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Theorem band-011x-is-unsigned-fix
⊦ 0 < i → band(j, 2 ^ i - 1) = bits2uint(fix(i→n(i), int2bits(j)))
Type: A user defined theorem
Validity: The proof is valid.
Features:
Comment:
Used by:
band-011x-is-unsigned-fix-01
,
Used by units in proved state:
Proof exists?: Yes
View
the proof
Infos about the proof
Proved?: Yes
Interactions: 10
Proof steps: 19
Used lemmas:
band-commutativity
,
band-associativity
,
band-zero
,
band-011x-is-unsigned-01
,
band-011x-is-lastn
,
Used spec theorems:
bitopsaux
/
fix-shorter
int2bits
/
int2bits-lslen-12
int-abs
/
Abs-pos
int2bits
/
int2bits-len-neg-02
bitopsaux
/
fix-longer
Used simplifier rules:
bitopsaux
/
fix-shorter
bitopsaux
/
fillsgn-longer
nat
/
lels
nat
/
anti
list-del
/bitlista/
lastN-all
nat-basic1
/
lf-01
nat-basic2
/
oz
nat
/
elim-pred-c
int-abs
/
neg-03
int-basic2
/
add-a
int-basic2
/
add-c
int-abs
/
neg-15
int-abs
/
sub-eq
int-basic2
/
add-zero
int-abs
/
neg-10
int-abs
/
neg-02
int-abs
/
neg-05
int-pot
/
pot2-pos
int-abs
/
lels-04
int2bits
/
int2bits-2pot-01
int-pot
/
two-zero
int-abs
/
zero-gels-04
int2bits
/
int2bits-2pot
nat-basic2
/
l
intnat
/
labs
int-abs
/
absle
int-basic1
/
irref
int-abs
/
forward-le-02
int-abs
/
negeq
int-abs
/
abs-08
int-basic1
/
lst-01
nat-basic1
/
ref-1
nat-basic2
/
succ
int2bits
/
int2bits-not-empty
list-data
/bitlista/
l
nat-basic1
/
trans-1
nat-basic1
/
trans
nat
/
succ-01
nat
/
le-num-02
nat
/
le
intnat
/
num-i2n-le-02
int-abs
/
leone
intnat
/
n2n
int-abs
/
abs-06
intnat
/
nat2int
int2bits
/
int2bits-zero
bitopsaux
/
fill-one-02
int2bits
/
bits2uint-zeros-04
int-pot
/
pot2-pos-01
int-abs
/
sub-ls-01
bitlista
/
inmklist-01
list
/bitlista/
c-07
int-abs
/
lels-02
int-basic1
/
ls-01
int-abs
/
lels-01
int2bits
/
int2bits-2pot-02
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
nat-basic1
/
ls-02
intnat
/
abs-zero
nat-basic1
/
f
int-abs
/
lels-03
int-abs
/
lels
nat
/
lels-01
int-abs
/
forward-le-05