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Proof step 4 from proof make (previous step)

⊦ rational(rational(i, i0).num, rational(i, i0).denom).num = rational(i, i0).num ∧ rational(rational(i, i0).num, rational(i, i0).denom).denom = rational(i, i0).denom

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 5:
⊦ i ≠ 0 ∧ 0 < j → rational(i, j).num = i / gcd(i, j)
Proof step 6:
¬(i ≠ 0 ∧ 0 < i0) ⊦ rational(rational(i, i0).num, rational(i, i0).denom).num = rational(i, i0).num ∧ rational(rational(i, i0).num, rational(i, i0).denom).denom = rational(i, i0).denom
Proof step 46:
i ≠ 0 ∧ 0 < i0 ⊦ rational(i / gcd(i, i0), rational(i, i0).denom).num = i / gcd(i, i0) ∧ rational(i / gcd(i, i0), rational(i, i0).denom).denom = rational(i, i0).denom

Rule argument

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

Additional information

Used terms: i0, i