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Theorem valid-peb-write-valid-peb
n < # apebs ⊦ valid-peb(apebs[n]) ∧ m0 ≥ apebs[n].fill ∧ m0 ≤ LEB_SIZE ∧ ubi-io-inv(apebs) → valid-peb(mkpeb(apebs[n].echdr, apebs[n].vidhdr, subarray(apebs[n].data, 0, m0) + buf1, m1, false))
Type: A user defined theorem
Validity: The proof is valid.
Features:
Comment:
Used by:
Used by units in proved state:
Proof exists?: Yes
View
the proof
Infos about the proof
Proved?: Yes
Interactions: 20
Proof steps: 48
Used lemmas:
ls-array-append-length0
,
ubi-io-inv-fwd
,
Used spec theorems:
ubi-io-inv
/
inv
ubi-io-inv
/
peb-inv
valid-peb
/
valid-peb0
valid-peb
/
valid-peb2
datasize
/
datasize-append
datasize
/
datasize-append-empty-h
datasize
/
datasize
checksum
/
checksum-append-left
array
/buffer/
Extension
array-splice
/buffer/
append-at1
array-splice
/buffer/
append-at2
Used simplifier rules:
apeb
/
elim
valid-peb
/
valid-peb0-vidhdr-empty
valid-peb
/
valid-peb0-bad
apeb
/
sel-07
avidheader
/
disj-02
apeb
/
sel-06
apeb
/
sel-08
apeb
/
sel-04
apeb
/
sel-05
datasize
/
datasize-subarray0
datasize
/
datasize-le-fwd
array-splice
/buffer/
subarray-append-left
datasize
/
datasize-empbuf
min-max
/
min-same
nat
/
ge
datasize
/
datasize-base
nat
/
zero
nat-basic
/
l-02
datasize
/
datasize-is-smaller
checksum
/
checksum-append-left
nat
/
le-def
nat
/
le-ls-simp
eraseblock
/
lebsize-neq-zero
array-splice
/buffer/
append-a
array-splice
/buffer/
append-len
array-copy
/buffer/
subarray-at
nat-basic
/
add-base
nat
/
lels-03
nat
/
fle-01
nat
/
fle
nat
/
let
oelem
/nat-set/
irreflexivity
array-copy
/buffer/
subarray-elim
array-splice
/buffer/
emparray-len
array-copy
/buffer/
size-subarray
nat-basic
/
l-06
array-splice
/buffer/
emparray-at
nat
/
lels
nat
/
sub-add
nat
/
add-01
nat
/
lep
nat-basic
/
a
nat-basic
/
c
nat-basic
/
eqs
nat-basic
/
lf-01
nat-basic
/
l-01
nat-basic
/
l
nat-basic
/
f
nat
/
lep-02
nat
/
ls-le-simp
nat
/
elim-sub