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Proof step 85 from proof lim-exists (previous step)

# σσ[0] = ⌜n⌝ , # σσ = ∞, σσ[m0] = σσ[0] + ⌜nf to ii(m0)⌝ , ii(0) = 0, ii(m0) < ii(m0 + 1), n0 < ii(m0 + 1), n2 < ii(m0 + 1), mon(σσ), ii(m0) ≤ n0, ∀ n. ii(n + 1) = ii(n) + # lf(n) ∧ (nf from ii(n)) to # lf(n) = lf(n), ∀ n. σσ[n + 1] = σσ[n] + ⌜lf(n)⌝ , ∀ m, n. m ≤ n → ii(m) ≤ ii(n) ⊦ ii(m0 + 1) + n = 0, ((σσ[0] + ⌜nf⌝ to n0 + n) + ⌜(nf to ii(m0 + 1)) from n0⌝ )[n2 + n] = nf(n2), ii(m0 + 1) = 0, σσ = [], ∃ n. # σσ[n] = ∞

User applied rule insert rewrite lemma

And obtained the following new goals

Rule argument

spec: stream name: get-append-notls seq: ⊦ ¬ ⌜m⌝ < # σ → (σ + σ1)[m] = σ1[m - (# σ).n] subst: [m, σ1, σ] → [n2 + n, ⌜(nf to ii(m0 + 1)) from n0⌝ , σσ[0] + ⌜nf⌝ to n0 + n] flags: <all paths>

Additional information

Used terms: n2 + n, ⌜(nf to ii(m0 + 1)) from n0⌝ , σσ[0] + ⌜nf⌝ to n0 + n