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Proof step 2 from proof max_exp-fac-add (previous step)

prime(i), j0 < i, 0 < j, 0 ≤ j0, 0 < i ⊦ max_exp(i, fac(i * j + j0)) = max_exp(i, fac(i * j))

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 3:
⊦ 0 ≤ i ∧ 0 ≤ j → fac(i + j) = fac(i) * Π countFun(1, j, λ j0. i + j0)
Proof step 4:
0 ≤ i * j ∧ 0 ≤ j0, prime(i), j0 < i, 0 < j, 0 ≤ j0, 0 < i ⊦ max_exp(i, fac(i * j) * Π countFun(1, j0, λ j0. i * j + j0)) = max_exp(i, fac(i * j))

Rule argument

spec: inst: name: fac-add seq: ⊦ 0 ≤ i ∧ 0 ≤ j → fac(i + j) = fac(i) * Π countFun(1, j, λ j0. i + j0) subst: [j, i] → [j0, i * j] flags: rewrite, current

Additional information

Used simplifier rules: zero-ge: ⊦ 0 < i → (0 ≤ i * j ↔ 0 ≤ j); from specification int-mult%associativity: ⊦ i * j * j0 = (i * j) * j0; from specification int-mult%commutativity: ⊦ i * j = j * i; from specification int-mult%zero-gels-04: ⊦ i ≤ 0 ∧ 0 ≤ j → i ≤ j; from specification int-abs%lels-01: ⊦ ¬ i ≤ j ↔ j < i; from specification int-abs%ls-01: ⊦ i < j → ¬ j < i; from specification int-basic1 Used terms: j0, i * j