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Proof step 6 from proof num-neg (previous step)

¬(0 < ~ i ∧ ~ j < 0), 0 < j ⊦ j = 0, i = 0, rational(~ i, ~ j).num = i / gcd(i, j)

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 7:
0 < j, 0 < i ⊦ j = 0, i = 0, rational(~ i, ~ j).num = i / gcd(i, j)

Rule argument

Additional information

Used simplifier rules: ⊦ i < j ∧ 0 ≤ i → 0 < j; (forward)% ⊦ i < j → ¬ j < i;% ⊦ ~ i < 0 ↔ 0 < i;% ⊦ i ≠ j → (i ≤ j ↔ i < j);% ⊦ ¬ i < j ↔ j ≤ i;% ⊦ 0 < ~ i ↔ i < 0;