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Proof step 764 from proof bitsand-cast (previous step)

false ' + true ' + bits ≠ [] ∧ bits1 ≠ [], # bits1 = 2 + # bits, # bits1 ≤ # bitsand(bits2, bits4) + # bitsand(bits1, false ' + true ' + bits), # bitsand(bits1, false ' + true ' + bits) < # bits1 ⊦ bits4 + bits1 = [], bits4 = [], bits2 = [], bits1 = [], bitsand(bits1, false ' + true ' + bits) = lastn(# bits1, bitsand(bits2, bits4) + bitsand(bits1, false ' + true ' + bits))

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 765:
# bits1 = 2 + # bits, # bitsand(bits1, false ' + true ' + bits) < # bits1, # bits1 ≤ # bitsand(bits2, bits4) + # bitsand(bits1, false ' + true ' + bits) ⊦ bits1 = [], bitsand(bits1, false ' + true ' + bits) = lastn(# bits1, bitsand(bits2, bits4) + bitsand(bits1, false ' + true ' + bits)), bits2 = [], bits4 = [], bits4 + bits1 = []

Rule argument

Additional information

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