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Theorem bib-neg-low
⊦ i < 0 ∧ i % 256 < ~128 → b2i(i2b(i)) = i % 256 + 256
Type: A user defined theorem
Validity: The proof is valid.
Features: simp, localsimp,
Comment:
Used by:
bib-lower
,
bib-ls-same
,
bib-ls-same-01
,
byte-law-neg
,
byte-mult-neg
,
getsetShort-theorem
,
Used by units in proved state:
Proof exists?: Yes
View
the proof
Infos about the proof
Proved?: Yes
Interactions: 25
Proof steps: 42
Used lemmas:
num-i2b-pos
,
num-i2b-neg
,
num-ibbi
,
Used spec theorems:
int2bits
/
int2bits-add-high
list-del
/bitlista/
lastN-rest-01
list-del
/bitlista/
lastN-append
bitopsaux
/
fill-length
list-data
/bitlista/
length-rest
int2bits
/
int2bits-lslen-05
int2bits
/
bits2int-fill
int2bits
/
int2int-rest-01
int2bits
/
int2bits-len-neg
int-basic1
/
lsrec
int-div
/
mod-zero-05
Used simplifier rules:
int-basic2
/
eq
int-abs
/
numlsledel-01
int2bits
/
int2bits-neg-num
bitopsaux
/
succ-zero
bitopsaux
/
sgn-rec
bitopsaux
/
sgn-base-01
list
/bitlista/
c-07
list
/bitlista/
e-01
int2bits
/
int2bits-true
int2bits
/
int2bits-eq
list
/bitlista/
app
list-data
/bitlista/
elim-list
list-last
/bitlista/
mk-len
bitopsaux
/
fillsgn-empty
nat
/
ls
nat-basic1
/
one-01
nat
/
pred-03
int2bits
/
int2bits-not-empty
list-data
/bitlista/
l
nat-basic1
/
f
nat
/
lels-01
int2bits
/
int2bits-pos-num
int2bits
/
uint2bits-pos-num
int2bits
/
uint2bits-one
list
/bitlista/
Two
list
/bitlista/
Last
list-del
/bitlista/
num-lastN
list-del
/bitlista/
lastN-zero
list
/bitlista/
Nil
list
/bitlista/
a
int2bits
/
bits2int-neg
list
/bitlista/
c
bitopsaux
/
invert-one
bitopsaux
/
invert-zero
bitopsaux
/
inv-false
bitopsaux
/
succ-rec
bitopsaux
/
succ-one
int2bits
/
bits2uint-zero
int2bits
/
bits2uint-one-03
int-basic1
/
numlslsdel-01
int-abs
/
numle-03
int-abs
/
numleledel-01
int-abs
/
numle-02
int-abs
/
forward-le-03
int-basic1
/
ls-01
int-basic1
/
numlslsdel
int-abs
/
numlelsdel
int-abs
/
zero-gels-01
int-basic2
/
add-zero
int-abs
/
anti
int-abs
/
numlelsdel-01
int-abs
/
numls-03
int-abs
/
neg-07
int-mult
/
commutativity
int-abs
/
forward-le-04
int-basic2
/
add-c
int-basic2
/
add-a
int-abs
/
numls-02
int-abs
/
neg-13
int-abs
/
abs-08
int-abs
/
zero-gels-03
int-abs
/
lels
int-abs
/
lels-03
int-div
/
div-elim-negpos
int-basic1
/
lst
int-abs
/
lels-01
int-abs
/
forward-le-02
int-basic1
/
numlsf