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Theorem byte-law-and-one
⊦ i2b(band(i, j)) = i2b(band(b2i(i2b(i)), j))
Type: A user defined theorem
Validity: The proof is valid.
Features:
Comment:
Used by:
Used by units in proved state:
Proof exists?: Yes
View
the proof
Infos about the proof
Proved?: Yes
Interactions: 111
Proof steps: 190
Used lemmas:
bib-on-bits
,
byte-equal
,
i2b-equal
,
i2b-noteq
,
Used spec theorems:
intops
/
band-def
intops
/
and-sgn
intops
/
band-num
int2bits
/
bits2bits-def
int2bits
/
bits2int-inj
intops
/
and-notempty
bitopsaux
/
lastn-fill-sgn
list-del
/bitlista/
lastN-all
bitopsaux
/
fill-length
intops
/
bitsand-fillsgn
bitopsaux
/
fill-fill
intops
/
add-ones-lelen
list
/bitlista/
a
bitopsaux
/
fill-rec
list
/bitlista/
split-rest
int2bits
/
int2bits-lslen-06
intops
/
bitsand-app
intops
/
bitsand-len-false
intops
/
and-com
intops
/
bitsand-app-true
intops
/
bitsand-app-false
bitopsaux
/
fillsgn-longer
list-del
/bitlista/
lastN-append-01
intops
/
bitsand-len-true
Used simplifier rules:
intops
/
bitsand-len-true
intops
/
bitsand-len-false
list-del
/bitlista/
lastN-append-01
int-abs
/
forward-lels
int-basic1
/
numlsf
int2bits
/
int2bits-leneq-neg
int-abs
/
numlelsdel
int-basic1
/
ls-01
int-basic1
/
forward-pos
int-abs
/
forward-le
int-abs
/
forward-le-05
int2bits
/
int2bits-leneq-pos
nat
/
lep
nat
/
add-num-03
list-del
/bitlista/
lastN-append
bitopsaux
/
fillsgn-longer
bitlista
/
inmklist-01
list-last
/bitlista/
mk-len
nat
/
ls-03
list-last
/bitlista/
mk-empty
nat
/
zero-01
nat-basic2
/
l-08
nat-basic2
/
l-06
nat
/
ler
nat
/
let
nat-basic2
/
l-01
nat-basic2
/
l-02
int2bits
/
int2bits-first-01
nat
/
ls-le-simp
list
/bitlista/
app-01
list-data
/bitlista/
size-01
nat
/
not-zero
list
/bitlista/
e
nat
/
succ-01
nat-basic2
/
s
bitopsaux
/
fill-nls
nat
/
l-num-04
nat-basic2
/
l
list
/bitlista/
c-08
list
/bitlista/
e-01
nat
/
fle
int2bits
/
int2bits-fillfirst
intops
/
and-notempty
bitopsaux
/
fill-empty
list
/bitlista/
app-02-ant
list
/bitlista/
Nil
int-abs
/
forward-le-02
nat
/
le-ls-simp
nat
/
fle-01
nat
/
lels
int-abs
/
lels-04
int-abs
/
forward-le-01
int-abs
/
zero-gels-04
int-abs
/
lels-03
nat
/
lels-03
nat-basic1
/
ref-1
intops
/
and-notempty-02
int-abs
/
lels
nat
/
add-num-04
list
/bitlista/
len-02
list
/bitlista/
len
int2bits
/
int2bits-first-02
bitopsaux
/
fill-rec
nat-basic2
/
c
nat-basic2
/
a
nat
/
l-num-05
nat-basic2
/
succ
list-data
/bitlista/
l
nat-basic1
/
trans-1
nat-basic1
/
trans
nat-basic1
/
lf-02
bitopsaux
/
fill-lastn
nat-basic1
/
lf-01
nat-basic1
/
ls-02
nat-basic1
/
f
nat
/
lels-01
list-del
/bitlista/
lastn-one-01
list-del
/bitlista/
num-lastN
list
/bitlista/
a
list
/bitlista/
app
list-last
/bitlista/
mk-zero
bitlista
/
mklist-num
bitopsaux
/
fillsgn-empty
bitopsaux
/
sgn-empty
int2bits
/
bits2int-inj
intops
/
and-sgn
intops
/
and-notempty-09
bitopsaux
/
sgn-empty-01
int2bits
/
int2bits-not-empty
list-del
/bitlista/
lastN-empty
intops
/
band-commutativity