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Proof step 8 from proof prime-ex-max (previous step)

j < i ∧ j | i ∧ prime(j) ∧ 2 ≤ i ∧ 0 ≤ i ∧ 0 < i, ∀ i0, j0. i→n(i0 - j0) < i→n(i - j) → j0 < i0 ∧ j0 | i0 ∧ prime(j0) ∧ 2 ≤ i0 ∧ 0 ≤ i0 ∧ 0 < i0 → (∃ j. prime(j) ∧ j | i0 ∧ j < i0 ∧ (∀ j0. j < j0 ∧ j0 < i0 ∧ prime(j0) → ¬ j0 | i0)) ⊦ ∃ j. prime(j) ∧ j | i ∧ j < i ∧ (∀ j0. j < j0 ∧ j0 < i ∧ prime(j0) → ¬ j0 | i)

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Rule argument

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