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Proof step 23 from proof num-neg-01 (previous step)

j < 0, 0 < i ⊦ i = 0, j = 0, rational(~ i, j).num = i / gcd(i, j)

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 24:
⊦ i < 0 ∧ j < 0 → rational(i, j).num = abs(i) / gcd(i, j)

Rule argument

name: numerator-neg2 rotate: F subst: [j, i] → [j, ~ i]

Additional information

Used simplifier rules: ⊦ gcd(~ i, j) = gcd(i, j);% ⊦ 0 < j → abs(j) = j;% ⊦ abs(~ i) = abs(i);% ⊦ ~ i < 0 ↔ 0 < i;% ⊦ ¬ i < j ↔ j ≤ i;% ⊦ i ≠ j → (i ≤ j ↔ i < j);% ⊦ i < j → ¬ j < i; Used terms: j, ~ i