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Proof step 18 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], mon<(nσf(n0)), ∀ n. nσf(n) ⊑ lim(nσf) ⊦ # lim(nσf) < ⌜n⌝ + ⌜2⌝

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 19:
⊦ mon<(nσ) ↔ (∀ n. ⌜n⌝ + ⌜1⌝ < # nσ → nσ[n] < nσ[n + 1])
Proof step 20:
(lim(nσf) to n + 2) + nσ = nσf(n0), ⌜n⌝ + ⌜1⌝ < # lim(nσf), mon(nσf), lim(nσf)[n + 1] ≤ lim(nσf)[n], ∀ n. ⌜n⌝ + ⌜1⌝ < # nσf(n0) → nσf(n0)[n] < nσf(n0)[n + 1], ∀ n. nσf(n) ⊑ lim(nσf) ⊦ # lim(nσf) < ⌜n⌝ + ⌜2⌝

Rule argument

spec: inst: name: monls-def seq: ⊦ mon<(nσ) ↔ (∀ n. ⌜n⌝ + ⌜1⌝ < # nσ → nσ[n] < nσ[n + 1]) subst: [nσ] → [nσf(n0)] flags: rewrite, current

Additional information

Used terms: nσf(n0)