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Theorem content-trunc
⊦ n = n0 * VFS_PAGE_SIZE + n1 ∧ n1 ≠ 0 ∧ n1 < VFS_PAGE_SIZE → (content upto n).stream = (content.stream to (n0 + 1) * VFS_PAGE_SIZE) + σ⊥
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: 13
Proof steps: 24
Used lemmas:
zerostream-size
,
getpage
,
getbyte
,
stream
,
Used spec theorems:
stream
/buffer-inf/
extensionality
stream
/buffer-inf/
get-append-ls
nat-basic
/
addex
nat
/
le-addex
Used simplifier rules:
stream
/buffer-inf/
to-inf
nat-mult
/
rsucc-02
afs-base
/
at-upto
afs-base
/
in-upto
stream
/buffer-inf/
size-append
nat-inf
/
add-inf2
nat-inf
/
less-inf2
stream
/buffer-inf/
size-inf
stream
/buffer-inf/
sel-inf
nat-div
/
div-elim
stream
/buffer-inf/
append-assoc
buffer-inf-conv
/
at-emptystream
nat-inf
/
sel
nat-inf
/
prime-add-fin
nat-inf
/
disj
stream
/buffer-inf/
get-append-notls
nat-basic
/
lf-01
nat-basic
/
l-01
nat-basic
/
one
nat-basic
/
succ
nat
/
fle-01
nat
/
lep-02
nat-basic
/
lf-02
nat-basic
/
lf
nat-basic
/
trans
nat-basic
/
f
nat-div
/
mod-eq
nat-div
/
mod-mult
nat-basic
/
add-base
nat-div
/
zero-01
nat-div
/
mult
page
/
page-size
stream
/buffer-inf/
get-infto
nat-inf
/
add-comm
nat-inf
/
add-assoc
nat
/
le-ls-simp
nat-inf
/
ls-natinf-to-nat-2-2
stream
/buffer-inf/
inf-size-to
nat-inf
/
add-fin
stream
/buffer-inf/
sel-fin
nat
/
lels
page
/
emptypage-at
nat-basic
/
l
nat-basic
/
nls-fst
nat-basic
/
a
nat-basic
/
c
nat-mult
/
modeq-01
nat-mult
/
mult-a
nat-mult
/
mult-c
nat-basic
/
z-01