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Proof step 6 from proof intshiftleft-is-mult-01 (previous step)

⊦ bits2int(int2bits(i) + mklist(false, i→n(band(j, 31)))) = i * 2 ^ band(j, 31), band(j, 31) ≠ 0 ∧ ¬ i < 0

User applied rule cut formula

And obtained the following new goals

Rule argument

fma: band(j, 31) ≠ 0

Additional information

Used simplifier rules: ⊦ mklist(boolvar, 0) = [];% ⊦ bits + [] = bits;% ⊦ (bits + bits0) + bits1 = bits + bits0 + bits1;% ⊦ bits2int(int2bits(i)) = i;% ⊦ 1 * i = i;% ⊦ i * j * j0 = (i * j) * j0;% ⊦ i * j = j * i; Used formulas: band(j, 31) ≠ 0