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Proof step 248 from proof bitsand-cast (previous step)

# bits2 ≠ 0, 2 + # bits1 = # bits, n0 + # bits = # fillsgn(n0 + # bits, mklist(false, m) + false ' + true ' + bits1), 2 + # bits1 + m < n0 + # bits, # bits2 < m, # bits2 + # bitsand(bits, 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 + # bitsand(bits, false ' + true ' + bits1)) + mklist(false, # bits2), bits2.first

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 249:
2 + # bits1 = # bits, n0 + # bits = # fillsgn(n0 + # bits, mklist(false, m) + false ' + true ' + bits1), 2 + # bits1 + m < n0 + # bits, # bits2 < m, # bits2 + # bitsand(bits, 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 + # bitsand(bits, false ' + true ' + bits1)) + mklist(false, # bits2), bits2.first

Rule argument

Additional information

Used simplifier rules: ⊦ (m + n0) + n1 = m + n0 + n1;% ⊦ # bits = 0 ↔ bits = [];% ⊦ m + n = n + m;