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Proofgold Proof

pf
Let x0 of type ι be given.
Let x1 of type ιο be given.
Assume H0: PNoLt x0 x1 x0 x1.
Apply PNoLtE with x0, x0, x1, x1, False leaving 4 subgoals.
The subproof is completed by applying H0.
Assume H1: PNoLt_ (binintersect x0 x0) x1 x1.
Apply PNoLt_irref_ with binintersect x0 x0, x1.
The subproof is completed by applying H1.
Assume H1: x0x0.
Apply FalseE with PNoEq_ x0 x1 x1x1 x0False.
Apply In_irref with x0.
The subproof is completed by applying H1.
Assume H1: x0x0.
Apply FalseE with PNoEq_ x0 x1 x1not (x1 x0)False.
Apply In_irref with x0.
The subproof is completed by applying H1.