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Proof step 10 from proof est-4-big-02 (previous step)

0 ≤ i0, 1 < j, 0 < j, 0 < i0, 0 < j0, 0 ≤ j0, j ≤ 2 * j0, 2 < i0 * j + j0, j ≤ i0 * j + j0, 2 * (i0 * j + j0) < 3 * j, j0 < j, 0 < i0 * j + j0, i0 * j < 2 * j0 ⊦ j = 3, j = 2

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 11:
⊦ (i + i0) * j = i * j + i0 * j
Proof step 12:
0 ≤ i0, 1 < j, 0 < j, 0 < i0, 0 < j0, 0 ≤ j0, j ≤ 2 * j0, 2 < i0 * j + j0, j ≤ i0 * j + j0, (i0 * j) * 2 + j0 * 2 < 3 * j, j0 < j, 0 < i0 * j + j0, i0 * j < 2 * j0 ⊦ j = 3, j = 2

Rule argument

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

Additional information

Used simplifier rules: commutativity: ⊦ i * j = j * i; from specification int-mult Used terms: 2, j0, i0 * j