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Theorem int2bits-len-range
~(2 ^ i) ≤ j, j < 2 ^ i ⊦ # int2bits(j) ≤ i→n(i + 1)
Type: A user defined theorem
Validity: The proof is valid.
Features:
Comment:
Used by:
int2bits-len-pos-01
,
Used by units in proved state:
bytes
,
byte
,
Proof exists?: Yes
View
the proof
Infos about the proof
Proved?: Yes
Interactions: 10
Proof steps: 20
Used lemmas:
int2bits-len-neg-01
,
int2bits-len-pos
,
int2bits-zero
,
int2bits-not-empty
,
Used spec theorems:
int-pot
/
exin2pot
int-abs
/
Abs-neg
intnat
/
add-01
Used simplifier rules:
int-basic1
/
lf-02
int-abs
/
numle-03
int-abs
/
mone-05
int-basic2
/
lst-04
int-mult
/
numls-08
int-abs
/
lels-02
int-abs
/
negeq
nat-basic2
/
l
int-abs
/
numsub
int-abs
/
leone
int-abs
/
anti
int-abs
/
sub-add-01
int-abs
/
sub-le
int-abs
/
succ-01
int-abs
/
lep-01
int-abs
/
Sub-def
int-basic1
/
lf-03
int-abs
/
numls-02
int-abs
/
mone-06
nat-basic2
/
l-02
int-abs
/
sub-le-01
int-mult
/
pred-rmerge
int-basic2
/
zero-02
int-abs
/
sub-ls
int-abs
/
neg-03
int-abs
/
neg-05
int-abs
/
neg-15
int-pot
/
two-zero
int-abs
/
neg-10
int-abs
/
subsub
intnat
/
rax-04
int-basic2
/
succ-01
int-basic2
/
ls-02
int-basic2
/
ls
int-mult
/
ls-same-01
int-basic2
/
ls-01
int-pot
/
two-le
int-abs
/
lep-02
int-abs
/
forward-lele
int-abs
/
neg-13
int-abs
/
negle-07
int-abs
/
neg-06
int-abs
/
lels-04
nat
/
l-num-01
nat-basic2
/
s
intnat
/
labs
int-abs
/
absle
int-abs
/
abs-16
nat-basic2
/
a
nat-basic2
/
c
nat-basic1
/
lf-01
int-abs
/
lels
int-abs
/
lels-03
intnat
/
abs-succ-03
int-abs
/
numlsf-01
int-mult
/
zero-gr
int-div
/
nummult-ls-02
int-pot
/
ls-pos
int-basic1
/
trans
int-basic1
/
lf-01
int-basic1
/
ls-01
int-abs
/
Abs-pos
int-basic1
/
lst-01
int-abs
/
forward-lsle
int-mult
/
commutativity
int-mult
/
associativity
int-mult
/
one
int-mult
/
numls-09
int-abs
/
forward-lels
int-pot
/
succ
int-pot
/
two-minus
int-basic1
/
numlsf
int-abs
/
lels-01
int-abs
/
numle-02
intnat
/
num-i2n-ls
int-abs
/
numls-03
int-abs
/
numadd-01
intnat
/
abs-zero
nat-basic1
/
one-01
list
/bitlista/
len-02
int-basic2
/
add-c
int-basic2
/
add-a
int-basic2
/
add-zero
int-abs
/
abs-06
list-data
/bitlista/
l
nat-basic1
/
f
nat
/
lels-01
int-abs
/
negle-13