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Theorem bytes2bytes-mone
1 < # bytes, b2i(bytes.first) = ~1, 0 ≤ b2i(bytes.rest.first) ⊦ int2bytes(bytes2int(bytes)) = bytes
Type: A user defined theorem
Validity: The proof is valid.
Features:
Comment:
Used by:
bytes2bytes-first-neg
,
bytes2bytes-fix
,
bytes2bytes-identity
,
bytes2bytes-length
,
Used by units in proved state:
Proof exists?: Yes
View
the proof
Infos about the proof
Proved?: Yes
Interactions: 31
Proof steps: 60
Used lemmas:
bytes2bits-empty
,
byte2bits-value
,
bits2bytes-base
,
byte2bits-length
,
bits2bytes-rec
,
byte2bits-first
,
byte2bits-empty
,
byte2bits
,
bytes2bits-one
,
bytes2bits-append
,
bytes2bits-empty-01
,
int2bytes
,
bytes2int
,
Used spec theorems:
list
/bytelist/
lastdiv-rew
bitopsaux
/
sgn-append-01
bitopsaux
/
sgn-base-03
byte
/
ibi
list-del
/bitlista/
lastN-rec-02
list-del
/bitlista/
lastN-all
bitopsaux
/
fill-in
int2bits
/
int2bits-ones
list-del
/bitlista/
lastN-append
bitopsaux
/
fill-length
int2bits
/
bits2int-fill
list
/bytelist/
first-01
Used simplifier rules:
list
/bitlista/
in-empty
nat-basic2
/
one-03
int-abs
/
zero-gels-01
int-abs
/
forward-le-02
int-abs
/
forward-lsle
int-abs
/
lels-01
nat-basic2
/
s
nat-basic1
/
ref-1
list
/bytelist/
app-03
int2bits
/
int2int-inj
nat
/
lels-01
byte
/
byte-len
nat-basic2
/
l-01
list-del
/bitlista/
firstN-len
nat-basic2
/
z
nat
/
add-01
nat
/
lels
nat
/
lep-01
list-data
/bitlista/
l
bitopsaux
/
sgn-empty-01
int-abs
/
forward-le-04
int-abs
/
forward-le-03
int2bits
/
int2bits-not-empty
list
/bitlista/
in-append
list
/bytelist/
e-01
byte
/
ibi
list
/bitlista/
c-07
list
/bytelist/
c-04
list
/bytelist/
app-01
int2bits
/
bits2int-one
list
/bytelist/
Last
list-del
/bitlista/
firstn-one
list
/bitlista/
len
list
/bitlista/
len-02
int-abs
/
zero-gels-04
int-abs
/
lels
int-abs
/
lels-04
list
/bitlista/
in-17
int2bits
/
int2bits-neg-num
int2bits
/
uint2bits-one
list
/bitlista/
Two
bitopsaux
/
invert-zero
bitopsaux
/
inv-one-01
list
/bitlista/
c
list
/bitlista/
a
bitopsaux
/
succ-zero
list
/bitlista/
Last
bitopsaux
/
sgn-two-01
bitopsaux
/
fill-rec-one
bitlista
/
mklist-num-01
list-last
/bitlista/
mk-zero
list
/bitlista/
app
bitopsaux
/
sgn-rec
list
/bitlista/
in-06
list
/bytelist/
e
list
/bytelist/
app
list
/bytelist/
c
list-data
/bytelist/
elim-list-c
list
/bytelist/
first
list
/bytelist/
Nil
list
/bytelist/
rest-01
list
/bytelist/
first-01
nat-basic2
/
c
nat-basic2
/
a
nat-basic2
/
one
list
/bytelist/
a
list
/bytelist/
len-02
list
/bytelist/
len
int-abs
/
forward-le-01
list-data
/bytelist/
l
nat-basic1
/
one
int2bits
/
bits2bits-def
list-data
/bytelist/
size-01