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Proof step 692 from proof bitsand-cast (previous step)

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

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 693:
# bits1 = 2 + # bits, # bits3 < m, # bits3 + # bitsand(bits1, false ' + true ' + bits) ≤ 2 + # bits + m ⊦ # bits3 = m, mklist(false, # bits3) + bitsand(bits1, false ' + true ' + bits) = [], bits1 = [], bits3 = [], bits3 + bits1 = [], bits2 + mklist(false, m) = [], mklist(false, m) = mklist ((mklist(false, # bits3) + bitsand(bits1, false ' + true ' + bits)).first, 2 + # bits + m - # bits3 + # bitsand(bits1, false ' + true ' + bits)) + mklist(false, # bits3), bits3.first

Rule argument

Additional information

Used simplifier rules: n ≤ m ⊦ (m - n) + n0 = n1 ↔ m + n0 = n + n1;% ⊦ bits + bits0 = bits1 + bits0 ↔ bits = bits1;% ⊦ ¬ m ≤ n ↔ n < m;% ⊦ m ≤ n → (n < m ↔ false);% ⊦ # mklist(boolvar, n) = n;% ⊦ #(bits + bits0) = # bits + # bits0;% ⊦ m + n = n + m;% ⊦ (m + n0) + n1 = m + n0 + n1;% ⊦ (bits + bits0) + bits1 = bits + bits0 + bits1;