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Proof step 13 from proof denom-neg-02 (previous step)

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

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 14:
gcd(i, j) = 1, 0 < j ⊦ (~ rational(i, j)).denom = j

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)