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Proof step 2 from proof num-pos (previous step)

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

User applied rule insert rewrite lemma

And obtained the following new goals

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

Rule argument

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

Additional information

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