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Proof step 4 from proof product-prime-divides (previous step)

prime(i), ∀ i. prime(i) → (i | Π ints0 ↔ (∃ j. j ∈ ints0 ∧ i | j)) ⊦ i | i0 * Π ints0 ↔ (∃ j. (j = i0 ∨ j ∈ ints0) ∧ i | j)

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 5:
⊦ prime(i) → (i | j * j0 ↔ i | j ∨ i | j0)
Proof step 6:
prime(i), prime(i), ∀ i. prime(i) → (i | Π ints0 ↔ (∃ j. j ∈ ints0 ∧ i | j)) ⊦ i | i0 ∨ i | Π ints0 ↔ (∃ j. (j = i0 ∨ j ∈ ints0) ∧ i | j)

Rule argument

spec: int-gcd inst: name: prime-divides seq: ⊦ prime(i) → (i | j * j0 ↔ i | j ∨ i | j0) subst: [j0, j, i] → [Π ints0, i0, i] flags: rewrite

Additional information

Used terms: Π ints0, i0, i