Let x0 of type ι → ι → ο be given.
Let x1 of type ι → ι → ο be given.
Assume H0: ∀ x2 x3 . x0 x2 x3 ⟶ x1 x2 x3.
Let x2 of type ι be given.
Let x3 of type ι be given.
Assume H2:
or (x0 x2 x3) (x2 = x3).
Apply H2 with
x1 x2 x3 leaving 2 subgoals.
Assume H3: x0 x2 x3.
Apply H0 with
x2,
x3.
The subproof is completed by applying H3.
Assume H3: x2 = x3.
Apply H3 with
λ x4 x5 . x1 x2 x4.
The subproof is completed by applying H1 with x2.