Let x0 of type ((ι → CT2 ι) → (((ι → ι) → ι → ι) → ι → ι) → ι → ι) → ((ι → ι) → ι) → ι be given.
Let x1 of type (((ι → ι) → CT2 ι) → ι) → ι → ι be given.
Let x2 of type ((CT2 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 be given.
Assume H0:
∀ x4 x5 x6 x7 . x3 (λ x8 . x2 (λ x9 : (ι → ι → ι) → ι . λ x10 . λ x11 : ι → ι → ι . λ x12 x13 . x2 (λ x14 : (ι → ι → ι) → ι . λ x15 . λ x16 : ι → ι → ι . λ x17 x18 . x16 (x3 (λ x19 . 0) (λ x19 . 0)) 0) (setsum 0 (x1 (λ x14 : (ι → ι) → (ι → ι → ι) → ι . 0) 0)) (λ x14 . λ x15 : ι → ι . x14)) 0 (λ x9 . λ x10 : ι → ι . x7)) (λ x8 . x8) = x2 (λ x8 : (ι → ι → ι) → ι . λ x9 . λ x10 : ι → ι → ι . λ x11 x12 . x12) (Inj0 x4) (λ x8 . λ x9 : ι → ι . x6).
Assume H1:
∀ x4 . ∀ x5 : (ι → ι) → ((ι → ι) → ι → ι) → ι . ∀ x6 x7 : ι → ι . x3 (λ x8 . setsum (x7 (x7 0)) (Inj0 0)) (λ x8 . 0) = setsum (x3 (λ x8 . x5 (λ x9 . 0) (λ x9 : ι → ι . λ x10 . x9 0)) (λ x8 . x7 (x0 (λ x9 : ι → (ι → ι → ι) → ι . λ x10 : ((ι → ι) → ι → ι) → ι → ι . λ x11 . 0) (λ x9 : ι → ι . x9 0)))) (setsum 0 (setsum 0 (setsum (x7 0) (setsum 0 0)))).
Assume H2:
∀ x4 : ι → ((ι → ι) → ι → ι) → ι . ∀ x5 . ∀ x6 : (ι → ι → ι) → ι . ∀ x7 . x2 (λ x8 : (ι → ι → ι) → ι . λ x9 . λ x10 : ι → ι → ι . λ x11 x12 . x2 (λ x13 : (ι → ι → ι) → ι . λ x14 . λ x15 : ι → ι → ι . λ x16 x17 . x16) (x10 0 (setsum x12 (Inj0 0))) (λ x13 . λ x14 : ι → ι . Inj1 0)) x7 (λ x8 . λ x9 : ι → ι . x0 (λ x10 : ι → (ι → ι → ι) → ι . λ x11 : ((ι → ι) → ι → ι) → ι → ι . λ x12 . x0 (λ x13 : ι → (ι → ι → ι) → ι . λ x14 : ((ι → ι) → ι → ι) → ι → ι . λ x15 . Inj1 (setsum 0 0)) (λ x13 : ι → ι . x11 (λ x14 : ι → ι . λ x15 . Inj0 0) (Inj1 0))) (λ x10 : ι → ι . 0)) = Inj1 (x3 (λ x8 . x2 (λ x9 : (ι → ι → ι) → ι . λ x10 . λ x11 : ι → ι → ι . λ x12 x13 . x1 (λ x14 : (ι → ι) → (ι → ι → ι) → ι . Inj1 0) 0) (x3 (λ x9 . x1 (λ x10 : (ι → ι) → (ι → ι → ι) → ι . 0) 0) (λ x9 . x9)) (λ x9 . λ x10 : ι → ι . setsum x9 (x1 (λ x11 : (ι → ι) → (ι → ι → ι) → ι . 0) 0))) (λ x8 . Inj1 x5)).
Assume H3:
∀ x4 : ι → ((ι → ι) → ι → ι) → ι → ι → ι . ∀ x5 : ι → ι → ι . ∀ x6 : ι → ι . ∀ x7 . x2 (λ x8 : (ι → ι → ι) → ι . λ x9 . λ x10 : ι → ι → ι . λ x11 x12 . x2 (λ x13 : (ι → ι → ι) → ι . λ x14 . λ x15 : ι → ι → ι . λ x16 x17 . 0) (setsum (setsum x11 (x0 (λ x13 : ι → (ι → ι → ι) → ι . λ x14 : ((ι → ι) → ι → ι) → ι → ι . λ x15 . 0) (λ x13 : ι → ι . 0))) 0) (λ x13 . λ x14 : ι → ι . 0)) (x3 (λ x8 . x2 (λ x9 : (ι → ι → ι) → ι . λ x10 . λ x11 : ι → ι → ι . λ x12 x13 . x1 (λ x14 : (ι → ι) → (ι → ι → ι) → ι . x14 (λ x15 . 0) (λ x15 x16 . 0)) x13) (Inj0 0) (λ x9 . λ x10 : ι → ι . 0)) (λ x8 . 0)) (λ x8 . λ x9 : ι → ι . setsum (setsum 0 (x3 (λ x10 . setsum 0 0) (λ x10 . setsum 0 0))) 0) = x2 (λ x8 : (ι → ι → ι) → ι . λ x9 . λ x10 : ι → ι → ι . λ x11 x12 . setsum (setsum x9 (Inj0 0)) (x3 ... ...)) ... ....