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Proof step 34 from proof infinite-append-prefixnextli-weak (previous step)

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

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 35:
ii(0) = 0, lf(0) = [], # x = ii(n), nextli(x) = x + nextli0(x), n ≤ m, ∀ 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)) ⊦ ii(m) = ii(n), ∃ n0. ii(n) = ii(n0) ∧ nextli(x) = x ∧ (∀ m. n0 ≤ m → ii(m) = ii(n0))

Proof step 34 from proof infinite-append-prefixnextli-weak (previous step)

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Rule argument

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