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 → ο be given.
Let x4 of type ι → ι → ι → ι be given.
Let x5 of type ι be given.
Let x6 of type ι be given.
Assume H1:
prim1 x6 (x1 x5).
Let x7 of type ι be given.
Assume H2:
prim1 x7 (x2 x5 x6).
Assume H3: x3 x5 x6 x7.
Apply UnionI with
94f9e.. x0 (λ x8 . 3b429.. (x1 x8) (x2 x8) (x3 x8) (x4 x8)),
x4 x5 x6 x7,
3b429.. (x1 x5) (x2 x5) (x3 x5) (x4 x5) leaving 2 subgoals.
Apply unknownprop_ad940adfb3a0d77735ec5efe28dee5c7c66104299e7bf6cd081b66c4c5ce99fb with
x1 x5,
x2 x5,
x3 x5,
x4 x5,
x6,
x7 leaving 3 subgoals.
The subproof is completed by applying H1.
The subproof is completed by applying H2.
The subproof is completed by applying H3.
Apply unknownprop_4785a7374559bd7d78314ce01f76cab97234c9b29cfa5b01c939c64f8ccf18e4 with
x0,
λ x8 . 3b429.. (x1 x8) (x2 x8) (x3 x8) (x4 x8),
x5.
The subproof is completed by applying H0.