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Proof step 15 from proof max_exp-fac-gen (previous step)

¬((∀ i1. 1 ≤ i1 ∧ i1 ≤ i0 → j2 / i ^ i1 = 0) ∧ 1 ≤ i0 ∧ 0 ≤ 1), 0 ≤ i0, 1 < i ^ i0, j2 < i, 0 < i ^ i0, 0 ≤ j2, prime(i), j2 < i ^ i0, 1 < i, 0 < i, 0 < j2, ∀ 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) ⊦ 0 = Σ countFun(1, i0, λ j. j2 / i ^ j)

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 16:
0 ≤ i0, 1 < i ^ i0, j2 < i, 0 < i ^ i0, 0 ≤ j2, prime(i), j2 < i ^ i0, 1 < i, 0 < i, 0 < j2, ∀ 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) ⊦ 0 = Σ countFun(1, i0, λ j. j2 / i ^ j), (0 < i1 ∧ i1 ≤ i0 → j2 / i ^ i1 = 0) ∧ 0 < i0

Rule argument

Additional information

Used simplifier rules: leone: ⊦ 1 ≤ i ↔ 0 < i; from specification int-abs