[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 and-011x-neg
¬ false ∈ bits0, bits ≠ [], bits.first, bitsand(false ' + bits0, bits) = false ' + bits1 ⊦ bits2uint(bits1) = 2 ^ n→i(# bits0) - bits2uint(bitsinvert(bits)) % 2 ^ n→i(# bits0) + 1
Type: A user defined theorem
Validity: The proof is valid.
Features:
Comment:
Used by:
band-011x-neg
,
Used by units in proved state:
Proof exists?: Yes
View
the proof
Infos about the proof
Proved?: Yes
Interactions: 15
Proof steps: 32
Used lemmas:
and-notempty-05
,
and-oner-01
,
and-zero-01
,
and-rec
,
Used spec theorems:
int2bits
/
bits2uint-ones
list-last
/bitlista/
splitlasteq
int2bits
/
bits2uint-rec-02
int-div
/
mod-twoodd
int-pot
/
succ
Used simplifier rules:
int-abs
/
sub-eq
list-data
/bitlista/
elim-list-c
int2bits
/
bits2uint-zeros-03
bitopsaux
/
invert-one
nat-basic2
/
one-03
list
/bitlista/
c-03
int-div
/
mod-one
int-abs
/
numadd-01
list
/bitlista/
in-empty
int-div
/
mod-zero-04
bitopsaux
/
invert-base
list
/bitlista/
app-01
int-abs
/
Sub-def
list-data
/bitlista/
size-01
int2bits
/
bits2uint-base
list-data
/bitlista/
l
list
/bitlista/
c
list-data
/bitlista/
lf-01
nat-basic2
/
one
nat-basic2
/
oz
nat-basic1
/
one
list
/bitlista/
Last
intnat
/
n2i-add
list
/bitlista/
in-15
bitopsaux
/
inv-one
bitopsaux
/
inv-append
list
/bitlista/
app
list
/bitlista/
c-05
list
/bitlista/
ni
list
/bitlista/
inapp-07
list
/bitlista/
app-02-ant
list
/bitlista/
e
list
/bitlista/
in-17
list
/bitlista/
in-append
list
/bitlista/
in-14
list-last
/bitlista/
lin-01
list-last
/bitlista/
l-02
list
/bitlista/
e-01
list-last
/bitlista/
l-in
list-last
/bitlista/
bapp
list-last
/bitlista/
last-elim
list
/bitlista/
e-02
list
/bitlista/
len
list
/bitlista/
len-02
nat-basic2
/
s
nat-basic1
/
ref-1
nat-basic2
/
a
nat-basic2
/
c
int2bits
/
bits2uint-one
int-basic1
/
lf-02
int-abs
/
lels-01
int2bits
/
bits2uint-not-neg-01
int-pot
/
grz
int-mult
/
succ-rmerge
list
/bitlista/
a
int2bits
/
bits2uint-zero
int-pot
/
two-zero-01
int-div
/
mod-mult-02
int-mult
/
associativity
int-mult
/
commutativity
int-mult
/
dist-rmerge
int-basic2
/
add-a
int-basic2
/
add-c
int-mult
/
eq-pos
intnat
/
nat2int