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 be given.
Let x4 of type ι be given.
Assume H1:
In x4 (x1 x3).
Apply unknownprop_bd19dfd009a9cdfd7e00e5a28a77c1545e733688b5ba89bd8cc2f4f90ec5aaa3 with
λ x5 x6 : ι → (ι → ι) → (ι → ι → ι) → ι . ap (ap (x6 x0 x1 x2) x3) x4 = x2 x3 x4.
Apply unknownprop_c5e2164052a280ad5b04f622e53815f0267ee33361e4345305e43303abef2c1b with
x0,
λ x5 . lam (x1 x5) (λ x6 . x2 x5 x6),
x3,
λ x5 x6 . ap x6 x4 = x2 x3 x4 leaving 2 subgoals.
The subproof is completed by applying H0.
Apply unknownprop_c5e2164052a280ad5b04f622e53815f0267ee33361e4345305e43303abef2c1b with
x1 x3,
λ x5 . x2 x3 x5,
x4.
The subproof is completed by applying H1.