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Proof step 14 from proof lim-exists (previous step)

# σσ[n] = ∞, # σσ = ∞, mon(σσ), n < n0 ⊦ σσ = [], n0 = 0, σσ[n0] = σσ[n]

User applied rule insert lemma

And obtained the following new goals

Proof step 15:
mon(σσ), m ≤ n, ⌜n⌝ < # σσ ⊦ σσ[m] ⊑ σσ[n]
Proof step 16:
σσ[n] ⊑ σσ[n0], # σσ[n] = ∞, # σσ = ∞, mon(σσ), n < n0 ⊦ σσ = [], n0 = 0, σσ[n0] = σσ[n]

Rule argument

spec: inst: name: mon-lem seq: mon(σσ), m ≤ n, ⌜n⌝ < # σσ ⊦ σσ[m] ⊑ σσ[n] subst: [σσ, m, n] → [σσ, n, n0] flags: current, []

Additional information

Used simplifier rules: lels-03: ⊦ m < n → m ≤ n; from specification nat%less-inf2: ⊦ ⌜m⌝ < ∞; from specification nat-inf Used terms: σσ, n, n0