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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 setminus x0 (binintersect x1 x2), binunion (setminus x0 x1) (setminus x0 x2) leaving 2 subgoals.
Apply unknownprop_c3fe42b21df0810041479a97b374de73f7754e07c8af1c88386a1e7dc0aad10f with setminus x0 (binintersect x1 x2), binunion (setminus x0 x1) (setminus x0 x2).
Let x3 of type ι be given.
Assume H0: In x3 (setminus x0 (binintersect x1 x2)).
Apply unknownprop_e02b92c94ff70655b8eb0623a7ec106c0c0c9c65ac0f52f9689f2e6c9f563b5d with x0, binintersect x1 x2, x3, In x3 (binunion (setminus x0 x1) (setminus x0 x2)) leaving 2 subgoals.
The subproof is completed by applying H0.
Assume H1: In x3 x0.
Assume H2: nIn x3 (binintersect x1 x2).
Apply unknownprop_75b5762e65badae8f9531d40fddd332ff95b59f608d93c7a55f19f4fa5ef37d5 with x3, binunion (setminus x0 x1) (setminus x0 x2).
Assume H3: nIn x3 (binunion (setminus x0 x1) (setminus x0 x2)).
Apply unknownprop_8369708f37c0d20e10b6156293f1b207e835dfc563ff7fbfa059bf26c84ddb80 with x3, binintersect x1 x2 leaving 2 subgoals.
The subproof is completed by applying H2.
Apply unknownprop_7e73699eda4c2a35af8db1aea1ddace7d2346405cd3944ace259823e1ec33cf3 with x1, x2, x3 leaving 2 subgoals.
Apply unknownprop_75b5762e65badae8f9531d40fddd332ff95b59f608d93c7a55f19f4fa5ef37d5 with x3, x1.
Assume H4: nIn x3 x1.
Apply unknownprop_8369708f37c0d20e10b6156293f1b207e835dfc563ff7fbfa059bf26c84ddb80 with x3, binunion (setminus x0 x1) (setminus x0 x2) leaving 2 subgoals.
The subproof is completed by applying H3.
Apply unknownprop_1598d20a62a395ced156dfcc7d767ab023594ea6ef7c5e3b53cecdbebaf0ec29 with setminus x0 x1, setminus x0 x2, x3.
Apply unknownprop_3fe7f97dcb00bcf31cf989081bd8403f8f0647acc7dd719f8a7da64cd4837dac with x0, x1, x3 leaving 2 subgoals.
The subproof is completed by applying H1.
The subproof is completed by applying H4.
Apply unknownprop_75b5762e65badae8f9531d40fddd332ff95b59f608d93c7a55f19f4fa5ef37d5 with x3, x2.
Assume H4: nIn x3 x2.
Apply unknownprop_8369708f37c0d20e10b6156293f1b207e835dfc563ff7fbfa059bf26c84ddb80 with x3, binunion (setminus x0 x1) (setminus x0 x2) leaving 2 subgoals.
The subproof is completed by applying H3.
Apply unknownprop_e6919c45bef19e01f88ce072c705412578331e9a3c7532de752ffb4187ed1265 with setminus x0 x1, setminus x0 x2, x3.
Apply unknownprop_3fe7f97dcb00bcf31cf989081bd8403f8f0647acc7dd719f8a7da64cd4837dac with x0, x2, x3 leaving 2 subgoals.
The subproof is completed by applying H1.
The subproof is completed by applying H4.
Apply unknownprop_fb26fe958e64ebbf533947db0048c8f1c2bfe1ee93c5358b327221e99f81f109 with setminus x0 x1, setminus x0 x2, setminus x0 (binintersect x1 x2) leaving 2 subgoals.
Apply unknownprop_23efa10145683812116a787fbe80411af9866a0e766c9c6a09762bdfcc92721f with x0, x1, binintersect x1 x2.
The subproof is completed by applying unknownprop_e0d452e0e0459ccd22d0a0ca66d8c6b520f69a835c0ebd50bbdd40077efd4a68 with x1, x2.
Apply unknownprop_23efa10145683812116a787fbe80411af9866a0e766c9c6a09762bdfcc92721f with x0, x2, binintersect x1 x2.
The subproof is completed by applying unknownprop_43a7b6a7250420244ab59ee561112cfc53c614b669837fc84c919b0df2ef6e0a with x1, x2.