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Theorem bytes2int-size-07
⊦ 0 ≤ b2i(by) → bytes2int(i2b(~1) ' + by ' + bytes) < ~(2 ^ (8 * (n→i(# bytes) + 1) - 1))
Type: A user defined theorem
Validity: The proof is valid.
Features:
Comment:
Used by:
int2bytes-len-le-neg-01
,
int2bytes-len-le-neg-03
,
Used by units in proved state:
Proof exists?: Yes
View
the proof
Infos about the proof
Proved?: Yes
Interactions: 9
Proof steps: 17
Used lemmas:
bytes2int-one
,
bytes2int-rec-01
,
Used spec theorems:
int-pot
/
pot-dist-pos
int-mult
/
modlep
Used simplifier rules:
intops
/
band-max-04
intops
/
band-notneg
int-abs
/
lels-03
int-abs
/
forward-le-05
int-mult
/
numls-12
int-mult
/
dist-rmerge
int-abs
/
leone
int-mult
/
zero-gr
int-abs
/
numls-02
int-abs
/
mone-06
intnat
/
nat2int
int-abs
/
sub-add-01
int-mult
/
succ-rmerge
int-abs
/
sub-eq
int-abs
/
Sub-def
int-mult
/
eq-pos
int-abs
/
zero-gels-01
int-mult
/
commutativity
int-mult
/
associativity
int-mult
/
numls-04
int-abs
/
forward-le-02
int-abs
/
forward-lsle
int-abs
/
lels-04
int-abs
/
lels-01
nat-basic2
/
s
nat-basic1
/
ref-1
intnat
/
n2i-add
list
/bytelist/
e-02
list-last
/bytelist/
last-elim
list-last
/bytelist/
l-02
list-last
/bytelist/
bapp
list
/bytelist/
app
list-last
/bytelist/
b
byte
/
num-ibbi
list-last
/bytelist/
l
intops
/
band-255-pos
byte
/
byte-mod-100x
intops
/
band-associativity
intops
/
band-commutativity
list-data
/bytelist/
size-01
int-abs
/
minus-add
int-basic2
/
add-a
int-basic2
/
add-c
int-abs
/
sub-le-01
byte
/
byte-nge
list-last
/bytelist/
bin
list-last
/bytelist/
l-05
list-data
/bytelist/
l
nat-basic2
/
one
list
/bytelist/
len
list
/bytelist/
len-02
list
/bytelist/
a
nat-basic1
/
one
nat-basic2
/
z-01
nat-basic2
/
a
nat-basic2
/
c
nat
/
add-num-03
int-abs
/
forward-le-01
int-abs
/
lels
int-abs
/
neg-07