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Proof step 20 from proof monls-exists-maxleq (previous step)

nσ[0] < nσ[m2], nσ[m2 + 1] ≤ nσ[m2], nσ[0] + 1 < nσ[2 + m2], m2 < m, ⌜m⌝ < # nσ, nσ[0] < nσ[m], mon<(nσ), nσ[0] < nσ[m2 + 1], nσ[0] + 1 < nσ[m], nσ[m2 + 1] < nσ[2 + m2], nσ[m2 + 1] < nσ[m], nσ[0] < nσ[2 + m2] ⊦ nσ[m] = 0, nσ[m2 + 1] = 0, nσ[2 + m2] = 0, m = 0, nσ[m2] = 0

User applied rule insert lemma

And obtained the following new goals

Rule argument

spec: inst: name: monls-ls seq: ⊦ mon<(nσ) ∧ m < n ∧ ⌜n⌝ < # nσ → nσ[m] < nσ[n] subst: [nσ, m, n] → [nσ, m2, m2 + 1] flags: current, []

Additional information

Used simplifier rules: s: ⊦ m < n + 1 ↔ ¬ n < m; from specification nat-basic2%ref-1: ⊦ ¬ n < n; from specification nat-basic1%a: ⊦ (m + n0) + n1 = m + n0 + n1; from specification nat-basic2%c: ⊦ m + n = n + m; from specification nat-basic2%add-fin: ⊦ ⌜m + n⌝ = ⌜m⌝ + ⌜n⌝ ; from specification nat-inf%le-ls-simp: ⊦ m ≤ n → (n < m ↔ false); from specification nat%lsle-trans: ⊦ n∞ < n∞1 ∧ ¬ n∞2 < n∞1 → n∞ < n∞2; (forward) from specification nat-inf%less-succ-leq: ⊦ ⌜n⌝ < ⌜1⌝ + n∞ ↔ ¬ n∞ < ⌜n⌝ ; from specification nat-inf%less-fin: ⊦ ⌜m⌝ < ⌜n⌝ ↔ m < n; from specification nat-inf%add-assoc: ⊦ (n∞ + n∞1) + n∞2 = n∞ + n∞1 + n∞2; from specification nat-inf%add-comm: ⊦ n∞1 + n∞2 = n∞2 + n∞1; from specification nat-inf Used terms: nσ, m2, m2 + 1