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Proof step 695 from proof bitsand-cast (previous step)

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

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 696:
# bits1 = 2 + # bits, # bits3 < m ⊦ mklist(false, m) = mklist((mklist(false, # bits3) + bitsand(bits1, false ' + true ' + bits)).first, m - # bits3) + mklist(false, # bits3), bits2 + mklist(false, m) = [], bits3 + bits1 = [], bits3 = [], bits1 = [], mklist(false, # bits3) + bitsand(bits1, false ' + true ' + bits) = [], # bits3 = m, bits3.first

Rule argument

Additional information

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