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Proof step 50 from proof make (previous step)

0 < i0 ⊦ i0 = 0, i = 0, rational(i / gcd(i, i0), i0 / gcd(i, i0)).num = i / gcd(i, i0) ∧ rational(i / gcd(i, i0), i0 / gcd(i, i0)).denom = i0 / gcd(i, i0)

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 51:
⊦ i ≠ 0 ∧ 0 < j → rational(i, j).num = i / gcd(i, j)
Proof step 52:
¬(i / gcd(i, i0) ≠ 0 ∧ 0 < i0 / gcd(i, i0)), 0 < i0 ⊦ i0 = 0, i = 0, rational(i / gcd(i, i0), i0 / gcd(i, i0)).num = i / gcd(i, i0) ∧ rational(i / gcd(i, i0), i0 / gcd(i, i0)).denom = i0 / gcd(i, i0)
Proof step 59:
i / gcd(i, i0) ≠ 0 ∧ 0 < i0 / gcd(i, i0), 0 < i0 ⊦ i0 = 0, i = 0, (i / gcd(i, i0)) / gcd(i / gcd(i, i0), i0 / gcd(i, i0)) = i / gcd(i, i0) ∧ rational(i / gcd(i, i0), i0 / gcd(i, i0)).denom = i0 / gcd(i, i0)

Rule argument

name: numerator-pos rotate: F subst: [j, i] → [i0 / gcd(i, i0), i / gcd(i, i0)]

Additional information

Used terms: i0 / gcd(i, i0), i / gcd(i, i0)