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Proof step 743 from proof bitsand-cast (previous step)

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

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 744:
# bits1 = # bitsand(bits1, false ' + true ' + bits), 2 + # bits = # bits1, # bits1 < # bitsand(false ' + true ' + bits, bits1) ⊦ (bits4 + bits0) + bits1 = [], bits4 = [], mklist(false, # bits0) + bitsand(bits1, false ' + true ' + bits) = lastn(2 + # bits + # bits0, mklist(false, # bits0) + bitsand(false ' + true ' + bits, bits1)), bits1 = [], bits0 = [], bits4 + bits0 = [], # bits1 = # bitsand(false ' + true ' + bits, bits1)

Rule argument

Additional information

Used simplifier rules: and-notempty-02: ⊦ bits0 ≠ [] → bitsand(boolvar ' + bits, bits0) ≠ [];% ⊦ # bits = 0 ↔ bits = [];% ⊦ m < n → n ≠ 0; (forward)% ⊦ m < n ∧ m = n0 → n0 < n; (forward)% ⊦ m ≠ n → (m ≤ n ↔ m < n);% ⊦ (m + n0) + n1 = m + n0 + n1;% ⊦ m + n = n + m;% ⊦ m + n = m + n0 ↔ n = n0;% ⊦ (bits + bits0) + bits1 = bits + bits0 + bits1;% ⊦ # mklist(boolvar, n) = n;% ⊦ #(bits + bits0) = # bits + # bits0;