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Proof step 12 from proof add-def-03 (previous step)

¬(0 < j2 ∧ 0 < ~ j1), j1 < 0 ⊦ j1 = 0, j2 = 0, rational(i2, j2) + rational(~ i1, ~ 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: ⊦ j < i ∧ i ≤ 0 → j < 0; (forward)% ⊦ i < j → ¬ j < i;% ⊦ 0 < ~ i ↔ i < 0;% ⊦ i ≠ j → (i ≤ j ↔ i < j);% ⊦ ¬ i < j ↔ j ≤ i;