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Proof step 7 from proof monls-exists-maxls (previous step)

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

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 8:
nσ[m] < nσ[m + 1], nσ[m] < nσ[m0], nσ[m] < nσ[m0 + 1], nσ[0] < nσ[m + 1], n < nσ[m + 1], ⌜m0⌝ < # nσ, nσ[0] < nσ[m0], n < nσ[m0], ⌜m0⌝ + ⌜1⌝ < # nσ, n < nσ[m0 + 1], nσ[0] < nσ[m0 + 1], mon<(nσ), m ≤ m0, nσ[m] ≤ n, nσ[0] ≤ n ⊦ ∃ m. nσ[m] ≤ n ∧ n < nσ[m + 1] ∧ m ≤ m0 + 1

Rule argument

Additional information

Used simplifier rules: ⊦ m < n → n ≠ 0; (s)%fle-01: ⊦ m ≤ n ∧ n < n0 → m < n0; (forward) from specification nat%f: ⊦ m < n → n ≠ 0; (forward) from specification nat-basic%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-basic%a: ⊦ (m + n0) + n1 = m + n0 + n1; from specification nat-basic% ⊦ ¬ m + n < m; (s)% ⊦ ⌜n⌝ + ⌜m⌝ < ⌜n0⌝ ↔ n + m < n0; (s)%lsle-trans: ⊦ n∞ < n∞1 ∧ ¬ n∞2 < n∞1 → n∞ < n∞2; (forward) from specification nat-inf