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Proof step 10 from proof prime-def-mod (previous step)

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

User applied rule insert rewrite lemma

And obtained the following new goals

Rule argument

spec: int-div inst: name: modex seq: j ≠ 0 ⊦ i % j = 0 ↔ (∃ j0. i = j0 * j) subst: [j, i] → [i, j] flags: rewrite

Additional information

Used simplifier rules: div-mult: ⊦ i | i * j;%ls-same-01: ⊦ 0 < i → (i < i * j ↔ 1 < j); from specification int-mult%associativity: ⊦ i * j * j0 = (i * j) * j0; from specification int-mult%commutativity: ⊦ i * j = j * i; from specification int-mult%le-pos: ⊦ 0 < i → (i * j ≤ i * i0 ↔ j ≤ i0); from specification int-mult%zero-gr: ⊦ 0 < i → (0 < i * j ↔ 0 < j); from specification int-mult%zero-ge: ⊦ 0 < i → (0 ≤ i * j ↔ 0 ≤ j); from specification int-mult%lels-02: ⊦ i ≠ j → (i ≤ j ↔ i < j); from specification int-abs%zero-gels-04: ⊦ i ≤ 0 ∧ 0 ≤ j → i ≤ j; from specification int-abs Used terms: i, j