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Proofgold Proof

pf
Let x0 of type ι be given.
Assume H0: x0u22.
Let x1 of type ιο 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.
Assume H13: x1 u12.
Assume H14: x1 u13.
Assume H15: x1 u14.
Assume H16: x1 u15.
Assume H17: x1 u16.
Assume H18: x1 u17.
Assume H19: x1 u18.
Assume H20: x1 u19.
Assume H21: x1 u20.
Assume H22: x1 u21.
Apply ordsuccE with u21, x0, x1 x0 leaving 3 subgoals.
The subproof is completed by applying H0.
Assume H23: x0u21.
Apply unknownprop_4755f906616e21172aaad401215d2e4f63743ca748efd3161fa96581302eb223 with x0, x1 leaving 22 subgoals.
The subproof is completed by applying H23.
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.
The subproof is completed by applying H12.
The subproof is completed by applying H13.
The subproof is completed by applying H14.
The subproof is completed by applying H15.
The subproof is completed by applying H16.
The subproof is completed by applying H17.
The subproof is completed by applying H18.
The subproof is completed by applying H19.
The subproof is completed by applying H20.
The subproof is completed by applying H21.
Assume H23: x0 = u21.
Apply H23 with λ x2 x3 . x1 x3.
The subproof is completed by applying H22.