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Proof step 3 from proof add-ones-grlen (previous step)

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

Heuristic simplifier applied rule simplifier

And obtained the following new goals

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

Rule argument

Additional information

Used simplifier rules: ⊦ # bits = 0 ↔ bits = [];% ⊦ m < n → n ≠ 0; (forward)% ⊦ m + n = n + m;% ⊦ (m + n0) + n1 = m + n0 + n1;% ⊦ m + 1 ≤ n ↔ m < n;% ⊦ mklist(boolvar, n) + boolvar ' = boolvar ' + mklist(boolvar, n);% ⊦ # boolvar ' = 0 +1;% ⊦ #(bits + bits0) = # bits + # bits0;% ⊦ (bits + bits0) + bits1 = bits + bits0 + bits1;% ⊦ boolvar ' + bits ≠ [];% ⊦ boolvar + bits = boolvar ' + bits;