[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 174 from proof bitsand-cast (previous step)

n = # fillsgn(n, mklist(false, n0 - 1) + false ' + true ' + bits1), sgn(mklist(false, n0 - 1) + false ' + true ' + bits1) = false ' + true ' + bits1, # bits = 2 + # bits1, n0 + 1 + # bits1 < n ⊦ n0 = 0, lastn(n, fillsgn(n, bitsand(bits, false ' + true ' + bits1))) = lastn(n, fillsgn(n, bitsand(mklist(false, n0 - 1) + false ' + true ' + bits1, bits2 + bits))), bits2 = [], bits2 + bits = []

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 175:
⊦ # bits = # bits1 ∧ bits0 ≠ [] ∧ bits2 ≠ [] ∧ bits ≠ [] → bitsand(bits0 + bits, bits2 + bits1) = bitsand(bits0, bits2) + bitsand(bits, bits1)
Proof step 176:
¬(#(false ' + true ' + bits1) = # bits ∧ mklist(false, n0 - 1) ≠ [] ∧ bits2 ≠ [] ∧ false ' + true ' + bits1 ≠ []), n = # fillsgn(n, mklist(false, n0 - 1) + false ' + true ' + bits1), sgn(mklist(false, n0 - 1) + false ' + true ' + bits1) = false ' + true ' + bits1, # bits = 2 + # bits1, n0 + 1 + # bits1 < n ⊦ n0 = 0, lastn(n, fillsgn(n, bitsand(bits, false ' + true ' + bits1))) = lastn(n, fillsgn(n, bitsand(mklist(false, n0 - 1) + false ' + true ' + bits1, bits2 + bits))), bits2 = [], bits2 + bits = []
Proof step 184:
#(false ' + true ' + bits1) = # bits ∧ mklist(false, n0 - 1) ≠ [] ∧ bits2 ≠ [] ∧ false ' + true ' + bits1 ≠ [], n = # fillsgn(n, mklist(false, n0 - 1) + false ' + true ' + bits1), sgn(mklist(false, n0 - 1) + false ' + true ' + bits1) = false ' + true ' + bits1, # bits = 2 + # bits1, n0 + 1 + # bits1 < n ⊦ n0 = 0, lastn(n, fillsgn(n, bitsand(bits, false ' + true ' + bits1))) = lastn(n, fillsgn(n, bitsand(mklist(false, n0 - 1), bits2) + bitsand(false ' + true ' + bits1, bits))), bits2 = [], bits2 + bits = []

Rule argument

name: bitsand-app rotate: F subst: [bits1, bits2, bits, bits0] → [bits, bits2, false ' + true ' + bits1, mklist(false, n0 - 1)]

Additional information

Used terms: bits, bits2, false ' + true ' + bits1, mklist(false, n0 - 1)