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Proof step 22 from proof monls-mon-implies-monls (previous step)

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

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 23:
(lim(nσf) to n + 2) + nσ = nσf(n0), ⌜n⌝ + ⌜1⌝ < # lim(nσf), mon(nσf), lim(nσf)[n + 1] ≤ lim(nσf)[n], # nσf(n0) < # lim(nσf), ∀ n. nσf(n) ⊑ lim(nσf) ⊦ ⌜n⌝ + ⌜1⌝ < # nσf(n0), # lim(nσf) < ⌜n⌝ + ⌜2⌝

Rule argument

Additional information

Used simplifier rules: lels-trans: ⊦ ¬ n∞1 < n∞ ∧ n∞1 < n∞2 → n∞ < n∞2; (forward) from specification nat-inf