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Theorem bytes2int-size-04
⊦ b2i(by) < 0 → ~(2 ^ ((n→i(# bytes) + 1) * 8 - 1)) ≤ bytes2int(by ' + bytes)
Type: A user defined theorem
Validity: The proof is valid.
Features:
Comment:
Used by:
int2bytes-len-le-neg
,
int2bytes-len-le-neg-02
,
Used by units in proved state:
Proof exists?: Yes
View
the proof
Infos about the proof
Proved?: Yes
Interactions: 8
Proof steps: 14
Used lemmas:
bytes2int-one
,
bytes2int-rec-01
,
Used spec theorems:
int-pot
/
pot-dist-pos
int-mult
/
modlsp-02
Used simplifier rules:
intops
/
band-max-04
byte
/
band-011x
int-abs
/
anti
int-abs
/
forward-le-04
int-basic2
/
add-zero
intops
/
band-notneg
intops
/
band-associativity
intops
/
band-commutativity
int-abs
/
zero-gels-01
int-abs
/
forward-lsle
int-abs
/
forward-le-01
int-abs
/
lels-03
int-abs
/
lels
nat-basic2
/
s
nat-basic1
/
ref-1
int-mult
/
dist-rmerge
int-abs
/
sub-le-01
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-mult
/
associativity
int-mult
/
commutativity
int-abs
/
sub-eq
int-abs
/
Sub-def
int-mult
/
eq-pos
intnat
/
n2i-add
list
/bytelist/
e-02
list-last
/bytelist/
last-elim
list-last
/bytelist/
bapp
list-last
/bytelist/
l-02
nat-basic2
/
one
list
/bytelist/
len
list
/bytelist/
len-02
list
/bytelist/
a
nat-basic1
/
one
nat-basic2
/
oz
nat-basic2
/
a
nat-basic2
/
c
nat-basic2
/
one-03
list-data
/bytelist/
l
list
/bytelist/
app
list-data
/bytelist/
size-01
int-abs
/
numls-03
byte
/
byte-nls
int-basic2
/
add-a
int-basic2
/
add-c
int-abs
/
forward-le-02
int-abs
/
lels-01
int-abs
/
negle-13