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Proof step 13 from proof distributivity (previous step)

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

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 14:
⊦ j1 ≠ 0 ∧ j2 ≠ 0 → rational(i1, j1) * rational(i2, j2) = rational(i1 * i2, j1 * j2)
Proof step 15:
j ≠ 0 ∧ j0 * j1 ≠ 0, 0 < j1, 0 < j0, 0 < j ⊦ j0 = 0, j1 = 0, rational(i * (i0 * j1 + j0 * i1), j * j0 * j1) = rational(i, j) * rational(i0, j0) + rational(i, j) * rational(i1, j1)

Rule argument

name: mult-def-03 rotate: F subst: [j2, i2, j1, i1] → [j0 * j1, i0 * j1 + j0 * i1, j, i]

Additional information

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