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Proof step 35 from proof Extsimple (previous step)

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

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 36:
⊦ i ≠ 0 ∧ 0 < j → rational(i, j).num = i / gcd(i, j)
Proof step 37:
¬(i2 ≠ 0 ∧ 0 < j2), i1 / gcd(i1, j1) + rational(i2, j2).num = 0, j1 / gcd(i1, j1) + abs(j2) / gcd(i2, j2) = 0, 0 < i1, j1 < 0 ⊦ i1 = 0, i2 = 0, j1 = 0, j2 = 0, ¬ i2 < 0 ∧ ¬ 0 < j2, i1 / gcd(i1, j1) = abs(i2) / gcd(i2, j2) ∧ ¬ 0 < i2 ∧ ¬ j2 < 0
Proof step 43:
i2 ≠ 0 ∧ 0 < j2, i1 / gcd(i1, j1) + i2 / gcd(i2, j2) = 0, j1 / gcd(i1, j1) + abs(j2) / gcd(i2, j2) = 0, 0 < i1, j1 < 0 ⊦ i1 = 0, i2 = 0, j1 = 0, j2 = 0, ¬ i2 < 0 ∧ ¬ 0 < j2, i1 / gcd(i1, j1) = abs(i2) / gcd(i2, j2) ∧ ¬ 0 < i2 ∧ ¬ j2 < 0

Rule argument

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

Additional information

Used terms: j2, i2