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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: 40dde.. x0 x2 x1 x3.
Let x4 of type ο be given.
Assume H1: PNoLt_ (d3786.. x0 x1) x2 x3x4.
Assume H2: prim1 x0 x1PNoEq_ x0 x2 x3x3 x0x4.
Assume H3: prim1 x1 x0PNoEq_ x1 x2 x3not (x2 x1)x4.
Apply H0 with x4 leaving 2 subgoals.
Assume H4: or (PNoLt_ (d3786.. x0 x1) x2 x3) (and (and (prim1 x0 x1) (PNoEq_ x0 x2 x3)) (x3 x0)).
Apply H4 with x4 leaving 2 subgoals.
The subproof is completed by applying H1.
Assume H5: and (and (prim1 x0 x1) (PNoEq_ x0 x2 x3)) (x3 x0).
Apply H5 with x4.
Assume H6: and (prim1 x0 x1) (PNoEq_ x0 x2 x3).
Apply H6 with x3 x0x4.
The subproof is completed by applying H2.
Assume H4: and (and (prim1 x1 x0) (PNoEq_ x1 x2 x3)) (not (x2 x1)).
Apply H4 with x4.
Assume H5: and (prim1 x1 x0) (PNoEq_ x1 x2 x3).
Apply H5 with not (x2 x1)x4.
The subproof is completed by applying H3.