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Proof step 557 from proof bitsand-cast (previous step)

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

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 558:
# bits1 = 2 + # bits, sgn(mklist(true, # bits0) + true ' + false ' + bits) = true ' + false ' + bits, # bitsand(bits1, true ' + false ' + bits) < # bits1, # bits1 ≤ # bits4 + # bitsand(bits1, true ' + false ' + bits), 2 + # bits + # bits0 ≤ # bitsand(bits0, mklist(true, # bits0)) + # bitsand(bits1, true ' + false ' + bits), mklist(true, # bits0).first ⊦ bits4 + bits0 = [], bits2 + mklist(true, # bits0) = [], lastn(2 + # bits + # bits0, bits4 + bits0 + bitsand(bits1, true ' + false ' + bits)) = lastn(2 + # bits + # bits0, bitsand(bits0, mklist(true, # bits0)) + bitsand(bits1, true ' + false ' + bits)), bits1 = [], (bits4 + bits0) + bits1 = [], bits2 = [], bits4 = [], bits0 = []

Rule argument

Additional information

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