Let x0 of type (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 be given.
Let x2 of type ((ι → CT2 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 → ι) → ι → (ι → ι) → ι → ι) → ι → (((ι → ι) → ι) → (ι → ι) → ι) → ι → ι be given.
Assume H0:
∀ x4 : (ι → ι → ι) → ι → ι . ∀ x5 . ∀ x6 : (ι → ι) → ι → ι → ι . ∀ x7 : ((ι → ι → ι) → (ι → ι) → ι) → ι → ι → ι . x3 (λ x8 : ι → ι → ι → ι → ι . λ x9 : ι → ι → ι → ι . λ x10 . λ x11 : ι → ι . λ x12 . 0) (x4 (λ x8 x9 . Inj1 0) (Inj1 (setsum (x7 (λ x8 : ι → ι → ι . λ x9 : ι → ι . 0) 0 0) 0))) (λ x8 : (ι → ι) → ι . λ x9 : ι → ι . 0) (x1 (λ x8 x9 . λ x10 : (ι → ι) → ι → ι . x2 (λ x11 : ι → (ι → ι → ι) → ι . λ x12 : (ι → ι) → (ι → ι) → ι → ι . λ x13 x14 x15 . 0) (x3 (λ x11 : ι → ι → ι → ι → ι . λ x12 : ι → ι → ι → ι . λ x13 . λ x14 : ι → ι . λ x15 . x3 (λ x16 : ι → ι → ι → ι → ι . λ x17 : ι → ι → ι → ι . λ x18 . λ x19 : ι → ι . λ x20 . 0) 0 (λ x16 : (ι → ι) → ι . λ x17 : ι → ι . 0) 0) x8 (λ x11 : (ι → ι) → ι . λ x12 : ι → ι . x10 (λ x13 . 0) 0) (setsum 0 0))) (Inj0 0)) = setsum (x0 (λ x8 x9 . λ x10 : (ι → ι) → ι . 0) (λ x8 : (ι → ι) → ι . λ x9 : ι → ι → ι . λ x10 : ι → ι . λ x11 . 0) (x4 (λ x8 x9 . 0) 0)) x5.
Assume H1:
∀ x4 : ι → (ι → ι → ι) → ι . ∀ x5 : ι → (ι → ι) → ι . ∀ x6 . ∀ x7 : (((ι → ι) → ι) → ι) → ι . x3 (λ x8 : ι → ι → ι → ι → ι . λ x9 : ι → ι → ι → ι . λ x10 . λ x11 : ι → ι . λ x12 . x11 (x0 (λ x13 x14 . λ x15 : (ι → ι) → ι . x2 (λ x16 : ι → (ι → ι → ι) → ι . λ x17 : (ι → ι) → (ι → ι) → ι → ι . λ x18 x19 x20 . setsum 0 0) 0) (λ x13 : (ι → ι) → ι . λ x14 : ι → ι → ι . λ x15 : ι → ι . λ x16 . setsum (x13 (λ x17 . 0)) (Inj0 0)) 0)) (Inj1 0) (λ x8 : (ι → ι) → ι . λ x9 : ι → ι . setsum x6 (setsum 0 (x0 (λ x10 x11 . λ x12 : (ι → ι) → ι . x2 (λ x13 : ι → (ι → ι → ι) → ι . λ x14 : (ι → ι) → (ι → ι) → ι → ι . λ x15 x16 x17 . 0) 0) (λ x10 : (ι → ι) → ι . λ x11 : ι → ι → ι . λ x12 : ι → ι . λ x13 . x11 0 0) (x3 (λ x10 : ι → ι → ι → ι → ι . λ x11 : ι → ι → ι → ι . λ x12 . λ x13 : ι → ι . λ x14 . 0) 0 (λ x10 : (ι → ι) → ι . λ x11 : ι → ι . 0) 0)))) (x7 (λ x8 : (ι → ι) → ι . x8 (λ x9 . x8 (λ x10 . 0)))) = x7 (λ x8 : (ι → ι) → ι . setsum 0 (x3 (λ x9 : ι → ι → ι → ι → ι . λ x10 : ι → ι → ι → ι . λ x11 . λ x12 : ι → ι . λ x13 . x12 (x10 0 0 0)) 0 (λ x9 : (ι → ι) → ι . λ x10 : ι → ι . x1 (λ x11 x12 . λ x13 : (ι → ι) → ι → ι . x13 (λ x14 . 0) 0) (x9 (λ x11 . 0))) (x5 x6 (λ x9 . x6)))).
Assume H2:
∀ x4 . ∀ x5 : (ι → ι) → ι . ∀ x6 x7 . x2 (λ x8 : ι → (ι → ι → ι) → ι . λ x9 : (ι → ι) → (ι → ι) → ι → ι . λ x10 x11 x12 . setsum (x1 (λ x13 x14 . λ x15 : (ι → ι) → ι → ι . setsum (x15 (λ x16 . 0) 0) (Inj1 0)) (Inj0 (x3 (λ x13 : ι → ι → ι → ι → ι . λ x14 : ι → ι → ι → ι . λ x15 . λ x16 : ι → ι . λ x17 . 0) 0 (λ x13 : (ι → ι) → ι . λ x14 : ι → ι . 0) 0))) (x1 (λ x13 x14 . λ x15 : (ι → ι) → ι → ι . x13) 0)) (setsum (setsum (Inj0 0) 0) (x0 (λ x8 x9 . λ x10 : (ι → ι) → ι . x0 (λ x11 x12 . λ x13 : (ι → ι) → ι . setsum 0 0) (λ x11 : (ι → ι) → ι . λ x12 : ι → ι → ι . λ x13 : ι → ι . λ x14 . Inj0 0) 0) (λ x8 : (ι → ι) → ι . λ x9 : ι → ι → ι . λ x10 : ι → ι . ...) ...)) = ....