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Theorem maxinf-def

⊦ (max∞(np) = ∞ ⊃ (∀ n. ∃ n0. n < n0 ∧ np(n0)) ∨ (∀ n. ¬ np(n));(∃ n. np(max∞(np).n)) ∧ (∀ m. np(m) → ¬ max∞(np) < ⌜m⌝ ))