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Proof step 819 from proof bitsand-cast (previous step)

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

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 820:
# bits1 = # bitsand(bits1, false ' + true ' + bits), 2 + # bits = # bits1, sgn(mklist(false, # bits0) + false ' + true ' + bits) = false ' + true ' + bits, 2 + # bits + # bits0 ≤ # bitsand(bits2, bits4) + # bitsand(mklist(false, # bits0), bits0) + # bits1, 2 + # bits + # bits0 < # bitsand(mklist(false, # bits0), bits0) + # bits1 ⊦ bits1 = [], bits4 = [], bits2 = [], mklist(false, # bits0) + bitsand(bits1, false ' + true ' + bits) = lastn(2 + # bits + # bits0, bitsand(mklist(false, # bits0), bits0) + bitsand(bits1, false ' + true ' + bits)), bits2 + mklist(false, # bits0) = [], bits4 + bits0 = [], (bits4 + bits0) + bits1 = [], bits0 = [], 2 + # bits + # bits0 = # bitsand(mklist(false, # bits0), bits0) + # bits1

Rule argument

Additional information

Used simplifier rules: ⊦ m < n → n ≠ 0;% ⊦ m < n → n ≠ 0; (forward)% ⊦ (bits + bits0) + bits1 = bits + bits0 + bits1;% ⊦ boolvar ' + bits ≠ [];% ⊦ m + n = n + m;% ⊦ (m + n0) + n1 = m + n0 + n1;