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Proof step 5 from proof zero-gr-01 (previous step)

i < 0, 0 < ~ i → (0 < ~ i * ~ j ↔ 0 < ~ j) ⊦ 0 < i * j ↔ j < 0

Heuristic simplifier applied rule simplifier

And closed the goal!

Rule argument

Additional information

Used simplifier rules: minus-left: ⊦ ~ i * j = ~(i * j);%associativity: ⊦ i * j * j0 = (i * j) * j0;%commutativity: ⊦ i * j = j * i;% ⊦ ~ ~ i = i; (s)% ⊦ 0 < ~ i ↔ i < 0; (s)