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Proof step 28 from proof max_exp-fac-gen (previous step)

i ^ (i0 - 1) * i ≤ i1 * i, 0 < i0, i ^ (i0 - 1) ≤ i1, i1 * i + j2 < i ^ (i0 - 1) * i, 0 ≤ i0, j2 < i, 0 < i1 * i + j2, 0 ≤ j2, prime(i), 0 < i ^ (i0 - 1), 1 < i ^ (i0 - 1), 1 < i ^ (i0 - 1) * i, 0 < i, 1 < i1, 0 < i1, ∀ j0, i2, i0. i→n(j0) < i→n(i1 * i + j2) → prime(i2) ∧ j0 < i2 ^ i0 ∧ 0 < j0 ∧ 0 < i2 ^ i0 ∧ 0 ≤ i0 ∧ 1 < i2 ^ i0 → max_exp(i2, fac(j0)) = Σ countFun(1, i0, λ j1. j0 / i2 ^ j1) ⊦ i1 * i + j2 < i1 * i, i1 + max_exp(i, fac(i1)) = Σ countFun(1, i0, λ j0. (i1 * i + j2) / i ^ j0)

User applied rule insert rewrite lemma

And obtained the following new goals

Rule argument

spec: int-abs inst: name: forward-lsle seq: ⊦ i < j ∧ j ≤ j0 → i < j0 subst: [j, j0, i] → [i ^ (i0 - 1) * i, i1 * i, i1 * i + j2] flags: rewrite

Additional information

Used simplifier rules: le-pos: ⊦ 0 < i → (i * j ≤ i * i0 ↔ j ≤ i0); from specification int-mult%associativity: ⊦ i * j * j0 = (i * j) * j0; from specification int-mult%commutativity: ⊦ i * j = j * i; from specification int-mult%ls: ⊦ i + j < j ↔ i < 0; from specification int-basic2%lels: ⊦ ¬ i < j ↔ j ≤ i; from specification int-abs%zero-gels-04: ⊦ i ≤ 0 ∧ 0 ≤ j → i ≤ j; from specification int-abs%add-a: ⊦ i + j + i0 = (i + j) + i0; from specification int-basic2%add-c: ⊦ i + j = j + i; from specification int-basic2 Used terms: i ^ (i0 - 1) * i, i1 * i, i1 * i + j2