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Proof step 14 from proof primes-divide (previous step)

i1 < Π ints0, 1 < i0 * Π ints0, prime(i0), j ∈ ints0, prime(j), j | i0, 0 < i0, 1 < Π ints0, 0 < Π ints0, 0 < i1, ∀ j. j ∈ ints0 → prime(j) ∧ j | i0 * i1 ⊦ i0 = 0, dups(ints0), i0 ∈ ints0, j | i1

User applied rule insert rewrite lemma

And obtained the following new goals

Rule argument

spec: int-gcd inst: name: divides-prime seq: ⊦ prime(j) → (i | j ↔ abs(i) = j ∨ abs(i) = 1) subst: [j, i] → [i0, j] flags: rewrite

Additional information

Used simplifier rules: prime-abs: ⊦ prime(j) → abs(j) = j; from specification int-gcd%lel: ⊦ i < i0 ∧ i = i1 → i1 < i0; (forward) from specification oelem[intlista]%numlelsdel-01: i0 ≠ 0, i0 ≤ i ⊦ (* i) < j → (* i0) < j; from specification int-abs%prime-one: ⊦ i ≤ 1 → ¬ prime(i); from specification int-gcd Used terms: i0, j