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Proof step 77 from proof infinite-append-prefixnextnli (previous step)

# lf(n0) = ii(n0), ii(0) = 0, lf(0) = [], (σ from ii(n0)) to # nextnli0(lf(n0), n0) = ⌜nextnli0(lf(n0), n0)⌝ , n1 < ii(n0) + # nextnli0(lf(n0), n0), (finp(σ) ⊃ # σ = ⌜ii(n)⌝ ∧ (∀ m. n ≤ m → nextnli0(lf(m), m) = [] ∧ ii(m) = ii(n));∀ n. ∃ m. ii(m) ≤ n ∧ n < ii(m + 1)), ∀ n2. n2 < ii(n0) → lf(n0)[n2] = σ[n2], ∀ m, n. m ≤ n → ii(m) ≤ ii(n) ⊦ (lf(n0) + nextnli0(lf(n0), n0))[n1] = σ[n1], # σ < ⌜ii(n0)⌝ + ⌜# nextnli0(lf(n0), n0)⌝

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 78:
⊦ σ0 = σ1 ↔ # σ0 = # σ1 ∧ (∀ n. ⌜n⌝ < # σ0 → σ0[n] = σ1[n])
Proof step 79:
#((σ from ii(n0)) to # nextnli0(lf(n0), n0)) = # ⌜nextnli0(lf(n0), n0)⌝ , # lf(n0) = ii(n0), ii(0) = 0, lf(0) = [], n1 < ii(n0) + # nextnli0(lf(n0), n0), (finp(σ) ⊃ # σ = ⌜ii(n)⌝ ∧ (∀ m. n ≤ m → nextnli0(lf(m), m) = [] ∧ ii(m) = ii(n));∀ n. ∃ m. ii(m) ≤ n ∧ n < ii(m + 1)), ∀ m, n. m ≤ n → ii(m) ≤ ii(n), ∀ n2. n2 < ii(n0) → lf(n0)[n2] = σ[n2], ∀ n. ⌜n⌝ < #((σ from ii(n0)) to # nextnli0(lf(n0), n0)) → ((σ from ii(n0)) to # nextnli0(lf(n0), n0))[n] = ⌜nextnli0(lf(n0), n0)⌝ [n] ⊦ (lf(n0) + nextnli0(lf(n0), n0))[n1] = σ[n1], # σ < ⌜ii(n0)⌝ + ⌜# nextnli0(lf(n0), n0)⌝

Rule argument

spec: stream name: extensionality seq: ⊦ σ0 = σ1 ↔ # σ0 = # σ1 ∧ (∀ n. ⌜n⌝ < # σ0 → σ0[n] = σ1[n]) subst: [σ1, σ0] → [⌜nextnli0(lf(n0), n0)⌝ , (σ from ii(n0)) to # nextnli0(lf(n0), n0)] flags: <all paths>

Additional information

Used terms: ⌜nextnli0(lf(n0), n0)⌝ , (σ from ii(n0)) to # nextnli0(lf(n0), n0)