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Proof step 2 from proof int2bits-2pot-05 (previous step)

0 ≤ i ⊦ int2bits(~(j * 2 ^ i)) = int2bits(~ j) + mklist(false, i→n(i)), 0 = j

User applied rule cut formula

And obtained the following new goals

Proof step 3:
~(j * 2 ^ i) = ~ j * 2 ^ i, 0 ≤ i ⊦ int2bits(~(j * 2 ^ i)) = int2bits(~ j) + mklist(false, i→n(i)), 0 = j

Rule argument

fma: ~(j * 2 ^ i) = ~ j * 2 ^ i

Additional information

Used simplifier rules: ⊦ i * j = j * i;% ⊦ ~ i * j = ~(i * j);% ⊦ i * j * j0 = (i * j) * j0;% ⊦ ~ i = ~ j ↔ i = j; Used formulas: ~(j * 2 ^ i) = ~ j * 2 ^ i