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Proof step 7 from proof lim-exists (previous step)

# σσ[n] = ∞, # σσ = ∞, mon(σσ) ⊦ σσ = [], (∀ n0. ∃ σ1. σσ[n0] + σ1 = σσ[n]) ∧ (∀ m. ¬ # σσ[n] < ⌜m⌝ → (∃ n0, σ1. (σσ[n] to m) + σ1 = σσ[n0]))

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 8:
# σσ = ∞, # σσ[n] = ∞, mon(σσ) ⊦ σσ = [], (∃ σ1. σσ[n0] + σ1 = σσ[n]) ∧ (∃ n0, σ1. (σσ[n] to m) + σ1 = σσ[n0])

Rule argument

Additional information

Used simplifier rules: less-inf1: ⊦ ¬ ∞ < n∞; from specification nat-inf