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Proof step 28 from proof abs-pos (previous step)

0 < j, 0 < j / gcd(i, 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, abs(i) / gcd(i, j) = 0

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 29:
⊦ i ≠ 0 ∧ 0 < j → rational(i, j).num = i / gcd(i, j)
Proof step 30:
abs(i) ≠ 0 ∧ 0 < j, 0 < j, 0 < j / gcd(i, j) ⊦ i = 0, j = 0, (abs(i) / gcd(i, j)) / gcd(abs(i) / gcd(i, j), j / gcd(i, j)) = abs(i) / gcd(abs(i), j), abs(i) / gcd(i, j) = 0

Rule argument

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

Additional information

Used simplifier rules: ⊦ abs(i) = 0 ↔ i = 0;% ⊦ ¬ i < j ↔ j ≤ i;% ⊦ i ≠ j → (i ≤ j ↔ i < j);% ⊦ i < j → ¬ j < i; Used terms: j, abs(i)