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Theorem int2bits-len-neg
0 ≤ i, ~(2 ^ (i + 1)) ≤ j, j < ~(2 ^ i) ⊦ # int2bits(j) = i→n(i + 2)
Type: A user defined theorem
Validity: The proof is valid.
Features:
Comment:
Used by:
bits2int-le8
,
int2bits-len-eq
,
int2bits-len-neg-01
,
int2bits-leneq-neg
,
int2bits-lslen-07
,
int2bits-lslen-08
,
Used by units in proved state:
intops
,
bytes
,
byte
,
Proof exists?: Yes
View
the proof
Infos about the proof
Proved?: Yes
Interactions: 19
Proof steps: 30
Used lemmas:
uint2bits-2pot
,
uint2bits-len
,
uint2bits-2pot-03
,
uint2bits-onein-01
,
uint2bits-expos1
,
uint2bits-sgn-2pot-01
,
int2bits-neg
,
Used spec theorems:
intnat
/
add
int-pot
/
two-le
intnat
/
num-n2i-eq
bitopsaux
/
succ-len
int-mult
/
commutativity
int-pot
/
succ
Used simplifier rules:
list-last
/bitlista/
mk-plus
list-last
/bitlista/
mklist-one
list-last
/bitlista/
mk-last
list-last
/bitlista/
mk-len
bitlista
/
inmklist
int-mult
/
numls-13
int-abs
/
zeroone
int-abs
/
anti
bitopsaux
/
inv-len
bitopsaux
/
succ-ones
bitopsaux
/
inv-inv
bitopsaux
/
inv-in-01
intnat
/
rax-04
int-mult
/
zero-ge-add-01
int-abs
/
ler
int-abs
/
succ-02
int-abs
/
numle-02
int-mult
/
numls-12
int-abs
/
mone-06
int-abs
/
numls-02
int-mult
/
numsucc
int-mult
/
dist-rmerge
int-abs
/
les
intnat
/
nat2int
int-pot
/
grz
int-div
/
nummult-ls-02
int-abs
/
numlsf-01
int-abs
/
sub-add-01
int-basic2
/
lst-01
int-abs
/
neg-05
int-abs
/
sub-ls-01
int-abs
/
mone-01
int-abs
/
sub-le-01
int-abs
/
sub-ls
int-abs
/
neg-15
int-basic2
/
zero-02
int-abs
/
neg-13
int-abs
/
neg-03
int-abs
/
numlef
list-data
/bitlista/
l
nat-basic1
/
z
intnat
/
num-n2i-ls-02
int-abs
/
forward-lels
int-pot
/
ls-pos
int-mult
/
zero-ge
int-abs
/
lep
int-abs
/
forward-lele
int-abs
/
negeq
int-abs
/
negle-07
int-basic2
/
add-zero
int-basic1
/
ls-01
nat-basic2
/
c
nat-basic2
/
a
nat
/
add-num-01
int-abs
/
lels-01
int-abs
/
lels-04
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
/
mone-08
int-basic1
/
lf-03
int-basic1
/
lf-02
int-abs
/
lels-03
int-abs
/
lels
int-abs
/
neg
int-abs
/
abs-08
int-mult
/
zero-gr
int-basic2
/
ls-02
int-basic1
/
numlsf
int-abs
/
numls-03
int-basic2
/
ls
int-basic2
/
succ-01
int-basic1
/
trans
int-basic1
/
lf-01
int-mult
/
commutativity
int-mult
/
associativity
int-mult
/
one
int-mult
/
numls-09
int-basic2
/
ls-01
int-abs
/
forward-lsle
int-abs
/
neg-07
int-abs
/
negle-13
int-basic2
/
add-c
int-basic2
/
add-a
int-pot
/
succ