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Proof step 101 from proof infinite-append-prefixnextli (previous step)

ii(0) = 0, lf(0) = [], # lf(n0) = ii(n0), nextli(lf(n0)) = lf(n0), nextli0(lf(n0)) = [], lf(n) = lf(n0), ii(n) = ii(n0), m < n, m < n0, ii(m + 1) ≤ ii(m), n0 < n, m + 1 < n, ∀ m. n0 < m → lf(m) = lf(n0) ∧ nextli0(lf(m)) = [] ∧ ii(m) = ii(n0), ∀ n0. lf(n0) = lf(n) to ii(n0), ∀ n0. ii(n0 + 1) = ii(n0) + # nextli0(lf(n0)) ∧ ¬ ii(n) < ii(n0 + 1) ∧ (lf(n) from ii(n0)) to # nextli0(lf(n0)) = nextli0(lf(n0)), ∀ m. nextli0(lf(m)) = [] ↔ n0 ≤ m, ∀ n. nextli0(lf(n)) = [] → (∀ m. n < m → lf(m) = lf(n) ∧ nextli0(lf(m)) = [] ∧ ii(m) = ii(n)), ∀ m, n. m ≤ n → ii(m) ≤ ii(n), ∀ n. lf(n + 1) = nextli(lf(n)), ∀ x. nextli(x) = x + nextli0(x), ∀ m. n ≤ m → nextli0(lf(m)) = [] ∧ ii(m) = ii(n0) ⊦ n0 = 0, n = 0

User applied rule all left

And obtained the following new goals

Proof step 102:
ii(0) = 0, lf(0) = [], # lf(n0) = ii(n0), nextli(lf(n0)) = lf(n0), nextli0(lf(n0)) = [], lf(n) = lf(n0), ii(n) = ii(n0), m < n, m < n0, ii(m + 1) ≤ ii(m), n0 < n, m + 1 < n, ∀ m. n0 < m → lf(m) = lf(n0) ∧ nextli0(lf(m)) = [] ∧ ii(m) = ii(n0), ∀ n0. lf(n0) = lf(n) to ii(n0), ∀ n0. ii(n0 + 1) = ii(n0) + # nextli0(lf(n0)) ∧ ¬ ii(n) < ii(n0 + 1) ∧ (lf(n) from ii(n0)) to # nextli0(lf(n0)) = nextli0(lf(n0)), ∀ m. nextli0(lf(m)) = [] ↔ n0 ≤ m, ∀ n. nextli0(lf(n)) = [] → (∀ m. n < m → lf(m) = lf(n) ∧ nextli0(lf(m)) = [] ∧ ii(m) = ii(n)), m ≤ m + 1 → ii(m) ≤ ii(m + 1), ∀ m, n. m ≤ n → ii(m) ≤ ii(n), ∀ n. lf(n + 1) = nextli(lf(n)), ∀ x. nextli(x) = x + nextli0(x), ∀ m. n ≤ m → nextli0(lf(m)) = [] ∧ ii(m) = ii(n0) ⊦ n0 = 0, n = 0

Rule argument

pos: left 18 terms: m, m + 1 abort: F discard: F computed: F

Additional information

Used terms: m, m + 1