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Proof step 8 from proof primes-divide (previous step)

i < i0 * Π ints0, 0 < i, 0 < i0 * Π ints0, 1 < i0 * Π ints0, prime(i0), i0 | i, j ∈ ints0 → prime(j) ∧ j | i, ∀ j. j ∈ ints0 → prime(j) ∧ j | i, (j ∈ ints0 → prime(j) ∧ j | i / i0) ∧ 0 < i / i0 → Π ints0 ≤ i / i0 ⊦ dups(ints0), i0 ∈ ints0

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 9:
⊦ i | j ↔ (∃ i0. i * i0 = j)
Proof step 10:
i < i0 * Π ints0, 0 < i, 0 < i0 * Π ints0, 1 < i0 * Π ints0, prime(i0), ∃ i1. i0 * i1 = i, j ∈ ints0 → prime(j) ∧ j | i, ∀ j. j ∈ ints0 → prime(j) ∧ j | i, (j ∈ ints0 → prime(j) ∧ j | i / i0) ∧ 0 < i / i0 → Π ints0 ≤ i / i0 ⊦ dups(ints0), i0 ∈ ints0

Rule argument

spec: int-gcd inst: name: divides seq: ⊦ i | j ↔ (∃ i0. i * i0 = j) subst: [j, i] → [i, i0] flags: rewrite

Additional information

Used terms: i, i0