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Proof step 3 from proof zero-gr-03 (previous step)

i ≤ 0 ⊦ 0 < i * j ↔ j < 0 ∧ i ≠ 0

User applied rule case distinction

And closed the goal!

Rule argument

pos: right 1

Additional information

Used simplifier rules: zero-gr-02: ⊦ 0 ≤ i → (0 < i * j ↔ 0 < j ∧ i ≠ 0);%associativity: ⊦ i * j * j0 = (i * j) * j0;%commutativity: ⊦ i * j = j * i;%zero-left: ⊦ 0 * i = 0;%zero-gr-01: ⊦ i < 0 → (0 < i * j ↔ j < 0);%associativity: ⊦ i * j * j0 = (i * j) * j0;%commutativity: ⊦ i * j = j * i;% ⊦ i ≠ j → (i ≤ j ↔ i < j); (s)% ⊦ i < j ↔ ¬ j ≤ i; (ss)% ⊦ i < j → (j ≤ i ↔ false); (as)% ⊦ i ≤ j → ¬ j < i; (s)