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Theorem nodes-append-subseteq-nodown
# gndx = # lax, # gndx1 = # lax1 ⊦ n ∈ gstore ∧ gstore[n] = groupblock(gndx, lax, m0) → nodes(gstore ↓, ginval) ⊆ nodes(gstore ↓[n, groupblock(gndx + gndx1, lax + lax1, m0)], ginval)
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: 28
Used lemmas:
nodes-write-at-other
,
valid-group-nodes-ls
,
down-store-write-same
,
down-block-explicit
,
down-store-adr-in-explicit-simp
,
nodes-gstore-at
,
down-store-in
,
down-store-at
,
down-store-adr-in-explicit
,
nodes-gstore-in
,
Used spec theorems:
store
/node-store/
Subset
ablock-store-inv
/group-store/
in
list-prefixn
/group-store/
in-prefixn-at-smaller
ablock-store-inv
/group-store/
at
Used simplifier rules:
address-data
/
elim
ablock
/group-store/
elim
store
/group-store-ablock-store-nat-store/
In-insert
groupnode
/
elim
list-prefixn
/laddress-list/
in-prefixn-samepos
store
/group-store-ablock-store-nat-store/
insin
list-prefixn
/laddress-list/
prefixn-in
list-prefixn
/laddress-list/
prefixn-notin
list-del
/laddress-list/
notin-03
list
/laddress-list/
in-append
list
/laddress-list/
in-11
list
/laddress-list/
a
list-del
/laddress-list/
app-05
store
/group-store-ablock-store-nat-store/
At-same
list-del
/group-store/
get-append-less
list
/group-store/
a
nat-basic
/
f
list-prefixn
/laddress-list/
in-prefixn-pos-smaller
list-del
/group-store/
get-append-grt
nat
/
lels
list-prefixn
/laddress-list/
in-prefixn-pos-smaller0
nat
/
le-def
nat
/
le-ls-simp
list-prefixn
/group-store/
prefixn-fulln
list-del
/laddress-list/
inl-01
ablock
/group-store/
inj
store
/group-store-ablock-store-nat-store/
in-neq
store
/group-store-ablock-store-nat-store/
At-other
store
/node-store/
notmemlookup
address-data
/
sel-03
address-data
/
sel-04
address-data
/
sel-05
ablock
/group-store/
sel-01
ablock
/group-store/
sel-02
groupnode
/
inj
store
/group-store-ablock-store-nat-store/
notmemlookup