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Proof step 709 from proof bitsand-cast (previous step)

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

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 710:
2 + # bits = # bits1, # bits1 = # bitsand(bits1, false ' + true ' + bits), 2 + # bits + m ≤ # bits3 + # bits1, # bits3 < m, # bits1 ≤ 2 + # bits + m ⊦ mklist(false, m) = lastn(2 + # bits + m - # bits1, mklist(false, # bits3)), # bits3 = m, bits1 = [], bits3 = [], bits3 + bits1 = [], bits2 + mklist(false, m) = [], bits3.first

Rule argument

Additional information

Used simplifier rules: ⊦ m ≤ m + n;% ⊦ n ≤ n0 ∧ n0 ≤ n1 → n ≤ n1; (forward)% ⊦ m + n = n + m;% ⊦ (m + n0) + n1 = m + n0 + n1;% ⊦ bits + bits0 = bits1 + bits0 ↔ bits = bits1;% ⊦ (bits + bits0) + bits1 = bits + bits0 + bits1;