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Theorem in-ri-update-in-ri
# ax0 = # ax ⊦ ax0.toSet ⊆ range ri ∧ ri-cons(ri, fs) → (key ∈ ri[keys(fs, ax0), ax] ↔ key ∈ ri)
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: 9
Proof steps: 19
Used lemmas:
key-cons
,
ri-cons
,
Used spec theorems:
store
/node-index/
In-insert
aubifs-base
/
index-update-in
store+set
/node-index/
Data-in
Used simplifier rules:
aubifs-base
/
keys-base
list+set
/address-list-set/
toSet-empty
set-basic
/node-store/
sub-e
aubifs-base
/
index-update-key-base
aubifs-base
/
range
set-basic
/node-store/
sub-add-03
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
/key-list-set/
c
aubifs-base
/
keys-rec
list-data
/address-list-set/
size-01
nat-basic
/
z-01
list-data
/address-list-set/
l
list
/key-list-set/
a
aubifs-base
/
index-update-key-rec
nat-basic
/
c
nat-basic
/
a
nat-basic
/
eq-01
list
/address-list-set/
a
nat-basic
/
succ
list
/address-list-set/
len-05
list
/address-list-set/
c
aubifs-base
/
keys-length