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Proof step 2 from proof product-prime-divides (previous step)

prime(i) ⊦ i | Π ints ↔ (∃ j. j ∈ ints ∧ i | j)

User applied rule structural induction

And obtained the following new goals

Proof step 3:
∀ i. prime(i) → (i | Π ints0 ↔ (∃ j. j ∈ ints0 ∧ i | j)), prime(i) ⊦ i | Π(i0 + ints0) ↔ (∃ j. j ∈ i0 + ints0 ∧ i | j)

Rule argument

indvar: ints

Additional information

Used simplifier rules: prod-empty: ⊦ Π [] = 1;%intlist freely generated by [], +;;%prime-divides-one: ⊦ prime(i) → ¬ i | 1; from specification int-gcd%in-empty: ⊦ ¬ i ∈ []; from specification list[intlista]