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

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

User applied rule insert rewrite lemma

And obtained the following new goals

Rule argument

name: denom-neg rotate: F subst: [j, i] → [j2, i2]

Additional information

Used simplifier rules: neg-neg: ⊦ j ≠ 0 → rational(~ i, ~ j) = rational(i, j);% ⊦ i < 0 → abs(i) = ~ i;% ⊦ ¬ i < j → (i ≠ j ↔ j < i);% ⊦ i < j → ¬ j < i;% ⊦ i < 0 ∧ 0 ≤ j → i < j;% ⊦ 0 < ~ i ↔ i < 0;% ⊦ ¬ i < j ↔ j ≤ i;% ⊦ i ≠ j → (i ≤ j ↔ i < j);% ⊦ i < j → (¬ ¬ j ≤ i ↔ false); Used terms: j2, i2