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Proof step 831 from proof bitsand-cast (previous step)

false ' + true ' + bits ≠ [] ∧ bits1 ≠ [], 2 + # bits + # bits0 = # bitsand(mklist(false, # bits0), bits0) + # bitsand(bits1, false ' + true ' + bits), sgn(mklist(false, # bits0) + false ' + true ' + bits) = false ' + true ' + bits, 2 + # bits = # bits1, # bits1 = # bitsand(bits1, false ' + true ' + bits) ⊦ bits0 = [], (bits4 + bits0) + bits1 = [], bits4 + bits0 = [], bits2 + mklist(false, # bits0) = [], bits1 = [], mklist(false, # bits0) + bitsand(bits1, false ' + true ' + bits) = bitsand(mklist(false, # bits0), bits0) + bitsand(bits1, false ' + true ' + bits), bits2 = [], bits4 = []

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 832:
2 + # bits + # bits0 = # bitsand(mklist(false, # bits0), bits0) + # bits1, sgn(mklist(false, # bits0) + false ' + true ' + bits) = false ' + true ' + bits, 2 + # bits = # bits1, # bits1 = # bitsand(bits1, false ' + true ' + bits) ⊦ bits2 = [], bits4 = [], bits1 = [], bits0 = [], (bits4 + bits0) + bits1 = [], bits4 + bits0 = [], bits2 + mklist(false, # bits0) = [], mklist(false, # bits0) = bitsand(mklist(false, # bits0), bits0)

Rule argument

Additional information

Used simplifier rules: ⊦ m + n = n + m;% ⊦ (m + n0) + n1 = m + n0 + n1;% ⊦ boolvar ' + bits ≠ [];% ⊦ bits + bits0 = bits1 + bits0 ↔ bits = bits1;% ⊦ (bits + bits0) + bits1 = bits + bits0 + bits1;