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Proof step 8 from proof make (previous step)

¬(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

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 9:
⊦ i < 0 ∧ j < 0 → rational(i, j).num = abs(i) / gcd(i, j)
Proof step 10:
¬(i < 0 ∧ i0 < 0), ¬(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 23:
i < 0 ∧ i0 < 0, ¬(0 < i ∧ i0 < 0), ¬(i ≠ 0 ∧ 0 < i0) ⊦ rational(abs(i) / gcd(i, i0), rational(i, i0).denom).num = abs(i) / gcd(i, i0) ∧ rational(abs(i) / gcd(i, i0), rational(i, i0).denom).denom = rational(i, i0).denom

Rule argument

name: numerator-neg2 rotate: F subst: [j, i] → [i0, i]

Additional information

Used terms: i0, i