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Theorem ri-inj-index-update
# ax = # kx ⊦ ri-inj(ri) ∧ ¬ dups(ax) ∧ ax.toSet ∩ range ri = ∅ → ri-inj(ri[kx, ax])
Type: A user defined theorem
Validity: The proof is valid.
Features: s, ls,
Comment:
Used by:
index-update-range
,
Used by units in proved state:
gjournal-asm
,
Proof exists?: Yes
View
the proof
Infos about the proof
Proved?: Yes
Interactions: 14
Proof steps: 27
Used lemmas:
Used spec theorems:
list
/key-list-set/
lastdiv-rew
list
/address-list-set/
lastdiv-rew
aubifs-base
/
keys-at-other
list
/key-list-set/
lastoc-rew
list
/address-list-set/
split-first
list-del
/address-list-set/
get-append-grt
store
/node-index/
At-other
Used simplifier rules:
aubifs-inv
/
ri-inj-variant1-01
list-data
/key-list-set/
size-01
list-data
/address-list-set/
l
aubifs-base
/
index-update-key-base
list-dup
/address-list-set/
e-01
list-dup
/address-list-set/
f
aubifs-base
/
update-index-app
list
/address-list-set/
len-02
store
/node-index/
At-other
store+set
/node-index/
In-data-in
aubifs-base
/
keys-at-other
aubifs-base
/
index-update-at-last-oc
nat
/
le-def
nat-basic
/
f
nat-basic
/
lf-02
nat-basic
/
l-02
aubifs-base
/
update-index-append
list
/key-list-set/
len-05
list
/address-list-set/
in-append
list
/address-list-set/
len
set-union
/node-store/
intu-empty
list+set
/address-list-set/
toSet-empty
set-union
/node-store/
int-e
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
/
index-update-in
aubifs-base
/
index-update-key-rec
nat-basic
/
eq-01
nat-basic
/
succ
list
/address-list-set/
len-05
set-union
/node-store/
int-a
aubifs-base
/
range
set-union
/node-store/
int-ins
set-union
/node-store/
unc
set-union
/node-store/
una
set-union
/node-store/
une
set-union
/node-store/
unadd
list+set
/address-list-set/
toSet-one
list+set
/address-list-set/
toSet-app
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-index/
in-neq
store
/node-index/
insin
store
/node-index/
At-same
set-union
/node-store/
int-c
list
/key-list-set/
len
list
/key-list-set/
len-02
list
/key-list-set/
a
nat-basic
/
s-04
oelem
/nat-set/
irreflexivity
nat-basic
/
a
nat-basic
/
c