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Proofgold Proof

pf
Let x0 of type ι be given.
Let x1 of type ι be given.
Let x2 of type ιο be given.
Let x3 of type ιο be given.
Assume H0: x0x1.
Assume H1: PNoEq_ x0 x2 x3.
Assume H2: x3 x0.
Apply or3I2 with PNoLt_ (binintersect x0 x1) x2 x3, and (and (x0x1) (PNoEq_ x0 x2 x3)) (x3 x0), and (and (x1x0) (PNoEq_ x1 x2 x3)) (not (x2 x1)).
Apply and3I with x0x1, PNoEq_ x0 x2 x3, x3 x0 leaving 3 subgoals.
The subproof is completed by applying H0.
The subproof is completed by applying H1.
The subproof is completed by applying H2.