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Proof step 6 from proof div-le-modzero (previous step)

i0 * j ≤ i, i % j = 0, 0 < j ⊦ i0 ≤ i / j

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 7:
⊦ i ≤ j ↔ ¬ j < i

Rule argument

spec: int-abs inst: name: le-def seq: ⊦ i ≤ j ↔ ¬ j < i subst: [j, i] → [i, i0 * j] flags: rewrite

Additional information

Used simplifier rules: mult-ls: ⊦ 0 < j ∧ i / j < i0 → i < i0 * j;%lels-01: ⊦ ¬ i ≤ j ↔ j < i; from specification int-abs%associativity: ⊦ i * j * j0 = (i * j) * j0; from specification int-mult%commutativity: ⊦ i * j = j * i; from specification int-mult Used terms: i, i0 * j