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Theorem band-011x-is-unsigned-03
⊦ i→n(i) = # int2bits(j) ∧ 0 < i → band(j, 2 ^ i - 1) = bits2uint(int2bits(j))
Type: A user defined theorem
Validity: The proof is valid.
Features:
Comment:
Used by:
band-011x-is-lastn
,
Used by units in proved state:
Proof exists?: Yes
View
the proof
Infos about the proof
Proved?: Yes
Interactions: 9
Proof steps: 16
Used lemmas:
band-commutativity
,
band-associativity
,
band-num
,
band-011x-is-unsigned-01
,
Used spec theorems:
intnat
/
num-i2n-eq
int2bits
/
int2bits-lslen-12
int-abs
/
Abs-neg
int2bits
/
int2bits-len-neg-02
Used simplifier rules:
nat
/
elim-pred-c
int-abs
/
neg-03
int-basic2
/
add-a
int-basic2
/
add-c
int-pot
/
two-minus
int2bits
/
int2bits-2pot-01
intnat
/
ini2-abs
int-abs
/
neg-15
int-abs
/
sub-eq
int-basic2
/
add-zero
int-abs
/
neg-10
int-abs
/
neg-05
int-pot
/
pot2-pos
int-abs
/
lels-04
intnat
/
n2i-add
intnat
/
i2i-pos-01
int-pot
/
succ
int2bits
/
bits2uint-2pot-02
int-abs
/
absle
int-pot
/
eq-two
int-abs
/
lels-02
int-abs
/
lels
int-abs
/
forward-le-02
int-abs
/
negeq
int-abs
/
neg-06
int-basic1
/
lst-01
int-abs
/
Abs-pos
nat-basic1
/
ref-1
nat-basic1
/
f
nat
/
succ-01
nat
/
le-num-02
nat
/
le
nat
/
lels-01
nat-basic1
/
one-01
int-abs
/
abs-06
int2bits
/
int2bits-zero
int2bits
/
bits2uint-one-02
int-pot
/
pot2-pos-01
int-abs
/
sub-ls-01
bitlista
/
inmklist-01
list
/bitlista/
c-07
int2bits
/
int2bits-2pot-02
intnat
/
n2n
list
/bitlista/
len
list
/bitlista/
len-02
list-last
/bitlista/
mk-len
list
/bitlista/
a
nat
/
add-01
nat-basic2
/
z
nat-basic2
/
a
nat-basic2
/
c
bitopsaux
/
fill-size
int2bits
/
int2bits-not-empty
list-data
/bitlista/
l
nat-basic1
/
z
intnat
/
num-n2i-ls-02
intnat
/
nat2int
int-abs
/
forward-le-05
int-abs
/
lels-01
int-basic1
/
ls-01