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Proof step 128 from proof lim-exists (previous step)

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

User applied rule insert equation

And closed the goal!

Rule argument

pos: left 2 flags: rotate, discard

Additional information

Used simplifier rules: ⊦ #(σ + σ1) = # σ + # σ1; (s)% ⊦ # ⌜nf⌝ = ∞; (s)% ⊦ n∞ + ∞ = ∞; (s)%add-assoc: ⊦ (n∞ + n∞1) + n∞2 = n∞ + n∞1 + n∞2; from specification nat-inf%add-comm: ⊦ n∞1 + n∞2 = n∞2 + n∞1; from specification nat-inf%append-assoc: ⊦ (σ + σ1) + σ2 = σ + σ1 + σ2; from specification stream