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Proof step 76 from proof Extsimple (previous step)

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

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 77:
abs(i1) / gcd(i1, j1) = abs(i2) / gcd(i2, j2), abs(j1) / gcd(i1, j1) = abs(j2) / gcd(i2, j2), (0 < i1 ∧ 0 < j1 ∨ i1 < 0 ∧ j1 < 0) ∧ (0 < i2 ∧ 0 < j2 ∨ i2 < 0 ∧ j2 < 0) ∨ (0 < i1 ∧ j1 < 0 ∨ i1 < 0 ∧ 0 < j1) ∧ (0 < i2 ∧ j2 < 0 ∨ i2 < 0 ∧ 0 < j2) ⊦ j2 = 0, j1 = 0, i2 = 0, i1 = 0, rational(i1, j1).num = rational(i2, j2).num

Rule argument

Additional information

Used simplifier rules: ⊦ i ≠ j → (i ≤ j ↔ i < j);% ⊦ ¬ i < j ↔ j ≤ i;