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Proof step 18 from proof max_exp-fac-gen (previous step)

i1 ≤ i0, 0 ≤ i0, 1 < i ^ i0, j2 < i, 0 < i ^ i0, 0 ≤ j2, prime(i), j2 < i ^ i0, 1 < i, 0 < i, 0 < j2, 0 < i1, 0 < i0, ∀ j0, i2, i0. i→n(j0) < i→n(0 * 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) ⊦ j2 / i ^ i1 = 0, 0 = Σ countFun(1, i0, λ j. j2 / i ^ j)

User applied rule insert rewrite lemma

And obtained the following new goals

Rule argument

spec: int-div inst: name: div-zero-03 seq: 0 < j ⊦ 0 ≤ i ∧ i < j → i / (* j) = 0 subst: [j, i] → [i ^ i1, j2] flags: rewrite

Additional information

Used simplifier rules: zero-gels-04: ⊦ i ≤ 0 ∧ 0 ≤ j → i ≤ j; from specification int-abs%grz: ⊦ 0 < i → (0 < i ^ j ↔ i = 1 ∨ 0 ≤ j); from specification int-pot%lels-01: ⊦ ¬ i ≤ j ↔ j < i; from specification int-abs%ls-01: ⊦ i < j → ¬ j < i; from specification int-basic1%lels: ⊦ ¬ i < j ↔ j ≤ i; from specification int-abs%forward-lels: ⊦ i ≤ j ∧ j < j0 → i < j0; (forward) from specification int-abs%pot-nls: ⊦ 0 < i ∧ 0 < j → ¬ i ^ j < i; from specification int-pot Used terms: i ^ i1, j2