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Proof step 20 from proof add-eq (previous step)

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

User applied rule cut formula

And obtained the following new goals

Proof step 21:
(i * j0 + j * i0) * j1 = (i * j1 + j * i1) * j0, (i * j0 + j * i0) * j * j1 = (i * j1 + j * i1) * j * j0, j ≠ 0 ∧ j1 ≠ 0, j ≠ 0 ∧ j0 ≠ 0, 0 < j0 * j1, rational(i * j0 + j * i0, j * j0) = rational(i * j1 + j * i1, j * j1), 0 < j, 0 < j0, 0 < j1 ⊦ i0 * j1 = i1 * j0, rational(i0, j0) = rational(i1, j1)

Rule argument

fma: (i * j0 + j * i0) * j1 = (i * j1 + j * i1) * j0

Additional information

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