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Proofgold Proof

pf
Let x0 of type ι be given.
Let x1 of type ι be given.
Assume H0: x0x1.
Apply set_ext with binintersect x0 x1, x0 leaving 2 subgoals.
The subproof is completed by applying binintersect_Subq_1 with x0, x1.
Let x2 of type ι be given.
Assume H1: x2x0.
Apply binintersectI with x0, x1, x2 leaving 2 subgoals.
The subproof is completed by applying H1.
Apply H0 with x2.
The subproof is completed by applying H1.