Let x0 of type ι be given.
Let x1 of type ι → ι be given.
Let x2 of type ι → ι → ι be given.
Let x3 of type ι → ι → ι → ι be given.
Let x4 of type ι → ι → ι → ι → ι be given.
Let x5 of type ι → ι → ι → ι → ι → ι be given.
Let x6 of type ι → ι → ι → ι → ι → ι → ι be given.
Let x7 of type ι → ι → ι → ι → ι → ι → ι → ο be given.
Let x8 of type ι → ι → ι → ι → ι → ι → ι → ι be given.
Let x9 of type ι be given.
Let x10 of type ο be given.
Assume H1:
∀ x11 . prim1 x11 x0 ⟶ ∀ x12 . prim1 x12 (x1 x11) ⟶ ∀ x13 . prim1 x13 (x2 x11 x12) ⟶ ∀ x14 . prim1 x14 (x3 x11 x12 x13) ⟶ ∀ x15 . prim1 x15 (x4 x11 x12 x13 x14) ⟶ ∀ x16 . prim1 x16 (x5 x11 x12 x13 x14 x15) ⟶ ∀ x17 . prim1 x17 (x6 x11 x12 x13 x14 x15 x16) ⟶ x7 x11 x12 x13 x14 x15 x16 x17 ⟶ x9 = x8 x11 x12 x13 x14 x15 x16 x17 ⟶ x10.
Apply UnionE_impred with
94f9e.. x0 (λ x11 . 6cd44.. (x1 x11) (x2 x11) (x3 x11) (x4 x11) (x5 x11) (x6 x11) (x7 x11) (x8 x11)),
x9,
x10 leaving 2 subgoals.
The subproof is completed by applying H0.
Let x11 of type ι be given.
Assume H3:
prim1 x11 (94f9e.. x0 (λ x12 . 6cd44.. (x1 x12) (x2 x12) (x3 x12) (x4 x12) (x5 x12) (x6 x12) (x7 x12) (x8 x12))).
Apply unknownprop_d908b89102f7b662c739e5a844f67efc8ae1cd05a2e9ce1e3546fa3885f40100 with
x0,
λ x12 . 6cd44.. (x1 x12) (x2 x12) (x3 x12) (x4 x12) (x5 x12) (x6 x12) (x7 x12) (x8 x12),
x11,
x10 leaving 2 subgoals.
The subproof is completed by applying H3.
Let x12 of type ι be given.
Assume H5:
x11 = 6cd44.. (x1 x12) (x2 x12) (x3 x12) (x4 x12) (x5 x12) (x6 x12) (x7 x12) (x8 x12).
Apply unknownprop_8ed5ef1390eae1529639ddf6c238e18ede5125e6622c691c2992c6b0424f0940 with
x1 x12,
x2 x12,
x3 x12,
x4 x12,
x5 x12,
x6 x12,
x7 x12,
x8 x12,
x9,
x10 leaving 2 subgoals.
The subproof is completed by applying L6.
Let x13 of type ι be given.
Assume H7:
prim1 x13 (x1 x12).
Let x14 of type ι be given.
Assume H8:
prim1 x14 (x2 x12 x13).
Let x15 of type ι be given.
Assume H9:
prim1 x15 (x3 x12 x13 x14).
Let x16 of type ι be given.
Assume H10:
prim1 x16 (x4 x12 x13 x14 x15).
Let x17 of type ι be given.
Assume H11:
prim1 x17 (x5 x12 x13 x14 x15 x16).
Let x18 of type ι be given.
Assume H12:
prim1 x18 (x6 x12 x13 x14 x15 x16 x17).
Assume H13: x7 x12 x13 x14 x15 x16 x17 x18.
Assume H14: x9 = x8 x12 x13 x14 ... ... ... ....