Let x0 of type (((((ι → ι) → 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 → 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 → ι → ι) → ι → (ι → (ι → ι) → ι → ι) → ι be given.
Assume H0:
∀ x4 x5 . ∀ x6 : (((ι → ι) → ι) → ι) → ι . ∀ x7 . x3 (λ x8 x9 . x3 (λ x10 x11 . setsum (x2 (λ x12 x13 x14 . 0) (λ x12 . λ x13 : ι → ι → ι . λ x14 . Inj0 0)) (setsum 0 x9)) (Inj1 (x6 (λ x10 : (ι → ι) → ι . setsum 0 0))) (λ x10 . λ x11 : ι → ι . λ x12 . setsum 0 x9)) (Inj0 (x1 (λ x8 . λ x9 : ι → (ι → ι) → ι → ι . λ x10 . setsum 0 0) (λ x8 . Inj0 (x3 (λ x9 x10 . 0) 0 (λ x9 . λ x10 : ι → ι . λ x11 . 0))))) (λ x8 . λ x9 : ι → ι . λ x10 . setsum 0 (Inj1 (x2 (λ x11 x12 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 . λ x12 : ι → ι → ι . λ x13 . x1 (λ x14 . λ x15 : ι → (ι → ι) → ι → ι . λ x16 . 0) (λ x14 . 0))))) = x3 (λ x8 x9 . setsum 0 (x1 (λ x10 . λ x11 : ι → (ι → ι) → ι → ι . λ x12 . x9) (λ x10 . x8))) (setsum (x1 (λ x8 . λ x9 : ι → (ι → ι) → ι → ι . λ x10 . 0) (λ x8 . x7)) (setsum 0 (Inj0 (x6 (λ x8 : (ι → ι) → ι . 0))))) (λ x8 . λ x9 : ι → ι . λ x10 . x10).
Assume H1:
∀ x4 : ι → (ι → ι → ι) → ι . ∀ x5 : ι → ι . ∀ x6 : (ι → ι) → ι → ι . ∀ x7 : ((ι → ι) → ι → ι → ι) → ι . x3 (λ x8 x9 . x8) 0 (λ x8 . λ x9 : ι → ι . λ x10 . x1 (λ x11 . λ x12 : ι → (ι → ι) → ι → ι . λ x13 . x10) (λ x11 . setsum x11 (x2 (λ x12 x13 x14 . x11) (λ x12 . λ x13 : ι → ι → ι . λ x14 . 0)))) = x1 (λ x8 . λ x9 : ι → (ι → ι) → ι → ι . λ x10 . x3 (λ x11 x12 . x3 (λ x13 x14 . x14) x10 (λ x13 . λ x14 : ι → ι . λ x15 . Inj0 x13)) (x2 (λ x11 x12 x13 . 0) (λ x11 . λ x12 : ι → ι → ι . λ x13 . x2 (λ x14 x15 x16 . x16) (λ x14 . λ x15 : ι → ι → ι . λ x16 . x1 (λ x17 . λ x18 : ι → (ι → ι) → ι → ι . λ x19 . 0) (λ x17 . 0)))) (λ x11 . λ x12 : ι → ι . λ x13 . Inj0 0)) (λ x8 . x8).
Assume H2:
∀ x4 : ι → ι → (ι → ι) → ι . ∀ x5 . ∀ x6 : ι → ι → ι . ∀ x7 : ι → (ι → ι) → ι . x2 (λ x8 x9 x10 . x7 x9 (λ x11 . Inj1 0)) (λ x8 . λ x9 : ι → ι → ι . λ x10 . x10) = x7 x5 (λ x8 . Inj1 (setsum (Inj0 (x1 (λ x9 . λ x10 : ι → (ι → ι) → ι → ι . λ x11 . 0) (λ x9 . 0))) (x1 (λ x9 . λ x10 : ι → (ι → ι) → ι → ι . λ x11 . 0) (λ x9 . 0)))).
Assume H3:
∀ x4 . ∀ x5 : (ι → ι) → ι . ∀ x6 : ι → ι → (ι → ι) → ι . ∀ x7 . x2 (λ x8 x9 x10 . Inj0 0) (λ x8 . λ x9 : ι → ι → ι . λ x10 . 0) = x4.
Apply FalseE with
... ⟶ ... ⟶ ... ⟶ (∀ x4 x5 . ∀ x6 : (ι → ι) → ι . ∀ x7 . x0 (λ x8 : (((ι → ι) → ι) → ι) → ι . λ x9 x10 . λ x11 : ι → ι . λ x12 . x2 (λ x13 x14 x15 . x3 (λ x16 x17 . x3 (λ x18 x19 . 0) x16 (λ x18 . λ x19 : ι → ι . λ x20 . x18)) (x3 (λ x16 x17 . Inj0 0) ... ...) ...) ...) ... ... = ...) ⟶ False.