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Proof step 3 from proof div2-neg-odd (previous step)

j < 0 ⊦ (j * 2 - 1) / 2 = j

User applied rule cut formula

And obtained the following new goals

Proof step 4:
j < 0 ⊦ (j * 2 - 1) / 2 = j, (j * 2 - 1) / 2 = ~((~ j * 2 + 1) / 2)

Rule argument

fma: (j * 2 - 1) / 2 = ~((~ j * 2 + 1) / 2)

Additional information

Used simplifier rules: div2-odd-01: ⊦ i < 0 → (1 - i * 2) / 2 = ~ i;% ⊦ ~ i * j = ~(i * j); (s)%associativity: ⊦ i * j * j0 = (i * j) * j0; from specification int-mult%commutativity: ⊦ i * j = j * i; from specification int-mult% ⊦ i + ~ j = i - j; (s)%add-a: ⊦ i + j + i0 = (i + j) + i0; from specification int-basic2%add-c: ⊦ i + j = j + i; from specification int-basic2% ⊦ ~ ~ i = i; (s) Used formulas: (j * 2 - 1) / 2 = ~((~ j * 2 + 1) / 2)