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

0 ≤ i1, 2 ≤ i0 * i1, 0 < i0, 2 < i0 * i1, 1 < i0, 1 < i1, 0 < 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) ⊦ i0 < i1

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 25:
0 ≤ i1, 2 ≤ i0 * i1, 0 < i0, 2 < i0 * i1, 1 < i1, 0 < i1, i1 ≤ i0, 1 < i0, 0 ≤ 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) ⊦

Rule argument

Additional information

Used simplifier rules: forward-lsle: ⊦ i < j ∧ j ≤ j0 → i < j0; (forward) from specification int-abs%forward-le-01: ⊦ i ≤ j ∧ 0 ≤ i → 0 ≤ j; (forward) from specification int-abs%lels: ⊦ ¬ i < j ↔ j ≤ i; from specification int-abs