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Proof step 667 from proof bitsand-cast (previous step)

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

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 668:
⊦ n ≤ # bits → fillsgn(n, bits) = bits
Proof step 669:
¬ 2 + # bits + m ≤ #(mklist(false, # bits3) + bitsand(false ' + true ' + bits, bits1)), # bits1 = # bitsand(bits1, false ' + true ' + bits), 2 + # bits = # bits1, # bits3 < m ⊦ # bits3 = m, mklist(false, m) + bitsand(bits1, false ' + true ' + bits) = lastn(2 + # bits + m, fillsgn(2 + # bits + m, mklist(false, # bits3) + bitsand(false ' + true ' + bits, bits1))), bits1 = [], bits2 + mklist(false, m) = [], bits3 + bits1 = [], bits3 = [], bits3.first
Proof step 703:
2 + # bits + m ≤ #(mklist(false, # bits3) + bitsand(false ' + true ' + bits, bits1)), # bits1 = # bitsand(bits1, false ' + true ' + bits), 2 + # bits = # bits1, # bits3 < m ⊦ # bits3 = m, mklist(false, m) + bitsand(bits1, false ' + true ' + bits) = lastn(2 + # bits + m, mklist(false, # bits3) + bitsand(false ' + true ' + bits, bits1)), bits1 = [], bits2 + mklist(false, m) = [], bits3 + bits1 = [], bits3 = [], bits3.first

Rule argument

seq: ⊦ n ≤ # bits → fillsgn(n, bits) = bits subst: [bits, n] → [ mklist(false, # bits3) + bitsand(false ' + true ' + bits, bits1), 2 + # bits + m] rotate: F spec: bitopsaux inst: name: fillsgn-longer

Additional information

Used terms: mklist(false, # bits3) + bitsand(false ' + true ' + bits, bits1), 2 + # bits + m