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Proof step 14 from proof num-neg-01 (previous step)

⊦ 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 15:
⊦ i ≠ 0 ∧ 0 < j → rational(i, j).num = i / gcd(i, j)
Proof step 16:
¬(i ≠ 0 ∧ 0 < j) ⊦ i = 0, j = 0, rational(i, j).num + rational(~ i, j).num = 0
Proof step 25:
i ≠ 0 ∧ 0 < j ⊦ i = 0, j = 0, i / gcd(i, j) + rational(~ i, j).num = 0

Rule argument

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

Additional information

Used terms: j, i