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Proof step 27 from proof make (previous step)

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

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 28:
⊦ 0 < i ∧ 0 < j → rational(i, j).num = i / gcd(i, j)
Proof step 29:
0 < ~(i / gcd(i, i0)) ∧ 0 < ~(i0 / gcd(i, i0)), i < 0, i0 < 0 ⊦ i0 = 0, i = 0, i / gcd(i, i0) + ~(i / gcd(i, i0)) / gcd(~(i / gcd(i, i0)), ~(i0 / gcd(i, i0))) = 0 ∧ i0 / gcd(i, i0) + rational(~(i / gcd(i, i0)), ~(i0 / gcd(i, i0))).denom = 0

Rule argument

name: num-pos rotate: F subst: [j, i] → [~(i0 / gcd(i, i0)), ~(i / gcd(i, i0))]

Additional information

Used simplifier rules: ⊦ 0 < ~ i ↔ i < 0;% ⊦ ¬ i < j ↔ j ≤ i;% ⊦ i0 < 0 → ¬ 0 ≤ i0 / gcd(i, i0);% ⊦ gcd(i, j) = gcd(j, i); Used terms: ~(i0 / gcd(i, i0)), ~(i / gcd(i, i0))