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Proof step 12 from proof int-add (previous step)

⊦ i = 0, rational(rational(j, 1).denom * i + rational(j, 1).num, rational(j, 1).denom).num = rational(i + j, 1).num

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 13:
⊦ i ≠ 0 ∧ j ≠ 0 → rational(i, j).denom = abs(j) / gcd(i, j)

Rule argument

name: denominator-pos rotate: F subst: [j, i] → [1, j]

Additional information

Used simplifier rules: numerator-zero: ⊦ rational(0, j).num = 0;%denominator-zero: ⊦ rational(0, j).denom = 1;%numerator-pos: ⊦ i ≠ 0 ∧ 0 < j → rational(i, j).num = i / gcd(i, j);%numerator-pos: ⊦ i ≠ 0 ∧ 0 < j → rational(i, j).num = i / gcd(i, j);% ⊦ 1 * i = i;% ⊦ i * j * j0 = (i * j) * j0;% ⊦ i * j = j * i;% ⊦ i + 0 = i;% ⊦ i + j + i0 = (i + j) + i0;% ⊦ i + j = j + i;% ⊦ gcd(i, 1) = 1;% ⊦ i / 1 = i; Used terms: 1, j