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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.
Apply unknownprop_a23ec6a55ac212526d74cbf0d04096929ad453b0eb0f8023e32b8a33930d39fb with binintersect x0 (binintersect x1 x2), binintersect (binintersect x0 x1) x2 leaving 2 subgoals.
Apply unknownprop_b493a75fcec57593a6576a7c6d850d3d24c9ed1931af4734bd2773dfce586a4d with binintersect x0 x1, x2, binintersect x0 (binintersect x1 x2) leaving 2 subgoals.
Apply unknownprop_b493a75fcec57593a6576a7c6d850d3d24c9ed1931af4734bd2773dfce586a4d with x0, x1, binintersect x0 (binintersect x1 x2) leaving 2 subgoals.
The subproof is completed by applying unknownprop_e0d452e0e0459ccd22d0a0ca66d8c6b520f69a835c0ebd50bbdd40077efd4a68 with x0, binintersect x1 x2.
Apply unknownprop_16d2e0ac4e61f9d6f4710f68fd29bc0751fdb2a43ae4ee41dc39565d6502f8a7 with binintersect x0 (binintersect x1 x2), binintersect x1 x2, x1 leaving 2 subgoals.
The subproof is completed by applying unknownprop_43a7b6a7250420244ab59ee561112cfc53c614b669837fc84c919b0df2ef6e0a with x0, binintersect x1 x2.
The subproof is completed by applying unknownprop_e0d452e0e0459ccd22d0a0ca66d8c6b520f69a835c0ebd50bbdd40077efd4a68 with x1, x2.
Apply unknownprop_16d2e0ac4e61f9d6f4710f68fd29bc0751fdb2a43ae4ee41dc39565d6502f8a7 with binintersect x0 (binintersect x1 x2), binintersect x1 x2, x2 leaving 2 subgoals.
The subproof is completed by applying unknownprop_43a7b6a7250420244ab59ee561112cfc53c614b669837fc84c919b0df2ef6e0a with x0, binintersect x1 x2.
The subproof is completed by applying unknownprop_43a7b6a7250420244ab59ee561112cfc53c614b669837fc84c919b0df2ef6e0a with x1, x2.
Apply unknownprop_b493a75fcec57593a6576a7c6d850d3d24c9ed1931af4734bd2773dfce586a4d with x0, binintersect x1 x2, binintersect (binintersect x0 x1) x2 leaving 2 subgoals.
Apply unknownprop_16d2e0ac4e61f9d6f4710f68fd29bc0751fdb2a43ae4ee41dc39565d6502f8a7 with binintersect (binintersect x0 x1) x2, binintersect x0 x1, x0 leaving 2 subgoals.
The subproof is completed by applying unknownprop_e0d452e0e0459ccd22d0a0ca66d8c6b520f69a835c0ebd50bbdd40077efd4a68 with binintersect x0 x1, x2.
The subproof is completed by applying unknownprop_e0d452e0e0459ccd22d0a0ca66d8c6b520f69a835c0ebd50bbdd40077efd4a68 with x0, x1.
Apply unknownprop_b493a75fcec57593a6576a7c6d850d3d24c9ed1931af4734bd2773dfce586a4d with x1, x2, binintersect (binintersect x0 x1) x2 leaving 2 subgoals.
Apply unknownprop_16d2e0ac4e61f9d6f4710f68fd29bc0751fdb2a43ae4ee41dc39565d6502f8a7 with binintersect (binintersect x0 x1) x2, binintersect x0 x1, x1 leaving 2 subgoals.
The subproof is completed by applying unknownprop_e0d452e0e0459ccd22d0a0ca66d8c6b520f69a835c0ebd50bbdd40077efd4a68 with binintersect x0 x1, x2.
The subproof is completed by applying unknownprop_43a7b6a7250420244ab59ee561112cfc53c614b669837fc84c919b0df2ef6e0a with x0, x1.
The subproof is completed by applying unknownprop_43a7b6a7250420244ab59ee561112cfc53c614b669837fc84c919b0df2ef6e0a with binintersect x0 x1, x2.