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Proof step 637 from proof bitsand-cast (previous step)

¬ (false ' + true ' + bits).first ∧ #(false ' + true ' + bits) ≤ # bits1 ∧ false ' + true ' + bits ≠ [], 2 + # bits = # bits1, # bits1 = #(false ' + true ' + bits), bits3.first, # bits3 ≤ m, # bits1 ≤ # bits2 + # bitsand(false ' + true ' + bits, bits1) ⊦ bits3 + bits1 = [], bits2 + mklist(false, m) = [], bits1 = [], mklist(false, m) + bitsand(bits1, false ' + true ' + bits) = lastn(2 + # bits + m, (bits2 + mklist(false, m)) + bitsand(false ' + true ' + bits, bits1)), bits3 = [], m = 0

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 638:
# bits1 = 2 + # bits, # bits1 ≤ # bits2 + # bitsand(false ' + true ' + bits, bits1), # bits3 ≤ m, bits3.first ⊦ m = 0, bits3 = [], mklist(false, m) + bitsand(bits1, false ' + true ' + bits) = lastn(2 + # bits + m, (bits2 + mklist(false, m)) + bitsand(false ' + true ' + bits, bits1)), bits1 = [], bits2 + mklist(false, m) = [], bits3 + bits1 = []

Rule argument

Additional information

Used simplifier rules: ⊦ m ≤ m;% ⊦ n ≤ n0 ∧ n0 ≤ n1 → n ≤ n1; (forward)% ⊦ (boolvar ' + bits).first ↔ boolvar;% ⊦ boolvar ' + bits ≠ [];% ⊦ m + n = n + m;% ⊦ (bits + bits0) + bits1 = bits + bits0 + bits1;% ⊦ # boolvar ' = 0 +1;% ⊦ #(bits + bits0) = # bits + # bits0;