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Proof step 6 from proof make (previous step)

¬(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

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 7:
⊦ 0 < i ∧ j < 0 → rational(i, j).num = ~(i / gcd(i, j))
Proof step 8:
¬(0 < i ∧ i0 < 0), ¬(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 32:
0 < i ∧ i0 < 0, ¬(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-neg1 rotate: F subst: [j, i] → [i0, i]

Additional information

Used terms: i0, i