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Proof step 3 from proof gcd-num-one (previous step)

⊦ rational(i, i0).num = 0, gcd(rational(i, i0).num, rational(i, i0).denom) = 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 < i0) ⊦ rational(i, i0).num = 0, gcd(rational(i, i0).num, rational(i, i0).denom) = 1
Proof step 11:
i ≠ 0 ∧ 0 < i0 ⊦ i / gcd(i, i0) = 0, gcd(i / gcd(i, i0), rational(i, i0).denom) = 1

Rule argument

name: numerator-pos rotate: F subst: [j, i] → [i0, i]

Additional information

Used terms: i0, i