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Proof step 24 from proof prime-def-prime (previous step)

0 < i0, 1 < i0, i0 < i1, 1 < i0 * i1, 1 < i1, 0 < i1, i0 ≤ i1, ∀ j. prime(j) ∧ j * j ≤ i0 * i1 → ¬ j | i0 * i1, ∀ i2. i→n(i2) < i→n(i0 * i1) → 0 < i2 ∧ 1 < i2 ∧ (∀ j. prime(j) ∧ j * j ≤ i2 → ¬ j | i2) → prime(i2) ⊦ prime(i0), 0 < i0 ∧ 1 < i0 ∧ (∀ j. prime(j) ∧ j * j ≤ i0 → ¬ j | i0)

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 25:
0 < i1, 1 < i1, 1 < i0 * i1, i0 < i1, 1 < i0, 0 < i0, j * j < i1, prime(j), j | i0, i0 ≤ i1, j * j ≤ i0, ∀ j. prime(j) ∧ j * j ≤ i0 * i1 → ¬ j | i0 * i1, ∀ i2. i→n(i2) < i→n(i0 * i1) → 0 < i2 ∧ 1 < i2 ∧ (∀ j. prime(j) ∧ j * j ≤ i2 → ¬ j | i2) → prime(i2) ⊦ prime(i0)

Rule argument

Additional information

Used simplifier rules: forward-lels: ⊦ i ≤ j ∧ j < j0 → i < j0; (forward) from specification int-abs