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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 set_ext with 1ad11.. x0 (0ac37.. x1 x2), 1ad11.. (1ad11.. x0 x1) x2 leaving 2 subgoals.
Let x3 of type ι be given.
Assume H0: prim1 x3 (1ad11.. x0 (0ac37.. x1 x2)).
Apply unknownprop_b29d0d66991b8737c3ef6109cea8b8736c6edd642ea721f35cfa04fecdda0905 with x0, 0ac37.. x1 x2, x3, prim1 x3 (1ad11.. (1ad11.. x0 x1) x2) leaving 2 subgoals.
The subproof is completed by applying H0.
Assume H1: prim1 x3 x0.
Assume H2: nIn x3 (0ac37.. x1 x2).
Apply unknownprop_3049ef35042a26417e6e2a411bca9b8d206847258db4e8c0544709df73c280e8 with x1, x2, x3, prim1 x3 (1ad11.. (1ad11.. 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_4469442df960b88f16925ae745a59dde3c3d26a1d7b003702e92e0a7ea2361ef with 1ad11.. x0 x1, x2, x3 leaving 2 subgoals.
Apply unknownprop_4469442df960b88f16925ae745a59dde3c3d26a1d7b003702e92e0a7ea2361ef 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.
Let x3 of type ι be given.
Assume H0: prim1 x3 (1ad11.. (1ad11.. x0 x1) x2).
Apply unknownprop_b29d0d66991b8737c3ef6109cea8b8736c6edd642ea721f35cfa04fecdda0905 with 1ad11.. x0 x1, x2, x3, prim1 x3 (1ad11.. x0 (0ac37.. x1 x2)) leaving 2 subgoals.
The subproof is completed by applying H0.
Assume H1: prim1 x3 (1ad11.. x0 x1).
Assume H2: nIn x3 x2.
Apply unknownprop_b29d0d66991b8737c3ef6109cea8b8736c6edd642ea721f35cfa04fecdda0905 with x0, x1, x3, prim1 x3 (1ad11.. x0 (0ac37.. x1 x2)) leaving 2 subgoals.
The subproof is completed by applying H1.
Assume H3: prim1 x3 x0.
Assume H4: nIn x3 x1.
Apply unknownprop_4469442df960b88f16925ae745a59dde3c3d26a1d7b003702e92e0a7ea2361ef with x0, 0ac37.. x1 x2, x3 leaving 2 subgoals.
The subproof is completed by applying H3.
Apply unknownprop_a86576b47858fc2ae965025628d64bfd5a3ebff151e086fcdccba31002fa5e9c with x1, x2, x3 leaving 2 subgoals.
The subproof is completed by applying H4.
The subproof is completed by applying H2.