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Proof step 23 from proof add-asso (previous step)

0 < j, 0 < j0, 0 < j1 ⊦ (i * j0 + j * i0) * j1 + (j * j0) * i1 = i * j0 * j1 + j * (i0 * j1 + j0 * i1), j0 = 0, rational((i * j0 + j * i0) * j1 + (j * j0) * i1, (j * j0) * j1) = rational(i * j0 * j1 + j * (i0 * j1 + j0 * i1), j * j0 * j1), j1 = 0, j = 0

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 24:
⊦ i * (j + j0) = i * j + i * j0
Proof step 25:
0 < j, 0 < j0, 0 < j1 ⊦ (j1 * i * j0 + j1 * j * i0) + (j * j0) * i1 = i * j0 * j1 + j * (i0 * j1 + j0 * i1), j0 = 0, rational((j1 * i * j0 + j1 * j * i0) + (j * j0) * i1, (j * j0) * j1) = rational(i * j0 * j1 + j * (i0 * j1 + j0 * i1), j * j0 * j1), j1 = 0, j = 0

Rule argument

seq: ⊦ i * (j + j0) = i * j + i * j0 subst: [i, j0, j] → [j1, j * i0, i * j0] rotate: F spec: int-mult inst: name: dist-rsplit

Additional information

Used simplifier rules: ⊦ i + j = j + i;% ⊦ i * j = j * i; Used terms: j1, j * i0, i * j0