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Theorem shiftright-neg-div
⊦ i < ~(2 ^ (abs(j) - 1)) ∧ j ≠ 0 → i >> j = (i - (2 ^ abs(j) - 1)) / 2 ^ abs(j)
Type: A user defined theorem
Validity: The proof is valid.
Features:
Comment:
Used by:
shiftright-neg-div-01
,
shiftright-neg-div-02
,
shiftright-rec-8-neg
,
Used by units in proved state:
Proof exists?: Yes
View
the proof
Infos about the proof
Proved?: Yes
Interactions: 29
Proof steps: 47
Used lemmas:
rightshift-zero
,
shiftright-rec-neg
,
shiftright-abs
,
Used spec theorems:
int-mult
/
dist-rsplit
int-div
/
divmult
int-abs
/
Abs-pos
int-pot
/
Pot-pos
int-div
/
div-two-intro
int-pot
/
two-zero
int-div
/
div-mult
int-div
/
div-add1-negneg
int-abs
/
zero-gels-02
int-mult
/
dist-sub-split
Used simplifier rules:
int-abs
/
Sub-def
int-mult
/
eq-pos
int-basic2
/
add-in
int-abs
/
neg-06
int-mult
/
two-zero
int-div
/
neg-01
int-div
/
div-mult-01
int-mult
/
minus-left
int-abs
/
subsub
int-abs
/
negeq
int-mult
/
zero-le
int-pot
/
two-lez-01
int-pot
/
pot2-pos
int-mult
/
zero-gr
int-abs
/
mone-08
int-abs
/
anti
int-div
/
mod-two-02
int-div
/
div-mult-03
int-mult
/
zero-ls
int-div
/
nummult-ls
int-mult
/
zero-eq
int-basic2
/
num-between
int-abs
/
numlelsdel
int-abs
/
sub-zero-01
int-mult
/
zero-neq-01
int-div
/
mod-zero-num
int-basic1
/
numlsf
int-mult
/
succ-rmerge
int-abs
/
sub-eq
int-abs
/
sub-ls
int-abs
/
zero-gels-03
int-mult
/
dist-rmerge
int-abs
/
zero-gels-04
int-abs
/
abs-08
int-abs
/
neg-13
int-abs
/
numls-02
int-basic1
/
minus-one
int-abs
/
forward-lele
int-abs
/
forward-le-04
int-abs
/
mone-06
int-basic2
/
add-zero
int-mult
/
numls-05
int-mult
/
numls-07
int-mult
/
minus-one-01
int-abs
/
neg
int-div
/
div-elim-negpos
int-abs
/
sub-add-01
int-abs
/
leone
int-basic1
/
ls-01
int-mult
/
zero-ge
int-abs
/
lels-01
int-abs
/
lels-04
int-abs
/
abs-06
int-mult
/
commutativity
int-mult
/
associativity
int-mult
/
one
int-mult
/
numls-03
int-basic1
/
forward-pos
int-abs
/
forward-le-05
int-abs
/
sub-pred
int-abs
/
abs-zero
int-abs
/
lsone
int-abs
/
lels-02
int-abs
/
sub-eq-01
int-abs
/
numls-03
int-abs
/
numsub
int-abs
/
minus-add
int-abs
/
sub-ls-01
int-abs
/
minus-ass
int-abs
/
zero-gels-01
int-abs
/
abs-10
int-abs
/
sub-le-01
int-abs
/
lep-01
intnat
/
labs
int-abs
/
abs-01
int-abs
/
lels
int-abs
/
abs-07
int-abs
/
forward-le-01
int-abs
/
forward-lsle
int-basic2
/
ls
int-pot
/
two-lsz
int-basic2
/
add-a
int-basic2
/
add-c
int-abs
/
forward-le-02
int-abs
/
neg-07
int-abs
/
sub-sub-04