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Proof step 1 from proof primes-divide (conclusion)

¬ dups(ints), ∀ j. j ∈ ints → prime(j) ∧ j | i, 0 < i ⊦ Π ints ≤ i

User applied rule structural induction

And obtained the following new goals

Proof step 2:
∀ i. ¬ dups(ints0) ∧ (∀ j. j ∈ ints0 → prime(j) ∧ j | i) ∧ 0 < i → Π ints0 ≤ i, ¬ dups(i0 + ints0), ∀ j. j ∈ i0 + ints0 → prime(j) ∧ j | i, 0 < i ⊦ Π(i0 + ints0) ≤ i

Rule argument

indvar: ints

Additional information

Used simplifier rules: intlist freely generated by [], +;;%prod-empty: ⊦ Π [] = 1; from specification intlist%leone: ⊦ 1 ≤ i ↔ 0 < i; from specification int-abs%lels: ⊦ ¬ i < j ↔ j ≤ i; from specification int-abs%lels-03: ⊦ i < j → (¬ ¬ j ≤ i ↔ false); from specification int-abs