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Proof step 543 from proof bitsand-cast (previous step)

(true ' + false ' + bits).first ∧ #(true ' + false ' + bits) ≤ # bits1 ∧ true ' + false ' + bits ≠ [], # bits1 = 2 + # bits, sgn(mklist(true, # bits0) + true ' + false ' + bits) = true ' + false ' + bits, # bitsand(bits0, mklist(true, # bits0)) + # bits1 < 2 + # bits + # bits0, mklist(true, # bits0).first ⊦ bits4 + bits0 = [], bits2 + mklist(true, # bits0) = [], lastn(2 + # bits + # bits0, fillsgn(2 + # bits + # bits0, (bits4 + bits0) + bitsand(bits1, true ' + false ' + bits))) = lastn(2 + # bits + # bits0, bitsand(bits2, bits4) + bitsand(bits0, mklist(true, # bits0)) + bitsand(bits1, true ' + false ' + bits)), bits1 = [], (bits4 + bits0) + bits1 = [], bits2 = [], bits4 = [], bits0 = []

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 544:
sgn(mklist(true, # bits0) + true ' + false ' + bits) = true ' + false ' + bits, # bits1 = 2 + # bits, mklist(true, # bits0).first, # bitsand(bits0, mklist(true, # bits0)) + # bits1 < 2 + # bits + # bits0 ⊦ bits0 = [], bits4 = [], bits2 = [], (bits4 + bits0) + bits1 = [], bits1 = [], lastn(2 + # bits + # bits0, fillsgn(2 + # bits + # bits0, (bits4 + bits0) + bitsand(bits1, true ' + false ' + bits))) = lastn(2 + # bits + # bits0, bitsand(bits2, bits4) + bitsand(bits0, mklist(true, # bits0)) + bitsand(bits1, true ' + false ' + bits)), bits2 + mklist(true, # bits0) = [], bits4 + bits0 = []

Rule argument

Additional information

Used simplifier rules: ⊦ m ≤ m;% ⊦ # boolvar ' = 0 +1;% ⊦ #(bits + bits0) = # bits + # bits0;% ⊦ (boolvar ' + bits).first ↔ boolvar;% ⊦ boolvar ' + bits ≠ [];% ⊦ (bits + bits0) + bits1 = bits + bits0 + bits1;