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Theorem size-0
⊦ ri-cons(ri, nodes(gstore ↓, ginval)) ∧ inv(gstore \ ginval) → ((range ri | m).size = 0 ↔ ¬(∃ adr. adr ∈ range ri ∧ adr.lnum = m))
Type: A user defined theorem
Validity: The proof is valid.
Features: s, ls,
Comment:
Used by:
lebs-dom-remove-refsize0
,
refsize-0-notin-index
,
refsize-nonzero-notin-ginval
,
Used by units in proved state:
Proof exists?: Yes
View
the proof
Infos about the proof
Proved?: Yes
Interactions: 14
Proof steps: 37
Used lemmas:
down-block
,
down-store-at
,
down-store-adr-in-explicit
,
nodes-gstore-in
,
Used spec theorems:
store+set
/node-index/
Data-in
aubifs-inv
/
ri-cons
gjournal-base
/
range-add-explicit
ablock-store-refsize-cons
/group-store/
restrict-add
ablock-store-refsize-cons
/group-store/
size-rec-rem
ablock-store-inv
/group-store/
inv-block
ablock-store-inv
/group-store/
inv-flashsize
list-prefixn
/laddress-list/
prefixn-notin
list
/laddress-list/
in-def
set-basic
/node-store/
Extension
Used simplifier rules:
address-data
/
elim
address-data
/
sel-03
ablock
/group-store/
elim
nat
/
sub-base
nat-basic
/
z-01
address-data
/
sel-05
gjournal-abs
/
in-ri
ablock-store-refsize-cons
/group-store/
restrict-in
ablock-store-refsize-cons
/group-store/
size-rem
ablock
/group-store/
inj
ablock
/group-store/
sel-02
ablock
/group-store/
sel-01
ablock-store-inv
/group-store/
inv-nodups-app-left
list-dup
/laddress-list/
a
apersistence-base
/
fwd-inv-gblock-rem
nat-basic
/
s-04
list-dup
/laddress-list/
f-01
nat-basic
/
succ
list
/laddress-list/
len-05
list
/laddress-list/
len
list
/laddress-list/
c
nat-basic
/
l-02
nat-basic
/
a
nat-basic
/
c
list-del
/laddress-list/
get-app
list
/laddress-list/
a
laddress
/
sel-01
ablock-store-inv
/group-store/
flashsize-neq-0
ablock-store-refsize-cons
/group-store/
size-emp
aubifs-base
/
range
ablock-store-refsize-cons
/group-store/
restrict-leb
set-basic
/node-store/
In-empty
set-basic
/node-store/
size-zero-01
set-basic
/node-store/
size-zero