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Proof step 22 from proof add-asso (previous step)

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

User applied rule cut formula

And obtained the following new goals

Proof step 23:
0 < j, 0 < j0, 0 < j1 ⊦ (i * j0 + j * i0) * j1 + (j * j0) * i1 = i * j0 * j1 + j * (i0 * j1 + j0 * i1), j0 = 0, rational((i * j0 + j * i0) * j1 + (j * j0) * i1, (j * j0) * j1) = rational(i * j0 * j1 + j * (i0 * j1 + j0 * i1), j * j0 * j1), j1 = 0, j = 0

Rule argument

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

Additional information

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