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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: ordinal x1.
Apply ordinal_In_Or_Subq with x0, x1, or (Subq x0 x1) (Subq x1 x0) leaving 4 subgoals.
The subproof is completed by applying H0.
The subproof is completed by applying H1.
Assume H2: prim1 x0 x1.
Apply orIL with Subq x0 x1, Subq x1 x0.
Apply ordinal_TransSet with x1, x0 leaving 2 subgoals.
The subproof is completed by applying H1.
The subproof is completed by applying H2.
Assume H2: Subq x1 x0.
Apply orIR with Subq x0 x1, Subq x1 x0.
The subproof is completed by applying H2.