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Proof step 9 from proof int-add (previous step)

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

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 10:
⊦ i ≠ 0 ∧ j ≠ 0 → rational(i, j).denom = abs(j) / gcd(i, j)
Proof step 11:
i ≠ 0 ∧ 1 ≠ 0 ⊦ i = 0, rational(abs(1) / gcd(i, 1) * rational(j, 1).num + rational(j, 1).denom * i, abs(1) / gcd(i, 1) * rational(j, 1).denom).num = rational(i + j, 1).num

Rule argument

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

Additional information

Used terms: 1, i