Let x0 of type ι be given.
Let x1 of type ι be given.
Let x2 of type ι be given.
Let x3 of type ι → ι → ι be given.
Let x4 of type ι → ι → ι be given.
Let x5 of type ι → ι → ο be given.
Let x6 of type ι → ι → ι be given.
Assume H0:
∀ x7 . x7 ∈ x0 ⟶ ∀ x8 . x8 ∈ x0 ⟶ x6 x7 x8 ∈ ReplSep2 x0 (λ x9 . x0) (λ x9 x10 . True) x6.
Assume H1:
∀ x7 . x7 ∈ x0 ⟶ ∀ x8 . x8 ∈ x0 ⟶ (λ x9 . prim0 (λ x10 . (λ x11 x12 : ο . ∀ x13 : ο . (x11 ⟶ x12 ⟶ x13) ⟶ x13) (x10 ∈ x0) (∃ x11 . and (x11 ∈ x0) (x9 = x6 x10 x11)))) (x6 x7 x8) = x7.
Assume H2:
∀ x7 . x7 ∈ x0 ⟶ ∀ x8 . x8 ∈ x0 ⟶ (λ x9 . prim0 (λ x10 . (λ x11 x12 : ο . ∀ x13 : ο . (x11 ⟶ x12 ⟶ x13) ⟶ x13) (x10 ∈ x0) (x9 = x6 ((λ x11 . prim0 (λ x12 . (λ x13 x14 : ο . ∀ x15 : ο . (x13 ⟶ x14 ⟶ x15) ⟶ x15) (x12 ∈ x0) (∃ x13 . and (x13 ∈ x0) (x11 = x6 x12 x13)))) x9) x10))) (x6 x7 x8) = x8.
Assume H3:
∀ x7 . x7 ∈ ReplSep2 x0 (λ x8 . x0) (λ x8 x9 . True) x6 ⟶ (λ x8 . prim0 (λ x9 . (λ x10 x11 : ο . ∀ x12 : ο . (x10 ⟶ x11 ⟶ x12) ⟶ x12) (x9 ∈ x0) (∃ x10 . and (x10 ∈ x0) (x8 = x6 x9 x10)))) x7 ∈ x0.
Assume H4:
∀ x7 . x7 ∈ ReplSep2 x0 (λ x8 . x0) (λ x8 x9 . True) x6 ⟶ (λ x8 . prim0 (λ x9 . (λ x10 x11 : ο . ∀ x12 : ο . (x10 ⟶ x11 ⟶ x12) ⟶ x12) (x9 ∈ x0) (x8 = x6 ((λ x10 . prim0 (λ x11 . (λ x12 x13 : ο . ∀ x14 : ο . (x12 ⟶ x13 ⟶ x14) ⟶ x14) (x11 ∈ x0) (∃ x12 . and (x12 ∈ x0) (x10 = x6 x11 x12)))) x8) x9))) x7 ∈ x0.
Assume H5:
∀ x7 . ... ⟶ ∀ x8 . ... ⟶ ... ⟶ (λ x9 . prim0 (λ x10 . (λ x11 x12 : ο . ∀ x13 : ο . (x11 ⟶ x12 ⟶ x13) ⟶ x13) (x10 ∈ x0) (x9 = x6 ((λ x11 . prim0 (λ x12 . (λ x13 x14 : ο . ∀ x15 : ο . (x13 ⟶ x14 ⟶ x15) ⟶ x15) (x12 ∈ x0) (∃ x13 . and (x13 ∈ x0) (x11 = x6 x12 x13)))) x9) x10))) x7 = (λ x9 . prim0 (λ x10 . (λ x11 x12 : ο . ∀ x13 : ο . (x11 ⟶ x12 ⟶ x13) ⟶ x13) (x10 ∈ x0) (x9 = x6 ((λ x11 . prim0 (λ x12 . (λ x13 x14 : ο . ∀ x15 : ο . (x13 ⟶ x14 ⟶ x15) ⟶ x15) (x12 ∈ x0) ...)) ...) ...))) ... ⟶ x7 = x8.