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Proof step 672 from proof bitsand-cast (previous step)

¬ (false ' + true ' + bits).first ∧ #(false ' + true ' + bits) ≤ # bits1 ∧ false ' + true ' + bits ≠ [], 2 + # bits = # bits1, # bits1 = #(false ' + true ' + bits), # bits3 + # bitsand(false ' + true ' + bits, bits1) < 2 + # bits + m, # bits3 < m ⊦ bits3 = [], 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, # bits3) + bitsand(false ' + true ' + bits, bits1))), # bits3 = m, bits3.first

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 673:
# bits1 = 2 + # bits, # bits3 < m, # bits3 + # bitsand(false ' + true ' + bits, bits1) < 2 + # bits + 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: ⊦ m ≤ m;% ⊦ (boolvar ' + bits).first ↔ boolvar;% ⊦ boolvar ' + bits ≠ [];% ⊦ m + n = n + m;% ⊦ (bits + bits0) + bits1 = bits + bits0 + bits1;% ⊦ # boolvar ' = 0 +1;% ⊦ #(bits + bits0) = # bits + # bits0;