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Proof step 7 from proof maxinf-inf (previous step)

max∞(np) = ⌜n1⌝ , np(n1), ∀ m. np(m) → ¬ max∞(np) < ⌜m⌝ , (∀ n. ∃ n0. n < n0 ∧ np(n0)) ∨ (∀ n. ¬ np(n)) ⊦ max∞(np) = ∞

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 8:
max∞(np) = ⌜n1⌝ , np(n1), ∀ m. np(m) → ¬ n1 < m, (∀ n. ∃ n0. n < n0 ∧ np(n0)) ∨ (∀ n. ¬ np(n)) ⊦

Rule argument

Additional information

Used simplifier rules: ⊦ ⌜m⌝ < ⌜n⌝ ↔ m < n; (s)% ⊦ ⌜m⌝ ≠ ∞; (s)