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Proof step 7 from proof num-neg (previous step)

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

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 8:
⊦ 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: ⊦ i < j → ¬ j < i;% ⊦ i ≠ j → (i ≤ j ↔ i < j);% ⊦ ¬ i < j ↔ j ≤ i;% ⊦ ~ i < 0 ↔ 0 < i;% ⊦ gcd(i, j) = gcd(j, i);% ⊦ abs(~ i) = abs(i);% ⊦ 0 < j → abs(j) = j;% ⊦ gcd(~ i, j) = gcd(i, j); Used terms: ~ j, ~ i