[Imprint]
[Data Privacy Statement]
[E-Mail]
View
long theorem info
. View
the proof
. Back to
main index
. View
the specification
. View
theorem base summary
, View
theorem base listing
, the
used properties by spec
, the
dependency list
, the
symbol table
,
Theorem div-div-rec
⊦ j < 0 ∧ 0 < i → ((j - (2 ^ i - 1)) / 2 ^ i - 1) / 2 = (j - (2 ^ (i + 1) - 1)) / 2 ^ (i + 1)
Type: A user defined theorem
Validity: The proof is valid.
Features:
Comment:
Used by:
div-div-rec-01
,
Used by units in proved state:
Proof exists?: Yes
View
the proof
Infos about the proof
Proved?: Yes
Interactions: 35
Proof steps: 44
Used lemmas:
ls-mult-2pot
,
two-zero
,
two-lsz
,
succ
,
two-lez-01
,
zero
,
pot2-pos
,
Used spec theorems:
int-abs
/
zero-gels-02
int-abs
/
numadd
int-mult
/
dist-lsplit
int-mult
/
one-01
int-abs
/
sub-add-01
int-abs
/
sub-shift
int-abs
/
sub-eq-01
int-basic2
/
add-c
int-mult
/
dist-rsplit
int-basic2
/
add-a
int-mult
/
associativity
int-mult
/
commutativity
int-div
/
div-mult-neg
int-abs
/
lstwo
int-abs
/
Abs-neg
Used simplifier rules:
int-abs
/
sub-sub-04
int-abs
/
numls-03
int-abs
/
mone-08
int-div
/
neg-01
int-div
/
div-same
int-basic1
/
ls-01
int-abs
/
forward-le-01
int-mult
/
ls-dist-03
int-abs
/
numsub
int-div
/
div-elim-negpos
int-abs
/
mone-05
int-abs
/
numle-03
int-abs
/
sub-eq
int-basic2
/
add-in
int-abs
/
sub-add-01
int-mult
/
zero-gr-03
int-basic2
/
ls-02
int-abs
/
lels-01
int-mult
/
zero-gr
int-mult
/
dist-rmerge
int-abs
/
abs-07
int-mult
/
zero-ls
int-mult
/
Mult-zero
int-abs
/
sub-sub-03
int-abs
/
forward-le-05
int-basic1
/
forward-pos
int-abs
/
abs-03
int-mult
/
one-01
int-abs
/
forward-lsle
int-abs
/
lsone
int-div
/
nummult-ls
int-abs
/
sub-le
int-abs
/
neg-15
int-mult
/
minus-one-01
int-abs
/
minus-add
int-abs
/
forward-le-02
int-abs
/
zero-gels-01
int-abs
/
zero-gels-03
int-abs
/
numadd-01
int-abs
/
negeq
int-mult
/
succ-rmerge
int-abs
/
Sub-def
int-div
/
div-mult-03
int-abs
/
forward-lele
int-abs
/
forward-le-04
int-abs
/
forward-lels
int-mult
/
one
int-mult
/
numle-13
int-abs
/
sub-le-01
int-abs
/
minus-sub
int-abs
/
sub-ls
int-abs
/
neg-06
int-abs
/
neg-13
int-abs
/
lels-04
int-abs
/
Abs-pos
int-abs
/
lels
int-abs
/
anti
int-basic2
/
add-zero
int-basic2
/
add-a
int-basic2
/
add-c
int-div
/
div-mult-01
int-mult
/
associativity
int-mult
/
commutativity
int-abs
/
zero-gels-04