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Proof step 6 from proof less-mult-div-01 (previous step)

j0 < j, i1 < j, 0 < j1, 0 < j, 0 < i0 * j + j0, 0 < ((i0 * j + j0) * i1) / j, 0 ≤ j0, 0 ≤ i0, i0 * j + j0 ≤ ((i0 * j + j0) * i1) / j, 0 ≤ i0 * j + j0, 0 ≤ ((i0 * j + j0) * i1) / j ⊦

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 7:
⊦ (i + i0) * j = i * j + i0 * j
Proof step 8:
0 < ((i0 * j) * i1 + j0 * i1) / j, 0 < i0 * j + j0, 0 < j, 0 < j1, i1 < j, j0 < j, 0 ≤ ((i0 * j) * i1 + j0 * i1) / j, 0 ≤ i0 * j + j0, i0 * j + j0 ≤ ((i0 * j) * i1 + j0 * i1) / j, 0 ≤ i0, 0 ≤ j0 ⊦

Rule argument

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

Additional information

Used terms: i1, j0, i0 * j