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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 (binunion x1 x2), setminus (setminus x0 x1) x2 leaving 2 subgoals.
Apply unknownprop_c3fe42b21df0810041479a97b374de73f7754e07c8af1c88386a1e7dc0aad10f with setminus x0 (binunion x1 x2), setminus (setminus x0 x1) x2.
Let x3 of type ι be given.
Assume H0: In x3 (setminus x0 (binunion x1 x2)).
Apply unknownprop_e02b92c94ff70655b8eb0623a7ec106c0c0c9c65ac0f52f9689f2e6c9f563b5d with x0, binunion x1 x2, x3, In x3 (setminus (setminus x0 x1) x2) leaving 2 subgoals.
The subproof is completed by applying H0.
Assume H1: In x3 x0.
Assume H2: nIn x3 (binunion x1 x2).
Apply unknownprop_7b9e293c61bcb3dc3488b0ba471f92772eec41ae9263c2ce6e2257cb44eb93fc with x1, x2, x3, In x3 (setminus (setminus x0 x1) x2) leaving 2 subgoals.
The subproof is completed by applying H2.
Assume H3: nIn x3 x1.
Assume H4: nIn x3 x2.
Apply unknownprop_3fe7f97dcb00bcf31cf989081bd8403f8f0647acc7dd719f8a7da64cd4837dac with setminus x0 x1, x2, x3 leaving 2 subgoals.
Apply unknownprop_3fe7f97dcb00bcf31cf989081bd8403f8f0647acc7dd719f8a7da64cd4837dac with x0, x1, x3 leaving 2 subgoals.
The subproof is completed by applying H1.
The subproof is completed by applying H3.
The subproof is completed by applying H4.
Apply unknownprop_c3fe42b21df0810041479a97b374de73f7754e07c8af1c88386a1e7dc0aad10f with setminus (setminus x0 x1) x2, setminus x0 (binunion x1 x2).
Let x3 of type ι be given.
Assume H0: In x3 (setminus (setminus x0 x1) x2).
Apply unknownprop_e02b92c94ff70655b8eb0623a7ec106c0c0c9c65ac0f52f9689f2e6c9f563b5d with setminus x0 x1, x2, x3, In x3 (setminus x0 (binunion x1 x2)) leaving 2 subgoals.
The subproof is completed by applying H0.
Assume H1: In x3 (setminus x0 x1).
Assume H2: nIn x3 x2.
Apply unknownprop_e02b92c94ff70655b8eb0623a7ec106c0c0c9c65ac0f52f9689f2e6c9f563b5d with x0, x1, x3, In x3 (setminus x0 (binunion x1 x2)) leaving 2 subgoals.
The subproof is completed by applying H1.
Assume H3: In x3 x0.
Assume H4: nIn x3 x1.
Apply unknownprop_3fe7f97dcb00bcf31cf989081bd8403f8f0647acc7dd719f8a7da64cd4837dac with x0, binunion x1 x2, x3 leaving 2 subgoals.
The subproof is completed by applying H3.
Apply unknownprop_511b477d6c59a05c03c208c1dd74b022107e0eff3c61d9283784d8417769059d with x1, x2, x3 leaving 2 subgoals.
The subproof is completed by applying H4.
The subproof is completed by applying H2.
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