Proofgold Proof

pf
Let x0 of type ι be given. Let x1 of type ι be given. Let x2 of type ι → ο be given. Let x3 of type ι → ο be given. Assume H0: PNoLt_ (binintersect x0 x1) x2 x3. Apply or3I1 with PNoLt_ (binintersect x0 x1) x2 x3, and (and (x0 ∈ x1) (PNoEq_ x0 x2 x3)) (x3 x0), and (and (x1 ∈ x0) (PNoEq_ x1 x2 x3)) (not (x2 x1)). The subproof is completed by applying H0. ■