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Proof step 25 from proof max_exp-fac-gen (previous step)

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

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Rule argument

Additional information

Used simplifier rules: forward-pos: ⊦ i < j ∧ 0 < i → 0 < j ∧ 1 < j; (forward) from specification int-basic1%forward-le-05: ⊦ i < j ∧ 0 ≤ i → 0 < j; (forward) from specification int-abs%forward-lsle: ⊦ i < j ∧ j ≤ j0 → i < j0; (forward) from specification int-abs%add-c: ⊦ i + j = j + i; from specification int-basic2%add-a: ⊦ i + j + i0 = (i + j) + i0; from specification int-basic2%lels-03: ⊦ i < j → (¬ ¬ j ≤ i ↔ false); from specification int-abs%ls-add: ⊦ 0 ≤ j1 ∧ j1 < j → (i0 * j + j1 < j ↔ i0 ≤ 0); from specification int-mult%one-01: ⊦ i = 1 → i * j = j; from specification int-mult%bet: ⊦ 0 < i → (i ≤ 1 ↔ i = 1); from specification int-abs%lels: ⊦ ¬ i < j ↔ j ≤ i; from specification int-abs%commutativity: ⊦ i * j = j * i; from specification int-mult%associativity: ⊦ i * j * j0 = (i * j) * j0; from specification int-mult%zero-gr: ⊦ 0 < i → (0 < i * j ↔ 0 < j); from specification int-mult%sub-pred: ⊦ i -1 = i - 1; from specification int-abs