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Proof step 5 from proof max_exp-fac-add (previous step)

prime(i), j0 < i, 0 < j, 0 ≤ j0, 0 < i, 0 ≤ j ⊦ max_exp(i, fac(i * j) * Π countFun(1, j0, λ j0. i * j + j0)) = max_exp(i, fac(i * j))

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 6:
⊦ 0 < j ∧ 0 < j0 ∧ prime(i) → max_exp(i, j * j0) = max_exp(i, j) + max_exp(i, j0)
Proof step 7:
¬(0 < fac(i * j) ∧ 0 < Π countFun(1, j0, λ j0. i * j + j0) ∧ prime(i)), prime(i), j0 < i, 0 < j, 0 ≤ j0, 0 < i, 0 ≤ j ⊦ max_exp(i, fac(i * j) * Π countFun(1, j0, λ j0. i * j + j0)) = max_exp(i, fac(i * j))
Proof step 13:
0 < fac(i * j) ∧ 0 < Π countFun(1, j0, λ j0. i * j + j0) ∧ prime(i), prime(i), j0 < i, 0 < j, 0 ≤ j0, 0 < i, 0 ≤ j ⊦ max_exp(i, fac(i * j)) + max_exp(i, Π countFun(1, j0, λ j0. i * j + j0)) = max_exp(i, fac(i * j))

Rule argument

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

Additional information

Used terms: Π countFun(1, j0, λ j0. i * j + j0), fac(i * j), i