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Theorem band-011x-is-unsigned
⊦ abs(j) ≤ 2 ^ (i - 1) ∧ 0 < i → band(j, 2 ^ i - 1) = bits2uint(fillsgn(i→n(i), int2bits(j)))
Type: A user defined theorem
Validity: The proof is valid.
Features:
Comment:
Used by:
band-011x-is-unsigned-01
,
Used by units in proved state:
Proof exists?: Yes
View
the proof
Infos about the proof
Proved?: Yes
Interactions: 9
Proof steps: 18
Used lemmas:
band-011x-neg
,
band-associativity
,
band-commutativity
,
band-011x-neg-02
,
band-011x-pos
,
Used spec theorems:
int2bits
/
ubits2bits
bitopsaux
/
fill-length
int2bits
/
int2bits-lslen-05
int2bits
/
int2bits-mone
int2bits
/
bits2int-fill
int-div
/
mod-zero-05
Used simplifier rules:
int-abs
/
forward-lele
int-pot
/
two-le
int-abs
/
lep-01
int-abs
/
absle
int2bits
/
int2uint-fill
bitopsaux
/
fill-fill
int2bits
/
int2int-inj
bitopsaux
/
fill-one-02
list-last
/bitlista/
mk-len
int-basic2
/
eq
int-abs
/
numadd-01
list-last
/bitlista/
mk-empty
intnat
/
abs-zero
list
/bitlista/
len-02
int-abs
/
lels-02
intnat
/
num-i2n-ls
int-abs
/
bet-01
int-abs
/
zero-gels-04
int-abs
/
minus-add
int-abs
/
mone-08
intnat
/
i2i-pos
int-abs
/
lels-04
list-data
/bitlista/
l
nat-basic1
/
f
nat
/
lels-01
bitopsaux
/
fill-empty
int2bits
/
int2bits-not-empty
int2bits
/
int2bits-fillfirst
int2bits
/
int2bits-first-01
int-basic2
/
add-in
int-abs
/
abs-05
int-abs
/
subsub
int-abs
/
neg-13
int-abs
/
numls-02
int-abs
/
mone-06
int-basic2
/
ls-01
int-pot
/
ls-pos-2pot
int-abs
/
sub-ls-01
int-basic2
/
ls
int-abs
/
sub-add-01
int-basic2
/
add-c
int-basic2
/
add-a
int-abs
/
Sub-def
int-abs
/
lels
int-abs
/
lels-03
int-abs
/
sub-eq
int-pot
/
pot2-pos
int-abs
/
leone
int-abs
/
sub-le-01
int2bits
/
int2bits-2pot-02
list
/bitlista/
c-07
list
/bitlista/
a
bitlista
/
inmklist-01
int-abs
/
zero-gels-01
int-abs
/
forward-le-02
int-abs
/
forward-lsle
int-abs
/
forward-le-01
int-abs
/
negle-13
int-abs
/
abs-08
int-basic1
/
ls-01
int-abs
/
lels-01
int-abs
/
forward-le-05