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Proof step 57 from proof Extsimple (previous step)

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)

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Rule argument

Additional information

Used simplifier rules: ⊦ i < j ∧ 0 ≤ i → 0 < j; (forward)% ⊦ i < j → ¬ j < i;% ⊦ 0 < j → abs(j) = j;% ⊦ ~ i = j ↔ i + j = 0;