Let x0 of type (ι → (CT2 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 be given.
Let x2 of type (((ι → ι) → (ι → ι → ι) → ι → ι) → ι) → ι → ι → ι be given.
Let x3 of type (ι → (CT2 ι) → ι → ι) → ι → ι be given.
Assume H0:
∀ x4 : ι → ι . ∀ x5 x6 x7 . x3 (λ x8 . λ x9 : (ι → ι → ι) → ι . λ x10 . x3 (λ x11 . λ x12 : (ι → ι → ι) → ι . λ x13 . x2 (λ x14 : (ι → ι) → (ι → ι → ι) → ι → ι . x3 (λ x15 . λ x16 : (ι → ι → ι) → ι . λ x17 . x0 (λ x18 . λ x19 : (ι → ι → ι) → ι . 0) 0) x11) x10 (x3 (λ x14 . λ x15 : (ι → ι → ι) → ι . λ x16 . x2 (λ x17 : (ι → ι) → (ι → ι → ι) → ι → ι . 0) 0 0) (x0 (λ x14 . λ x15 : (ι → ι → ι) → ι . 0) 0))) 0) 0 = x3 (λ x8 . λ x9 : (ι → ι → ι) → ι . λ x10 . x0 (λ x11 . λ x12 : (ι → ι → ι) → ι . x1 (λ x13 : ι → ι . x12 (λ x14 x15 . x0 (λ x16 . λ x17 : (ι → ι → ι) → ι . 0) 0)) (λ x13 x14 . λ x15 : ι → ι . λ x16 . 0) (Inj0 (x3 (λ x13 . λ x14 : (ι → ι → ι) → ι . λ x15 . 0) 0)) (λ x13 x14 . setsum (x2 (λ x15 : (ι → ι) → (ι → ι → ι) → ι → ι . 0) 0 0) (Inj1 0)) (λ x13 . 0) 0) (x0 (λ x11 . λ x12 : (ι → ι → ι) → ι . x2 (λ x13 : (ι → ι) → (ι → ι → ι) → ι → ι . x2 (λ x14 : (ι → ι) → (ι → ι → ι) → ι → ι . 0) 0 0) (setsum 0 0) (x9 (λ x13 x14 . 0))) x8)) (Inj1 (x0 (λ x8 . λ x9 : (ι → ι → ι) → ι . 0) x6)).
Assume H1: ∀ x4 x5 . ∀ x6 : ((ι → ι) → ι → ι → ι) → ι . ∀ x7 : ι → (ι → ι → ι) → ι . x3 (λ x8 . λ x9 : (ι → ι → ι) → ι . λ x10 . x8) 0 = x4.
Apply FalseE with
... ⟶ ... ⟶ ... ⟶ (∀ x4 : (ι → (ι → ι) → ι) → ι . ∀ x5 . ∀ x6 : ι → ι → ι → ι → ι . ∀ x7 . x1 (λ x8 : ι → ι . x6 (Inj0 (x0 (λ x9 . λ x10 : (ι → ι → ι) → ι . setsum 0 0) (x8 0))) (x2 (λ x9 : (ι → ι) → (ι → ι → ι) → ι → ι . 0) (Inj0 (x0 (λ x9 . λ x10 : (ι → ι → ι) → ι . 0) 0)) (setsum 0 0)) 0 0) (λ x8 x9 . λ x10 : ι → ι . λ x11 . Inj1 0) (x3 (λ x8 . λ x9 : (ι → ι → ι) → ι . λ x10 . setsum 0 0) (x6 x5 x7 0 (x1 (λ x8 : ι → ι . x7) (λ x8 x9 . λ x10 : ι → ι . λ x11 . x2 (λ x12 : (ι → ι) → (ι → ι → ι) → ι → ι . 0) 0 0) ... ... ... ...))) ... ... 0 = ...) ⟶ (∀ x4 : ι → ι . ∀ x5 : ι → ι → ι . ∀ x6 x7 . x0 (λ x8 . λ x9 : (ι → ι → ι) → ι . x8) (x2 (λ x8 : (ι → ι) → (ι → ι → ι) → ι → ι . setsum (setsum x6 0) (setsum 0 (setsum 0 0))) (x5 x6 (Inj1 0)) (x4 (setsum (Inj0 0) x7))) = setsum 0 (x0 (λ x8 . λ x9 : (ι → ι → ι) → ι . setsum (setsum (x0 (λ x10 . λ x11 : (ι → ι → ι) → ι . 0) 0) (x1 (λ x10 : ι → ι . 0) (λ x10 x11 . λ x12 : ι → ι . λ x13 . 0) 0 (λ x10 x11 . 0) (λ x10 . 0) 0)) (x2 (λ x10 : (ι → ι) → (ι → ι → ι) → ι → ι . x3 (λ x11 . λ x12 : (ι → ι → ι) → ι . λ x13 . 0) 0) 0 (Inj0 0))) 0)) ⟶ (∀ x4 . ∀ x5 : ι → ι . ∀ x6 : (ι → ι) → ι . ∀ x7 . x0 (λ x8 . λ x9 : (ι → ι → ι) → ι . x7) (x3 (λ x8 . λ x9 : (ι → ι → ι) → ι . λ x10 . Inj0 0) x4) = x7) ⟶ False.