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Proof step 15 from proof distributivity (previous step)

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)

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 16:
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)

Rule argument

Additional information

Used simplifier rules: mult-def-03: ⊦ j1 ≠ 0 ∧ j2 ≠ 0 → rational(i1, j1) * rational(i2, j2) = rational(i1 * i2, j1 * j2);%mult-ass: ⊦ (ri * rj) * rj1 = ri * rj * rj1;%mult-comm: ⊦ ri * rj = rj * ri;% ⊦ i * j = j * i;% ⊦ i * j * j0 = (i * j) * j0;% ⊦ 0 < i → (i * j = 0 ↔ j = 0);