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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: prim1 x1 x0.
Assume H1: PNoEq_ x1 x2 x3.
Assume H2: not (x2 x1).
Apply or3I3 with PNoLt_ (d3786.. x0 x1) x2 x3, and (and (prim1 x0 x1) (PNoEq_ x0 x2 x3)) (x3 x0), and (and (prim1 x1 x0) (PNoEq_ x1 x2 x3)) (not (x2 x1)).
Apply and3I with prim1 x1 x0, PNoEq_ x1 x2 x3, not (x2 x1) leaving 3 subgoals.
The subproof is completed by applying H0.
The subproof is completed by applying H1.
The subproof is completed by applying H2.