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Proof step 16 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(i1 * i, j1 * j) + rational(i0 * i, j0 * j)

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 17:
⊦ j1 ≠ 0 ∧ j2 ≠ 0 → rational(i1, j1) + rational(i2, j2) = rational(i1 * j2 + j1 * i2, j1 * j2)
Proof step 18:
j1 * j ≠ 0 ∧ j0 * j ≠ 0, 0 < j1, 0 < j0, 0 < j ⊦ j = 0, j0 = 0, j1 = 0, rational(i * (i0 * j1 + j0 * i1), j * j0 * j1) = rational((i1 * i) * j0 * j + (j1 * j) * i0 * i, (j1 * j) * j0 * j)

Rule argument

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