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 ι be given.
Assume H1:
prim1 x10 (x1 x9).
Let x11 of type ι be given.
Assume H2:
prim1 x11 (x2 x9 x10).
Let x12 of type ι be given.
Assume H3:
prim1 x12 (x3 x9 x10 x11).
Let x13 of type ι be given.
Assume H4:
prim1 x13 (x4 x9 x10 x11 x12).
Let x14 of type ι be given.
Assume H5:
prim1 x14 (x5 x9 x10 x11 x12 x13).
Let x15 of type ι be given.
Assume H6:
prim1 x15 (x6 x9 x10 x11 x12 x13 x14).
Assume H7: x7 x9 x10 x11 x12 x13 x14 x15.
Apply UnionI with
94f9e.. x0 (λ x16 . 6cd44.. (x1 x16) (x2 x16) (x3 x16) (x4 x16) (x5 x16) (x6 x16) (x7 x16) (x8 x16)),
x8 x9 x10 x11 x12 x13 x14 x15,
6cd44.. (x1 x9) (x2 x9) (x3 x9) (x4 x9) (x5 x9) (x6 x9) (x7 x9) (x8 x9) leaving 2 subgoals.
Apply unknownprop_a321e8a09b36511124aca1092fe58e4da6ea72e03b9a17af9e17f135f775e8dc with
x1 x9,
x2 x9,
x3 x9,
x4 x9,
x5 x9,
x6 x9,
x7 x9,
x8 x9,
x10,
x11,
x12,
x13,
x14,
x15 leaving 7 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.
The subproof is completed by applying H6.
The subproof is completed by applying H7.
Apply unknownprop_4785a7374559bd7d78314ce01f76cab97234c9b29cfa5b01c939c64f8ccf18e4 with
x0,
λ x16 . 6cd44.. (x1 x16) (x2 x16) (x3 x16) (x4 x16) (x5 x16) (x6 x16) (x7 x16) (x8 x16),
x9.
The subproof is completed by applying H0.