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Proof step 9 from proof est-4-big (previous step)

0 ≤ j0, 2 * j0 < j, (2 * (i0 * j + j0)) / 3 < j, j ≤ i0 * j + j0, 2 < i0 * j + j0, 2 * (i0 * j + j0) < j * j, j0 < j, j0 < i0 * j, 0 < i0 * j + j0, 0 ≤ i0, 0 < j, 0 < i0 ⊦ (2 * (i0 * j + j0)) / j = 2 * i0

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 10:
⊦ i * (j + j0) = i * j + i * j0
Proof step 11:
0 ≤ j0, 2 * j0 < j, (2 * i0 * j + 2 * j0) / 3 < j, j ≤ i0 * j + j0, 2 < i0 * j + j0, 2 * i0 * j + 2 * j0 < j * j, j0 < j, j0 < i0 * j, 0 < i0 * j + j0, 0 ≤ i0, 0 < j, 0 < i0 ⊦ (2 * i0 * j + 2 * j0) / j = 2 * i0

Rule argument

spec: int-mult inst: name: dist-rsplit seq: ⊦ i * (j + j0) = i * j + i * j0 subst: [j0, j, i] → [j0, i0 * j, 2] flags: rewrite

Additional information

Used terms: j0, i0 * j, 2