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Proof step 77 from proof inv-ls-succ (previous step)

nσ[n1] = n + 1, nσ[n0] = n + 1, nσ[m] = n + 1, m < n1, ⌜n1⌝ < # nσ, m0 < n1, n < nσ[m0], ⌜n0⌝ < # nσ, m < n0, m < m0, ∞.n ≤ max∞(λ n0. ⌜n0⌝ < # nσ ∧ nσ[n0] = n).n, ⌜m⌝ < # nσ, stutf(nσ), ⌜m0⌝ < # nσ, n + 1 < nσ[m0], m + 1 < n1, ∀ m2. (∃ m0. ⌜m0⌝ < # nσ ∧ nσ[m0] = m2 - 1 ∧ (# nσ ≠ ∞ ∨ ¬(∀ m1. m0 < m1 → nσ[m1] = m2 - 1))) → ¬ 2 + n < m2 ⊦ nσ[m0] = n + 1

User applied rule insert lemma

And obtained the following new goals

Rule argument

spec: inst: name: monle-leq seq: ⊦ mon≤(nσ) ∧ m ≤ n ∧ ⌜n⌝ < # nσ → nσ[m] ≤ nσ[n] subst: [nσ, m, n] → [nσ, m0, n1] flags: current, []

Additional information

Used simplifier rules: stutf-monle: ⊦ stutf(nσ) → (¬ mon≤(nσ) ↔ false);%lels-03: ⊦ m < n → m ≤ n; from specification nat%le-one: ⊦ m ≤ n + 1 ∧ n < n0 → m ≤ n0; (forward) from specification nat%a: ⊦ (m + n0) + n1 = m + n0 + n1; from specification nat-basic2%c: ⊦ m + n = n + m; from specification nat-basic2%fle-01: ⊦ m ≤ n ∧ n < n0 → m < n0; (forward) from specification nat%fle: ⊦ m < n ∧ n ≤ n0 → m < n0; (forward) from specification nat%ref-1: ⊦ ¬ n < n; from specification nat-basic1 Used terms: nσ, m0, n1