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Proof step 19 from proof add-def-03 (previous step)

j1 < 0, 0 < j2 ⊦ j1 = 0, j2 = 0, rational(~(j1 * i2 + i1 * j2), ~(j1 * j2)) = rational(i1 * j2 + j1 * i2, j1 * j2)

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 20:
⊦ j ≠ 0 → rational(~ i, ~ j) = rational(i, j)

Rule argument

name: neg-neg rotate: F subst: [j, i] → [j1 * j2, j1 * i2 + i1 * j2]

Additional information

Used simplifier rules: ⊦ i + j = j + i;% ⊦ i * j = 0 ↔ i = 0 ∨ j = 0;% ⊦ i * j * j0 = (i * j) * j0;% ⊦ i * j = j * i; Used terms: j1 * j2, j1 * i2 + i1 * j2