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Theorem index-update-adr-in
⊦ ¬ dups(kx) ∧ # kx = # ax → (adr ∈ ri[kx, ax] ↔ adr ∈ ax ∨ adr ∈ range(ri \ kx.toSet))
Type: A user defined theorem
Validity: The proof is valid.
Features: ws, lws,
Comment:
Used by:
Used by units in proved state:
Proof exists?: Yes
View
the proof
Infos about the proof
Proved?: Yes
Interactions: 14
Proof steps: 31
Used lemmas:
toSet-diff-in
,
toSet-diff-get
,
Used spec theorems:
store+set
/node-index/
Diff-rec
store+set
/node-index/
Data-in
Used simplifier rules:
aubifs-base
/
range
list-data
/key-list-set/
size-01
list-data
/address-list-set/
l
list+set
/key-list-set/
toSet-empty
store+set
/node-index/
Diff-base
aubifs-base
/
update-index-data-notin
list-dup
/key-list-set/
e-01
aubifs-base
/
index-update-key-base
list
/address-list-set/
in-empty
list-dup
/key-list-set/
dups-cons
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/
c
list-data
/address-list-set/
size-01
nat-basic
/
z-01
list-data
/key-list-set/
l
list
/address-list-set/
in-rec
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
store
/node-index/
in-neq
store
/node-index/
At-other
store
/node-index/
insin
store
/node-index/
At-same
store
/node-index/
Del-at
list+set
/key-list-set/
toSet-ext
store+set
/node-index/
Diff-ext
store
/node-index/
Del-in