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Theorem intshiftrsign-rec-neg
⊦ i < 0 ∧ 0 < j ∧ j < 32 → i i>> j = (i - 1) / 2 i>> (j - 1)
Type: A user defined theorem
Validity: The proof is valid.
Features:
Comment:
Used by:
intshiftrsign-2pot-neg
,
intshiftrsign-2pot-neg-01
,
Used by units in proved state:
Proof exists?: Yes
View
the proof
Infos about the proof
Proved?: Yes
Interactions: 15
Proof steps: 28
Used lemmas:
band-commutativity
,
band-associativity
,
bitsand-oner
,
band-num
,
band-011x-pos-02
,
intshiftrsign
,
Used spec theorems:
int-div
/
mod-zero-05
int2bits
/
int2bits-rec-neg
list-del
/bitlista/
sublist-num-01
list
/bitlista/
a
list-del
/bitlista/
sublist-append
int2bits
/
bits2int-sign
list-del
/bitlista/
sublist-rec
list-last
/bitlista/
mk-rec
intnat
/
rax-01
Used simplifier rules:
int-abs
/
bet
int-abs
/
sub-eq-01
list
/bitlista/
e-01
list
/bitlista/
c-08
nat
/
pred-03
list
/bitlista/
app-02-ant
list-last
/bitlista/
mk-empty
int2bits
/
int2bits-not-empty
list-data
/bitlista/
l
list-del
/bitlista/
sublist-empty
nat
/
lep
nat-basic2
/
z
list-last
/bitlista/
mk-len
nat
/
lels-01
nat-basic2
/
l-02
nat-basic2
/
pred
nat-basic2
/
oz
nat-basic2
/
a
nat-basic2
/
c
int-abs
/
lels-02
intnat
/
abs-zero
list
/bitlista/
len
int-div
/
mod2-neg-odd
list
/bitlista/
len-02
list-last
/bitlista/
mk-last
list-del
/bitlista/
sublist-num-01
list-del
/bitlista/
sub-zerozero
int2bits
/
bits2int-one
int-abs
/
abs-09
int-abs
/
sub-ls
int-basic1
/
numlslsdel
int-abs
/
sub-le-01
int-abs
/
leone
int-abs
/
anti
list-last
/bitlista/
mk-zero
list
/bitlista/
Nil
list-del
/bitlista/
sub-zero
int2bits
/
int2int-inj
int2bits
/
int2bits-neg-num
bitopsaux
/
invert-zero
bitopsaux
/
inv-one-01
list
/bitlista/
c
bitopsaux
/
succ-zero
bitopsaux
/
sgn-two-01
int2bits
/
bits2int-pos
int2bits
/
bits2uint-one
int2bits
/
bits2uint-one-03
bitlista
/
mklist-num-01
list
/bitlista/
app
int-abs
/
abs-16
int-abs
/
numlelsdel
int-abs
/
zero-gels-01
int-abs
/
forward-le-01
int-abs
/
forward-lsle
list
/bitlista/
in-06
int-abs
/
lels-01
int-basic1
/
ls-01
int2bits
/
int2bits-pos-num
int2bits
/
uint2bits-pos-num
int2bits
/
uint2bits-one
list
/bitlista/
Two
list
/bitlista/
Last
list
/bitlista/
c-07
list
/bitlista/
a
list
/bitlista/
in-append
list
/bitlista/
in-17
int-abs
/
lels-03
int-abs
/
lels
int-abs
/
mone-05
int-abs
/
numle-03
int-basic2
/
add-c
int-basic2
/
add-a
int-abs
/
numsub
int-abs
/
sub-add-01
int-div
/
div-ls-zero
int2bits
/
int2bits-first-02
int2bits
/
int2bits-first-01
int-abs
/
forward-le-02
int-abs
/
forward-le-05
int-basic1
/
forward-pos