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Proof step 22 from proof num-neg-01 (previous step)

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

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 23:
j < 0, 0 < i ⊦ i = 0, j = 0, rational(~ i, j).num = i / gcd(i, j)

Rule argument

Additional information

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