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Theorem bits2int-pos
⊦ bits ≠ [] → (0 ≤ bytes2int(bits2bytes(bits)) ↔ ¬ bits.first)
Type: A user defined theorem
Validity: The proof is valid.
Features: localsimp, simp,
Comment:
Used by:
bits2int-neg
,
fix-bits2bytes
,
fix-bits2bytes-01
,
Used by units in proved state:
Proof exists?: Yes
View
the proof
Infos about the proof
Proved?: Yes
Interactions: 34
Proof steps: 58
Used lemmas:
bytes2int-one
,
byte2bits
,
bytes2bits-rec
,
bits2bytes-rec-01
,
bits2bits-inj
,
bytes2int
,
bits2bytes-base
,
Used spec theorems:
nat-div
/
mod-nls
int2bits
/
bits2int-neg
int2bits
/
bits2bits-def
int2bits
/
bits2int-neg-03
int2bits
/
int2bits-pos
int2bits
/
bits2int-lez
list
/bitlista/
first-01
bitopsaux
/
fill-first
byte
/
num-ibbi
int2bits
/
bits2int-le8
int2bits
/
bits2uint-ls
int2bits
/
bits2uint-not-zero
Used simplifier rules:
int-abs
/
sub-le
int-abs
/
minus-add
int-abs
/
numle-02
int-abs
/
negle-13
int-abs
/
numls-03
int-abs
/
neg-07
int2bits
/
uint2bits-first-02
int-abs
/
zero-gels-04
int2bits
/
uint2bits-empty
int-abs
/
numleledel-01
int-basic2
/
num-between
int-abs
/
lels
int-abs
/
forward-le-02
bitopsaux
/
inv-append
bitopsaux
/
sgn-first
bitopsaux
/
fill-empty
bitopsaux
/
sgn-not-empty-01
int-abs
/
forward-lele
int-abs
/
neg
int-basic1
/
numlslsdel-01
int-basic1
/
forward-pos
int-abs
/
forward-le-05
nat
/
le-ls-simp
int-abs
/
zero-gels-01
int-abs
/
forward-lsle
int-basic1
/
numlsf
int-abs
/
forward-le-01
list
/bytelist/
a
nat
/
fle-01
list-del
/bitlista/
first-length
list-del
/bitlista/
restN-rec
list
/bitlista/
c-07
list
/bitlista/
c-08
list-del
/bitlista/
firstN-rec
nat-div
/
mod-succ-06
nat-basic2
/
oz
nat
/
l-num-04
nat
/
lels
nat
/
ls-le-simp
int2bits
/
bits2uint-zeros
bitopsaux
/
succ-truein-01
int2bits
/
bits2uint-not-neg-01
int-abs
/
lels-01
int2bits
/
bits2int-pos
int2bits
/
bits2uint-not-neg
int-basic2
/
add-c
int-basic2
/
add-a
int-basic2
/
add-zero
int-abs
/
negle-07
bitopsaux
/
invert-one
int2bits
/
bits2int-neg
list
/bitlista/
app-02-ant
list
/bitlista/
e
list-data
/bitlista/
l
nat-basic1
/
f
nat-basic2
/
c
nat-basic2
/
a
nat
/
lels-01
nat
/
le-num-05
list
/bitlista/
len-02
list
/bitlista/
len
list
/bitlista/
a
list
/bitlista/
e-01
list
/bitlista/
c
list-data
/bitlista/
elim-list-c