[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 int2bits-rec-2pot-neg-02
⊦ j ≤ ~(2 ^ i) ∧ 0 < i ∧ j % 2 ^ i ≠ 0 → int2bits(j) = int2bits(j / 2 ^ i - 1) + fillsgn(i→n(i + 1), int2bits(j % 2 ^ i)).rest
Type: A user defined theorem
Validity: The proof is valid.
Features:
Comment:
Used by:
int2bits-rec-2pot-neg-03
,
Used by units in proved state:
intops
,
bytes
,
Proof exists?: Yes
View
the proof
Infos about the proof
Proved?: Yes
Interactions: 48
Proof steps: 82
Used lemmas:
int2int-inj
,
uint2int-01
,
bits2int-inv
,
int2bits-neg-01
,
uint2bits-len-max
,
bits2int-sgn
,
bits2int-inj
,
uint2bits-first-05
,
uint2bits-empty-01
,
uint2bits-first-04
,
uint2bits-one
,
uint2bits-zero
,
uint2bits-onein
,
uint2bits-truein
,
uint2bits-onein-01
,
uint2bits-empty
,
uint2bits-2potrec
,
int2bits-neg
,
Used spec theorems:
bitopsaux
/
succ-zero-02
int-div
/
mod-grz-01
int-div
/
div-zero-ngr
bitopsaux
/
sgn-append-01
int-div
/
div-eq-zero-01
list
/bitlista/
In
int-div
/
mod-grz
bitopsaux
/
invert-rest
bitopsaux
/
inv-fill
bitopsaux
/
succ-rest
bitopsaux
/
fill-fill
bitopsaux
/
fillsgn-longer
list-last
/bitlista/
mk-rest-01
bitopsaux
/
succ-fill
bitopsaux
/
fill-sgn-01
bitopsaux
/
succ-len
int-abs
/
numle-03
int-abs
/
minus-neg
int-basic2
/
add-zero-rev
int-div
/
mod-neg-01
int-div
/
mod-les
Used simplifier rules:
int-abs
/
sub-eq
int-abs
/
neg-02
int-abs
/
subsub
int-abs
/
minus-sub
int-abs
/
negeq
int-abs
/
Sub-def
int-abs
/
sub-ls-01
nat
/
ls-le-simp
list
/bitlista/
e-01
list
/bitlista/
len
list
/bitlista/
len-02
nat-basic2
/
l
nat
/
lep-02
nat
/
zero
nat
/
cancel-01
nat
/
pred-03
bitopsaux
/
inv-mklist
nat
/
zero-02
nat
/
lels-02
nat-basic2
/
s
nat-basic2
/
z
nat-basic2
/
pred
bitopsaux
/
inv-inv
bitopsaux
/
inv-rest
bitopsaux
/
inv-len
bitopsaux
/
succ-ones
bitopsaux
/
fill-empty
list
/bitlista/
app-01
bitopsaux
/
sgn-sgn
bitopsaux
/
sgn-empty-01
bitopsaux
/
inv-empty
bitopsaux
/
succ-empty-01
list
/bitlista/
in-14
list
/bitlista/
app-03
list
/bitlista/
c-04
bitopsaux
/
inv-one
list-data
/bitlista/
elim-list
list
/bitlista/
Nil
int-abs
/
zero-gels-03
int-pot
/
abs-2pot
int-abs
/
neg-13
list
/bitlista/
in-17
bitopsaux
/
sgn-two-01
list
/bitlista/
Last
bitopsaux
/
succ-zero
list
/bitlista/
c
bitopsaux
/
inv-one-01
bitopsaux
/
invert-zero
list
/bitlista/
Two
bitopsaux
/
inv-false
int-abs
/
anti
bitopsaux
/
inv-in-01
bitopsaux
/
inv-in-02
int-abs
/
neg-15
int-abs
/
minus-02
int-abs
/
lsone
int-abs
/
sub-ls
int-abs
/
lels-02
int-abs
/
neg
int-pot
/
pot2-pos
int-basic1
/
lst-01
list
/bitlista/
in-append
list-last
/bitlista/
mklist-one
nat
/
add-01
int-abs
/
lels-03
int-basic2
/
add-zero
bitlista
/
inmklist
nat
/
lez
list-data
/bitlista/
size-01
list
/bitlista/
c-07
list-last
/bitlista/
mk-last
list
/bitlista/
app
list-last
/bitlista/
mk-zero
bitlista
/
mklist-num
list-last
/bitlista/
mk-plus
bitopsaux
/
fillsgn-empty
nat-basic2
/
l-02
list-data
/bitlista/
l
nat-basic1
/
f
nat
/
fle
nat
/
lels-01
nat-basic2
/
a
nat
/
lels
nat
/
succ-01
nat-basic2
/
c
bitopsaux
/
succ-zeros
int-abs
/
zero-gels-01
int-abs
/
forward-lsle
int-abs
/
zero-gels-04
list
/bitlista/
a
bitopsaux
/
inv-append
int-div
/
mod-neg-01
int-div
/
neg-01
int-pot
/
two-zero
int-abs
/
lels-01
int-abs
/
lels-04
int-abs
/
forward-le-02
int-abs
/
abs-08
int-abs
/
forward-le-05
int-abs
/
forward-le-04
int-abs
/
forward-lels
int-abs
/
negle-07
intnat
/
abs-succ-03
int-abs
/
lels
int-abs
/
forward-le-01
int-abs
/
forward-lele
int-abs
/
lep-01
int-pot
/
two-lez-01
int-basic1
/
ls-01
int-basic2
/
add-a
int-basic2
/
add-c