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Proof step 4 from proof zero-ls-03 (previous step)

i < 0 → (i * j < i * 0 ↔ 0 < j), i ≤ 0 ⊦ i * j < 0 ↔ 0 < j ∧ i ≠ 0

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 5:
i ≤ 0, i < 0 → i * j < 0 → 0 < j ⊦ i * j < 0 ↔ 0 < j ∧ i ≠ 0

Rule argument

Additional information

Used simplifier rules: zero-left: ⊦ 0 * i = 0;%associativity: ⊦ i * j * j0 = (i * j) * j0;%commutativity: ⊦ i * j = j * i;%zero-ls: ⊦ 0 < i → (i * j < 0 ↔ j < 0);%zero-gels-01: ⊦ i < 0 ∧ 0 ≤ j → i < j; from specification int-abs