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Proof step 810 from proof bitsand-cast (previous step)

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

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 811:
sgn(mklist(false, # bits0) + false ' + true ' + bits) = false ' + true ' + bits, 2 + # bits = # bits1, # bits1 = # bitsand(bits1, false ' + true ' + bits), # bitsand(bits0, mklist(false, # bits0)) + # bits1 < 2 + # bits + # bits0, 2 + # bits + # bits0 ≤ # bitsand(bits2, bits4) + # bitsand(bits0, mklist(false, # bits0)) + # bits1, mklist(false, # bits0).first ⊦ bits0 = [], (bits4 + bits0) + bits1 = [], bits4 + bits0 = [], bits2 + mklist(false, # bits0) = [], mklist(false, # bits0) + bitsand(bits1, false ' + true ' + bits) = lastn(2 + # bits + # bits0, bitsand(bits2, bits4) + bitsand(bits0, mklist(false, # bits0)) + bitsand(bits1, false ' + true ' + bits)), bits2 = [], bits4 = [], bits1 = []

Rule argument

Additional information

Used simplifier rules: ⊦ # bits = 0 ↔ bits = [];% ⊦ mklist(boolvar, m) = [] ↔ m = 0;% ⊦ ¬ n < n;% ⊦ ¬ m ≤ n ↔ n < m;% ⊦ # mklist(boolvar, n) = n;% ⊦ m + n = n + m;% ⊦ (m + n0) + n1 = m + n0 + n1;