[Imprint][Data Privacy Statement][E-Mail]

View long theorem info. View the proof. Back to main index. View the specification. View theorem base summary, View theorem base listing, the used properties by spec, the dependency list, the symbol table,

Proof step 538 from proof bitsand-cast (previous step)

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

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 539:
⊦ n ≤ # bits → lastn(n, bits0 + bits) = lastn(n, bits)
Proof step 540:
¬ 2 + # bits + # bits0 ≤ #(bitsand(bits0, mklist(true, # bits0)) + bitsand(bits1, true ' + false ' + bits)), sgn(mklist(true, # bits0) + true ' + false ' + bits) = true ' + false ' + bits, # bits1 = 2 + # bits, mklist(true, # bits0).first ⊦ bits0 = [], bits4 = [], bits2 = [], (bits4 + bits0) + bits1 = [], bits1 = [], lastn(2 + # bits + # bits0, fillsgn(2 + # bits + # bits0, (bits4 + bits0) + bitsand(bits1, true ' + false ' + bits))) = lastn(2 + # bits + # bits0, bitsand(bits2, bits4) + bitsand(bits0, mklist(true, # bits0)) + bitsand(bits1, true ' + false ' + bits)), bits2 + mklist(true, # bits0) = [], bits4 + bits0 = []
Proof step 546:
2 + # bits + # bits0 ≤ #(bitsand(bits0, mklist(true, # bits0)) + bitsand(bits1, true ' + false ' + bits)), sgn(mklist(true, # bits0) + true ' + false ' + bits) = true ' + false ' + bits, # bits1 = 2 + # bits, mklist(true, # bits0).first ⊦ bits0 = [], bits4 = [], bits2 = [], (bits4 + bits0) + bits1 = [], bits1 = [], lastn(2 + # bits + # bits0, fillsgn(2 + # bits + # bits0, (bits4 + bits0) + bitsand(bits1, true ' + false ' + bits))) = lastn(2 + # bits + # bits0, bitsand(bits0, mklist(true, # bits0)) + bitsand(bits1, true ' + false ' + bits)), bits2 + mklist(true, # bits0) = [], bits4 + bits0 = []

Rule argument

seq: ⊦ n ≤ # bits → lastn(n, bits0 + bits) = lastn(n, bits) subst: [bits, bits0, n] → [ bitsand(bits0, mklist(true, # bits0)) + bitsand(bits1, true ' + false ' + bits), bitsand(bits2, bits4), 2 + # bits + # bits0] rotate: F spec: list-del inst: bitlista name: lastN-append-01

Additional information

Used simplifier rules: ⊦ (m + n0) + n1 = m + n0 + n1;% ⊦ m + n = n + m; Used terms: bitsand(bits0, mklist(true, # bits0)) + bitsand(bits1, true ' + false ' + bits), bitsand(bits2, bits4), 2 + # bits + # bits0