((ι → ι) → ι) → ι) → ι → ι . ∀ x3 : (ι → (((ι → ι) → ι) → ι) → ι) → (((ι → ι) → ι) → ι) → ι → ι . (∀ x4 : ι → ι → ι → ι → ι . ∀ x5 x6 x7 . x3 (λ x9 . λ x10 : ((ι → ι) → ι) → ι . Inj1 x7) (λ x9 : (ι → ι) → ι . setsum (setsum 0 (x2 (λ x10 . x9 (λ x11 . 0)) (λ x10 . λ x11 : (ι → ι) → ι . setsum 0 0) (x3 (λ x10 . λ x11 : ((ι → ι) → ι) → ι . 0) (λ x10 : (ι → ι) → ι . 0) 0))) 0) (x2 (λ x9 . x0 (λ x10 x11 . Inj0 0) (x0 (λ x10 x11 . 0) 0)) (λ x9 . λ x10 : (ι → ι) → ι . x1 (λ x11 x12 . x2 (λ x13 . 0) (λ x13 . λ x14 : (ι → ι) → ι . 0) x9) (λ x11 x12 . λ x13 : ι → ι . λ x14 . setsum 0 (Inj1 0))) x5) = x2 (λ x9 . x1 (λ x10 x11 . x9) (λ x10 x11 . λ x12 : ι → ι . λ x13 . Inj0 (Inj1 0))) (λ x9 . λ x10 : (ι → ι) → ι . Inj0 (x0 (λ x11 x12 . 0) x9)) (x0 (λ x9 x10 . x2 (λ x11 . 0) (λ x11 . λ x12 : (ι → ι) → ι . setsum 0 (x3 (λ x13 . λ x14 : ((ι → ι) → ι) → ι . 0) (λ x13 : (ι → ι) → ι . 0) 0)) (Inj1 (x2 (λ x11 . 0) (λ x11 . λ x12 : (ι → ι) → ι . 0) 0))) (x0 (λ x9 x10 . x1 (λ x11 x12 . x3 (λ x13 . λ x14 : ((ι → ι) → ι) → ι . 0) (λ x13 : (ι → ι) → ι . 0) 0) (λ x11 x12 . λ x13 : ι → ι . λ x14 . x3 (λ x15 . λ x16 : ((ι → ι) → ι) → ι . 0) (λ x15 : (ι → ι) → ι . 0) 0)) 0))) ⟶ (∀ x4 : (ι → ι → ι → ι) → ι . ∀ x5 . ∀ x6 : ((ι → ι) → ι → ι → ι) → ι → ι . ∀ x7 : ((ι → ι → ι) → ι) → ι → ι → ι . x3 (λ x9 . λ x10 : ((ι → ι) → ι) → ι . x9) (λ x9 : (ι → ι) → ι . setsum 0 (x9 (λ x10 . x0 (λ x11 x12 . x11) (Inj1 0)))) (x1 (λ x9 x10 . x3 (λ x11 . λ x12 : ((ι → ι) → ι) → ι . x2 (λ x13 . x3 (λ x14 . λ x15 : ((ι → ι) → ι) → ι . 0) (λ x14 : (ι → ι) → ι . 0) 0) (λ x13 . λ x14 : (ι → ι) → ι . 0) (x2 (λ x13 . 0) (λ x13 . λ x14 : (ι → ι) → ι . 0) 0)) (λ x11 : (ι → ι) → ι . x0 (λ x12 x13 . x10) 0) x10) (λ x9 x10 . λ x11 : ι → ι . Inj1)) = Inj0 (x2 (λ x9 . 0) (λ x9 . λ x10 : (ι → ι) → ι . 0) 0)) ⟶ (∀ x4 x5 . ∀ x6 : (ι → ι → ι → ι) → ι . ∀ x7 : (ι → (ι → ι) → ι) → ι → ι . x2 (λ x9 . setsum 0 (x6 (λ x10 x11 x12 . setsum (x0 (λ x13 x14 . 0) 0) (Inj0 0)))) (λ x9 . λ x10 : (ι → ι) → ι . x0 (λ x11 x12 . setsum (Inj1 (Inj0 0)) (Inj0 x11)) (x7 (λ x11 . λ x12 : ι → ι . x1 (λ x13 x14 . Inj1 0) (λ x13 x14 . λ x15 : ι → ι . λ x16 . setsum 0 0)) 0)) (x6 (λ x9 x10 x11 . 0)) = x0 (λ x9 x10 . Inj1 (x0 (λ x11 x12 . setsum 0 (x2 (λ x13 . 0) (λ x13 . λ x14 : (ι → ι) → ι . 0) 0)) (x3 (λ x11 . λ x12 : ((ι → ι) → ι) → ι . x1 (λ x13 x14 . 0) (λ x13 x14 . λ x15 : ι → ι . λ x16 . 0)) (λ x11 : (ι → ι) → ι . x11 (λ x12 . 0)) (Inj1 0)))) (setsum (Inj0 0) (Inj0 (setsum (setsum 0 0) (setsum 0 0))))) ⟶ (∀ x4 : (ι → ι) → ι . ∀ x5 x6 . ∀ x7 : ι → ι . x2 (λ x9 . x2 (λ x10 . x3 (λ x11 . λ x12 : ((ι → ι) → ι) → ι . x12 (λ x13 : ι → ι . 0)) (λ x11 : (ι → ι) → ι . x9) 0) (λ x10 . λ x11 : (ι → ι) → ι . x9) (setsum (setsum x5 x6) (x1 (λ x10 x11 . x2 (λ x12 . 0) (λ x12 . λ x13 : (ι → ι) → ι . 0) 0) (λ x10 x11 . λ x12 : ι → ι . λ x13 . 0)))) (λ x9 . λ x10 : (ι → ι) → ι . x2 (λ x11 . 0) (λ x11 . λ x12 : (ι → ι) → ι . x3 (λ x13 . λ x14 : ((ι → ι) → ι) → ι . 0) (λ x13 : (ι → ι) → ι . Inj1 x11) (x12 (λ x13 . setsum 0 0))) 0) 0 = x2 (λ x9 . x6) (λ x9 . λ x10 : (ι → ι) → ι . setsum (setsum 0 (Inj0 0)) (setsum (setsum (x0 (λ x11 x12 . 0) 0) x9) 0)) (x0 (λ x9 x10 . setsum x6 0) (x7 (setsum (x3 (λ x9 . λ x10 : ((ι → ι) → ι) → ι . 0) (λ x9 : (ι → ι) → ι . 0) 0) x5)))) ⟶ (∀ x4 . ∀ x5 : (((ι → ι) → ι) → (ι → ι) → ι → ι) → ι → ι . ∀ x6 : ι → ι . ∀ x7 : (ι → ι → ι → ι) → ι → (ι → ι) → ι . x1 (λ x9 x10 . Inj0 0) (λ x9 x10 . λ x11 : ι → ι . λ x12 . 0) = x4) ⟶ (∀ x4 : ι → (ι → ι) → (ι → ι) → ι → ι . ∀ x5 x6 . ∀ x7 : ((ι → ι) → ι) → ι → (ι → ι) → ι . x1 (λ x9 x10 . 0) (λ x9 x10 . λ x11 : ι → ι . λ x12 . 0) = setsum (Inj1 0) x6) ⟶ (∀ x4 : ι → ι . ∀ x5 . ∀ x6 : ((ι → ι → ι) → ι) → ι → ι → ι . ∀ x7 : (ι → ι → ι) → ι . x0 (λ x9 x10 . x6 (λ x11 : ι → ι → ι . x7 (λ x12 x13 . x3 (λ x14 . λ x15 : ((ι → ι) → ι) → ι . x13) (λ x14 : (ι → ι) → ι . x13) (x1 (λ x14 x15 . 0) (λ x14 x15 . λ x16 : ι → ι . λ x17 . 0)))) (setsum (setsum (Inj1 0) (x1 (λ x11 x12 . 0) (λ x11 x12 . λ x13 : ι → ι . λ x14 . 0))) 0) (setsum (x3 (λ x11 . λ x12 : ((ι → ι) → ι) → ι . setsum 0 0) (λ x11 : (ι → ι) → ι . 0) (setsum 0 0)) (Inj1 (x1 (λ x11 x12 . 0) (λ x11 x12 . λ x13 : ι → ι . λ x14 . 0))))) (setsum (Inj0 (Inj1 0)) (x1 (λ x9 x10 . x2 (λ x11 . x10) (λ x11 . λ x12 : (ι → ι) → ι . x1 (λ x13 x14 . 0) (λ x13 x14 . λ x15 : ι → ι . λ x16 . 0)) (x6 (λ x11 : ι → ι → ι . 0) 0 0)) (λ x9 x10 . λ x11 : ι → ι . λ x12 . 0))) = x6 (λ x9 : ι → ι → ι . setsum (setsum x5 x5) (x9 (x0 (λ x10 x11 . x1 (λ x12 x13 . 0) (λ x12 x13 . λ x14 : ι → ι . λ x15 . 0)) (x9 0 0)) (setsum (x6 (λ x10 : ι → ι → ι . 0) 0 0) (x0 (λ x10 x11 . 0) 0)))) x5 (Inj0 (x7 (λ x9 x10 . x9)))) ⟶ (∀ x4 : ι → ι → ι . ∀ x5 x6 . ∀ x7 : ι → ι . x0 (λ x9 x10 . x2 (λ x11 . x7 0) (λ x11 . λ x12 : (ι → ι) → ι . x1 (λ x13 x14 . Inj1 (Inj1 0)) (λ x13 x14 . λ x15 : ι → ι . λ x16 . setsum 0 x13)) 0) (x0 (λ x9 x10 . x2 (λ x11 . x0 (λ x12 x13 . 0) (setsum 0 0)) (λ x11 . λ x12 : (ι → ι) → ι . x1 (λ x13 x14 . x0 (λ x15 x16 . 0) 0) (λ x13 x14 . λ x15 : ι → ι . λ x16 . 0)) (x7 (x2 (λ x11 . 0) (λ x11 . λ x12 : (ι → ι) → ι . 0) 0))) (setsum (x2 (λ x9 . x0 (λ x10 x11 . 0) 0) (λ x9 . λ x10 : (ι → ι) → ι . setsum 0 0) (x0 (λ x9 x10 . 0) 0)) (x7 (Inj1 0)))) = x2 (λ x9 . Inj1 0) (λ x9 . λ x10 : (ι → ι) → ι . Inj0 (setsum x9 0)) (x7 (x4 (Inj1 (x7 0)) (x0 (λ x9 x10 . x1 (λ x11 x12 . 0) (λ x11 x12 . λ x13 : ι → ι . λ x14 . 0)) 0)))) ⟶ False (proof) |
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