Let x0 of type (ι → ι → ι → ο) → ο be given.
Let x1 of type (ι → ι → ι → ο) → ο be given.
Assume H0:
∃ x2 : ι → ι → ι → ο . and (x0 x2) (x1 x2).
Let x2 of type ο be given.
Assume H1: ∀ x3 : ι → ι → ι → ο . x0 x3 ⟶ x1 x3 ⟶ x2.
Apply H0 with
x2.
Let x3 of type ι → ι → ι → ο be given.
Assume H2:
(λ x4 : ι → ι → ι → ο . and (x0 x4) (x1 x4)) x3.
Apply andE with
x0 x3,
x1 x3,
x2 leaving 2 subgoals.
The subproof is completed by applying H2.
Assume H3: x0 x3.
Assume H4: x1 x3.
Apply H1 with
x3 leaving 2 subgoals.
The subproof is completed by applying H3.
The subproof is completed by applying H4.