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Proof step 10 from proof num-neg (previous step)

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

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 11:
⊦ 0 < i ∧ j < 0 → rational(i, j).num = ~(i / gcd(i, j))

Rule argument

name: numerator-neg1 rotate: F subst: [j, i] → [j, i]

Additional information

Used simplifier rules: numerator-neg2: ⊦ i < 0 ∧ j < 0 → rational(i, j).num = abs(i) / gcd(i, j);% ⊦ gcd(i, j) = gcd(j, i);% ⊦ ¬ i < j ↔ j ≤ i;% ⊦ i ≠ j → (i ≤ j ↔ i < j);% ⊦ i < j → ¬ j < i;% ⊦ i < 0 → abs(i) = ~ i;% ⊦ gcd(i, j) = 0 ↔ i = 0 ∧ j = 0;%j ≠ 0 ⊦ ~ i / j = ~(i / j);% ⊦ ~ i + i = 0;% ⊦ i + j + i0 = (i + j) + i0;% ⊦ i + j = j + i; Used terms: j, i