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Proof step 11 from proof prime-def-mod (previous step)

j % i = 0, 1 < i, 0 < i, 0 < j, i < j, 0 ≤ j, 2 ≤ j, i * i ≤ 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 name: modex seq: j ≠ 0 ⊦ i % j = 0 ↔ (∃ j0. i = j0 * j) subst: [j, i] → [i, j] flags: <all paths>

Additional information

Used simplifier rules: div-mult: ⊦ i | i * j;% ⊦ 0 < i → (0 ≤ i * j ↔ 0 ≤ j); (s)%associativity: ⊦ i * j * j0 = (i * j) * j0; from specification int-mult%commutativity: ⊦ i * j = j * i; from specification int-mult% ⊦ 0 < i → (i * j ≤ i * i0 ↔ j ≤ i0); (s)% ⊦ 0 < i → (0 < i * j ↔ 0 < j); (s)% ⊦ 0 < i → (i < i * j ↔ 1 < j); (s)% ⊦ i ≤ 0 ∧ 0 ≤ j → i ≤ j; (s) Used terms: i, j