Let x0 of type ι be given.
Let x1 of type ι → ι be given.
Let x2 of type ι → ι → ο be given.
Let x3 of type ι → ι → ι be given.
Let x4 of type ι be given.
Let x5 of type ι be given.
Assume H1:
prim1 x5 (x1 x4).
Assume H2: x2 x4 x5.
Apply UnionI with
94f9e.. x0 (λ x6 . a4c2a.. (x1 x6) (λ x7 . x2 x6 x7) (λ x7 . x3 x6 x7)),
x3 x4 x5,
a4c2a.. (x1 x4) (λ x6 . x2 x4 x6) (λ x6 . x3 x4 x6) leaving 2 subgoals.
Apply unknownprop_9c424e90871cd9e3a05e6a3be208792c52ad17517e2db8ef40187e46ac0e9a6e with
x1 x4,
x2 x4,
x3 x4,
x5 leaving 2 subgoals.
The subproof is completed by applying H1.
The subproof is completed by applying H2.
Apply unknownprop_4785a7374559bd7d78314ce01f76cab97234c9b29cfa5b01c939c64f8ccf18e4 with
x0,
λ x6 . a4c2a.. (x1 x6) (λ x7 . x2 x6 x7) (λ x7 . x3 x6 x7),
x4.
The subproof is completed by applying H0.