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