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Theorem int2bytes-len-le-neg-03
⊦ int2bytes(i).first = i2b(~1) → (# int2bytes(i) ≤ n ↔ ~(2 ^ (8 * n→i(n) - 1)) ≤ i)
Type: A user defined theorem
Validity: The proof is valid.
Features:
Comment:
Used by:
int2bytes-len-eq-neg-01
,
int2bytes-len-ls-neg-01
,
rightshift-8-01-01
,
Used by units in proved state:
Proof exists?: Yes
View
the proof
Infos about the proof
Proved?: Yes
Interactions: 18
Proof steps: 34
Used lemmas:
no-leading-zero-04
,
int2bytes-byte
,
int2bytes-minus-one
,
int2bytes-empty
,
int2int
,
bytes2int-size-07
,
bytes2int-size-05
,
Used spec theorems:
list-data
/bytelist/
length-rest
nat-basic1
/
lstwo
intnat
/
n2i-sub
int-pot
/
ls-pos-2pot
Used simplifier rules:
list
/bytelist/
app-04
list
/bytelist/
e-01
nat-basic1
/
lf-01
nat
/
fle
int-abs
/
sub-ls-01
nat-basic1
/
one
nat
/
lels-02
int-mult
/
ls-pos
intnat
/
le
nat
/
ls-le-simp
nat
/
let
nat
/
lez-01
int-mult
/
zero-gr
int-pot
/
ls-pos-2pot-01
int-abs
/
succ-02
int-mult
/
le-pos
intnat
/
le-int-le-nat
nat
/
succ-01
nat
/
le-ls-simp
nat-basic2
/
a
nat-basic2
/
c
nat-basic1
/
z
intnat
/
num-n2i-ls-02
int-abs
/
leone
int-abs
/
sub-le-01
intnat
/
nat2int
int-abs
/
Sub-def
list
/bytelist/
in-14
list
/bytelist/
onein
list
/bytelist/
c-03
nat
/
not-zero
int-abs
/
lels-03
int-basic2
/
add-zero
int-abs
/
forward-lels
int-basic1
/
numlsf
int-abs
/
numls-03
nat-basic1
/
lf-02
nat-basic1
/
f
nat
/
ls-02
list-data
/bytelist/
l
nat
/
pred-03
list
/bytelist/
c
list
/bytelist/
app
list
/bytelist/
len-02
int-abs
/
minus-add
int-abs
/
sub-ls
int-pot
/
2pot-leone
int-div
/
nummult-ls
intnat
/
nat2int-14
nat
/
lels-01
nat-basic1
/
one-01
list-data
/bytelist/
elim-list
int-abs
/
zero-gels-01
int-mult
/
associativity
int-basic2
/
add-a
intnat
/
num-n2i-ls-07
int-abs
/
numle-02
int-mult
/
zero-ge
int-pot
/
pot2-ls-pred
int-basic2
/
ls-01
int-abs
/
forward-le-01
int-abs
/
forward-le-02
int-abs
/
forward-lsle
int-abs
/
lels-04
int-abs
/
lels
list
/bytelist/
a
int-mult
/
commutativity
int-basic2
/
add-c
int-abs
/
neg-07
int-abs
/
lels-01
int-abs
/
negle-13