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Proof step 62 from proof infinite-append-prefixnextli-weak (previous step)

# lf(n0) = ii(n0), ii(0) = 0, lf(0) = [], (σ from ii(n0)) to # nextli0(lf(n0)) = ⌜nextli0(lf(n0))⌝ , n1 < ii(n0) + # nextli0(lf(n0)), (finp(σ) ⊃ # σ = ⌜ii(n)⌝ ∧ (∀ m. n ≤ m → nextli0(lf(m)) = [] ∧ ii(m) = ii(n));∀ n. ∃ m. ii(m) ≤ n ∧ n < ii(m + 1)), ∀ n. ii(n + 1) = ii(n) + # nextli0(lf(n)) ∧ ¬ # σ < ⌜ii(n + 1)⌝ ∧ (σ from ii(n)) to # nextli0(lf(n)) = ⌜nextli0(lf(n))⌝ , ∀ m, n. m ≤ n → ii(m) ≤ ii(n), ∀ n. lf(n + 1) = nextli(lf(n)), ∀ x. nextli(x) = x + nextli0(x), ∀ n2. n2 < ii(n0) → lf(n0)[n2] = σ[n2] ⊦ (lf(n0) + nextli0(lf(n0)))[n1] = σ[n1], # σ < ⌜ii(n0)⌝ + ⌜# nextli0(lf(n0))⌝

User applied rule insert rewrite lemma

And obtained the following new goals

Rule argument

spec: list-del name: get-append-less seq: ⊦ n < # x → (x + y)[n] = x[n] subst: [n, y, x] → [n1, nextli0(lf(n0)), lf(n0)] flags: <all paths>

Additional information

Used terms: n1, nextli0(lf(n0)), lf(n0)