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Proof step 20 from proof num-neg-01 (previous step)

j < 0, i < 0 ⊦ 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 21:
⊦ 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: ⊦ i < j → ¬ j < i;% ⊦ i ≠ j → (i ≤ j ↔ i < j);% ⊦ ¬ i < j ↔ j ≤ i;% ⊦ 0 < ~ i ↔ i < 0;% ⊦ gcd(~ i, j) = gcd(i, j);% ⊦ gcd(i, j) = 0 ↔ i = 0 ∧ j = 0;%j ≠ 0 ⊦ ~ i / j = ~(i / j);% ⊦ ~ ~ i = i; Used terms: j, ~ i