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Proof step 69 from proof Extsimple (previous step)

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

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 70:
i1 / gcd(i1, j1) = i2 / gcd(i2, j2), j1 / gcd(i1, j1) = j2 / gcd(i2, j2), 0 < j1, 0 < j2 ⊦ j2 = 0, j1 = 0, i1 = 0, i2 = 0, abs(i1) / gcd(i1, j1) = abs(i2) / gcd(i2, j2) ∧ (¬ i1 < 0 ∧ ¬ i2 < 0 ∨ ¬ 0 < i1 ∧ ¬ 0 < i2), ¬ 0 < i1 ∧ ¬ i2 < 0

Rule argument

Additional information

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