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Proof step 2 from proof num-div-denom-01 (previous step)

⊦ i1 = 0, j = 0, (rational(i, i1).num * j) / rational(i, i1).denom = (i * j) / i1

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 3:
⊦ i ≠ 0 ∧ 0 < j → rational(i, j).num = i / gcd(i, j)
Proof step 4:
¬(i ≠ 0 ∧ 0 < i1) ⊦ i1 = 0, j = 0, (rational(i, i1).num * j) / rational(i, i1).denom = (i * j) / i1
Proof step 13:
i ≠ 0 ∧ 0 < i1 ⊦ i1 = 0, j = 0, (i / gcd(i, i1) * j) / rational(i, i1).denom = (i * j) / i1

Rule argument

name: numerator-pos rotate: F subst: [j, i] → [i1, i]

Additional information

Used terms: i1, i