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Theorem getsetShort-theorem
⊦ j ∈short → bor(b2i(i2b(j i>> 8)) i<< 8, band(255, b2i(i2b(j)))) = 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: 35
Proof steps: 68
Used lemmas:
bib-pos-high
,
bib-pos-low
,
bib-ls-same-01
,
byte-neq
,
byte
,
byte-mult
,
bib-neg-low
,
bib-neg-high
,
ubyte-pos
,
ubyte-neg
,
ubyte-pos-03
,
byte-mult-256
,
inbyte
,
bib-in
,
band-ff
,
inshort
,
Used spec theorems:
intops
/
bor-shift-plus
intops
/
intshiftright-unbounded-same
intops
/
shiftright-pos-div
intops
/
shiftright-rec-8-neg
int-mult
/
numle-06
int-abs
/
forward-lele
int-abs
/
le-rew-succ
int-mult
/
numls-06
intops
/
intshiftrsign-pos-8
intops
/
intshiftrsign-neg-01
intops
/
intshiftrsign-neg-02
int-div
/
modex
Used simplifier rules:
int-div
/
mod-nle-01
int-basic1
/
ls-01
int-abs
/
sub-add-01
int-abs
/
sub-eq
int-mult
/
eq-succ
int-abs
/
forward-le
int-div
/
div-mult-num
int-mult
/
one
int-div
/
nummult-le-03
int-abs
/
numls-02
int-abs
/
numadd-01
int-abs
/
lels-02
int-basic2
/
eq
int-div
/
divmult
int-div
/
mod-lsz
int-div
/
divmod-rew
int-basic1
/
numlslsdel
int-abs
/
numlsledel-01
int-div
/
mod-ls-zero
int-mult
/
succ-rmerge
int-div
/
mod-ngez
int-abs
/
sub-le-01
int-basic2
/
ls
int-mult
/
zero-ls
int-abs
/
sub-ls
int-basic2
/
num-between
int-abs
/
numlelsdel
int-mult
/
zero-ge-add
int-mult
/
eq-pos
int-basic2
/
add-in
int-div
/
div-elim-pospos
int-basic1
/
numlslsdel-01
int-abs
/
zero-gels
int-div
/
num-ls
int-abs
/
numleledel-01
int-div
/
nummult-le-02
int-abs
/
leone
int-abs
/
lels-04
int-abs
/
forward-lels
int-basic2
/
add-less
int-basic2
/
ls-02
int-abs
/
sub-le
int-abs
/
minus-add
int-abs
/
zero-gels-04
int-mult
/
commutativity
int-mult
/
associativity
int-div
/
div-elim-negpos
int-abs
/
forward-le-04
int-abs
/
numlsledel
int-abs
/
numle-03
int-div
/
div-ls-zero
int-basic1
/
lst
int-div
/
div-zero-ngr
int-basic1
/
forward-pos
int-abs
/
forward-le-05
int-basic1
/
numlsf
int-abs
/
numle-02
int-basic2
/
add-c
int-basic2
/
add-a
int-abs
/
numls-03
int-abs
/
elim-sub
intops
/
rightshift-zero
int-abs
/
lels-03
int-abs
/
zero-gels-01
int-abs
/
forward-le-02
int-abs
/
forward-lsle
int-abs
/
zero-gels-03
int-abs
/
forward-le-01
int-abs
/
forward-lele
int-abs
/
lels
intops
/
band-max-04
intops
/
band-associativity
intops
/
band-commutativity
int-abs
/
lels-01
intops
/
band-notneg