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Proof step 8 from proof maxinf-fin (previous step)

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

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 9:
max∞(np) = ∞, n < n0, np(n0), np(n), ∀ n. ∃ n0. n < n0 ∧ np(n0), ∀ m. np(m) → ¬ n < m ⊦ n0 = 0

Rule argument

Additional information

Used simplifier rules: f: ⊦ m < n → n ≠ 0; (forward) from specification nat-basic1