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Proof step 6 from proof primes-rec (previous step)

∀ i0. i0 = i ∨ i0 ∈ ints → prime(i0) ⊦ prime(i) ∧ (∀ i. i ∈ ints → prime(i))

Heuristic structural induction applied rule structural induction

And obtained the following new goals

Proof step 7:
∀ i. (∀ i0. i0 = i ∨ i0 ∈ ints0 → prime(i0)) → prime(i) ∧ (∀ i. i ∈ ints0 → prime(i)), ∀ i1. i1 = i ∨ i1 ∈ i0 + ints0 → prime(i1) ⊦ prime(i) ∧ (∀ i. i ∈ i0 + ints0 → prime(i))

Rule argument

term: ints

Additional information

Used simplifier rules: intlist freely generated by [], +;;%in-empty: ⊦ ¬ i ∈ []; from specification list[intlista]