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Proof step 22 from proof abs-pos (previous step)

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

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 23:
⊦ i ≠ 0 ∧ 0 < j → rational(i, j).num = i / gcd(i, j)
Proof step 24:
¬(abs(i) / gcd(i, j) ≠ 0 ∧ 0 < j / gcd(i, j)), 0 < j ⊦ i = 0, j = 0, rational(abs(i) / gcd(i, j), j / gcd(i, j)).num = rational(abs(i), j).num
Proof step 27:
abs(i) / gcd(i, j) ≠ 0 ∧ 0 < j / gcd(i, j), 0 < j ⊦ i = 0, j = 0, (abs(i) / gcd(i, j)) / gcd(abs(i) / gcd(i, j), j / gcd(i, j)) = rational(abs(i), j).num

Rule argument

name: numerator-pos rotate: F subst: [j, i] → [j / gcd(i, j), abs(i) / gcd(i, j)]

Additional information

Used terms: j / gcd(i, j), abs(i) / gcd(i, j)