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Proof step 3 from proof lim-exists (previous step)

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

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 4:
# σσ = ∞, mon(σσ) ⊦ σσ = [], ∃ σ. (∀ n. ∃ σ1. σσ[n] + σ1 = σ) ∧ (∀ m. ¬ # σ < ⌜m⌝ → (∃ n, σ1. (σ to m) + σ1 = σσ[n]))

Rule argument

Additional information

Used simplifier rules: less-inf2: ⊦ ⌜m⌝ < ∞; from specification nat-inf