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Proof step 19 from proof distributivity (previous step)

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

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 20:
⊦ i * j = j * i
Proof step 21:
0 < j1, 0 < j0, 0 < j ⊦ j = 0, j0 = 0, j1 = 0, rational(i * (i0 * j1 + j0 * i1), j * j0 * j1) = rational((j * (j1 * i0 + i1 * j0)) * i, (j1 * j) * j0 * j)

Rule argument

seq: ⊦ i * j = j * i subst: [j, i] → [j * (j1 * i0 + i1 * j0), i] rotate: F spec: int-mult inst: name: commutativity

Additional information

Used terms: j * (j1 * i0 + i1 * j0), i