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Theorem ls-subarray-datasize
n ≤ # buf ⊦ LEB_SIZE = align↑(datasize(buf, n), EB_PAGE_SIZE) + n0 ∧ LEB_SIZE = n + n1 ∧ is-aligned(n, EB_PAGE_SIZE) → subarray(buf, 0, align↑(datasize(buf, n), EB_PAGE_SIZE)) + mkempbuf(n0) = subarray(buf, 0, n) + mkempbuf(n1)
Type: A user defined theorem
Validity: The proof is valid.
Features: ls,
Comment:
Used by:
prepost-atomic-leb-change
,
Used by units in proved state:
Proof exists?: Yes
View
the proof
Infos about the proof
Proved?: Yes
Interactions: 8
Proof steps: 16
Used lemmas:
subbarray-alignup-datasize-empty
,
ls-array-append-length0
,
nat-sum-leq
,
Used spec theorems:
array-splice
/buffer/
subarray-split-at
array-copy
/buffer/
subarray-subarray-elim
Used simplifier rules:
align
/
alignup-le-is-aligned
datasize
/
datasize-is-smaller-help
nat
/
elim-sub
nat
/
lels
nat-basic
/
eqs
nat
/
lels-02
nat
/
le-def
nat-basic
/
lf-02
nat-basic
/
lf-01
nat
/
fle-01
nat-basic
/
f
nat-basic
/
l
oelem
/nat-set/
irreflexivity
array-copy
/buffer/
subarray-elim
array-copy
/buffer/
size-subarray
array-splice
/buffer/
emparray-len
nat
/
ler
nat
/
let
nat-basic
/
add-base
array-splice
/buffer/
mkemparray-eq
array-splice
/buffer/
append-eq-left
array-splice
/buffer/
append-a
array-splice
/buffer/
mkemparray-append
eraseblock
/
page-size
nat-basic
/
eq-01
nat-basic
/
a
nat-basic
/
c
align
/
alignup-same