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Proof step 17 from proof num-neg-01 (previous step)

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

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 18:
⊦ 0 < i ∧ j < 0 → rational(i, j).num = ~(i / gcd(i, j))
Proof step 19:
¬(0 < i ∧ j < 0), j < 0 ⊦ i = 0, j = 0, rational(i, j).num + rational(~ i, j).num = 0
Proof step 22:
0 < i ∧ j < 0, j < 0 ⊦ i = 0, j = 0, ~(i / gcd(i, j)) + rational(~ i, j).num = 0

Rule argument

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

Additional information

Used terms: j, i