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Proof step 115 from proof lim-exists (previous step)

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

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 116:
⊦ n < # x → (x + y)[n] = x[n]
Proof step 117:
# σσ = ∞, ii(0) = 0, ii(n0 + 1) = ii(n0) + # lf(n0), n < ii(n0 + 1), mon(σσ), ∀ m, n. m ≤ n → ii(m) ≤ ii(n), ∀ n. ∃ m. ii(m) ≤ n ∧ n < ii(m + 1) ⊦ # σσ[0] = ∞, ((nf to ii(n0)) + ((nf from ii(n0)) to # lf(n0)))[n] = nf(n), ii(n0 + 1) = 0, σσ = [], n < #(nf to ii(n0)), ∃ n. # σσ[n] = ∞

Rule argument

spec: list-del name: get-append-less seq: ⊦ n < # x → (x + y)[n] = x[n] subst: [n, y, x] → [n, (nf from ii(n0)) to # lf(n0), nf to ii(n0)] flags: <all paths>

Additional information

Used simplifier rules: ⊦ m < n ↔ ¬ n ≤ m; (ss)% ⊦ #(nf to n) = n; (s)% ⊦ m ≤ n → (n < m ↔ false); (s)%m < n ⊦ (nf to n)[m] = nf(m); (s) Used terms: n, (nf from ii(n0)) to # lf(n0), nf to ii(n0)