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Proofgold Proof

pf
Let x0 of type ι be given.
Assume H0: x0 ∈ setminus u16 u6.
Let x1 of type ι → ο be given.
Assume H1: x1 u6.
Assume H2: x1 u7.
Assume H3: x1 u8.
Assume H4: x1 u9.
Assume H5: x1 u10.
Assume H6: x1 u11.
Assume H7: x1 u12.
Assume H8: x1 u13.
Assume H9: x1 u14.
Assume H10: x1 u15.
Apply setminusE with u16, u6, x0, x1 x0 leaving 2 subgoals.
The subproof is completed by applying H0.
Assume H11: x0 ∈ u16.
Assume H12: nIn x0 u6.
Apply xm with x0 ∈ u12, x1 x0 leaving 2 subgoals.
Assume H13: x0 ∈ u12.
Apply unknownprop_0fab5122556b271f6fd5ccb0ad45cb01192affd855cb92d430b4ab8c0e6f785a with x0, x1 leaving 7 subgoals.
Apply setminusI with u12, u6, x0 leaving 2 subgoals.
The subproof is completed by applying H13.
The subproof is completed by applying H12.
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.
The subproof is completed by applying H6.
Assume H13: 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 H11.
The subproof is completed by applying H13.
The subproof is completed by applying H7.
The subproof is completed by applying H8.
The subproof is completed by applying H9.
The subproof is completed by applying H10.
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