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 → ο be given.
Let x7 of type ι → ι → ι → ι → ι → ι → ι be given.
Let x8 of type ι be given.
Let x9 of type ι be given.
Assume H1:
prim1 x9 (x1 x8).
Let x10 of type ι be given.
Assume H2:
prim1 x10 (x2 x8 x9).
Let x11 of type ι be given.
Assume H3:
prim1 x11 (x3 x8 x9 x10).
Let x12 of type ι be given.
Assume H4:
prim1 x12 (x4 x8 x9 x10 x11).
Let x13 of type ι be given.
Assume H5:
prim1 x13 (x5 x8 x9 x10 x11 x12).
Assume H6: x6 x8 x9 x10 x11 x12 x13.
Apply UnionI with
94f9e.. x0 (λ x14 . 2aab0.. (x1 x14) (x2 x14) (x3 x14) (x4 x14) (x5 x14) (x6 x14) (x7 x14)),
x7 x8 x9 x10 x11 x12 x13,
2aab0.. (x1 x8) (x2 x8) (x3 x8) (x4 x8) (x5 x8) (x6 x8) (x7 x8) leaving 2 subgoals.
Apply unknownprop_49096b1ce91015c116eb3af9e4b2caad39c195eb8e177209af133a01558f12db with
x1 x8,
x2 x8,
x3 x8,
x4 x8,
x5 x8,
x6 x8,
x7 x8,
x9,
x10,
x11,
x12,
x13 leaving 6 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.
Apply unknownprop_4785a7374559bd7d78314ce01f76cab97234c9b29cfa5b01c939c64f8ccf18e4 with
x0,
λ x14 . 2aab0.. (x1 x14) (x2 x14) (x3 x14) (x4 x14) (x5 x14) (x6 x14) (x7 x14),
x8.
The subproof is completed by applying H0.