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Proof step 5 from proof div-sub-01 (previous step)

i0 % j = 0 ⊦ j = 0, j0 = (j0 * j - i0) / j + i0 / j

User applied rule insert rewrite lemma

And obtained the following new goals

Rule argument

spec: inst: name: modex seq: j ≠ 0 ⊦ i % j = 0 ↔ (∃ j0. i = j0 * j) subst: [j, i] → [j, i0] flags: rewrite, current

Additional information

Used simplifier rules: div-mult-03: j ≠ 0 ⊦ (i * j) / j = i;%dist-sub-merge: ⊦ i * j - i * j0 = i * (j - j0); from specification int-mult%associativity: ⊦ i * j * j0 = (i * j) * j0; from specification int-mult%commutativity: ⊦ i * j = j * i; from specification int-mult%Sub-def: ⊦ i + (j - i) = j; from specification int-abs%add-a: ⊦ i + j + i0 = (i + j) + i0; from specification int-basic2%add-c: ⊦ i + j = j + i; from specification int-basic2 Used terms: j, i0