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Theorem content-write
⊦ # buf = VFS_PAGE_SIZE → content[n, buf].stream = (content.stream to n * VFS_PAGE_SIZE) + ⌜buf⌝ + (content.stream from (n + 1) * VFS_PAGE_SIZE)
Type: A user defined theorem
Validity: The proof is valid.
Features:
Comment:
Used by:
Used by units in proved state:
afs-contracts
,
Proof exists?: Yes
View
the proof
Infos about the proof
Proved?: Yes
Interactions: 14
Proof steps: 29
Used lemmas:
getpage
,
getbyte
,
stream
,
Used spec theorems:
stream
/buffer-inf/
extensionality
store
/file-content/
In-insert
stream
/buffer-inf/
get-append-notls
stream
/buffer-inf/
get-append-ls
store
/file-content/
At-other
nat-basic
/
addex
nat-mult
/
dist
nat-basic
/
a
nat-mult
/
succ
nat-mult
/
modeq
Used simplifier rules:
stream
/buffer-inf/
from-inf
stream
/buffer-inf/
to-inf
nat-inf
/
less-inf2
nat-inf
/
add-inf2
stream
/buffer-inf/
size-append
stream
/buffer-inf/
size-inf
nat-div
/
mod-eq
stream
/buffer-inf/
get-infto
stream
/buffer-inf/
sel-fin
stream
/buffer-inf/
get-append-ls
page
/
emptypage-at
nat-basic
/
ref
store
/file-content/
At-other
nat-inf
/
add-comm
nat-inf
/
add-assoc
nat-inf
/
ls-natinf-to-nat-2-1
nat-inf
/
add-fin
stream
/buffer-inf/
inf-size-to
nat
/
le-def
nat-mult
/
modls
nat
/
le-ls-simp
buffer-inf-conv
/
tostream-at
store
/file-content/
k-At-same
nat
/
fle
nat
/
lels
nat-inf
/
less-fin
stream
/buffer-inf/
append-assoc
nat-div
/
mod-once
nat-div
/
mod-mult
nat-div
/
mult
stream
/buffer-inf/
get-from-inf
stream
/buffer-inf/
sel-inf
nat-inf
/
sel
buffer-inf-conv
/
tostream-size
stream
/buffer-inf/
get-append-notls
nat
/
elim-sub
nat
/
lep
store
/file-content/
At-same
nat
/
ler
nat-div
/
zero-01
nat-basic
/
add-base
nat-basic
/
l-05
nat
/
lels-02
nat-basic
/
eq-02
nat-basic
/
eq-01
nat-div
/
div-elim
nat-mult
/
zero-06
nat-basic
/
l-01
nat-basic
/
lf-02
nat-mult
/
modeq
nat-basic
/
f
nat-basic
/
lf-01
page
/
page-size
nat-basic
/
a
nat-basic
/
c
nat-mult
/
rsucc-02
nat-mult
/
mult-a
nat-mult
/
mult-c