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Proof step 2 from proof zero-gr-case (previous step)

⊦ 0 < i * j ↔ 0 < i ∧ 0 < j ∨ i < 0 ∧ j < 0

User applied rule insert rewrite lemma

And obtained the following new goals

Rule argument

spec: int-mult inst: name: zero-gr seq: ⊦ 0 < i → (0 < i * j ↔ 0 < j) subst: [j, i] → [j, i] flags: rewrite, current

Additional information

Used simplifier rules: zero-gr-01: ⊦ i < 0 → (0 < i * j ↔ j < 0);%associativity: ⊦ i * j * j0 = (i * j) * j0;%commutativity: ⊦ i * j = j * i;%zero-gr-03: ⊦ i ≤ 0 → (0 < i * j ↔ ¬ ¬(j < 0 ∧ i ≠ 0));%ls-01: ⊦ i < j → ¬ j < i; from specification int-basic1%zero-gels-01: ⊦ i < 0 ∧ 0 ≤ j → i < j; from specification int-abs%lels: ⊦ ¬ i < j ↔ j ≤ i; from specification int-abs%lels-02: ⊦ i ≠ j → (i ≤ j ↔ i < j); from specification int-abs Used terms: j, i