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Proof step 814 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, 2 + # bits + # bits0 ≤ # bitsand(bits2, bits4) + # bitsand(mklist(false, # bits0), bits0) + # bitsand(false ' + true ' + bits, bits1), 2 + # bits + # bits0 ≤ # bitsand(mklist(false, # bits0), bits0) + # bitsand(false ' + true ' + bits, bits1) ⊦ bits4 = [], bits2 = [], mklist(false, # bits0) + bitsand(bits1, false ' + true ' + bits) = lastn(2 + # bits + # bits0, 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 815:
⊦ n = # bits → lastn(n, bits) = bits
Proof step 816:
2 + # bits + # bits0 ≠ #(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, 2 + # bits + # bits0 ≤ # bitsand(bits2, bits4) + # bitsand(mklist(false, # bits0), bits0) + # bitsand(false ' + true ' + bits, bits1), 2 + # bits + # bits0 ≤ # bitsand(mklist(false, # bits0), bits0) + # bitsand(false ' + true ' + bits, bits1) ⊦ bits4 = [], bits2 = [], mklist(false, # bits0) + bitsand(bits1, false ' + true ' + bits) = lastn(2 + # bits + # bits0, bitsand(mklist(false, # bits0), bits0) + bitsand(false ' + true ' + bits, bits1)), bits1 = [], bits2 + mklist(false, # bits0) = [], bits4 + bits0 = [], (bits4 + bits0) + bits1 = [], bits0 = []
Proof step 828:
2 + # bits + # bits0 = #(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, 2 + # bits + # bits0 ≤ # bitsand(bits2, bits4) + # bitsand(mklist(false, # bits0), bits0) + # bitsand(false ' + true ' + bits, bits1), 2 + # bits + # bits0 ≤ # bitsand(mklist(false, # bits0), bits0) + # bitsand(false ' + true ' + bits, bits1) ⊦ bits4 = [], bits2 = [], mklist(false, # bits0) + bitsand(bits1, false ' + true ' + bits) = 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 → lastn(n, bits) = bits subst: [bits, n] → [ bitsand(mklist(false, # bits0), bits0) + bitsand(false ' + true ' + bits, bits1), 2 + # bits + # bits0] rotate: F spec: list-del inst: bitlista name: lastN-all

Additional information

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