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Proof step 15 from proof num-neg-03 (previous step)

∃ i, j. ri = rational(i, j) ∧ ri.num = i ∧ ri.denom = j ∧ 0 < j ∧ gcd(i, j) = 1 ⊦ ri.num + (~ ri).num = 0

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 16:
gcd(i, j) = 1, 0 < j ⊦ (~ rational(i, j)).num + i = 0

Rule argument

Additional information

Used simplifier rules: num-id: ⊦ gcd(i, j) = 1 ∧ 0 < j → rational(i, j).num = i;%denom-id: ⊦ gcd(i, j) = 1 ∧ 0 < j → rational(i, j).denom = j;% ⊦ i < j ∧ 0 ≤ i → 0 < j; (forward)