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Proof step 70 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 ⊦ 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

User applied rule cut formula

And obtained the following new goals

Rule argument

fma: 0 < i1

Additional information

Used simplifier rules: ⊦ ¬ 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;% ⊦ i < 0 ∧ 0 ≤ j → i < j;% ⊦ i + ~ j = i - j;% ⊦ i = j → i - j = 0;% ⊦ i + j + i0 = (i + j) + i0;% ⊦ i + j = j + i; Used formulas: 0 < i1