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Proof step 32 from proof stutf-maxinf-is-fin (previous step)

m1 ≤ n, nσ[m1] ≤ nσ[n], stutf(nσ), ⌜n⌝ < # nσ, ⌜nσ[m1]⌝ < # nσ ∧ nσ[m1] ≤ nσ[nσ[m1]] → m0 ≤ nσ[m0] ∧ nσ[m0] = nσ[m1], ∀ n. ¬ ⌜n⌝ < # nσ ∨ nσ[n] ≠ nσ[m1] ⊦ # nσ = ∞ ∧ (∃ n. ∀ n0. ¬ n0 < n → nσ[n0] = nσ[m1])

Heuristic quantifier closing applied rule all left

And closed the goal!

Rule argument

pos: left 6 terms: m1

Additional information

Used simplifier rules: lsle-trans: ⊦ n∞ < n∞1 ∧ ¬ n∞2 < n∞1 → n∞ < n∞2; (forward) from specification nat-inf%less-fin: ⊦ ⌜m⌝ < ⌜n⌝ ↔ m < n; from specification nat-inf%le-ls-simp: ⊦ m ≤ n → (n < m ↔ false); from specification nat Used terms: m1