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Proof step 8 from proof max_exp-fac-add (previous step)

Π countFun(1, j0, λ j0. i * j + j0) < fac(i * j), Π countFun(1, j0, λ j0. i * j + j0) < i, Π countFun(1, j0, λ j0. i * j + j0) < j, Π countFun(1, j0, λ j0. i * j + j0) ≤ 0, 0 < fac(i * j), 0 ≤ j, 0 < i, 0 ≤ j0, 0 < j, j0 < i, prime(i) ⊦ 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 9:
∀ i. i ∈ ints → 0 < i ⊦ ¬ Π ints ≤ 0
Proof step 10:
¬(∀ i0. i0 ∈ countFun(1, j0, λ j0. i * j + j0) → 0 < i0), Π countFun(1, j0, λ j0. i * j + j0) < fac(i * j), Π countFun(1, j0, λ j0. i * j + j0) < i, Π countFun(1, j0, λ j0. i * j + j0) < j, Π countFun(1, j0, λ j0. i * j + j0) ≤ 0, 0 < fac(i * j), 0 ≤ j, 0 < i, 0 ≤ j0, 0 < j, j0 < i, prime(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: intlist inst: name: product-positive seq: ∀ i. i ∈ ints → 0 < i ⊦ ¬ Π ints ≤ 0 subst: [ints] → [countFun(1, j0, λ j0. i * j + j0)] flags: rewrite

Additional information

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