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Proof step 669 from proof bitsand-cast (previous step)

¬ 2 + # bits + m ≤ #(mklist(false, # bits3) + bitsand(false ' + true ' + bits, bits1)), # 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

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 670:
2 + # bits = # bits1, # bits1 = # bitsand(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

Rule argument

Additional information

Used simplifier rules: n < n0 ⊦ (* n) ≠ m0 + (* n0);% ⊦ m < n → n ≠ 0; (forward)% ⊦ m + n = n + m;% ⊦ (m + n0) + n1 = m + n0 + n1;% ⊦ ¬ m ≤ n ↔ n < m;% ⊦ (bits + bits0) + bits1 = bits + bits0 + bits1;% ⊦ # mklist(boolvar, n) = n;% ⊦ #(bits + bits0) = # bits + # bits0;