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Proofgold Proof

pf
Let x0 of type ι be given.
Assume H0: x0 ∈ u12.
Let x1 of type ι → ο be given.
Assume H1: x1 0.
Assume H2: x1 u1.
Assume H3: x1 u2.
Assume H4: x1 u3.
Assume H5: x1 u4.
Assume H6: x1 u5.
Assume H7: x1 u6.
Assume H8: x1 u7.
Assume H9: x1 u8.
Assume H10: x1 u9.
Assume H11: x1 u10.
Assume H12: x1 u11.
Apply ordsuccE with u11, x0, x1 x0 leaving 3 subgoals.
The subproof is completed by applying H0.
Assume H13: x0 ∈ u11.
Apply unknownprop_16a583b27c846cbf24441f77a51593d3d8c71d1e4798e971e3bf25553934797a with x0, x1 leaving 12 subgoals.
The subproof is completed by applying H13.
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.
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.
The subproof is completed by applying H11.
Assume H13: x0 = u11.
Apply H13 with λ x2 x3 . x1 x3.
The subproof is completed by applying H12.
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