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Proof step 3 from proof int-mult (previous step)

⊦ rational(rational(i, 1).num * rational(j, 1).num, rational(i, 1).denom * rational(j, 1).denom) = rational(i * j, 1)

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 4:
⊦ i ≠ 0 ∧ 0 < j → rational(i, j).num = i / gcd(i, j)
Proof step 5:
¬(i ≠ 0 ∧ 0 < 1) ⊦ rational(rational(i, 1).num * rational(j, 1).num, rational(i, 1).denom * rational(j, 1).denom) = rational(i * j, 1)
Proof step 8:
i ≠ 0 ∧ 0 < 1 ⊦ rational(i / gcd(i, 1) * rational(j, 1).num, rational(i, 1).denom * rational(j, 1).denom) = rational(i * j, 1)

Rule argument

name: numerator-pos rotate: F subst: [j, i] → [1, i]

Additional information

Used terms: 1, i