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Proof step 57 from proof lim-exists (previous step)

ii(0) = 0, # σσ = ∞, mon(σσ), ∀ n. σσ[n] = σσ[0] + ⌜nf to ii(n)⌝ , ∀ n. ∃ m. ii(m) ≤ n ∧ n < ii(m + 1), ∀ m, n. m ≤ n → ii(m) ≤ ii(n), ∀ n. σσ[n + 1] = σσ[n] + ⌜lf(n)⌝ , ∀ n. ii(n + 1) = ii(n) + # lf(n) ∧ (nf from ii(n)) to # lf(n) = lf(n) ⊦ ∃ σ1. (σσ[0] + ⌜nf to ii(n)⌝ ) + σ1 = σσ[0] + ⌜nf⌝ , σσ = [], ∃ n. # σσ[n] = ∞

User applied rule exists right

And closed the goal!

Rule argument

pos: right 1 terms: ⌜nf from ii(n)⌝ abort: F discard: T computed: F

Additional information

Used simplifier rules: append-cut1: ⊦ σ + σ1 = σ + σ2 ↔ σ1 = σ2 ∨ # σ = ∞; from specification stream%to-plus-from-inf-simp: ⊦ ⌜nf to n⌝ + ⌜nf from n⌝ ≠ ⌜nf⌝ ↔ false; from specification stream%append-assoc: ⊦ (σ + σ1) + σ2 = σ + σ1 + σ2; from specification stream Used terms: ⌜nf from ii(n)⌝