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Proof step 12 from proof monls-mon-implies-monls (previous step)

⌜n⌝ + ⌜1⌝ < # lim(nσf), # lim(nσf) < ⌜n⌝ + ⌜2⌝ , mon(nσf), lim(nσf)[n + 1] ≤ lim(nσf)[n], ¬ # lim(nσf) < ⌜n⌝ + ⌜2⌝ → lim(nσf) to n + 2 ⊑ nσf(n0), ∀ n. nσf(n) ⊑ lim(nσf), ∀ n. mon<(nσf(n)) ⊦

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Rule argument

Additional information

Used simplifier rules: 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% ⊦ ⌜m⌝ = ⌜m0⌝ ↔ m = m0; (s)% ⊦ ⌜1⌝ < n∞ ↔ n∞ ≠ ⌜0⌝ ∧ n∞ ≠ ⌜1⌝ ; (s)% ⊦ ⌜n⌝ + n∞1 < ⌜n⌝ + n∞2 ↔ n∞1 < n∞2; (s)%ls-trans: ⊦ n∞ < n∞1 ∧ n∞1 < n∞2 → n∞ < n∞2; (forward) from specification nat-inf