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Proof step 16 from proof Extsimple (previous step)

i1 / gcd(i1, j1) + rational(i2, j2).num = 0, j1 / gcd(i1, j1) + abs(j2) / gcd(i2, j2) = 0, i1 < 0, j1 < 0 ⊦ i1 = 0, i2 = 0, j1 = 0, j2 = 0, ¬ 0 < i2 ∧ ¬ 0 < j2, i2 / gcd(i2, j2) + i1 / gcd(i1, j1) = 0 ∧ ¬ i2 < 0 ∧ ¬ j2 < 0

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 17:
⊦ 0 < i ∧ j < 0 → rational(i, j).num = ~(i / gcd(i, j))
Proof step 18:
¬(0 < i2 ∧ j2 < 0), i1 / gcd(i1, j1) + rational(i2, j2).num = 0, j1 / gcd(i1, j1) + abs(j2) / gcd(i2, j2) = 0, i1 < 0, j1 < 0 ⊦ i1 = 0, i2 = 0, j1 = 0, j2 = 0, ¬ 0 < i2 ∧ ¬ 0 < j2, i2 / gcd(i2, j2) + i1 / gcd(i1, j1) = 0 ∧ ¬ i2 < 0 ∧ ¬ j2 < 0
Proof step 26:
0 < i2 ∧ j2 < 0, i1 / gcd(i1, j1) + ~(i2 / gcd(i2, j2)) = 0, j1 / gcd(i1, j1) + abs(j2) / gcd(i2, j2) = 0, i1 < 0, j1 < 0 ⊦ i1 = 0, i2 = 0, j1 = 0, j2 = 0, ¬ 0 < i2 ∧ ¬ 0 < j2, i2 / gcd(i2, j2) + i1 / gcd(i1, j1) = 0 ∧ ¬ i2 < 0 ∧ ¬ j2 < 0

Rule argument

name: numerator-neg1 rotate: F subst: [j, i] → [j2, i2]

Additional information

Used terms: j2, i2