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Proof step 3 from proof prime-def-mod (previous step)

⊦ 1 < j → (2 ≤ j ∧ (∀ i. 1 < i ∧ i < j → ¬ i | j) ↔ (∀ i. 1 < i ∧ i * i ≤ j → j % i ≠ 0))

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 4:
0 < j, 1 < j ⊦ 2 ≤ j ∧ (∀ i. 1 < i ∧ i < j → ¬ i | j) ↔ (∀ i. 1 < i ∧ i * i ≤ j → j % i ≠ 0)

Rule argument

Additional information

Used simplifier rules: forward-le-05: ⊦ i < j ∧ 0 ≤ i → 0 < j; (forward) from specification int-abs%forward-pos: ⊦ i < j ∧ 0 < i → 0 < j ∧ 1 < j; (forward) from specification int-basic1