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Proof step 49 from proof Extsimple (previous step)

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

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 50:
⊦ i ≠ 0 ∧ 0 < j → rational(i, j).num = i / gcd(i, j)
Proof step 51:
¬(i2 ≠ 0 ∧ 0 < j2), i1 / gcd(i1, j1) = rational(i2, j2).num, j1 / gcd(i1, j1) = abs(j2) / gcd(i2, j2), 0 < j1 ⊦ j2 = 0, j1 = 0, i2 = 0, i1 = 0, abs(i1) / gcd(i1, j1) = abs(i2) / gcd(i2, j2) ∧ (¬ i1 < 0 ∧ (¬ i2 < 0 ∧ ¬ j2 < 0 ∨ ¬ 0 < i2 ∧ ¬ 0 < j2) ∨ ¬ 0 < i1 ∧ (¬ i2 < 0 ∧ ¬ 0 < j2 ∨ ¬ 0 < i2 ∧ ¬ j2 < 0))
Proof step 62:
i2 ≠ 0 ∧ 0 < j2, i1 / gcd(i1, j1) = i2 / gcd(i2, j2), j1 / gcd(i1, j1) = abs(j2) / gcd(i2, j2), 0 < j1 ⊦ j2 = 0, j1 = 0, i2 = 0, i1 = 0, abs(i1) / gcd(i1, j1) = abs(i2) / gcd(i2, j2) ∧ (¬ i1 < 0 ∧ (¬ i2 < 0 ∧ ¬ j2 < 0 ∨ ¬ 0 < i2 ∧ ¬ 0 < j2) ∨ ¬ 0 < i1 ∧ (¬ i2 < 0 ∧ ¬ 0 < j2 ∨ ¬ 0 < i2 ∧ ¬ j2 < 0))

Rule argument

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

Additional information

Used terms: j2, i2