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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 x0.
Apply unknownprop_b30a94f49240f0717f4ecb200a605aa8a4e6dad6dc5d1afa60c37866ee96baab with x2, binintersect x0 x1.
Assume H1: In x2 (binintersect x0 x1).
Apply unknownprop_8369708f37c0d20e10b6156293f1b207e835dfc563ff7fbfa059bf26c84ddb80 with x2, x0 leaving 2 subgoals.
The subproof is completed by applying H0.
Apply unknownprop_625f5facc6d0cfc120b9f58035b73c3c65ed740e13bf862e9499b972625669a5 with x0, x1, x2.
The subproof is completed by applying H1.