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Proof step 699 from proof bitsand-cast (previous step)

# bits1 = 2 + # bits, # bits3 < m ⊦ mklist(false, m) = mklist(mklist(false, # bits3).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

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 700:
⊦ m ≠ 0 → (mklist(boolvar, m).first ↔ boolvar)
Proof step 701:
# bits3 ≠ 0, # bits1 = 2 + # bits, # bits3 < m ⊦ mklist(false, m) = mklist(false, 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

seq: ⊦ m ≠ 0 → (mklist(boolvar, m).first ↔ boolvar) subst: [m, boolvar] → [# bits3, false] rotate: F spec: list-last inst: bitlista name: mk-first-01

Additional information

Used simplifier rules: ⊦ # bits = 0 ↔ bits = []; Used terms: # bits3, false