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Proof step 63 from proof infinite-append-prefixnextnli (previous step)

ii(0) = 0, lf(0) = [], lf(n0) = (σ to ii(n0)).l, ii(n0 + 1) = ii(n0) + # nextnli0(lf(n0), n0), (σ from ii(n0)) to # nextnli0(lf(n0), n0) = ⌜nextnli0(lf(n0), n0)⌝ , ∀ m, n. m ≤ n → ii(m) ≤ ii(n), ∀ n. lf(n + 1) = nextnli(lf(n), n), ∀ x, n. nextnli(x, n) = x + nextnli0(x, 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 + 1) = (σ to ii(n0 + 1)).l, # σ < ⌜ii(n0 + 1)⌝

User applied rule all left

And obtained the following new goals

Proof step 64:
ii(0) = 0, lf(0) = [], lf(n0) = (σ to ii(n0)).l, ii(n0 + 1) = ii(n0) + # nextnli0(lf(n0), n0), (σ from ii(n0)) to # nextnli0(lf(n0), n0) = ⌜nextnli0(lf(n0), n0)⌝ , ∀ m, n. m ≤ n → ii(m) ≤ ii(n), lf(n0 + 1) = nextnli(lf(n0), n0), ∀ x, n. nextnli(x, n) = x + nextnli0(x, 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 + 1) = (σ to ii(n0 + 1)).l, # σ < ⌜ii(n0 + 1)⌝

Rule argument

pos: left 7 terms: n0 abort: F discard: T computed: T

Additional information

Used terms: n0