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Proof step 8 from proof monls-exists-maxleq (previous step)

nσ[0] < nσ[m1], nσ[m1 + 1] ≤ nσ[m1], nσ[0] < nσ[m1 + 1], ⌜m1⌝ + ⌜1⌝ < # nσ, mon<(nσ) ⊦ nσ[m1 + 1] = 0, nσ[m1] = 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, m1, m1 + 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 Used terms: nσ, m1, m1 + 1