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

# nσ = ∞, ∀ n. ∃ n0. n < n0 ∧ ⌜n0⌝ < # nσ ∧ nσ[n0] = m, stutf(nσ) ⊦ # nσ = ∞ ∧ (∃ n. ∀ n0. ¬ n0 < n → nσ[n0] = m) ∨ (∀ n. ⌜n⌝ < # nσ → nσ[n] < m)

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 9:
# nσ = ∞, m ≤ nσ[n], stutf(nσ), ∀ n1. ∃ n0. n1 < n0 ∧ nσ[n0] = m ⊦ ∃ n. ∀ n0. ¬ n0 < n → nσ[n0] = m

Rule argument

Additional information

Used simplifier rules: less-inf2: ⊦ ⌜m⌝ < ∞; from specification nat-inf%lels: ⊦ ¬ m < n ↔ n ≤ m; from specification nat