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Proof step 1 from proof num-neg (conclusion)

⊦ j ≠ 0 → rational(~ i, ~ j).num = rational(i, j).num

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 2:
⊦ i ≠ 0 ∧ 0 < j → rational(i, j).num = i / gcd(i, j)
Proof step 3:
¬(~ i ≠ 0 ∧ 0 < ~ j) ⊦ j ≠ 0 → rational(~ i, ~ j).num = rational(i, j).num
Proof step 9:
~ i ≠ 0 ∧ 0 < ~ j ⊦ j ≠ 0 → ~ i / gcd(~ i, ~ j) = rational(i, j).num

Rule argument

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

Additional information

Used terms: ~ j, ~ i