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Theorem lim-extractprefix
⊦ mon(⌜σf⌝ ) → lim(⌜λ n. ⌜x⌝ + σf(n)⌝ ) = ⌜x⌝ + lim(⌜σf⌝ )
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: 80
Proof steps: 158
Used lemmas:
mon-lem
,
mon-rmprefix
,
lim-def
,
Used spec theorems:
stream
/
extensionality
stream
/
get-append-ls
stream
/
prefix-def
stream
/
get-append-notls
nat-inf
/
notinf-fin
list-getput
/
extension
stream-basic
/
sel-embed-fin
Used simplifier rules:
stream
/
sel-inf
nat-inf
/
less-inf2
stream
/
size-inf
stream
/
fun-nonempty
nat-inf
/
less-inf1
nat-inf
/
add-comm
nat-inf
/
add-assoc
nat-inf
/
add-inf2
stream
/
append-assoc
stream
/
size-fin
stream
/
size-append
nat
/
lels
nat-inf
/
less-fin
nat-inf
/
sel-rqui-dotn
stream
/
get-append-notls
nat
/
elim-sub
nat-basic
/
c
nat-basic
/
a
nat
/
lep
nat-inf
/
less-succ-leq
nat-inf
/
add-fin
stream
/
size-to
stream
/
size-to-02
nat-inf
/
add-not-less
nat-inf
/
disj-rqui-infty
nat-inf
/
prime-add-fin
nat-basic
/
refl-nat
stream
/
get-to
nat-basic
/
s-04
stream
/
sel-fin
nat-inf
/
add-cancel-01
nat-inf
/
add-ls-cancel-01
nat-inf
/
addeqinf-cancel
nat
/
cancel-01
nat-basic
/
l
stream
/
get-append-ls
nat-inf
/
ls-natinf-to-nat-2-1
nat-basic
/
l-02
nat
/
eq-01
nat-basic
/
f
nat
/
le-def
nat
/
lels-03
nat-inf
/
lels-trans
stream
/
size-empty-equiv
nat-inf
/
add-less
nat-inf
/
elim-rqui
nat-inf
/
add-less-fin-01
nat-inf
/
add-cancel-03
nat-inf
/
sum-zero-fin
nat-inf
/
add-cancel-num-02
nat-inf
/
add-cancel-num-03
nat-inf
/
add-all-zero
list-data
/
l
nat-inf
/
less-notgeqinf
nat-inf
/
ls-lsadd
nat
/
ls-le-simp
nat-inf
/
add-all-inf
nat-inf
/
eq-natinf-to-nat-2-1
stream
/
neq-fin-inf-02
stream
/
neq-fin-inf-01
stream
/
eq-stream-to-list-2-2
list
/
len
list
/
a
nat-basic
/
eq-01
nat-basic
/
eq-02
nat-basic
/
z-01
nat-basic
/
oz
stream
/
leq-append-both
stream
/
append-split-fin
nat-inf
/
eq-natinf-to-nat-3-1
stream
/
finlen-tolen-02
stream
/
leq-trans
stream-basic
/
elim-finp-suc
stream
/
to-fin
stream
/
leq-refl
nat-inf
/
inj-rqui
stream-basic
/
elim-finp-ant
stream
/
leq-symm-2
stream
/
eq-stream-to-list-2-1
stream
/
fin-finlen-tolen
stream
/
append-inf
stream-basic
/
disj-rqui-rqui0
stream
/
appendend-equal
stream
/
append-empty-01
stream
/
prefixself-equal
stream
/
fin-empty
stream
/
append-finfin
stream
/
empty
stream
/
append-empty
list-data
/
size-nil
nat-basic
/
add-base
list
/
app