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Proof step 14 from proof max_exp-fac-add (previous step)

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

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 15:
⊦ prime(i) → (i | Π ints ↔ (∃ j. j ∈ ints ∧ i | j))
Proof step 16:
prime(i), prime(i), j0 < i, 0 < j, 0 ≤ j0, 0 < i, 0 ≤ j, ∃ j1. j1 ∈ countFun(1, j0, λ j0. i * j + j0) ∧ i | j1, 0 < fac(i * j), 0 < Π countFun(1, j0, λ j0. i * j + j0) ⊦

Rule argument

spec: intlist inst: name: product-prime-divides seq: ⊦ prime(i) → (i | Π ints ↔ (∃ j. j ∈ ints ∧ i | j)) subst: [ints, i] → [countFun(1, j0, λ j0. i * j + j0), i] flags: rewrite

Additional information

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