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Proof step 9 from proof primes-rec (previous step)

prime(i), ∀ 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))

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 10:
prime(i), ∀ i. (∀ i0. i0 = i ∨ i0 ∈ ints0 → prime(i0)) → prime(i) ∧ (∀ i. i ∈ ints0 → prime(i)), ∀ i2. i2 = i0 ∨ i2 ∈ ints0 → prime(i2), i1 = i0 ∨ i1 ∈ ints0 ⊦ prime(i1)

Proof step 9 from proof primes-rec (previous step)

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Rule argument

Additional information