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Proofgold Proof

pf
Let x0 of type ι be given.
Let x1 of type ι be given.
Let x2 of type ι be given.
Assume H0: nIn x2 (binintersect x0 x1).
Apply not_and_or_demorgan with x2x0, x2x1.
Assume H1: and (x2x0) (x2x1).
Apply H1 with False.
Assume H2: x2x0.
Assume H3: x2x1.
Apply H0.
Apply binintersectI with x0, x1, x2 leaving 2 subgoals.
The subproof is completed by applying H2.
The subproof is completed by applying H3.