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Proof step 666 from proof bitsand-cast (previous step)

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

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 667:
# bits1 = # bitsand(bits1, false ' + true ' + bits), 2 + # bits = # bits1, # bits3 < m ⊦ # bits3 = m, mklist(false, m) + bitsand(bits1, false ' + true ' + bits) = lastn(2 + # bits + m, fillsgn(2 + # bits + m, mklist(false, # bits3) + bitsand(false ' + true ' + bits, bits1))), bits1 = [], bits2 + mklist(false, m) = [], bits3 + bits1 = [], bits3 = [], bits3.first

Rule argument

Additional information

Used simplifier rules: ⊦ ¬ true ∈ mklist(false, n);% ⊦ # mklist(boolvar, n) = n;% ⊦ m < n → n ≠ 0;% ⊦ mklist(boolvar, m) = [] ↔ m = 0;% ⊦ bits + bits0 = bits + bits1 ↔ bits0 = bits1;% ⊦ (bits + bits0) + bits1 = bits + bits0 + bits1;% ⊦ sgn(false ' + true ' + bits) = false ' + true ' + bits;% ⊦ ¬ true ∈ bits → sgn(bits + false ' + bits0) = sgn(false ' + bits0);