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Proof step 1 from proof max_exp-fac-gen-stronger (conclusion)

⊦ prime(i) ∧ 0 < j ∧ 0 ≤ i0 ∧ j < i ^ i0 → max_exp(i, fac(j)) = Σ countFun(1, i0 - 1, λ j0. j / i ^ j0)

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 2:
prime(i), j < i ^ i0, 0 < j, 0 < i ^ i0, 0 ≤ i0, 1 < i ^ i0 ⊦ max_exp(i, fac(j)) = Σ countFun(1, i0 - 1, λ j0. j / i ^ j0)

Rule argument

Additional information

Used simplifier rules: forward-le-05: ⊦ i < j ∧ 0 ≤ i → 0 < j; (forward) from specification int-abs%transitivity: ⊦ i < i0 ∧ i0 < i1 → i < i1; (forward) from specification oelem[intlista]%forward-le-01: ⊦ i ≤ j ∧ 0 ≤ i → 0 ≤ j; (forward) from specification int-abs%forward-pos: ⊦ i < j ∧ 0 < i → 0 < j ∧ 1 < j; (forward) from specification int-basic1