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Proofgold Proof

pf
Let x0 of type ι be given.
Assume H0: x0setminus u17 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.
Apply setminusE with u17, u12, x0, x1 x0 leaving 2 subgoals.
The subproof is completed by applying H0.
Assume H6: x0u17.
Assume H7: nIn x0 u12.
Apply ordsuccE with u16, x0, x1 x0 leaving 3 subgoals.
The subproof is completed by applying H6.
Assume H8: x0u16.
Apply unknownprop_bf17ea03608bec2ab1db40555d0b2aea03020efffda1ccd3dabfc161366b81c8 with x0, x1 leaving 5 subgoals.
Apply setminusI with u16, u12, x0 leaving 2 subgoals.
The subproof is completed by applying H8.
The subproof is completed by applying H7.
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.
Assume H8: x0 = u16.
Apply H8 with λ x2 x3 . x1 x3.
The subproof is completed by applying H5.