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Proof step 13 from proof Extsimple (previous step)

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

User applied rule insert rewrite lemma

And obtained the following new goals

Rule argument

name: numerator-neg2 rotate: F subst: [j, i] → [j2, i2]

Additional information

Used simplifier rules: ⊦ i < 0 → abs(i) = ~ i;% ⊦ gcd(i, j) = 0 ↔ i = 0 ∧ j = 0;%j ≠ 0 ⊦ ~ i / j = ~(i / j);% ⊦ i + ~ j = i - j;% ⊦ i + j + i0 = (i + j) + i0;% ⊦ i + j = j + i;% ⊦ i - j = i0 ↔ i = i0 + j;% ⊦ i + 0 = i;% ⊦ i = j → i - j = 0;% ⊦ i < 0 ∧ 0 ≤ j → i < j;% ⊦ i < j → ¬ j < i; Used terms: j2, i2