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Theorem bytes2bytes-zero
1 < # bytes, b2i(bytes.first) = 0, b2i(bytes.rest.first) < 0 ⊦ 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
,
no-leading-zero-03
,
Used by units in proved state:
Proof exists?: Yes
View
the proof
Infos about the proof
Proved?: Yes
Interactions: 25
Proof steps: 49
Used lemmas:
byte2bits-value
,
byte2bits-length
,
bits2bytes-base
,
bits2bytes-rec
,
byte2bits
,
bytes2bits-empty
,
byte2bits-empty
,
int2bytes
,
bytes2bits-one
,
bytes2bits-append
,
bytes2int
,
Used spec theorems:
bitopsaux
/
sgn-append-04
bitopsaux
/
sgn-base-03
bitopsaux
/
fill-length
int2bits
/
bits2int-fill
list-del
/bitlista/
firstn-one-01
list
/bytelist/
lastdiv-rew
list
/bitlista/
a
bitopsaux
/
sgn-append-01
bitopsaux
/
fill-in
list-del
/bitlista/
lastN-append
Used simplifier rules:
int-abs
/
lels-03
int-abs
/
lels
nat-basic2
/
s
nat-basic1
/
ref-1
nat-basic2
/
l-01
list-del
/bitlista/
firstN-len
nat-basic2
/
z
nat
/
add-01
nat
/
lep-01
bitopsaux
/
sgn-empty-01
int2bits
/
int2bits-truein
int-abs
/
forward-le-05
list
/bitlista/
in-06
list
/bitlista/
in-append
int2bits
/
bits2int-zero
list
/bytelist/
c-04
byte
/
byte-equal-01
list
/bitlista/
e-01
list
/bitlista/
c-08
list
/bytelist/
app-03
byte
/
ibi
int2bits
/
int2int-inj
nat-basic1
/
lf-01
list-data
/bitlista/
l
nat-basic1
/
f
list
/bytelist/
Last
nat
/
lels-01
byte
/
byte-len
nat
/
lels
nat
/
l-num-04
list
/bitlista/
len-02
list
/bitlista/
len
bitopsaux
/
fill-empty
int2bits
/
int2bits-not-empty
int2bits
/
int2bits-fillfirst
int2bits
/
int2bits-first-01
list
/bitlista/
in-17
list
/bitlista/
e
bitopsaux
/
sgn-rec
list-last
/bitlista/
mk-zero
bitlista
/
mklist-num
bitopsaux
/
fill-rec-one
int2bits
/
int2bits-zero
list
/bytelist/
app
list
/bitlista/
app
int2bits
/
bits2bits-def
list
/bitlista/
app-02-ant
list
/bitlista/
a
list
/bytelist/
e-01
nat-basic2
/
c
nat-basic2
/
a
nat-basic2
/
one
list
/bytelist/
a
list
/bytelist/
len-02
list
/bytelist/
len
list
/bytelist/
c
int-abs
/
forward-le-02
list-data
/bytelist/
l
nat-basic1
/
one
list-data
/bytelist/
elim-list-c