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Proof step 8 from proof div-mult-shift-holds (previous step)

j0 < j, j0 * i0 < j, 0 ≤ i0, 0 < j, 0 ≤ j0, 0 ≤ i1 ⊦ (i0 * (i1 * j + j0)) / j = i1 * i0

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 9:
⊦ (i + i0) * j = i * j + i0 * j
Proof step 10:
j0 < j, j0 * i0 < j, 0 ≤ i0, 0 < j, 0 ≤ j0, 0 ≤ i1 ⊦ ((i1 * j) * i0 + j0 * i0) / j = i1 * i0

Rule argument

spec: int-mult inst: name: dist-lsplit seq: ⊦ (i + i0) * j = i * j + i0 * j subst: [j, i0, i] → [i0, j0, i1 * j] flags: rewrite

Additional information

Used simplifier rules: commutativity: ⊦ i * j = j * i; from specification int-mult Used terms: i0, j0, i1 * j