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Proof step 10 from proof prime-def-prime (previous step)

0 < i ∧ 1 < i ∧ (∀ j. prime(j) ∧ j * j ≤ i → ¬ j | i), ∀ i0. i→n(i0) < i→n(i) → 0 < i0 ∧ 1 < i0 ∧ (∀ j. prime(j) ∧ j * j ≤ i0 → ¬ j | i0) → prime(i0) ⊦ prime(i)

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Rule argument

Additional information