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Proof step 147 from proof infinite-append-prefixnextli (previous step)

nextli0(lf(n0)) = [], ii(0) = 0, lf(0) = [], # x = ii(n), lf(m0 + 1) = nextli(lf(m0)), lf(2 + m0) = nextli(nextli(lf(m0))), ii(m0 + 1) = ii(m0) + # nextli0(lf(m0)), (x from ii(m0)) to # nextli0(lf(m0)) = nextli0(lf(m0)), n0 ≤ m0, ii(m0 + 1) ≤ 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(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)), n0 < m0 → lf(m0) = lf(n0) ∧ nextli0(lf(m0)) = [] ∧ ii(m0) = ii(n0) ⊦ nextli(lf(m0)) = lf(n0) ∧ nextli0(nextli(lf(m0))) = [] ∧ ii(m0 + 1) = ii(n0)

User applied rule all left

And obtained the following new goals

Proof step 148:
nextli0(lf(n0)) = [], ii(0) = 0, lf(0) = [], # x = ii(n), lf(m0 + 1) = nextli(lf(m0)), lf(2 + m0) = nextli(nextli(lf(m0))), ii(m0 + 1) = ii(m0) + # nextli0(lf(m0)), (x from ii(m0)) to # nextli0(lf(m0)) = nextli0(lf(m0)), n0 ≤ m0, ii(m0 + 1) ≤ ii(n), ∀ m, n. m ≤ n → ii(m) ≤ ii(n), ∀ n. lf(n + 1) = nextli(lf(n)), nextli(lf(m0)) = lf(m0) + nextli0(lf(m0)), ∀ x. nextli(x) = x + nextli0(x), ∀ 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)), n0 < m0 → lf(m0) = lf(n0) ∧ nextli0(lf(m0)) = [] ∧ ii(m0) = ii(n0) ⊦ nextli(lf(m0)) = lf(n0) ∧ nextli0(nextli(lf(m0))) = [] ∧ ii(m0 + 1) = ii(n0)

Rule argument

pos: left 13 terms: lf(m0) abort: F discard: F computed: T

Additional information

Used terms: lf(m0)