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Proof step 3 from proof bitsand-zeros-01 (previous step)

bits0 = boolvar + bits1, # bits0 < # bits ⊦ bits = [], bits0 = [], bitsand(bits, bits0) = mklist(false, # bits0), true ∈ bits, boolvar

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 4:
1 + # bits1 < # bits ⊦ bits = [], bitsand(bits, false ' + bits1) = false ' + mklist(false, # bits1), true ∈ bits

Rule argument

Additional information

Used simplifier rules: ⊦ m + n = n + m;% ⊦ (m + n0) + n1 = m + n0 + n1;% ⊦ bits + [] = bits;% ⊦ mklist(boolvar, 0) = [];%n ≠ 0 ⊦ mklist(false, (* n)) = false ' + mklist(false, n -1);% ⊦ mklist(boolvar, m + n) = mklist(boolvar, m) + mklist(boolvar, n);% ⊦ # boolvar ' = 0 +1;% ⊦ #(bits + bits0) = # bits + # bits0;% ⊦ (bits + bits0) + bits1 = bits + bits0 + bits1;% ⊦ boolvar ' + bits ≠ [];% ⊦ boolvar + bits = boolvar ' + bits;