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Proofgold Proof

pf
Let x0 of type ι be given.
Let x1 of type ι be given.
Apply prop_ext_2 with x0x1, binintersect x0 x1 = x0 leaving 2 subgoals.
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.
Apply binintersect_Subq_max with x0, x1, x0 leaving 2 subgoals.
The subproof is completed by applying Subq_ref with x0.
The subproof is completed by applying H0.
Assume H0: binintersect x0 x1 = x0.
Apply H0 with λ x2 x3 . x2x1.
The subproof is completed by applying binintersect_Subq_2 with x0, x1.