Let x0 of type ((ι → (ι → ι) → ι) → ι) → ι → ι → ι be given.
Let x1 of type (((ι → ι → ι) → (ι → ι → ι) → ι → ι) → ((ι → ι → ι) → (ι → ι) → ι) → ι → ι → ι) → ι → (CT2 ι) → ι be given.
Let x2 of type (ι → ((ι → ι) → ι → ι) → ((ι → ι) → ι → ι) → ι) → ι → ((ι → ι) → ι) → ι be given.
Let x3 of type ((((ι → ι) → (ι → ι) → ι) → ι) → ι → CT2 ι) → (ι → ι → (ι → ι) → ι) → (((ι → ι) → ι → ι) → ι) → ι be given.
Assume H0: ∀ x4 x5 . ∀ x6 : (((ι → ι) → ι → ι) → ι → ι) → ι → ι → ι . ∀ x7 : ι → ι → (ι → ι) → ι → ι . x3 (λ x8 : ((ι → ι) → (ι → ι) → ι) → ι . λ x9 . λ x10 : ι → ι → ι . x8 (λ x11 x12 : ι → ι . x11 (x10 (x0 (λ x13 : ι → (ι → ι) → ι . 0) 0 0) 0))) (λ x8 x9 . λ x10 : ι → ι . 0) (λ x8 : (ι → ι) → ι → ι . 0) = x5.
Apply FalseE with
... ⟶ ... ⟶ ... ⟶ ... ⟶ (∀ x4 . ...) ⟶ (∀ x4 : ι → ι → ι . ∀ x5 : (ι → ι → ι) → ι → ι . ∀ x6 : ι → ι . ∀ x7 . x0 (λ x8 : ι → (ι → ι) → ι . 0) (x5 (λ x8 x9 . setsum x8 0) 0) (Inj1 (setsum (x3 (λ x8 : ((ι → ι) → (ι → ι) → ι) → ι . λ x9 . λ x10 : ι → ι → ι . x2 (λ x11 . λ x12 x13 : (ι → ι) → ι → ι . 0) 0 (λ x11 : ι → ι . 0)) (λ x8 x9 . λ x10 : ι → ι . x8) (λ x8 : (ι → ι) → ι → ι . x8 (λ x9 . 0) 0)) (Inj1 (x0 (λ x8 : ι → (ι → ι) → ι . 0) 0 0)))) = x5 (λ x8 x9 . x6 (x1 (λ x10 : (ι → ι → ι) → (ι → ι → ι) → ι → ι . λ x11 : (ι → ι → ι) → (ι → ι) → ι . λ x12 x13 . x1 (λ x14 : (ι → ι → ι) → (ι → ι → ι) → ι → ι . λ x15 : (ι → ι → ι) → (ι → ι) → ι . λ x16 x17 . x2 (λ x18 . λ x19 x20 : (ι → ι) → ι → ι . 0) 0 (λ x18 : ι → ι . 0)) (Inj0 0) (λ x14 : ι → ι → ι . x12)) (x1 (λ x10 : (ι → ι → ι) → (ι → ι → ι) → ι → ι . λ x11 : (ι → ι → ι) → (ι → ι) → ι . λ x12 x13 . x2 (λ x14 . λ x15 x16 : (ι → ι) → ι → ι . 0) 0 (λ x14 : ι → ι . 0)) (Inj0 0) (λ x10 : 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 . 0) (λ x11 : (ι → ι) → ι → ι . 0))) (λ x10 : ι → ι → ι . x8))) (x4 0 (Inj1 0))) ⟶ (∀ x4 x5 . ∀ x6 x7 : ι → ι . x0 (λ x8 : ι → (ι → 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 . Inj1 (x2 (λ x15 . λ x16 x17 : (ι → ι) → ι → ι . 0) 0 (λ x15 : ι → ι . 0))) (λ x12 x13 . λ x14 : ι → ι . x1 (λ x15 : (ι → ι → ι) → (ι → ι → ι) → ι → ι . λ x16 : (ι → ι → ι) → (ι → ι) → ι . λ x17 x18 . x17) 0 (λ x15 : ι → ι → ι . x2 (λ x16 . λ x17 x18 : (ι → ι) → ι → ι . 0) 0 (λ x16 : ι → ι . 0))) (λ x12 : (ι → ι) → ι → ι . 0)) (x6 0) (λ x9 : ι → ι . x9 0)) (x3 (λ x8 : ((ι → ι) → (ι → ι) → ι) → ι . λ x9 . λ x10 : ι → ι → ι . x8 (λ x11 x12 : ι → ι . 0)) (λ x8 x9 . λ x10 : ι → ι . x8) (λ x8 : (ι → ι) → ι → ι . x6 0)) 0 = x2 (λ x8 . λ x9 x10 : (ι → ι) → ι → ι . setsum (setsum x8 (x3 (λ x11 : ((ι → ι) → (ι → ι) → ι) → ι . λ x12 . λ x13 : ι → ι → ι . x2 (λ x14 . λ x15 x16 : (ι → ι) → ι → ι . 0) 0 (λ x14 : ι → ι . 0)) (λ x11 x12 . λ x13 : ι → ι . x10 (λ x14 . 0) 0) (λ x11 : (ι → ι) → ι → ι . setsum 0 0))) 0) (x2 (λ x8 . λ x9 x10 : (ι → ι) → ι → ι . setsum 0 0) (x6 0) (λ x8 : ι → ι . setsum (x0 (λ x9 : ι → (ι → ι) → ι . x2 (λ x10 . λ x11 x12 : (ι → ι) → ι → ι . 0) 0 (λ x10 : ι → ι . 0)) 0 0) (x6 (x6 0)))) (λ x8 : ι → ι . Inj1 (x2 (λ x9 . λ x10 x11 : (ι → ι) → ι → ι . x9) (x0 (λ x9 : ι → (ι → ι) → ι . setsum 0 0) 0 (Inj0 0)) (λ x9 : ι → ι . setsum (setsum 0 0) (x6 0))))) ⟶ False.