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Proof step 1 from proof num-neg-02 (conclusion)

⊦ 0 < j → (rational(i, j).num < 0 ↔ i < 0)

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 2:
0 < j ⊦ rational(i, j).num < 0 ↔ ¬ 0 ≤ i

Rule argument

Additional information

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