Let x0 of type (CT3 ι) → ((((ι → ι) → ι → ι) → ι) → CT2 ι) → ι be given.
Let x1 of type (((((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) → ι) → (ι → (ι → ι) → (ι → ι) → ι → ι) → ι be given.
Let x3 of type (ι → ι) → (ι → ι → (ι → ι) → ι) → ι be given.
Assume H0: ∀ x4 x5 x6 x7 . x3 (λ x8 . 0) (λ x8 x9 . λ x10 : ι → ι . 0) = x6.
Apply FalseE with
... ⟶ (∀ x4 : (((ι → ι) → ι → ι) → ι) → ((ι → ι) → ι) → (ι → ι) → ι → ι . ∀ x5 . ∀ x6 : ι → ι . ∀ x7 : (ι → ι) → ι → ι . x2 (λ x8 : (((ι → ι) → ι → ι) → (ι → ι) → ι) → ι → ι → ι → ι . 0) (λ x8 . λ x9 x10 : ι → ι . λ x11 . x0 (λ x12 : ι → ι → ι → ι . 0) (λ x12 : ((ι → ι) → ι → ι) → ι . λ x13 : ι → ι → ι . x2 (λ x14 : (((ι → ι) → ι → ι) → (ι → ι) → ι) → ι → ι → ι → ι . 0) (λ x14 . λ x15 x16 : ι → ι . λ x17 . setsum (x0 (λ x18 : ι → ι → ι → ι . 0) (λ x18 : ((ι → ι) → ι → ι) → ι . λ x19 : ι → ι → ι . 0)) (setsum 0 0)))) = x0 ... ...) ⟶ (∀ x4 : ι → ι → (ι → ι) → ι . ∀ x5 . ∀ x6 : ((ι → ι → ι) → ι → ι → ι) → ι → ι . ∀ x7 : ((ι → ι → ι) → ι) → ι . x2 (λ x8 : (((ι → ι) → ι → ι) → (ι → ι) → ι) → ι → ι → ι → ι . Inj0 0) (λ x8 . λ x9 x10 : ι → ι . λ x11 . 0) = setsum 0 (x4 (setsum (x4 (setsum 0 0) (x1 (λ x8 : (((ι → ι) → ι → ι) → ι → ι) → ι . 0) 0) (λ x8 . 0)) (x3 (λ x8 . 0) (λ x8 x9 . λ x10 : ι → ι . setsum 0 0))) (x2 (λ x8 : (((ι → ι) → ι → ι) → (ι → ι) → ι) → ι → ι → ι → ι . x0 (λ x9 : ι → ι → ι → ι . x7 (λ x10 : ι → ι → ι . 0)) (λ x9 : ((ι → ι) → ι → ι) → ι . λ x10 : ι → ι → ι . x7 (λ x11 : ι → ι → ι . 0))) (λ x8 . λ x9 x10 : ι → ι . λ x11 . 0)) (λ x8 . x1 (λ x9 : (((ι → ι) → ι → ι) → ι → ι) → ι . x2 (λ x10 : (((ι → ι) → ι → ι) → (ι → ι) → ι) → ι → ι → ι → ι . 0) (λ x10 . λ x11 x12 : ι → ι . λ x13 . 0)) (setsum 0 (x1 (λ x9 : (((ι → ι) → ι → ι) → ι → ι) → ι . 0) 0))))) ⟶ (∀ x4 x5 . ∀ x6 : ι → ι . ∀ x7 . x1 (λ x8 : (((ι → ι) → ι → ι) → ι → ι) → ι . setsum (x0 (λ x9 : ι → ι → ι → ι . x9 0 x7 0) (λ x9 : ((ι → ι) → ι → ι) → ι . λ x10 : ι → ι → ι . x3 (λ x11 . x9 (λ x12 : ι → ι . λ x13 . 0)) (λ x11 x12 . λ x13 : ι → ι . 0))) (Inj0 0)) 0 = Inj1 x4) ⟶ (∀ x4 : (((ι → ι) → ι → ι) → ι) → ι . ∀ x5 . ∀ x6 : ((ι → ι) → (ι → ι) → ι) → (ι → ι) → ι . ∀ x7 : ι → ι → (ι → ι) → ι → ι . x1 (λ x8 : (((ι → ι) → ι → ι) → ι → ι) → ι . x5) (Inj1 0) = Inj0 (x3 (λ x8 . x7 (x2 (λ x9 : (((ι → ι) → ι → ι) → (ι → ι) → ι) → ι → ι → ι → ι . x6 (λ x10 x11 : ι → ι . 0) (λ x10 . 0)) (λ x9 . λ x10 x11 : ι → ι . λ x12 . setsum 0 0)) (Inj1 0) (λ x9 . x2 (λ x10 : (((ι → ι) → ι → ι) → (ι → ι) → ι) → ι → ι → ι → ι . x9) (λ x10 . λ x11 x12 : ι → ι . λ x13 . x11 0)) (Inj0 0)) (λ x8 x9 . λ x10 : ι → ι . x8))) ⟶ (∀ x4 x5 x6 . ∀ x7 : (ι → (ι → ι) → ι → ι) → ι → ι . x0 (λ x8 : ι → ι → ι → ι . x6) (λ x8 : ((ι → ι) → ι → ι) → ι . λ x9 : ι → ι → ι . x3 (λ x10 . Inj0 (setsum x10 (x7 (λ x11 . λ x12 : ι → ι . λ x13 . 0) 0))) (λ x10 x11 . λ x12 : ι → ι . setsum (setsum (setsum 0 0) (setsum 0 0)) (Inj0 (x12 0)))) = x6) ⟶ (∀ x4 . ∀ x5 : ((ι → ι) → ι) → (ι → ι → ι) → ι . ∀ x6 . ∀ x7 : ι → ((ι → ι) → ι) → ι . x0 (λ x8 : ι → ι → ι → ι . setsum (Inj1 (setsum 0 (x1 (λ x9 : (((ι → ι) → ι → ι) → ι → ι) → ι . 0) 0))) (Inj1 0)) (λ x8 : ((ι → ι) → ι → ι) → ι . λ x9 : ι → ι → ι . setsum x6 (Inj0 (x9 (x2 (λ x10 : (((ι → ι) → ι → ι) → (ι → ι) → ι) → ι → ι → ι → ι . 0) (λ x10 . λ x11 x12 : ι → ι . λ x13 . 0)) (x9 0 0)))) = x7 0 (λ x8 : ι → ι . x8 0)) ⟶ False.