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Proof step 25 from proof modmod-mult (previous step)

0 < j, j0 < j, j1 < j, 0 ≤ i2, 0 ≤ j0, 0 ≤ j1, 0 ≤ i1 ⊦ (j0 * j1) % j = ((i1 * j) * (i2 * j + j1) + j0 * (i2 * j + j1)) % j, (i1 * j) * (i2 * j + j1) + j0 * (i2 * j + j1) = (i1 * (j1 + i2 * j) + j0 * i2) * j + j0 * j1

User applied rule insert rewrite lemma

And obtained the following new goals

Rule argument

spec: int-mult name: dist-rsplit seq: ⊦ i * (j + j0) = i * j + i * j0 subst: [j0, j, i] → [j1, i2 * j, j0] flags: <all paths>

Additional information

Used simplifier rules: ⊦ i * j + i * j0 = i * (j + j0); (s)%associativity: ⊦ i * j * j0 = (i * j) * j0; from specification int-mult%commutativity: ⊦ i * j = j * i; from specification int-mult%add-a: ⊦ i + j + i0 = (i + j) + i0; from specification int-basic2%add-c: ⊦ i + j = j + i; from specification int-basic2% ⊦ i + j = i + i0 ↔ j = i0; (s) Used terms: j1, i2 * j, j0