[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 458 from proof bitsand-cast (previous step)

2 + # bits + n = n0 + # bits1, sgn((mklist(true, n) + mklist(true, # bits3)) + true ' + false ' + bits) = true ' + false ' + bits, # bits1 = 2 + # bits, bits3.first ⊦ mklist(true, n0) = lastn(n0, mklist(true, n)), bits3 + bitsand(bits1, true ' + false ' + bits) = [], bits2 + mklist(true, n) + mklist(true, # bits3) = [], bits3 = [], bits3 + bits1 = [], bits1 = []

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 459:
⊦ m ≤ n → lastn(m, mklist(boolvar, n)) = mklist(boolvar, m)
Proof step 460:
¬ n0 ≤ n, 2 + # bits + n = n0 + # bits1, sgn((mklist(true, n) + mklist(true, # bits3)) + true ' + false ' + bits) = true ' + false ' + bits, # bits1 = 2 + # bits, bits3.first ⊦ mklist(true, n0) = lastn(n0, mklist(true, n)), bits3 + bitsand(bits1, true ' + false ' + bits) = [], bits2 + mklist(true, n) + mklist(true, # bits3) = [], bits3 = [], bits3 + bits1 = [], bits1 = []

Rule argument

seq: ⊦ m ≤ n → lastn(m, mklist(boolvar, n)) = mklist(boolvar, m) subst: [n, boolvar, m] → [n, true, n0] rotate: F spec: list-del inst: bitlista name: lastn-mklist

Additional information

Used terms: n, true, n0