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 → ο be given.
Let x6 of type ι → ι → ι → ι → ι → ι be given.
Let x7 of type ι be given.
Let x8 of type ι be given.
Assume H1:
prim1 x8 (x1 x7).
Let x9 of type ι be given.
Assume H2:
prim1 x9 (x2 x7 x8).
Let x10 of type ι be given.
Assume H3:
prim1 x10 (x3 x7 x8 x9).
Let x11 of type ι be given.
Assume H4:
prim1 x11 (x4 x7 x8 x9 x10).
Assume H5: x5 x7 x8 x9 x10 x11.
Apply UnionI with
94f9e.. x0 (λ x12 . f6efa.. (x1 x12) (x2 x12) (x3 x12) (x4 x12) (x5 x12) (x6 x12)),
x6 x7 x8 x9 x10 x11,
f6efa.. (x1 x7) (x2 x7) (x3 x7) (x4 x7) (x5 x7) (x6 x7) leaving 2 subgoals.
Apply unknownprop_b68ba48b91e9c0d00a54e6d5c382e699ba20b9f9b79173ffcffc71424fcd0134 with
x1 x7,
x2 x7,
x3 x7,
x4 x7,
x5 x7,
x6 x7,
x8,
x9,
x10,
x11 leaving 5 subgoals.
The subproof is completed by applying H1.
The subproof is completed by applying H2.
The subproof is completed by applying H3.
The subproof is completed by applying H4.
The subproof is completed by applying H5.
Apply unknownprop_4785a7374559bd7d78314ce01f76cab97234c9b29cfa5b01c939c64f8ccf18e4 with
x0,
λ x12 . f6efa.. (x1 x12) (x2 x12) (x3 x12) (x4 x12) (x5 x12) (x6 x12),
x7.
The subproof is completed by applying H0.