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Proof step 246 from proof bitsand-cast (previous step)

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(mklist(false, # bits2).first, n0 + # bits - # bits2 + # bitsand(bits, false ' + true ' + bits1)) + mklist(false, # bits2), bits2.first

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 247:
⊦ m ≠ 0 → (mklist(boolvar, m).first ↔ boolvar)
Proof step 248:
# 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

Rule argument

seq: ⊦ m ≠ 0 → (mklist(boolvar, m).first ↔ boolvar) subst: [m, boolvar] → [# bits2, false] rotate: F spec: list-last inst: bitlista name: mk-first-01

Additional information

Used simplifier rules: ⊦ # bits = 0 ↔ bits = []; Used terms: # bits2, false