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Proof step 711 from proof bitsand-cast (previous step)

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

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 712:
# bits1 = # bitsand(bits1, false ' + true ' + bits), 2 + # bits = # bits1 ⊦ bits3 = [], mklist(false, # bits3) + bitsand(bits1, false ' + true ' + bits) = lastn(2 + # bits + # bits3, fillsgn(2 + # bits + # bits3, mklist(false, # bits3) + bitsand(false ' + true ' + bits, bits1))), bits1 = [], bits2 + mklist(false, # bits3) = [], bits3 + bits1 = [], bits3.first

Rule argument

Additional information

Used simplifier rules: ⊦ m ≤ m;% ⊦ # bits = 0 ↔ bits = [];% ⊦ m ≤ n → (n ≤ m ↔ m = n);% ⊦ # mklist(boolvar, n) = n;% ⊦ ¬ true ∈ mklist(false, n);% ⊦ 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);