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Proof step 807 from proof bitsand-cast (previous step)

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

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 808:
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 = []

Rule argument

Additional information

Used simplifier rules: and-notempty: ⊦ bits ≠ [] ∧ bits0 ≠ [] → bitsand(bits, bits0) ≠ [];% ⊦ m < m + n ↔ n ≠ 0;% ⊦ m + n < m + n0 ↔ n < n0;% ⊦ m < n ∧ n ≤ n0 → m < n0; (forward)% ⊦ # bits = 0 ↔ bits = [];% ⊦ mklist(boolvar, m) = [] ↔ m = 0;% ⊦ m + n = n + m;% ⊦ (m + n0) + n1 = m + n0 + n1;