Let x0 of type ι be given.
Let x1 of type ι be given.
Let x2 of type ι → ι → ι be given.
Let x3 of type ι → ι → ι be given.
Assume H0:
∀ x4 . prim1 x4 x0 ⟶ ∀ x5 . prim1 x5 x1 ⟶ x2 x4 x5 = x3 x4 x5.
Apply unknownprop_59be5eee144fb0f12156456c7f9888c3f0525fea126d0d8cdf71e5c53005d86a with
ac767.. x0 x1,
λ x4 . x2 (f482f.. x4 4a7ef..) (f482f.. x4 (4ae4a.. 4a7ef..)),
λ x4 . x3 (f482f.. x4 4a7ef..) (f482f.. x4 (4ae4a.. 4a7ef..)).
Let x4 of type ι be given.
Apply H0 with
f482f.. x4 4a7ef..,
f482f.. x4 (4ae4a.. 4a7ef..) leaving 2 subgoals.
Apply unknownprop_a84e7b83bd5a8bec9717474837d8a3466c738bfe80d317693d21dd132b10f7db with
x0,
λ x5 . x1,
x4.
The subproof is completed by applying H1.
Apply unknownprop_e18efd509b680f433a069707c2a704dd064e01f14c3ae7cd35fcb2837fcff9a4 with
x0,
λ x5 . x1,
x4.
The subproof is completed by applying H1.