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

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

User applied rule insert rewrite lemma

And obtained the following new goals

Rule argument

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

Additional information

Used simplifier rules: zero-le-03: ⊦ i ≤ 0 → (i * j ≤ 0 ↔ ¬ ¬(i = 0 ∨ 0 ≤ j));%associativity: ⊦ i * j * j0 = (i * j) * j0;%commutativity: ⊦ i * j = j * i;%lels-02: ⊦ i ≠ j → (i ≤ j ↔ i < j); from specification int-abs%zero-gels-01: ⊦ i < 0 ∧ 0 ≤ j → i < j; from specification int-abs%ls-01: ⊦ i < j → ¬ j < i; from specification int-basic1%lels-01: ⊦ ¬ i ≤ j ↔ j < i; from specification int-abs%forward-le-05: ⊦ i < j ∧ 0 ≤ i → 0 < j; (forward) from specification int-abs%lf-02: ⊦ i < j ∧ j = i0 → i < i0; (forward) from specification int-basic1%lels: ⊦ ¬ i < j ↔ j ≤ i; from specification int-abs Used terms: j, i