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Proof step 2 from proof mod-mult (previous step)

⊦ j = 0, (i * j) |%| j = 0

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 3:
⊦ i % j < 0 → i |%| j = i % j + j
Proof step 4:
¬ (i * j) % j < 0 ⊦ j = 0, (i * j) |%| j = 0

Rule argument

spec: int-mod inst: name: mod-neg-def seq: ⊦ i % j < 0 → i |%| j = i % j + j subst: [j, i] → [j, i * j] flags: rewrite, current

Additional information

Used simplifier rules: mod-mult-04: j ≠ 0 ⊦ (i * j) % j = 0; from specification int-div%associativity: ⊦ i * j * j0 = (i * j) * j0; from specification int-mult%commutativity: ⊦ i * j = j * i; from specification int-mult%ax-04: ⊦ i + 0 = i; from specification int-basic2%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, i * j