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Proofgold Proof

pf
Let x0 of type ι(ιο) → ο be given.
Let x1 of type ι(ιο) → ο be given.
Let x2 of type ι be given.
Assume H0: ordinal x2.
Let x3 of type ιο be given.
Let x4 of type ιο be given.
Assume H1: PNoEq_ x2 x3 x4.
Assume H2: PNo_rel_strict_imv x0 x1 x2 x3.
Apply H2 with PNo_rel_strict_imv x0 x1 x2 x4.
Assume H3: PNo_rel_strict_upperbd x0 x2 x3.
Assume H4: PNo_rel_strict_lowerbd x1 x2 x3.
Apply andI with PNo_rel_strict_upperbd x0 x2 x4, PNo_rel_strict_lowerbd x1 x2 x4 leaving 2 subgoals.
Apply PNoEq_rel_strict_upperbd with x0, x2, x3, x4 leaving 3 subgoals.
The subproof is completed by applying H0.
The subproof is completed by applying H1.
The subproof is completed by applying H3.
Apply PNoEq_rel_strict_lowerbd with x1, x2, x3, x4 leaving 3 subgoals.
The subproof is completed by applying H0.
The subproof is completed by applying H1.
The subproof is completed by applying H4.