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Proof step 11 from proof one (previous step)

i < 0 ⊦ rational(~(i / gcd(i, i)), ~(i / gcd(i, i))) = rational(1, 1)

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 12:
⊦ i ≠ 0 → gcd(i, i) = abs(i)

Rule argument

seq: ⊦ i ≠ 0 → gcd(i, i) = abs(i) subst: [i] → [i] rotate: F spec: int-gcd inst: name: gcd-same

Additional information

Used simplifier rules: equal-same: ⊦ 0 < j → (rational(i, j) = rational(i0, j) ↔ i = i0);% ⊦ gcd(0, 0) = 0;% ⊦ i < 0 → abs(i) = ~ i;%j ≠ 0 ⊦ i / ~ j = ~(i / j);%i ≠ 0 ⊦ i / i = 1; Used terms: i