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Proof step 44 from proof Extsimple (previous step)

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

User applied rule cut formula

And obtained the following new goals

Rule argument

fma: 0 < i2

Additional information

Used simplifier rules: ⊦ i + j = j + i;% ⊦ ¬ i < j → (i ≠ j ↔ j < i);% ⊦ i < j → ¬ j < i;% ⊦ i < 0 → abs(i) = ~ i;% ⊦ gcd(i, j) = 0 ↔ i = 0 ∧ j = 0;%j ≠ 0 ⊦ ~ i / j = ~(i / j);% ⊦ ~ i = j ↔ i + j = 0; Used formulas: 0 < i2