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Proof step 18 from proof add-def-03 (previous step)

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

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Rule argument

Additional information

Used simplifier rules: ⊦ i < j ∧ 0 ≤ i → 0 < j; (forward)% ⊦ i < 0 ∧ 0 ≤ j → i < j;% ⊦ 0 < ~ i ↔ i < 0;% ⊦ i + j = j + i;% ⊦ i + j + i0 = (i + j) + i0;% ⊦ ~ i + ~ j = ~(i + j);% ⊦ i * j = j * i;% ⊦ i * j * j0 = (i * j) * j0;% ⊦ ~ i * j = ~(i * j);