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Proof step 7 from proof primes-rec (previous step)

∀ 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))

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 8:
∀ i. (∀ i0. i0 = i ∨ i0 ∈ ints0 → prime(i0)) → prime(i) ∧ (∀ i. i ∈ ints0 → prime(i)), ∀ i1. i1 = i ∨ i1 = i0 ∨ i1 ∈ ints0 → prime(i1) ⊦ prime(i) ∧ (i1 = i0 ∨ i1 ∈ ints0 → prime(i1))

Rule argument

Additional information

Used simplifier rules: 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]%c: ⊦ i + ints = i ' + ints; from specification list[intlista]