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Proofgold Proof

pf
Let x0 of type ι be given.
Assume H0: x0setminus u16 u10.
Let x1 of type ιο be given.
Assume H1: x1 u10.
Assume H2: x1 u11.
Assume H3: x1 u12.
Assume H4: x1 u13.
Assume H5: x1 u14.
Assume H6: x1 u15.
Apply setminusE with u16, u10, x0, x1 x0 leaving 2 subgoals.
The subproof is completed by applying H0.
Assume H7: x0u16.
Assume H8: nIn x0 u10.
Apply xm with x0u12, x1 x0 leaving 2 subgoals.
Assume H9: x0u12.
Apply unknownprop_fe3434c13e4d9f957110bf39b27112a1224a05dbf0d1a39a1c9cb87663b7ee08 with x0, x1 leaving 3 subgoals.
Apply setminusI with u12, u10, 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.
Assume H9: nIn x0 u12.
Apply unknownprop_bf17ea03608bec2ab1db40555d0b2aea03020efffda1ccd3dabfc161366b81c8 with x0, x1 leaving 5 subgoals.
Apply setminusI with u16, u12, x0 leaving 2 subgoals.
The subproof is completed by applying H7.
The subproof is completed by applying H9.
The subproof is completed by applying H3.
The subproof is completed by applying H4.
The subproof is completed by applying H5.
The subproof is completed by applying H6.