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Proof step 2 from proof monls-mon-implies-monls (previous step)

mon(nσf), ∀ n. mon<(nσf(n)) ⊦ mon<(lim(nσf))

User applied rule insert spec-lemma

And obtained the following new goals

Proof step 3:
⊦ mon(nσf) → (∀ n. nσf(n) ⊑ lim(nσf)) ∧ (∀ m. ¬ # lim(nσf) < ⌜m⌝ → (∃ n. lim(nσf) to m ⊑ nσf(n)))
Proof step 4:
mon(nσf) → (∀ n. nσf(n) ⊑ lim(nσf)) ∧ (∀ m. ¬ # lim(nσf) < ⌜m⌝ → (∃ n. lim(nσf) to m ⊑ nσf(n))), mon(nσf), ∀ n. mon<(nσf(n)) ⊦ mon<(lim(nσf))

Rule argument

spec: mon-lim-filter-count inst: natstream name: lim-def seq: ⊦ mon(nσf) → (∀ n. nσf(n) ⊑ lim(nσf)) ∧ (∀ m. ¬ # lim(nσf) < ⌜m⌝ → (∃ n. lim(nσf) to m ⊑ nσf(n))) subst: [nσf] → [nσf] flags: []

Additional information

Used terms: nσf