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Proof step 6 from proof monls-exists-maxls (previous step)

mon<(nσ), nσ[0] ≤ n, n < nσ[m0 + 1], ⌜m0⌝ + ⌜1⌝ < # nσ, nσ[0] < nσ[m0 + 1], n < nσ[m0], nσ[0] < nσ[m0], mon<(nσ) ∧ nσ[0] ≤ n ∧ n < nσ[m0] ∧ ⌜m0⌝ < # nσ → (∃ m1. nσ[m1] ≤ n ∧ n < nσ[m1 + 1] ∧ m1 ≤ m0) ⊦ nσ[m0 + 1] = 0, nσ[m0] = 0, ∃ m. nσ[m] ≤ n ∧ n < nσ[m + 1] ∧ m ≤ m0 + 1

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 7:
nσ[0] < nσ[m0], n < nσ[m0], nσ[0] < nσ[m0 + 1], ⌜m0⌝ + ⌜1⌝ < # nσ, n < nσ[m0 + 1], nσ[0] ≤ n, mon<(nσ), ⌜m0⌝ < # nσ, nσ[m] ≤ n, n < nσ[m + 1], m ≤ m0, nσ[0] < nσ[m + 1], nσ[m] < nσ[m0], nσ[m] < nσ[m0 + 1], nσ[m] < nσ[m + 1] ⊦ nσ[m0] = 0, nσ[m0 + 1] = 0, nσ[m + 1] = 0, ∃ m. nσ[m] ≤ n ∧ n < nσ[m + 1] ∧ m ≤ m0 + 1

Rule argument

Additional information

Used simplifier rules: fle-01: ⊦ m ≤ n ∧ n < n0 → m < n0; (forward) from specification nat%f: ⊦ m < n → n ≠ 0; (forward) from specification nat-basic1%add-comm: ⊦ n∞1 + n∞2 = n∞2 + n∞1; from specification nat-inf%add-assoc: ⊦ (n∞ + n∞1) + n∞2 = n∞ + n∞1 + n∞2; from specification nat-inf%c: ⊦ m + n = n + m; from specification nat-basic2%a: ⊦ (m + n0) + n1 = m + n0 + n1; from specification nat-basic2%l-02: ⊦ ¬ m + n < m; from specification nat-basic2%ls-natinf-to-nat-2-1: ⊦ ⌜n⌝ + ⌜m⌝ < ⌜n0⌝ ↔ n + m < n0; from specification nat-inf%lsle-trans: ⊦ n∞ < n∞1 ∧ ¬ n∞2 < n∞1 → n∞ < n∞2; (forward) from specification nat-inf