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Proof step 7 from proof mod-shift (previous step)

j0 < j, 0 ≤ i, 0 < j, 0 ≤ j0, 0 ≤ i1 ⊦ (i * j0) % j = ((i1 * j) * i + j0 * i) % j

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 8:
⊦ i + j = j + i
Proof step 9:
j0 < j, 0 ≤ i, 0 < j, 0 ≤ j0, 0 ≤ i1 ⊦ (i * j0) % j = (j0 * i + (i1 * j) * i) % j

Rule argument

spec: int-basic2 inst: name: add-c seq: ⊦ i + j = j + i subst: [j, i] → [j0 * i, (i1 * j) * i] flags: rewrite

Additional information

Used terms: j0 * i, (i1 * j) * i