Let x0 of type (((ι → ο) → ο) → ο) → ο be given.
Let x1 of type (((ι → ο) → ο) → ο) → ο be given.
Let x2 of type ((((ι → ο) → ο) → ο) → ο) → ο be given.
Assume H1:
∀ x3 : ((ι → ο) → ο) → ο . x1 x3 ⟶ x2 (a327b.. x3).
Apply H0 with
x2 x0.
Let x3 of type ((ι → ο) → ο) → ο be given.
Assume H2:
(λ x4 : ((ι → ο) → ο) → ο . and (x0 = a327b.. x4) (x1 x4)) x3.
Apply andE with
x0 = a327b.. x3,
x1 x3,
x2 x0 leaving 2 subgoals.
The subproof is completed by applying H2.
Assume H4: x1 x3.
Apply H3 with
λ x4 x5 : (((ι → ο) → ο) → ο) → ο . x2 x5.
Apply H1 with
x3.
The subproof is completed by applying H4.