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Proof step 523 from proof bitsand-cast (previous step)

2 + # bits + # bits0 ≤ #((bitsand(bits2, bits4) + bitsand(mklist(true, # bits0), bits0)) + bitsand(bits1, true ' + false ' + bits)), sgn(mklist(true, # bits0) + true ' + false ' + bits) = true ' + false ' + bits, # bits1 = 2 + # bits ⊦ bits4 = [], bits2 = [], (bits4 + bits0) + bits1 = [], bits1 = [], lastn(2 + # bits + # bits0, fillsgn(2 + # bits + # bits0, (bits4 + bits0) + bitsand(bits1, true ' + false ' + bits))) = lastn(2 + # bits + # bits0, (bitsand(bits2, bits4) + bitsand(mklist(true, # bits0), bits0)) + bitsand(bits1, true ' + false ' + bits)), bits2 + mklist(true, # bits0) = [], bits4 + bits0 = [], bits0 = []

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 524:
sgn(mklist(true, # bits0) + true ' + false ' + bits) = true ' + false ' + bits, # bits1 = 2 + # bits, 2 + # bits + # bits0 ≤ # bitsand(bits2, bits4) + # bitsand(mklist(true, # bits0), bits0) + # bitsand(bits1, true ' + false ' + bits) ⊦ bits4 = [], bits2 = [], (bits4 + bits0) + bits1 = [], bits1 = [], lastn(2 + # bits + # bits0, fillsgn(2 + # bits + # bits0, (bits4 + bits0) + bitsand(bits1, true ' + false ' + bits))) = lastn(2 + # bits + # bits0, (bitsand(bits2, bits4) + bitsand(mklist(true, # bits0), bits0)) + bitsand(bits1, true ' + false ' + bits)), bits2 + mklist(true, # bits0) = [], bits4 + bits0 = [], bits0 = []

Rule argument

Additional information

Used simplifier rules: ⊦ (bits + bits0) + bits1 = bits + bits0 + bits1;% ⊦ #(bits + bits0) = # bits + # bits0;% ⊦ m + n = n + m;% ⊦ (m + n0) + n1 = m + n0 + n1;