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Proofgold Proof

pf
Let x0 of type ιο be given.
Let x1 of type ιο be given.
Assume H0: ∃ x2 . and (x0 x2) (x1 x2).
Let x2 of type ο be given.
Assume H1: ∀ x3 . x0 x3x1 x3x2.
Apply H0 with x2.
Let x3 of type ι be given.
Assume H2: (λ x4 . and (x0 x4) (x1 x4)) x3.
Apply H2 with x2.
The subproof is completed by applying H1 with x3.