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Proof step 782 from proof bitsand-cast (previous step)

# bits1 = # bitsand(bits1, false ' + true ' + bits), 2 + # bits = # bits1, sgn(mklist(false, # bits0) + false ' + true ' + bits) = false ' + true ' + bits ⊦ bits4 = [], bits2 = [], mklist(false, # bits0) + bitsand(bits1, false ' + true ' + bits) = lastn (2 + # bits + # bits0, fillsgn(2 + # bits + # bits0, (bitsand(bits2, bits4) + bitsand(mklist(false, # bits0), bits0)) + bitsand(false ' + true ' + bits, bits1))), bits1 = [], bits2 + mklist(false, # bits0) = [], bits4 + bits0 = [], (bits4 + bits0) + bits1 = [], bits0 = []

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 783:
⊦ n ≤ # bits → fillsgn(n, bits) = bits
Proof step 784:
¬ 2 + # bits + # bits0 ≤ #((bitsand(bits2, bits4) + bitsand(mklist(false, # bits0), bits0)) + bitsand(false ' + true ' + bits, bits1)), # bits1 = # bitsand(bits1, false ' + true ' + bits), 2 + # bits = # bits1, sgn(mklist(false, # bits0) + false ' + true ' + bits) = false ' + true ' + bits ⊦ bits4 = [], bits2 = [], mklist(false, # bits0) + bitsand(bits1, false ' + true ' + bits) = lastn (2 + # bits + # bits0, fillsgn(2 + # bits + # bits0, (bitsand(bits2, bits4) + bitsand(mklist(false, # bits0), bits0)) + bitsand(false ' + true ' + bits, bits1))), bits1 = [], bits2 + mklist(false, # bits0) = [], bits4 + bits0 = [], (bits4 + bits0) + bits1 = [], bits0 = []
Proof step 796:
2 + # bits + # bits0 ≤ #((bitsand(bits2, bits4) + bitsand(mklist(false, # bits0), bits0)) + bitsand(false ' + true ' + bits, bits1)), # bits1 = # bitsand(bits1, false ' + true ' + bits), 2 + # bits = # bits1, sgn(mklist(false, # bits0) + false ' + true ' + bits) = false ' + true ' + bits ⊦ bits4 = [], bits2 = [], mklist(false, # bits0) + bitsand(bits1, false ' + true ' + bits) = lastn(2 + # bits + # bits0, (bitsand(bits2, bits4) + bitsand(mklist(false, # bits0), bits0)) + bitsand(false ' + true ' + bits, bits1)), bits1 = [], bits2 + mklist(false, # bits0) = [], bits4 + bits0 = [], (bits4 + bits0) + bits1 = [], bits0 = []

Rule argument

seq: ⊦ n ≤ # bits → fillsgn(n, bits) = bits subst: [bits, n] → [ ( bitsand(bits2, bits4) + bitsand(mklist(false, # bits0), bits0)) + bitsand(false ' + true ' + bits, bits1), 2 + # bits + # bits0] rotate: F spec: bitopsaux inst: name: fillsgn-longer

Additional information

Used terms: (bitsand(bits2, bits4) + bitsand(mklist(false, # bits0), bits0)) + bitsand(false ' + true ' + bits, bits1), 2 + # bits + # bits0