Let x0 of type (ι → ι) → ((ι → (ι → ι) → ι) → ι → (ι → ι) → ι) → (ι → ι → ι → ι) → ((ι → ι) → ι → ι) → ι be given.
Let x1 of type (ι → ι → ι) → ((ι → ι) → ι) → ι be given.
Let x2 of type (((CT2 ι) → ι → ι) → ι) → (ι → ι) → ι → CT2 ι be given.
Let x3 of type ((ι → ι) → ι) → (ι → ((ι → ι) → ι) → ι → ι → ι) → ι be given.
Assume H0:
∀ x4 : (ι → ι) → ι . ∀ x5 x6 . ∀ x7 : (ι → ι) → (ι → ι → ι) → ι . x3 (λ x8 : ι → ι . setsum (x0 (λ x9 . setsum 0 0) (λ x9 : ι → (ι → ι) → ι . λ x10 . λ x11 : ι → ι . 0) (λ x9 x10 x11 . x10) (λ x9 : ι → ι . λ x10 . x7 (λ x11 . Inj1 0) (λ x11 x12 . x2 (λ x13 : ((ι → ι → ι) → ι) → ι → ι . 0) (λ x13 . 0) 0 (λ x13 x14 . 0)))) 0) (λ x8 . λ x9 : (ι → ι) → ι . λ x10 x11 . Inj0 (x2 (λ x12 : ((ι → ι → ι) → ι) → ι → ι . x1 (λ x13 x14 . x14) (λ x13 : ι → ι . 0)) (λ x12 . x3 (λ x13 : ι → ι . 0) (λ x13 . λ x14 : (ι → ι) → ι . λ x15 x16 . x1 (λ x17 x18 . 0) (λ x17 : ι → ι . 0))) 0 (λ x12 x13 . setsum 0 x13))) = x6.
Apply FalseE with
... ⟶ ... ⟶ ... ⟶ (∀ x4 . ∀ x5 : ι → (ι → ι → ι) → ι → ι . ∀ x6 x7 . x1 (λ x8 x9 . 0) (λ x8 : ι → ι . x1 (λ x9 x10 . Inj1 0) (λ x9 : ι → ι . 0)) = x1 (λ x8 x9 . x0 (λ x10 . x1 (λ x11 x12 . x11) ...) ... ... ...) ...) ⟶ (∀ x4 x5 . ∀ x6 : ((ι → ι → ι) → ι) → ι . ∀ x7 . x1 (λ x8 x9 . 0) (λ x8 : ι → ι . x8 (x8 (setsum (x8 0) x5))) = x5) ⟶ (∀ x4 x5 x6 . ∀ x7 : ι → ι . x0 (λ x8 . x6) (λ x8 : ι → (ι → ι) → ι . λ x9 . λ x10 : ι → ι . x2 (λ x11 : ((ι → ι → ι) → ι) → ι → ι . setsum (x2 (λ x12 : ((ι → ι → ι) → ι) → ι → ι . x12 (λ x13 : ι → ι → ι . 0) 0) (λ x12 . x10 0) 0 (λ x12 x13 . setsum 0 0)) (x0 (λ x12 . 0) (λ x12 : ι → (ι → ι) → ι . λ x13 . λ x14 : ι → ι . 0) (λ x12 x13 x14 . x14) (λ x12 : ι → ι . λ x13 . x13))) (λ x11 . x10 x11) 0 (λ x11 x12 . x0 (λ x13 . x3 (λ x14 : ι → ι . x1 (λ x15 x16 . 0) (λ x15 : ι → ι . 0)) (λ x14 . λ x15 : (ι → ι) → ι . λ x16 x17 . x3 (λ x18 : ι → ι . 0) (λ x18 . λ x19 : (ι → ι) → ι . λ x20 x21 . 0))) (λ x13 : ι → (ι → ι) → ι . λ x14 . λ x15 : ι → ι . x15 0) (λ x13 x14 x15 . setsum (Inj0 0) 0) (λ x13 : ι → ι . λ x14 . x1 (λ x15 x16 . x3 (λ x17 : ι → ι . 0) (λ x17 . λ x18 : (ι → ι) → ι . λ x19 x20 . 0)) (λ x15 : ι → ι . x14)))) (λ x8 x9 x10 . x8) (λ x8 : ι → ι . λ x9 . x3 (λ x10 : ι → ι . x9) (λ x10 . λ x11 : (ι → ι) → ι . λ x12 x13 . 0)) = Inj0 (Inj0 (x2 (λ x8 : ((ι → ι → ι) → ι) → ι → ι . x1 (λ x9 x10 . 0) (λ x9 : ι → ι . 0)) (λ x8 . x5) 0 (λ x8 x9 . x1 (λ x10 x11 . x11) (λ x10 : ι → ι . Inj1 0))))) ⟶ (∀ x4 x5 x6 x7 . x0 (λ x8 . x6) (λ x8 : ι → (ι → ι) → ι . λ x9 . λ x10 : ι → ι . x1 (λ x11 x12 . 0) (λ x11 : ι → ι . Inj0 (setsum (x3 (λ x12 : ι → ι . 0) (λ x12 . λ x13 : (ι → ι) → ι . λ x14 x15 . 0)) (x8 0 (λ x12 . 0))))) (λ x8 x9 x10 . x7) (λ x8 : ι → ι . λ x9 . x1 (λ x10 x11 . Inj1 x9) (λ x10 : ι → ι . Inj1 (Inj0 0))) = x6) ⟶ False.