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Proof step 21 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((j * (j1 * i0 + i1 * j0)) * i, (j1 * j) * j0 * j)

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 22:
⊦ i * j * j0 = (i * j) * j0
Proof step 23:
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 * j0 = (i * j) * j0 subst: [j0, j, i] → [i, j1 * i0 + i1 * j0, j] rotate: T spec: int-mult inst: name: associativity

Additional information

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