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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 (1ad11.. x1 x2), 0ac37.. (1ad11.. x0 x1) (d3786.. x0 x2) leaving 2 subgoals.
Let x3 of type ι be given.
Assume H0: prim1 x3 (1ad11.. x0 (1ad11.. x1 x2)).
Apply unknownprop_b29d0d66991b8737c3ef6109cea8b8736c6edd642ea721f35cfa04fecdda0905 with x0, 1ad11.. x1 x2, x3, prim1 x3 (0ac37.. (1ad11.. x0 x1) (d3786.. x0 x2)) leaving 2 subgoals.
The subproof is completed by applying H0.
Assume H1: prim1 x3 x0.
Assume H2: nIn x3 (1ad11.. x1 x2).
Apply unknownprop_d6451fc69fbe08714e8831021b9f2447054d88e18bdd01e2b77f6eb9ba73fa61 with x1, x2, x3, prim1 x3 (0ac37.. (1ad11.. x0 x1) (d3786.. x0 x2)) leaving 3 subgoals.
The subproof is completed by applying H2.
Assume H3: nIn x3 x1.
Apply unknownprop_0b5b61a66a1ed2eb843dbce5c5f6930c63a284fe5e33704d9f0cc564310ec40b with 1ad11.. x0 x1, d3786.. x0 x2, x3.
Apply unknownprop_4469442df960b88f16925ae745a59dde3c3d26a1d7b003702e92e0a7ea2361ef with x0, x1, x3 leaving 2 subgoals.
The subproof is completed by applying H1.
The subproof is completed by applying H3.
Assume H3: prim1 x3 x2.
Apply unknownprop_e4d6e0bfb4ef6d52ee13edd54a77c8cc7f0a3af8ffb1b8da66d4f98842dd28b5 with 1ad11.. x0 x1, d3786.. x0 x2, x3.
Apply unknownprop_0eb2245dc687a56a5adef9ad3fc675715803356fcfbd14168f93f22b67fac4c1 with x0, x2, x3 leaving 2 subgoals.
The subproof is completed by applying H1.
The subproof is completed by applying H3.
Apply unknownprop_c16c0737d29e3b3e820cf0e7f73a8868a90e8434c78c164566097cca1a566416 with 1ad11.. x0 x1, d3786.. x0 x2, 1ad11.. x0 (1ad11.. x1 x2) leaving 2 subgoals.
Let x3 of type ι be given.
Assume H0: prim1 x3 (1ad11.. x0 x1).
Apply unknownprop_b29d0d66991b8737c3ef6109cea8b8736c6edd642ea721f35cfa04fecdda0905 with x0, x1, x3, prim1 x3 (1ad11.. x0 (1ad11.. x1 x2)) leaving 2 subgoals.
The subproof is completed by applying H0.
Assume H1: prim1 x3 x0.
Assume H2: nIn x3 x1.
Apply unknownprop_4469442df960b88f16925ae745a59dde3c3d26a1d7b003702e92e0a7ea2361ef with x0, 1ad11.. x1 x2, x3 leaving 2 subgoals.
The subproof is completed by applying H1.
Apply unknownprop_1e19e245fe2a6915cced7ba5d31744ce21c833015f3fda47eabe25fcd1195b5b with x1, x2, x3.
The subproof is completed by applying H2.
Let x3 of type ι be given.
Assume H0: prim1 x3 (d3786.. x0 x2).
Apply unknownprop_1ac99d32a7ae5dc08fd640ea6c8b661df6b3535fe85e88b30b17c3701cb4c7ce with x0, x2, x3, prim1 x3 (1ad11.. x0 (1ad11.. x1 x2)) leaving 2 subgoals.
The subproof is completed by applying H0.
Assume H1: prim1 x3 x0.
Assume H2: prim1 x3 x2.
Apply unknownprop_4469442df960b88f16925ae745a59dde3c3d26a1d7b003702e92e0a7ea2361ef with x0, 1ad11.. x1 x2, x3 leaving 2 subgoals.
The subproof is completed by applying H1.
Apply unknownprop_991aad6ad920d57b07c64812bdcfe3d8d1bbe968590265c6414344edc5b13b23 with x1, x2, x3.
The subproof is completed by applying H2.
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