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Theorem byte-mult-256
⊦ i2b(i * 256 + j) = i2b(j)
Type: A user defined theorem
Validity: The proof is valid.
Features: simp, localsimp,
Comment:
Used by:
byte-add-256
,
byte-law-add-one
,
byte-law-add-pos
,
byte-law-mult-one
,
byte-mult-256-01
,
getsetShort-theorem
,
Used by units in proved state:
bytes
,
Proof exists?: Yes
View
the proof
Infos about the proof
Proved?: Yes
Interactions: 44
Proof steps: 71
Used lemmas:
byte-in
,
num-i2b-neg
,
num-i2b-equal
,
byte-mult
,
bib-upper
,
num-ibbi
,
bib-lower
,
bib-in-01
,
byte-mult-neg
,
byte-equal
,
i2b-equal
,
byte-mult-pos
,
i2b-noteq
,
Used spec theorems:
int-basic1
/
lsrec
int-div
/
modex
Used simplifier rules:
int-basic2
/
num-between
int2bits
/
int2bits-neg-num
int2bits
/
uint2bits-pos-num
int2bits
/
uint2bits-one
list
/bitlista/
Two
list
/bitlista/
Last
bitopsaux
/
invert-zero
bitopsaux
/
invert-one
bitopsaux
/
inv-false
list
/bitlista/
c
list
/bitlista/
a
bitopsaux
/
succ-rec
bitopsaux
/
succ-zero
bitopsaux
/
sgn-rec
bitopsaux
/
sgn-base-01
list-del
/bitlista/
num-lastN
list-del
/bitlista/
lastn-one
list-last
/bitlista/
last-def
int2bits
/
bits2int-pos
int2bits
/
bits2uint-zero
int2bits
/
bits2uint-one-02
int-abs
/
minus-add
int-mult
/
eq-succ
int-abs
/
elim-sub
int-abs
/
mone-06
int-mult
/
eq-same
int-abs
/
sub-ls
int-abs
/
mone-08
int-abs
/
sub-add-01
int-abs
/
sub-eq
int-mult
/
zero-ls
int-basic2
/
ls
int-abs
/
forward-lsle
int-abs
/
forward-le-01
int-abs
/
zero-gels-04
int-mult
/
zero-ge-add
int-div
/
mod-zero
int-abs
/
lels-04
int-div
/
div-elim-pospos
int-div
/
mod-zero-01
int-div
/
mod-ngez
int-abs
/
numsub
int-abs
/
numlsledel-01
int-basic2
/
succ-01
int-abs
/
numadd-01
int-abs
/
numls-03
int-basic1
/
numlslsdel-01
int-abs
/
numle-03
int-abs
/
numleledel-01
int-basic1
/
lst
int-abs
/
numlelsdel-01
int-abs
/
numlelsdel
int-abs
/
sub-le-01
int-abs
/
leone
int-basic1
/
ls-01
int-abs
/
numle-02
int-mult
/
succ-rmerge
int-abs
/
Sub-def
int-basic2
/
add-zero
int-abs
/
anti
int-mult
/
eq-pos
int-basic2
/
add-in
int-abs
/
forward-le-04
int-abs
/
forward-lels
int-abs
/
numls-02
int-abs
/
neg-13
int-abs
/
abs-08
int-abs
/
zero-gels-03
int-mult
/
dist-rmerge
int-div
/
div-elim-negpos
int-abs
/
forward-le-05
int-abs
/
lels-03
int-abs
/
lels-02
int-abs
/
lels
int-abs
/
forward-le-02
int-abs
/
zero-gels-01
int-abs
/
lels-01
int-basic2
/
add-c
int-basic2
/
add-a
int-mult
/
commutativity
int-mult
/
associativity
int-mult
/
zero-eq
int-basic2
/
eq