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Theorem shiftright-rec-neg
⊦ i < 0 ∧ j ≠ 0 → i >> j = (i - 1) / 2 >> (abs(j) - 1)
Type: A user defined theorem
Validity: The proof is valid.
Features:
Comment:
Used by:
shiftright-neg-div
,
shiftright-rec-8-neg
,
shiftright-shift
,
Used by units in proved state:
Proof exists?: Yes
View
the proof
Infos about the proof
Proved?: Yes
Interactions: 31
Proof steps: 57
Used lemmas:
shiftrsign-01
,
Used spec theorems:
int2bits
/
int2bits-rec-neg-01
int2bits
/
int2bits-mone
list-del
/bitlista/
sublist-def
list-del
/bitlista/
firstn-one-01
list-del
/bitlista/
sublist-num
list-del
/bitlista/
firstn-butlast-intro
list-last
/bitlista/
bapp
list-del
/bitlista/
firstN-rec
intnat
/
abs-succ-02
int2bits
/
bits2int-neg-1bit
int2bits
/
bits2int-neg-1bit-01
list-del
/bitlista/
firstn-first
list-last
/bitlista/
mk-first
list-del
/bitlista/
extension
list-last
/bitlista/
lb
int2bits
/
int2bits-mod2-len
Used simplifier rules:
list-data
/bitlista/
size-01
nat-basic1
/
less-1
list-del
/bitlista/
firstN-empty
nat-basic2
/
oz
intnat
/
abs
intnat
/
abs-eq
int2bits
/
int2int-inj
list-del
/bitlista/
first-all
int-abs
/
abs-06
nat
/
pred-03
list-last
/bitlista/
mk-rest-01
list
/bitlista/
c
list
/bitlista/
app
int2bits
/
int2bits-not-empty
list-data
/bitlista/
l
nat-basic2
/
one
nat-basic2
/
one-03
nat-basic2
/
c
nat-basic2
/
a
nat-basic2
/
z-01
nat-basic1
/
one
nat-basic2
/
l
list-last
/bitlista/
mk-len
int-abs
/
zero-gels-03
int-abs
/
lels-01
int-basic1
/
ls-01
list
/bitlista/
len
int-abs
/
sub-eq-01
list-last
/bitlista/
mk-zero
list
/bitlista/
Nil
list
/bitlista/
first
int2bits
/
bits2int-one
list
/bitlista/
e-02
list
/bitlista/
app-02-ant
list-last
/bitlista/
mk-empty
intnat
/
abs-zero
int-abs
/
sub-eq
list
/bitlista/
e
list
/bitlista/
a
list-del
/bitlista/
restN-zero
list
/bitlista/
len-02
int-abs
/
mone-08
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