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Proof step 33 from proof make (previous step)

0 < i, i0 < 0 ⊦ i / gcd(i, i0) + rational(~(i / gcd(i, i0)), rational(i, i0).denom).num = 0 ∧ rational(~(i / gcd(i, i0)), rational(i, i0).denom).denom = rational(i, i0).denom

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 34:
⊦ i ≠ 0 ∧ j ≠ 0 → rational(i, j).denom = abs(j) / gcd(i, j)
Proof step 35:
i ≠ 0 ∧ i0 ≠ 0, 0 < i, i0 < 0 ⊦ i / gcd(i, i0) + rational(~(i / gcd(i, i0)), abs(i0) / gcd(i, i0)).num = 0 ∧ rational(~(i / gcd(i, i0)), abs(i0) / gcd(i, i0)).denom = abs(i0) / gcd(i, i0)

Rule argument

name: denominator-pos rotate: F subst: [j, i] → [i0, i]

Additional information

Used terms: i0, i