Let x0 of type ι be given.
Let x1 of type ι → ι be given.
Let x2 of type ι → ι → ο be given.
Let x3 of type ι → ι → ι be given.
Let x4 of type ι be given.
Let x5 of type ο be given.
Assume H1:
∀ x6 . prim1 x6 x0 ⟶ ∀ x7 . prim1 x7 (x1 x6) ⟶ x2 x6 x7 ⟶ x4 = x3 x6 x7 ⟶ x5.
Apply UnionE_impred with
94f9e.. x0 (λ x6 . a4c2a.. (x1 x6) (λ x7 . x2 x6 x7) (λ x7 . x3 x6 x7)),
x4,
x5 leaving 2 subgoals.
The subproof is completed by applying H0.
Let x6 of type ι be given.
Apply unknownprop_d908b89102f7b662c739e5a844f67efc8ae1cd05a2e9ce1e3546fa3885f40100 with
x0,
λ x7 . a4c2a.. (x1 x7) (λ x8 . x2 x7 x8) (λ x8 . x3 x7 x8),
x6,
x5 leaving 2 subgoals.
The subproof is completed by applying H3.
Let x7 of type ι be given.
Assume H5:
x6 = a4c2a.. (x1 x7) (λ x8 . x2 x7 x8) (λ x8 . x3 x7 x8).
Claim L6:
prim1 x4 (a4c2a.. (x1 x7) (λ x8 . x2 x7 x8) (λ x8 . x3 x7 x8))Apply H5 with
λ x8 x9 . prim1 x4 x8.
The subproof is completed by applying H2.
Apply unknownprop_e546e9a8cc28c7314a8604ada98e2a83641f2ef6b8078441570ffe037b28d26f with
x1 x7,
x2 x7,
x3 x7,
x4,
x5 leaving 2 subgoals.
The subproof is completed by applying L6.
Let x8 of type ι be given.
Assume H7:
prim1 x8 (x1 x7).
Assume H8: x2 x7 x8.
Assume H9: x4 = x3 x7 x8.
Apply H1 with
x7,
x8 leaving 4 subgoals.
The subproof is completed by applying H4.
The subproof is completed by applying H7.
The subproof is completed by applying H8.
The subproof is completed by applying H9.