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Theorem intshiftrsign-2pot-neg-01
⊦ i < 0 ∧ 0 < j ∧ j < 32 → i i>> j = (i - (2 ^ j - 1)) / 2 ^ j
Type: A user defined theorem
Validity: The proof is valid.
Features:
Comment:
Used by:
intshiftright-ls-02
,
intshiftrsign-2pot-neg-02
,
intshiftrsign-abs-le
,
intshiftrsign-neg-02
,
Used by units in proved state:
byte
,
Proof exists?: Yes
View
the proof
Infos about the proof
Proved?: Yes
Interactions: 19
Proof steps: 29
Used lemmas:
intshiftrsign-rec-neg
,
intshiftrsign-zero
,
Used spec theorems:
int-div
/
two-mult
int-div
/
neg-01
int-div
/
div-twoodd
int-abs
/
Abs-neg
int-pot
/
Pot-pos
int-div
/
div-two-01
int-pot
/
two-zero
Used simplifier rules:
int-mult
/
dist-sub-merge
int-div
/
nummult-ls-01
int-abs
/
numlsledel
int-abs
/
Abs-pos
int-abs
/
neg-13
int-abs
/
numls-02
int-basic1
/
minus-one
int-div
/
minus-add
int-abs
/
succ-01
int-abs
/
minus-sub
int-mult
/
minus-left
int-pot
/
two-lsz
int-abs
/
anti
int-abs
/
leone
int-abs
/
sub-le-01
int-pot
/
pot2-pos
int-mult
/
two-zero
int-abs
/
neg-15
int-abs
/
num-subadd
int-abs
/
neg-06
int-abs
/
negeq
int-abs
/
sub-add-05
int-abs
/
sub-add-06
int-basic2
/
add-zero
int-abs
/
succ-02
int-abs
/
zero-gels-02
int-abs
/
Sub-def
int-mult
/
dist-rmerge
int-mult
/
eq-pos
int-abs
/
sub-pred
int-abs
/
forward-le-01
int-abs
/
zero-gels-01
int-div
/
nummult-ls
int-mult
/
zero-ls
int-abs
/
mone-06
int-abs
/
minus-ass
int-basic1
/
numlsf
int-abs
/
numls-03
int-mult
/
commutativity
int-mult
/
associativity
int-mult
/
succ-rmerge
int-abs
/
forward-le-04
int-abs
/
forward-lels
int-abs
/
zero-gels-03
int-abs
/
sub-eq
int-abs
/
lsone
int-abs
/
lels-01
int-basic1
/
ls-01
int-div
/
div-elim-negpos
int-abs
/
minus-add
int-basic1
/
numlslsdel
int-abs
/
sub-ls
int-abs
/
bet
int-abs
/
sub-ls-01
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
intnat
/
abs-pred
int-abs
/
lels
int-abs
/
lels-03
int-abs
/
numlelsdel
int-abs
/
forward-le-02
int-abs
/
forward-le-05
int-basic1
/
forward-pos
int-abs
/
sub-sub-04