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Proof step 5 from proof monls-mon-implies-monls (previous step)

mon(nσf), ∀ n. mon<(nσf(n)), ∀ n. nσf(n) ⊑ lim(nσf), ∀ m. ¬ # lim(nσf) < ⌜m⌝ → (∃ n. lim(nσf) to m ⊑ nσf(n)) ⊦ mon<(lim(nσf))

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 6:
⊦ mon<(nσ) ↔ (∀ n. ⌜n⌝ + ⌜1⌝ < # nσ → nσ[n] < nσ[n + 1])
Proof step 7:
mon(nσf), ∀ n. mon<(nσf(n)), ∀ n. nσf(n) ⊑ lim(nσf), ∀ m. ¬ # lim(nσf) < ⌜m⌝ → (∃ n. lim(nσf) to m ⊑ nσf(n)) ⊦ ∀ n. ⌜n⌝ + ⌜1⌝ < # lim(nσf) → lim(nσf)[n] < lim(nσf)[n + 1]

Rule argument

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

Additional information

Used terms: lim(nσf)