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Proof step 8 from proof monls-notsmall (previous step)

nσ[0] = 0, mon<(nσ), ⌜2⌝ + ⌜n0⌝ < # nσ, nσ[2 + n0] ≤ n0 + 1, mon<(nσ) ∧ nσ[0] = 0 ∧ ⌜n0⌝ + ⌜1⌝ < # nσ → n0 < nσ[n0 + 1] ⊦

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Rule argument

Additional information

Used simplifier rules: le-one: ⊦ m ≤ n + 1 ∧ 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%add-ls-cancel-num-02: ⊦ m ≤ n → (⌜(* n)⌝ + n∞1 < ⌜(* m)⌝ + n∞2 ↔ ⌜n - m⌝ + n∞1 < n∞2); from specification nat-inf%lsle-trans: ⊦ n∞ < n∞1 ∧ ¬ n∞2 < n∞1 → n∞ < n∞2; (forward) from specification nat-inf