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Proofgold Proof

pf
Let x0 of type (((ιο) → ο) → ο) → ο be given.
Let x1 of type (((ιο) → ο) → ο) → ο be given.
Assume H0: 8fddf.. x0 x1.
Let x2 of type ((((ιο) → ο) → ο) → ο) → ο be given.
Assume H1: ∀ x3 : ((ι → ο) → ο) → ο . x1 x3x2 (a327b.. x3).
Apply H0 with x2 x0.
Let x3 of type ((ιο) → 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 H3: x0 = a327b.. x3.
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.