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Proof step 679 from proof bitsand-cast (previous step)

# bits1 = 2 + # bits, # bits3 < m ⊦ bits1 = [], bits3 = [], bits3 + bits1 = [], bits2 + mklist(false, m) = [], mklist(false, m) + bitsand(bits1, false ' + true ' + bits) = lastn(2 + # bits + m, fillsgn(2 + # bits + m, 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 680:
⊦ n = # bits → lastn(n, bits) = bits
Proof step 681:
2 + # bits + m ≠ # fillsgn(2 + # bits + m, mklist(false, # bits3) + bitsand(bits1, false ' + true ' + bits)), # bits1 = 2 + # bits, # bits3 < m ⊦ bits1 = [], bits3 = [], bits3 + bits1 = [], bits2 + mklist(false, m) = [], mklist(false, m) + bitsand(bits1, false ' + true ' + bits) = lastn(2 + # bits + m, fillsgn(2 + # bits + m, mklist(false, # bits3) + bitsand(bits1, false ' + true ' + bits))), # bits3 = m, bits3.first
Proof step 687:
2 + # bits + m = # fillsgn(2 + # bits + m, mklist(false, # bits3) + bitsand(bits1, false ' + true ' + bits)), # bits1 = 2 + # bits, # bits3 < m ⊦ bits1 = [], bits3 = [], bits3 + bits1 = [], bits2 + mklist(false, m) = [], mklist(false, m) + bitsand(bits1, false ' + true ' + bits) = fillsgn(2 + # bits + m, mklist(false, # bits3) + bitsand(bits1, false ' + true ' + bits)), # bits3 = m, bits3.first

Rule argument

seq: ⊦ n = # bits → lastn(n, bits) = bits subst: [bits, n] → [fillsgn (2 + # bits + m, mklist(false, # bits3) + bitsand(bits1, false ' + true ' + bits)), 2 + # bits + m] rotate: F spec: list-del inst: bitlista name: lastN-all

Additional information

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