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Proof step 612 from proof bitsand-cast (previous step)

bits1 ≠ [] ∧ false ' + true ' + bits ≠ [], sgn(mklist(false, m) + false ' + true ' + bits) = false ' + true ' + bits, 2 + # bits = # bits1 ⊦ lastn(2 + # bits + m, mklist(bits1.first ∧ (false ' + true ' + bits).first, m) + bitsand(bits1, false ' + true ' + bits)) = lastn(2 + # bits + m, fillsgn(2 + # bits + m, bitsand(bits2 + mklist(false, m), bits3) + bitsand(false ' + true ' + bits, bits1))), bitsand(bits1, false ' + true ' + bits) = [], bits3 + bits1 = [], bits3 = [], bits2 + mklist(false, m) = []

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 613:
sgn(mklist(false, m) + false ' + true ' + bits) = false ' + true ' + bits, 2 + # bits = # bits1 ⊦ bits3 + bits1 = [], bits3 = [], bits2 + mklist(false, m) = [], bits1 = [], lastn(2 + # bits + m, mklist(false, m) + bitsand(bits1, false ' + true ' + bits)) = lastn(2 + # bits + m, fillsgn(2 + # bits + m, bitsand(bits2 + mklist(false, m), bits3) + bitsand(false ' + true ' + bits, bits1)))

Rule argument

Additional information

Used simplifier rules: and-notempty-01: ⊦ bits ≠ [] → bitsand(bits, boolvar ' + bits0) ≠ [];% ⊦ boolvar ' + bits ≠ [];% ⊦ (bits + bits0) + bits1 = bits + bits0 + bits1;% ⊦ (boolvar ' + bits).first ↔ boolvar;