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Proofgold Proof

pf
Let x0 of type ι be given.
Assume H0: x0setminus u18 u12.
Let x1 of type ιο be given.
Assume H1: x1 u12.
Assume H2: x1 u13.
Assume H3: x1 u14.
Assume H4: x1 u15.
Assume H5: x1 u16.
Assume H6: x1 u17.
Apply setminusE with u18, u12, x0, x1 x0 leaving 2 subgoals.
The subproof is completed by applying H0.
Assume H7: x0u18.
Assume H8: nIn x0 u12.
Apply ordsuccE with u17, x0, x1 x0 leaving 3 subgoals.
The subproof is completed by applying H7.
Assume H9: x0u17.
Apply unknownprop_d2eb1da8f945e97882f3b17888a7fe6e441c3a4b20ad156ba00c22e721803915 with x0, x1 leaving 6 subgoals.
Apply setminusI with u17, u12, x0 leaving 2 subgoals.
The subproof is completed by applying H9.
The subproof is completed by applying H8.
The subproof is completed by applying H1.
The subproof is completed by applying H2.
The subproof is completed by applying H3.
The subproof is completed by applying H4.
The subproof is completed by applying H5.
Assume H9: x0 = u17.
Apply H9 with λ x2 x3 . x1 x3.
The subproof is completed by applying H6.