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Theorem read-lookup-copy
# ax = # kx ⊦ new(ax, fs) ∧ ¬ dups(ax) ∧ ¬ dups(kx) ∧ ri-cons(ri, fs) ∧ kx.toSet ⊆ dom ri ∧ key ∈ ri → fs[ax, fs[ri[kx]]][ri[kx, ax][key]] = fs[ri[key]]
Type: A user defined theorem
Validity: The proof is valid.
Features: s, ls,
Comment:
Used by:
Used by units in proved state:
Proof exists?: Yes
View
the proof
Infos about the proof
Proved?: Yes
Interactions: 12
Proof steps: 27
Used lemmas:
ri-cons
,
Used spec theorems:
aubifs-base
/
write-shift
aubifs-base
/
update-index-shift
store
/node-index/
At-other
store
/node-store/
At-other
aubifs-base
/
keys-at-other
list
/key-list-set/
in-def
list
/address-list-set/
split-first
list-del
/address-list-set/
get-append-grt
Used simplifier rules:
aubifs-base
/
new-base
list-dup
/address-list-set/
e-01
aubifs-base
/
index-lookup-base
aubifs-base
/
read-base
aubifs-base
/
write-base
aubifs-base
/
index-update-key-base
list-data
/key-list-set/
size-01
list-data
/address-list-set/
l
list-dup
/key-list-set/
dups-cons
aubifs-base
/
index-update-key-rec
list
/node-list/
a
aubifs-base
/
write-rec
list
/node-list/
c
aubifs-base
/
read-rec
aubifs-base
/
index-lookup-rec
aubifs-base
/
index-lookup-length
aubifs-base
/
read-length
store
/node-index/
At-same
store
/node-store/
At-same
list-dup
/key-list-set/
a
aubifs-base
/
index-update-at-last-oc
list-dup
/key-list-set/
f-01
list
/key-list-set/
in-rec
list
/key-list-set/
in-append
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
/
f
nat-basic
/
lf-02
nat-basic
/
l-02
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-data
/key-list-set/
l
list-dup
/address-list-set/
a
list-dup
/address-list-set/
f-01
list-dup
/address-list-set/
dups-cons
list
/address-list-set/
in-06
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
nat
/
lels
nat
/
zero
list-del
/address-list-set/
get-zero-01
list
/address-list-set/
a
list-del
/address-list-set/
get-append-less
list-del
/address-list-set/
get-in
store
/node-store/
notmemlookup