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Proof step 7 from proof abs-pos (previous step)

0 < j ⊦ abs(rational(i, j)).num = rational(abs(i), j).num ∧ rational(i, j).denom = rational(abs(i), j).denom

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 8:
⊦ i ≠ 0 ∧ j ≠ 0 → rational(i, j).denom = abs(j) / gcd(i, j)
Proof step 9:
¬(i ≠ 0 ∧ j ≠ 0), 0 < j ⊦ abs(rational(i, j)).num = rational(abs(i), j).num ∧ rational(i, j).denom = rational(abs(i), j).denom
Proof step 12:
i ≠ 0 ∧ j ≠ 0, 0 < j ⊦ abs(rational(i, j)).num = rational(abs(i), j).num ∧ abs(j) / gcd(i, j) = rational(abs(i), j).denom

Rule argument

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

Additional information

Used terms: j, i