Let x0 of type ι → ο be given.
Let x1 of type (ι → ι) → ο be given.
Assume H0: ∀ x2 : ι → ι . x1 x2 ⟶ ∀ x3 . x0 x3 ⟶ x0 (x2 x3).
Let x2 of type ι → ι be given.
Let x3 of type ι → ι be given.
Assume H1: x1 x2.
Assume H2: x1 x3.
Let x4 of type ι be given.
Assume H3: x0 x4.
Apply H0 with
x3,
x2 x4 leaving 2 subgoals.
The subproof is completed by applying H2.
Apply H0 with
x2,
x4 leaving 2 subgoals.
The subproof is completed by applying H1.
The subproof is completed by applying H3.