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Proof step 8 from proof one (previous step)

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

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 9:
⊦ 0 < j → rational(i, j) = rational(i / gcd(i, j), j / gcd(i, j))
Proof step 10:
0 < ~ i, i < 0 ⊦ rational(~ i / gcd(~ i, ~ i), ~ i / gcd(~ i, ~ i)) = rational(1, 1)

Rule argument

name: canon-any rotate: F subst: [j, i] → [~ i, ~ i]

Additional information

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