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Proof step 14 from proof div-addthree-rew (previous step)

j2 < j, j1 < j, j0 < j, 0 < j, 0 ≤ j0, 0 ≤ i2, 0 ≤ j1, 0 ≤ i3, 0 ≤ j2, 0 ≤ i0 ⊦ ((i2 * j + j0) + (i3 * j + j1) + i0 * j + j2) / j = ((i2 + i3 + i0) * j + j0 + j1 + j2) / j

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 15:
⊦ (i + i0) * j = i * j + i0 * j
Proof step 16:
j2 < j, j1 < j, j0 < j, 0 < j, 0 ≤ j0, 0 ≤ i2, 0 ≤ j1, 0 ≤ i3, 0 ≤ j2, 0 ≤ i0 ⊦ ((i2 * j + j0) + (i3 * j + j1) + i0 * j + j2) / j = ((i2 * j + (i3 + i0) * j) + j0 + j1 + j2) / j

Rule argument

spec: int-mult inst: name: dist-lsplit seq: ⊦ (i + i0) * j = i * j + i0 * j subst: [j, i0, i] → [j, i3 + i0, i2] flags: rewrite

Additional information

Used terms: j, i3 + i0, i2