[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 ri-cons-copy-new
# ax = # kx ⊦ ri-cons(ri, fs) ∧ kx.toSet ⊆ dom ri ∧ new(ax, fs) ∧ ¬ dups(kx) ∧ ¬ dups(ax) → ri-cons(ri[kx, ax], fs[ax, fs[ri[kx]]])
Type: A user defined theorem
Validity: The proof is valid.
Features: ss, lss,
Comment:
Used by:
Used by units in proved state:
aubifs-internal-asm
,
Proof exists?: Yes
View
the proof
Infos about the proof
Proved?: Yes
Interactions: 9
Proof steps: 26
Used lemmas:
ri-cons
,
Used spec theorems:
aubifs-base
/
index-update-in
list
/key-list-set/
in-def
list
/address-list-set/
split-first
list-del
/address-list-set/
get-append-grt
aubifs-base
/
at-write-other
Used simplifier rules:
aubifs-base
/
in-write
aubifs-base
/
toSet-subseteq-domri-notin
list-dup
/key-list-set/
a
list
/node-list/
c
aubifs-base
/
read-rec
aubifs-base
/
read-app
aubifs-base
/
index-lookup-rec
aubifs-base
/
index-lookup-app
aubifs-base
/
index-update-at-last-oc
list-dup
/key-list-set/
f-01
set-union
/node-index/
unsub-union-01
store+set
/node-index/
Dom
set-basic
/node-index/
sub-add-03
set-union
/node-index/
unc
set-union
/node-index/
una
set-union
/node-index/
une
set-union
/node-index/
unadd
list+set
/key-list-set/
toSet-one
list+set
/key-list-set/
toSet-app
list
/key-list-set/
len-05
list
/key-list-set/
len
list
/key-list-set/
a
list
/key-list-set/
c
nat
/
le-def
nat-basic
/
l-02
aubifs-base
/
write-app
list
/node-list/
len-05
list
/address-list-set/
in-append
aubifs-base
/
new-append
list
/address-list-set/
len
list-data
/address-list-set/
size-01
nat-basic
/
z-01
list-dup
/address-list-set/
a
list
/node-list/
a
aubifs-base
/
write-rec
list
/address-list-set/
in-rec
list-dup
/address-list-set/
f-01
list-dup
/address-list-set/
dups-cons
aubifs-base
/
new-rec
nat-basic
/
c
nat-basic
/
a
nat-basic
/
eq-01
nat-basic
/
succ
list
/address-list-set/
len-05
list
/address-list-set/
c
list-del
/address-list-set/
get-append-less
list-del
/address-list-set/
get-in
nat-basic
/
f
nat-basic
/
lf-02
nat-basic
/
lf-01
list-data
/key-list-set/
l
nat-basic
/
ls-02
list
/address-list-set/
a
list-del
/address-list-set/
get-zero-01
nat
/
zero
nat
/
ler
nat
/
lels
store
/node-store/
At-same
aubifs-base
/
keys-at-other
aubifs-base
/
index-lookup-length
aubifs-base
/
read-length
aubifs-base
/
new-not-new