Let x0 of type (ι → ι) → ο be given.
Let x1 of type ι be given.
Let x2 of type ι be given.
Let x3 of type ι → ι be given.
Assume H1: x0 x3.
Let x4 of type ι → ι → ο be given.
Apply H0 with
x3,
λ x5 x6 . x4 x6 x5.
The subproof is completed by applying H1.