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Proof step 9 from proof stutf-maxinf-is-fin (previous step)

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

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 10:
# nσ = ∞, stutf(nσ), m ≤ nσ[n], ∀ n1. ∃ n0. n1 < n0 ∧ nσ[n0] = m ⊦ ∃ n. ∀ n0. ¬ n0 < n → nσ[n0] = m

Rule argument

Additional information

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