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Proof step 801 from proof bitsand-cast (previous step)

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

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 802:
sgn(mklist(false, # bits0) + false ' + true ' + bits) = false ' + true ' + bits, 2 + # bits = # bits1, # bits1 = # bitsand(bits1, false ' + true ' + bits), # bitsand(mklist(false, # bits0), bits0) + # bitsand(false ' + true ' + bits, bits1) < 2 + # bits + # bits0, 2 + # bits + # bits0 ≤ # bitsand(bits2, bits4) + # bitsand(mklist(false, # bits0), bits0) + # bitsand(false ' + true ' + bits, bits1) ⊦ bits0 = [], (bits4 + bits0) + bits1 = [], bits4 + bits0 = [], bits2 + mklist(false, # bits0) = [], bits1 = [], mklist(false, # bits0) + bitsand(bits1, false ' + true ' + bits) = lastn(2 + # bits + # bits0, bitsand(bits2, bits4) + bitsand(mklist(false, # bits0), bits0) + bitsand(false ' + true ' + bits, bits1)), bits2 = [], bits4 = []

Rule argument

Additional information

Used simplifier rules: and-notempty: ⊦ bits ≠ [] ∧ bits0 ≠ [] → bitsand(bits, bits0) ≠ [];% ⊦ # bits = 0 ↔ bits = [];% ⊦ m < m + n ↔ n ≠ 0;% ⊦ m + n < m + n0 ↔ n < n0;%n < n0 ⊦ (* n) ≠ m0 + (* n0);% ⊦ m < n → n ≠ 0; (forward)% ⊦ m < n ∧ n ≤ n0 → m < n0; (forward)% ⊦ ¬ m ≤ n ↔ n < m;% ⊦ (bits + bits0) + bits1 = bits + bits0 + bits1;% ⊦ #(bits + bits0) = # bits + # bits0;% ⊦ m + n = n + m;% ⊦ (m + n0) + n1 = m + n0 + n1;