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Proofgold Proof

pf
Let x0 of type ι be given.
Let x1 of type ι be given.
Assume H0: ordinal x0.
Assume H1: (λ x2 . SetAdjoin x2 (Sing 1)) x0 = (λ x2 . SetAdjoin x2 (Sing 1)) x1.
Apply unknownprop_c3fe42b21df0810041479a97b374de73f7754e07c8af1c88386a1e7dc0aad10f with x0, x1.
Let x2 of type ι be given.
Assume H2: In x2 x0.
Claim L3: In x2 ((λ x3 . SetAdjoin x3 (Sing 1)) x1)
Apply H1 with λ x3 x4 . In x2 x3.
Apply unknownprop_c8252e4c83bb4898d143266bc455e2432960bbe927d91a6293e89e924042d02d with x0, Sing 1, x2.
The subproof is completed by applying H2.
Apply unknownprop_e0504d591aa31271c5372c445c216da1b623d835d8188df9ffa1d2ea977ac098 with x1, Sing 1, x2, In x2 x1 leaving 3 subgoals.
The subproof is completed by applying L3.
Assume H4: In x2 x1.
The subproof is completed by applying H4.
Assume H4: x2 = Sing 1.
Apply FalseE with In x2 x1.
Apply unknownprop_831031d8fe8dbf34401419f1bd72d9257a766bdbb899a9b13b9b87ffc267e396.
Apply H4 with λ x3 x4 . ordinal x3.
Apply unknownprop_df95567eaac7dcf742571a06351d685ef037c3575a0b273f643efe646824ac1a with x0, x2 leaving 2 subgoals.
The subproof is completed by applying H0.
The subproof is completed by applying H2.