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Proof step 682 from proof bitsand-cast (previous step)

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

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 683:
⊦ # bits ≤ n → # fillsgn(n, bits) = n
Proof step 684:
¬ #(mklist(false, # bits3) + bitsand(bits1, false ' + true ' + bits)) ≤ 2 + # bits + m, # bits1 = 2 + # bits, # bits3 < m ⊦ 2 + # bits + m = # fillsgn(2 + # bits + m, mklist(false, # bits3) + bitsand(bits1, false ' + true ' + bits)), # bits3 = 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))), bits2 + mklist(false, m) = [], bits3 + bits1 = [], bits3 = [], bits1 = [], bits3.first

Rule argument

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

Additional information

Used simplifier rules: ⊦ (m + n0) + n1 = m + n0 + n1;% ⊦ m + n = n + m; Used terms: mklist(false, # bits3) + bitsand(bits1, false ' + true ' + bits), 2 + # bits + m