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Proof step 71 from proof infinite-append-prefixnextnli (previous step)

ii(0) = 0, lf(0) = [], lf(n0) = (σ to ii(n0)).l, (σ from ii(n0)) to # nextnli0(lf(n0), n0) = ⌜nextnli0(lf(n0), n0)⌝ , ∀ m, n. m ≤ n → ii(m) ≤ ii(n), (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)) ⊦ lf(n0) + nextnli0(lf(n0), n0) = (σ to ii(n0) + # nextnli0(lf(n0), n0)).l, # σ < ⌜ii(n0)⌝ + ⌜# nextnli0(lf(n0), n0)⌝

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 72:
⊦ x = y ↔ # x = # y ∧ (∀ n. n < # x → x[n] = y[n])
Proof step 73:
ii(0) = 0, lf(0) = [], lf(n0) = (σ to ii(n0)).l, (σ from ii(n0)) to # nextnli0(lf(n0), n0) = ⌜nextnli0(lf(n0), n0)⌝ , ∀ m, n. m ≤ n → ii(m) ≤ ii(n), (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)) ⊦ #(lf(n0) + nextnli0(lf(n0), n0)) = # (σ to ii(n0) + # nextnli0(lf(n0), n0)).l ∧ (∀ n. n < #(lf(n0) + nextnli0(lf(n0), n0)) → (lf(n0) + nextnli0(lf(n0), n0))[n] = (σ to ii(n0) + # nextnli0(lf(n0), n0)).l[n]), # σ < ⌜ii(n0)⌝ + ⌜# nextnli0(lf(n0), n0)⌝

Rule argument

spec: list-del inst: name: extension seq: ⊦ x = y ↔ # x = # y ∧ (∀ n. n < # x → x[n] = y[n]) subst: [y, x] → [(σ to ii(n0) + # nextnli0(lf(n0), n0)).l, lf(n0) + nextnli0(lf(n0), n0)] flags: rewrite

Additional information

Used terms: (σ to ii(n0) + # nextnli0(lf(n0), n0)).l, lf(n0) + nextnli0(lf(n0), n0)