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Theorem nodes-append-subseteq
# gndx = # lax, n0 ≤ m0 ⊦ n ∈ gstore ∧ gstore[n] = groupblock(gndx, lax, n0) → nodes(gstore ↓, ginval) ⊆ nodes(gstore ↓[n, groupblock(gndx + gnd ', lax + ladr ', 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: 14
Proof steps: 39
Used lemmas:
nodes-write-at-other
,
valid-group-nodes-ls
,
down-store-write-same
,
nodes-gstore-at
,
down-store-in
,
down-store-at
,
down-store-adr-in-explicit
,
nodes-gstore-in
,
valid-group-nodes-rec
,
down-block-explicit
,
Used spec theorems:
store
/node-store/
Subset
ablock-store-inv
/group-store/
in
store
/group-store-ablock-store-nat-store/
At-other
list-prefixn
/laddress-list/
prefixn-shift-right
ablock-store-inv
/group-store/
at
list-del
/group-store/
get-append-grt
list-prefixn
/group-store/
prefixn-append-left
list-del
/laddress-list/
app-05-neg
list-prefixn
/group-store/
in-prefixn-at-smaller
Used simplifier rules:
address-data
/
elim
groupnode
/
elim
ablock
/group-store/
elim
store
/group-store-ablock-store-nat-store/
In-insert
store
/group-store-ablock-store-nat-store/
in-neq
store
/group-store-ablock-store-nat-store/
insin
ablock
/group-store/
inj
list-prefixn
/laddress-list/
prefixn-in
list
/laddress-list/
in-11
nat
/
lels-03
store
/group-store-ablock-store-nat-store/
At-same
list-prefixn
/group-store/
prefixn-append-left
list-prefixn
/laddress-list/
in-prefixn-samepos
ablock
/group-store/
sel-02
ablock
/group-store/
sel-01
address-data
/
sel-05
address-data
/
sel-04
address-data
/
sel-03
list-data
/laddress-list/
l
list-del
/laddress-list/
app-05-neg
nat
/
lep-02
list-del
/laddress-list/
inl-01
list-del
/group-store/
get-butlast
list
/group-store/
len
list
/group-store/
len-02
list
/group-store/
a
nat
/
succ-01
nat-basic
/
a
nat-basic
/
c
list
/laddress-list/
len
list
/laddress-list/
len-02
nat
/
ls-le-simp
list
/laddress-list/
in-append
list
/laddress-list/
in-17
nat-basic
/
f
list-data
/group-store/
l
oelem
/nat-set/
irreflexivity
nat
/
fle
list-prefixn
/laddress-list/
prefixn-append-left
nat-basic
/
succ
nat-basic
/
lf-02
oelem
/nat-set/
transitivity
nat
/
le-def
list-del
/laddress-list/
notin-03
list-prefixn
/laddress-list/
prefixn-notin
nat
/
le-ls-simp
list-del
/laddress-list/
inl
list
/laddress-list/
a
list-del
/laddress-list/
app-05
groupnode
/
inj
list-prefixn
/laddress-list/
in-prefixn-pos-smaller
nat
/
anti
nat
/
lels-02
nat
/
lels
nat
/
fle-01
nat-basic
/
lf-01
nat-basic
/
lf
list-prefixn
/laddress-list/
in-prefixn-pos-smaller0
nat-basic
/
ls-02
list-prefixn
/group-store/
prefixn-fulln
list-prefixn
/laddress-list/
prefixn-fulln
nat
/
let