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Proof step 13 from proof primes-divide (previous step)

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

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 14:
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

Rule argument

Additional information

Used simplifier rules: forward-pos: ⊦ i < j ∧ 0 < i → 0 < j ∧ 1 < j; (forward) from specification int-basic1%forward-le-05: ⊦ i < j ∧ 0 ≤ i → 0 < j; (forward) from specification int-abs%transitivity: ⊦ i < i0 ∧ i0 < i1 → i < i1; (forward) from specification oelem[intlista]%prime-divides: ⊦ prime(i) → (i | j * j0 ↔ i | j ∨ i | j0); from specification int-gcd%lels-03: ⊦ i < j → (¬ ¬ j ≤ i ↔ false); from specification int-abs%commutativity: ⊦ i * j = j * i; from specification int-mult%associativity: ⊦ i * j * j0 = (i * j) * j0; from specification int-mult%zero-gr: ⊦ 0 < i → (0 < i * j ↔ 0 < j); from specification int-mult