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

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

User applied rule insert rewrite lemma

And obtained the following new goals

Rule argument

name: mult-def-02 rotate: F subst: [j2, i2, j1, i1] → [abs(j2), ~ i2, j1, i1]

Additional information

Used simplifier rules: neg-neg: ⊦ j ≠ 0 → rational(~ i, ~ j) = rational(i, j);% ⊦ i < 0 → abs(i) = ~ i;% ⊦ ¬ i < j ↔ j ≤ i;% ⊦ i < j → (¬ ¬ j ≤ i ↔ false);% ⊦ 0 < ~ i ↔ i < 0;% ⊦ i ≠ j → (i ≤ j ↔ i < j);% ⊦ i < j → ¬ j < i; Used terms: abs(j2), ~ i2, j1, i1