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Proofgold Proof

pf
Let x0 of type ι → (ι → ο) → ο be given.
Let x1 of type ι → (ι → ο) → ο be given.
Assume H0: PNoLt_pwise x0 x1.
Let x2 of type ι be given.
Assume H1: ordinal x2.
Assume H2: PNo_lenbdd x2 x0.
Assume H3: PNo_lenbdd x2 x1.
Apply PNo_bd_pred with x0, x1, x2, PNo_strict_imv x0 x1 (PNo_bd x0 x1) (PNo_pred x0 x1) 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 H3.
Assume H4: and (ordinal (PNo_bd x0 x1)) (PNo_strict_imv x0 x1 (PNo_bd x0 x1) (PNo_pred x0 x1)).
Assume H5: ∀ x3 . x3 ∈ PNo_bd x0 x1 ⟶ ∀ x4 : ι → ο . not (PNo_strict_imv x0 x1 x3 x4).
Apply H4 with PNo_strict_imv x0 x1 (PNo_bd x0 x1) (PNo_pred x0 x1).
Assume H6: ordinal (PNo_bd x0 x1).
Assume H7: PNo_strict_imv x0 x1 (PNo_bd x0 x1) (PNo_pred x0 x1).
The subproof is completed by applying H7.
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