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Proof step 251 from proof bitsand-cast (previous step)

¬ (false ' + true ' + bits1).first ∧ #(false ' + true ' + bits1) ≤ # bits ∧ false ' + true ' + bits1 ≠ [], 2 + # bits1 = # bits, n0 + # bits = # fillsgn(n0 + # bits, mklist(false, m) + false ' + true ' + bits1), 2 + # bits1 + m < n0 + # bits, # bits2 < m, # bits2 + #(false ' + true ' + bits1) ≤ n0 + # bits ⊦ mklist(false, # bits2) + bitsand(bits, false ' + true ' + bits1) = [], bits2 = [], bits = [], bits2 + bits = [], mklist(false, n0) = mklist(false, n0 + # bits - # bits2 + #(false ' + true ' + bits1)) + mklist(false, # bits2), bits2.first

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 252:
n0 + # bits = # fillsgn(n0 + # bits, mklist(false, m) + false ' + true ' + bits1), 2 + # bits1 = # bits, # bits2 < m, 2 + # bits1 + m < n0 + # bits, # bits2 ≤ n0 ⊦ bits2 + bits = [], bits = [], bits2 = [], mklist(false, # bits2) + bitsand(bits, false ' + true ' + bits1) = [], mklist(false, n0) = mklist(false, n0 - # bits2) + mklist(false, # bits2), bits2.first

Rule argument

Additional information

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