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Theorem replay-log-gc-copy
# ax = # kx ⊦ ri-cons(ri, fs) ∧ kx.toSet ⊆ dom ri ∧ new(ax, fs) ∧ ¬ dups(ax) ∧ ¬ dups(kx) ∧ orphans-cons(fs, ri, ro) ∧ ri-closed(ri, fs, ro) ∧ ro.inodes? → replay-log(ax, fs[ax, fs[ri[kx]]], ri ⊖ ro) = ri[kx, ax] ⊖ ro
Type: A user defined theorem
Validity: The proof is valid.
Features: s, ls,
Comment:
Used by:
Used by units in proved state:
aubifs-asm
,
Proof exists?: Yes
View
the proof
Infos about the proof
Proved?: Yes
Interactions: 8
Proof steps: 17
Used lemmas:
orphans-cons-gc-one
,
replay-one-update
,
replay-log-write
,
replay-log-rec
,
replay-log-empty
,
Used spec theorems:
aubifs-base
/
write-shift
aubifs-base
/
read-write-other-fs
store+set
/node-index/
Data-in
Used simplifier rules:
list-data
/address-list-set/
size-01
list-data
/key-list-set/
l
aubifs-base
/
new-base
list-dup
/address-list-set/
e-01
aubifs-base
/
index-update-key-base
list-dup
/address-list-set/
dups-cons
aubifs-base
/
new-rec
list
/address-list-set/
len-05
list-data
/key-list-set/
size-01
nat-basic
/
z-01
list-data
/address-list-set/
l
list-dup
/key-list-set/
dups-cons
store+set
/node-index/
Dom
set-basic
/node-index/
sub-add-03
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
aubifs-base
/
index-update-key-rec
list
/node-list/
a
aubifs-base
/
write-rec
list
/address-list-set/
a
list
/node-list/
c
aubifs-base
/
read-rec
list
/address-list-set/
c
aubifs-base
/
index-lookup-rec
nat-basic
/
c
nat-basic
/
a
nat-basic
/
eq-01
list
/key-list-set/
a
nat-basic
/
succ
list
/key-list-set/
len-05
list
/key-list-set/
c
store
/node-store/
At-same
aubifs-base
/
new-write
aubifs-base
/
read-write-other
store+set
/node-index/
dom-add-in
store+set
/node-index/
dom-ins
aubifs-inv
/
ri-cons-gc-one
aubifs-inv
/
ri-closed-gc-one
aubifs-base
/
index-lookup-length
aubifs-base
/
read-length
aubifs-base
/
in-read-in-dom
aubifs-inv
/
ri-cons-in