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Theorem fill-stream-append
⊦ n + m = # buf → ⌜fill(buf, zero, n, m)⌝ = (⌜buf⌝ to n) + (σ⊥ to m)
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: 6
Proof steps: 13
Used lemmas:
zerostream-size
,
Used spec theorems:
stream
/buffer-inf/
extensionality
stream
/buffer-inf/
get-append-ls
buffer-inf-conv
/
tostream-at
array-copy
/buffer/
at-fill-h
Used simplifier rules:
nat-basic
/
lf-01
nat-inf
/
add-comm
nat-inf
/
add-assoc
nat-inf
/
eq-natinf-to-nat-2-1
stream
/buffer-inf/
size-append
array-copy
/buffer/
size-fill-h
nat-basic
/
l-01
buffer-inf-conv
/
at-emptystream
nat-inf
/
less-inf1
nat
/
ls-01
nat
/
le-ls-simp
nat
/
le-def
stream
/buffer-inf/
append-assoc
nat-inf
/
sel
stream
/buffer-inf/
get-append-notls
nat-basic
/
l
nat-basic
/
ref
stream
/buffer-inf/
get-to
stream
/buffer-inf/
size-to
nat-basic
/
lf-02
nat-basic
/
f
nat-inf
/
less-fin
buffer-inf-conv
/
tostream-size
nat
/
ls-le-simp
nat
/
lels
nat
/
fle-01
nat
/
fle
nat-basic
/
a
nat-basic
/
c
nat-basic
/
l-08
nat-basic
/
l-02