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Proof step 18 from proof prime-def-prime (previous step)

i0 < i1, 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) ⊦

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 19:
i0 < i1, 0 ≤ i1, 2 ≤ i0 * i1, 0 < i0, 2 < i0 * i1, 1 < i0, 0 < i1, 1 < i1, 2 < 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) ⊦

Rule argument

Additional information

Used simplifier rules: trans: ⊦ i < j ∧ j < j0 → i < j0; (forward) from specification int-basic1%lf-01: ⊦ i < j ∧ j < i0 → i +1 < i0; (forward) from specification int-basic1