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Proof step 5 from proof prime-def-mod (previous step)

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

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 6:
j % i = 0, i * i ≤ j, 2 ≤ j, 0 < j, 0 < i, 1 < i, 0 ≤ j, ∀ i. 1 < i ∧ i < j → ¬ i | j ⊦

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%forward-le-01: ⊦ i ≤ j ∧ 0 ≤ i → 0 ≤ j; (forward) from specification int-abs%numlsledel-01: i0 ≠ 0, i0 < i ⊦ (* i) ≤ j → (* i0) < j; from specification int-abs