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Proof step 3 from proof primes-rec (previous step)

⊦ (∀ i0. i0 ∈ i ' + ints → prime(i0)) ↔ prime(i) ∧ primes(ints)

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Rule argument

Additional information

Used simplifier rules: primes-in: ⊦ primes(ints) ∧ i ∈ ints → (¬ prime(i) ↔ false);%a: ⊦ (ints + ints0) + ints1 = ints + ints0 + ints1; from specification list[intlista]%in-17: ⊦ i ∈ i0 ' ↔ i = i0; from specification list[intlista]%in-append: ⊦ i ∈ ints + ints0 ↔ ¬ ¬(i ∈ ints ∨ i ∈ ints0); from specification list[intlista]