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Theorem int2uint-neg
⊦ j < 0 → bits2uint(int2bits(j)) = 2 ^ n→i(# int2bits(j)) + j
Type: A user defined theorem
Validity: The proof is valid.
Features:
Comment:
Used by:
int2int-rest-01
,
Used by units in proved state:
intops
,
bytes
,
Proof exists?: Yes
View
the proof
Infos about the proof
Proved?: Yes
Interactions: 9
Proof steps: 16
Used lemmas:
uint2uint-inv-01
,
uint2bits-2pot-03
,
bits2uint-2pot
,
uint2bits-onein-01
,
uint2bits-expos0
,
uint2bits-sgn-2pot-01
,
int2bits-neg
,
Used spec theorems:
int-pot
/
succ
bitopsaux
/
succ-len
Used simplifier rules:
bitopsaux
/
inv-len
bitopsaux
/
succ-ones
bitopsaux
/
inv-inv
bitopsaux
/
inv-in-01
int-abs
/
neg-03
int-abs
/
sub-eq
int-pot
/
grz
int-mult
/
numeq-04
int-mult
/
one
int-mult
/
associativity
int-mult
/
commutativity
intnat
/
nat2int
int-basic2
/
succ-01
int-basic2
/
ls
int-basic1
/
trans
int-basic1
/
lf-01
int-basic1
/
lf-03
int-basic2
/
ls-02
int-basic1
/
lf-02
int-abs
/
negeq
int-abs
/
negle-07
int-basic2
/
add-zero
int-basic2
/
add-a
int-basic2
/
add-c
int-abs
/
lels-01
int-basic1
/
ls-01
nat-basic2
/
c
nat-basic2
/
a
intnat
/
n2i-add
list
/bitlista/
len-02
list
/bitlista/
len
bitopsaux
/
sgn-base-04
bitopsaux
/
sgn-rec
bitopsaux
/
succ-one
bitopsaux
/
succ-zeros
list
/bitlista/
c-07
list
/bitlista/
in-17
list
/bitlista/
in-append
bitopsaux
/
succ-prefix
list
/bitlista/
c
bitopsaux
/
invert-one
bitopsaux
/
invert-zero
list
/bitlista/
in-13
list
/bitlista/
a
list
/bitlista/
in-14
int-abs
/
lels-03
int-abs
/
lels
int-abs
/
neg
int-abs
/
abs-08