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Proof step 52 from proof Extsimple (previous step)

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

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 53:
⊦ 0 < i ∧ j < 0 → rational(i, j).num = ~(i / gcd(i, j))
Proof step 54:
¬(0 < i2 ∧ j2 < 0), i1 / gcd(i1, j1) = rational(i2, j2).num, j2 / gcd(i2, j2) + j1 / gcd(i1, j1) = 0, 0 < j1, j2 < 0 ⊦ j2 = 0, j1 = 0, i2 = 0, i1 = 0, abs(i1) / gcd(i1, j1) = abs(i2) / gcd(i2, j2) ∧ (¬ i1 < 0 ∧ ¬ 0 < i2 ∨ ¬ 0 < i1 ∧ ¬ i2 < 0)
Proof step 57:
0 < i2 ∧ j2 < 0, i1 / gcd(i1, j1) = ~(i2 / gcd(i2, j2)), j2 / gcd(i2, j2) + j1 / gcd(i1, j1) = 0, 0 < j1, j2 < 0 ⊦ j2 = 0, j1 = 0, i2 = 0, i1 = 0, abs(i1) / gcd(i1, j1) = abs(i2) / gcd(i2, j2) ∧ (¬ i1 < 0 ∧ ¬ 0 < i2 ∨ ¬ 0 < i1 ∧ ¬ i2 < 0)

Rule argument

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

Additional information

Used terms: j2, i2