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Theorem intshiftrzero-prop-01
i < 0, ~(2 ^ 31) ≤ i, band(j, 31) ≠ 0 ⊦ i i>>> j = (i i>> j) + (2 i<< bcompl(j))
Type: A user defined theorem
Validity: The proof is valid.
Features:
Comment:
Used by:
Used by units in proved state:
Proof exists?: Yes
View
the proof
Infos about the proof
Proved?: Yes
Interactions: 26
Proof steps: 50
Used lemmas:
intshiftrsign32
,
band-ls-zero-01
,
band-associativity
,
band-max-02
,
band-011x-eq-01
,
band-commutativity
,
band-011x-neg-03
,
intshiftleft
,
compl-def
,
intshiftrzero-def
,
Used spec theorems:
intnat
/
sub
int2bits
/
int2bits-pos
list-last
/bitlista/
mk-succ
int2bits
/
int2bits-lslen-05
int2bits
/
int2bits-mone
list-del
/bitlista/
sublist-def
list-del
/bitlista/
firstn-app-02
nat
/
zero-02
int2bits
/
bits2int-mklist-05
int2bits
/
ubits2bits
list-del
/bitlista/
firstn-first
int2bits
/
bits2int-sign
intnat
/
n2i-sub
int-pot
/
Pot-pos
Used simplifier rules:
int-abs
/
numlsledel
int-basic2
/
add-zero
int-abs
/
sub-ls-01
int-abs
/
sub-pred
int-abs
/
minus-ass
int-mult
/
eq-pos
nat
/
zero-02
int-basic2
/
add-in
list-del
/bitlista/
first-length
bitopsaux
/
fill-empty
int2bits
/
int2bits-fillfirst
list-del
/bitlista/
firstN-empty
int2bits
/
bits2int-mklist-05
intnat
/
abs-zero
intnat
/
num-i2n-eq
int-abs
/
sub-eq-01
int-mult
/
eq-one
int-mult
/
associativity
int-mult
/
commutativity
list-del
/bitlista/
firstN-zero
nat
/
lep
list-last
/bitlista/
mk-len
nat-basic2
/
l-02
list-del
/bitlista/
restN-zero
int2bits
/
int2bits-first-01
bitopsaux
/
fill-length
bitopsaux
/
fill-rec-one
bitlista
/
mklist-num-01
list
/bitlista/
len
list
/bitlista/
len-02
int-abs
/
mone-08
int-abs
/
lels
int-abs
/
numle-02
int-abs
/
numleledel-01
list-data
/bitlista/
l
nat-basic1
/
f
nat
/
lels-01
intnat
/
i2i-pos
intnat
/
num-i2n-le
int-abs
/
numleledel
int2bits
/
bits2uint-2pot-02
int2bits
/
bits2uint-zero
nat-basic2
/
c
nat-basic2
/
a
list
/bitlista/
app
list-last
/bitlista/
mk-zero
bitlista
/
mklist-num
list-last
/bitlista/
mk-plus
int2bits
/
bits2int-pos
int-abs
/
forward-le-05
int-abs
/
lels-02
int-abs
/
lels-01
int-basic2
/
add-c
int-basic2
/
add-a
int-abs
/
num-subadd
int2bits
/
uint2bits-pos-num
int2bits
/
uint2bits-one
list
/bitlista/
Two
list
/bitlista/
Last
list
/bitlista/
app-01
list
/bitlista/
in-append
list
/bitlista/
in-17
list
/bitlista/
in-15
list
/bitlista/
in-14
list
/bitlista/
a
int2bits
/
int2bits-first-05
list
/bitlista/
c
int2bits
/
int2bits-not-empty
list-data
/bitlista/
elim-list-c
int-abs
/
subsub
int-abs
/
forward-le-02
int-abs
/
forward-lels