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Proof step 2 from proof sgn-01-01 (previous step)

i < 0 ⊦ sgn(i) * j = ~ j

Heuristic simplifier applied rule simplifier

And closed the goal!

Rule argument

Additional information

Used simplifier rules: Sign-neg: ⊦ j < 0 → sgn(j) = 0 -1;% ⊦ i * j = 0 ↔ i = 0 ∨ j = 0; (ws)%commutativity: ⊦ i * j = j * i; from specification int-mult%associativity: ⊦ i * j * j0 = (i * j) * j0; from specification int-mult%add-c: ⊦ i + j = j + i; from specification int-basic2%add-a: ⊦ i + j + i0 = (i + j) + i0; from specification int-basic2% ⊦ i * j + i = i * (j + 1); (s)% ⊦ ~ i = j ↔ i + j = 0; (s)