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Proof step 75 from proof infinite-append-prefixnextli (previous step)

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

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Rule argument

Additional information

Used simplifier rules: to-zero-l: ⊦ x to 0 = []; from specification stream%size-01: ⊦ # [] = 0; from specification list-data%ler: ⊦ m ≤ m; from specification nat%l: ⊦ # x = 0 ↔ x = []; from specification list-data%eq: ⊦ m = m + n ↔ n = 0; from specification nat-basic2%anti: ⊦ m ≤ n → (n ≤ m ↔ m = n); from specification nat%c: ⊦ m + n = n + m; from specification nat-basic2%a: ⊦ (m + n0) + n1 = m + n0 + n1; from specification nat-basic2%lep: ⊦ m ≤ m + n; from specification nat