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Proof step 142 from proof inv-ls-succ (previous step)

leninv(nσ) = ⌜n1⌝ , nσ[n0] = nσ[m] + 1, m ≤ ((λ m. max∞(λ n. ⌜n⌝ < # nσ ∧ nσ[n] = m).n) to n1)[nσ[m]], ⌜n0⌝ < # nσ, stutf(nσ), n0 ≤ ((λ m. max∞(λ n. ⌜n⌝ < # nσ ∧ nσ[n] = m).n) to n1)[nσ[m]], nσ[n0] < n1, m ≤ n0, ∀ m0. ⌜m0⌝ < # nσ ∧ nσ[m0] = nσ[n0] → ¬ n0 < m0, ∀ n2. ¬ ⌜n2⌝ < # nσ ∨ nσ[n2] ≠ nσ[m] ⊦

Heuristic quantifier closing applied rule all left

And closed the goal!

Rule argument

pos: left 10 terms: m

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: m