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Theorem copy-stream-append
⊦ n0 + m ≤ # buf0 ∧ n1 + m ≤ # buf1 → ⌜copy(buf0, n0, buf1, n1, m)⌝ = (⌜buf1⌝ to n1) + ((⌜buf0⌝ from n0) to m) + ((⌜buf1⌝ from n1 + m) to (# buf1 - n1 + m))
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: 17
Proof steps: 41
Used lemmas:
Used spec theorems:
stream
/buffer-inf/
extensionality
stream
/buffer-inf/
get-append-ls
buffer-inf-conv
/
tostream-at
stream
/buffer-inf/
get-from
nat-inf
/
add-cancel-num-01
stream
/buffer-inf/
size-to
stream
/buffer-inf/
fin-size-from
stream
/buffer-inf/
fin-size-from2
Used simplifier rules:
buffer-inf-conv
/
from-to-rest
stream
/buffer-inf/
size-append
array-copy
/buffer/
size-copy
array-copy
/buffer/
at-copy
nat
/
add-01
nat-basic
/
l-05
nat-basic
/
succ
nat-basic
/
trans
nat-basic
/
lf
nat-basic
/
lf-01
stream
/buffer-inf/
append-assoc
stream
/buffer-inf/
get-append-notls
nat-inf
/
add-all-zero
nat
/
sub-base
nat-basic
/
zero
nat
/
lez
nat-basic
/
l-01
nat
/
fle-01
nat-inf
/
ls-natinf-to-nat-3-1
nat-basic
/
l-06
stream
/buffer-inf/
get-to
nat-inf
/
ls-natinf-to-nat-2-1
buffer-inf-conv
/
tostream-at
nat
/
ls-le-simp
nat
/
lep-02
nat
/
lep
nat
/
eq-01
stream
/buffer-inf/
fin-size-from
nat-inf
/
less-fin
nat
/
le-def
nat-basic
/
ls-02
nat
/
ls-01
nat
/
le-ls-simp
stream
/buffer-inf/
size-to
nat
/
lels-03
nat
/
let
nat
/
le-add
nat-inf
/
not-less-zero
nat-basic
/
add-base
nat
/
anti
nat-inf
/
add-cancel-01
buffer-inf-conv
/
finp-buf
nat-basic
/
lf-02
nat-basic
/
f
nat-basic
/
l
nat-basic
/
l-02
stream-basic
/buffer-inf/
inj-02
stream-basic
/buffer-inf/
test-02
stream-basic
/buffer-inf/
stream-fin-forward
nat-inf
/
add-comm
nat-inf
/
add-assoc
nat
/
lels
nat-inf
/
ls-natinf-to-nat-1-2
nat-inf
/
add-fin
nat-inf
/
inj
nat-inf
/
sel
buffer-inf-conv
/
tostream-size
nat-basic
/
a
nat-basic
/
c
nat-basic
/
eqs
nat
/
elim-sub