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Proof step 27 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, j * j1 * j0 * j)

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 28:
⊦ j ≠ 0 ∧ i1 ≠ 0 → rational(i1 * i, i1 * j) = rational(i, j)

Rule argument

name: factor-rat-01 rotate: F subst: [j, i, i1] → [j1 * j0 * j, (j1 * i0 + i1 * j0) * i, j]

Additional information

Used simplifier rules: ⊦ 0 < i → (i * j = 0 ↔ j = 0);% ⊦ i * j = j * i;% ⊦ i + j = j + i;% ⊦ i * j * j0 = (i * j) * j0; Used terms: j1 * j0 * j, (j1 * i0 + i1 * j0) * i, j