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Proof step 119 from proof lim-exists (previous step)

# σσ = ∞, mon(σσ) ⊦ σσ = [], ∃ x. σσ[n + 1] = σσ[n] + ⌜x⌝ , ∃ n. # σσ[n] = ∞, ∃ σ. (∀ n. ∃ σ1. σσ[n] + σ1 = σ) ∧ (∀ m. ¬ # σ < ⌜m⌝ → (∃ n, σ1. (σ to m) + σ1 = σσ[n]))

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 120:
⊦ mon(σσ) ↔ (∀ n. ⌜n⌝ + ⌜1⌝ < # σσ → σσ[n] ⊑ σσ[n + 1])
Proof step 121:
# σσ = ∞, ∀ n. ⌜n⌝ + ⌜1⌝ < # σσ → σσ[n] ⊑ σσ[n + 1] ⊦ σσ = [], ∃ x. σσ[n + 1] = σσ[n] + ⌜x⌝ , ∃ n. # σσ[n] = ∞, ∃ σ. (∀ n. ∃ σ1. σσ[n] + σ1 = σ) ∧ (∀ m. ¬ # σ < ⌜m⌝ → (∃ n, σ1. (σ to m) + σ1 = σσ[n]))

Rule argument

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

Additional information

Used terms: σσ