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Proof step 21 from proof Extsimple (previous step)

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

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 22:
⊦ i < 0 ∧ j < 0 → i + j ≠ 0

Rule argument

seq: ⊦ i < 0 ∧ j < 0 → i + j ≠ 0 subst: [j, i] → [i1 / gcd(i1, j1), i2 / gcd(i2, j2)] rotate: F spec: int-basic2 inst: name: zero

Additional information

Used simplifier rules: ⊦ ¬ i < j ↔ j ≤ i;% ⊦ i0 < 0 → ¬ 0 ≤ i0 / gcd(i, i0);% ⊦ gcd(i, j) = gcd(j, i); Used terms: i1 / gcd(i1, j1), i2 / gcd(i2, j2)