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Proof step 26 from proof Extsimple (previous step)

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

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 27:
i1 / gcd(i1, j1) = i2 / gcd(i2, j2), j1 / gcd(i1, j1) = j2 / gcd(i2, j2), i1 < 0, j1 < 0, 0 < i2, j2 < 0 ⊦ i1 = 0, i2 = 0, j1 = 0, j2 = 0

Rule argument

Additional information

Used simplifier rules: ⊦ i < j ∧ 0 ≤ i → 0 < j; (forward)% ⊦ j < i ∧ i ≤ 0 → j < 0; (forward)% ⊦ i < 0 ∧ 0 ≤ j → i < j;% ⊦ i < j → ¬ j < i;%j ≠ 0 ⊦ ~ i / j = ~(i / j);% ⊦ gcd(i, j) = 0 ↔ i = 0 ∧ j = 0;% ⊦ i < 0 → abs(i) = ~ i;% ⊦ i + 0 = i;% ⊦ i - j = i0 ↔ i = i0 + j;% ⊦ i + j = j + i;% ⊦ i + j + i0 = (i + j) + i0;% ⊦ i + ~ j = i - j;