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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 ι be given.
Assume H0: ordinal x0.
Assume H1: ordinal x1.
Assume H2: ordinal x2.
Let x3 of type ι → ο be given.
Let x4 of type ι → ο be given.
Let x5 of type ι → ο be given.
Assume H3: or (PNoLt x0 x3 x1 x4) (and (x0 = x1) (PNoEq_ x0 x3 x4)).
Assume H4: PNoLt x1 x4 x2 x5.
Apply H3 with PNoLt x0 x3 x2 x5 leaving 2 subgoals.
Assume H5: PNoLt x0 x3 x1 x4.
Apply PNoLt_tra with x0, x1, x2, x3, x4, x5 leaving 5 subgoals.
The subproof is completed by applying H0.
The subproof is completed by applying H1.
The subproof is completed by applying H2.
The subproof is completed by applying H5.
The subproof is completed by applying H4.
Assume H5: and (x0 = x1) (PNoEq_ x0 x3 x4).
Apply H5 with PNoLt x0 x3 x2 x5.
Assume H6: x0 = x1.
Assume H7: PNoEq_ x0 x3 x4.
Apply H6 with λ x6 x7 . PNoLt x7 x3 x2 x5.
Apply PNoEqLt_tra with x1, x2, x3, x4, x5 leaving 4 subgoals.
The subproof is completed by applying H1.
The subproof is completed by applying H2.
Apply H6 with λ x6 x7 . PNoEq_ x6 x3 x4.
The subproof is completed by applying H7.
The subproof is completed by applying H4.
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