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Proof step 14 from proof int-add (previous step)

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

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 15:
⊦ i ≠ 0 ∧ 0 < j → rational(i, j).num = i / gcd(i, j)
Proof step 16:
i ≠ 0 ∧ 0 < 1 ⊦ rational(i / gcd(i, 1) * rational(j, 1).denom + rational(i, 1).denom * rational(j, 1).num, rational(i, 1).denom * rational(j, 1).denom).denom = rational(i + j, 1).denom

Rule argument

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

Additional information

Used simplifier rules: denominator-zero: ⊦ rational(0, j).denom = 1;%numerator-zero: ⊦ rational(0, j).num = 0;%make: ⊦ rational(ri.num, ri.denom) = ri;% ⊦ 1 * i = i;% ⊦ i * j * j0 = (i * j) * j0;% ⊦ i * j = j * i;% ⊦ i * 0 = 0;% ⊦ i + 0 = i;% ⊦ i + j + i0 = (i + j) + i0;% ⊦ i + j = j + i; Used terms: 1, i