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Theorem conttr-thm
⊦ cont(βf) ∧ mon(⌜σf⌝ ) ∧ mon(⌜αf⌝ ) ∧ (∀ n. # σf(n) = # αf(n) + ⌜1⌝ ) → lim(⌜λ n. βf(σf(n), αf(n))⌝ ) = βf(lim(⌜σf⌝ ), lim(⌜αf⌝ ))
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: 114
Proof steps: 219
Used lemmas:
fun-neq
,
pbdtr-def
,
montr-def
,
conttr-def
,
twomon-limsize
,
Used spec theorems:
streamseq-mon-lim
/
lim-def
streamseq-mon-lim
/
mon-def
streamseq-mon-lim
/
equal-prepostfix
stream
/
prefix-def
list-last
/
prefix-eq
streamseq-mon-lim
/
mon-lem
stream
/
leq-trans
list-last
/
prefix
list-getput
/
extension
stream
/
add-list-fun-def
Used simplifier rules:
stream
/
sel-inf
nat-inf
/
less-inf2
stream
/
size-inf
stream
/
fun-nonempty
nat-inf
/
add-comm
nat-inf
/
add-assoc
nat-inf
/
disj-rqui-infty
nat-inf
/
addeqinf-cancel
nat-inf
/
inf-less
stream
/
to-fin
nat-inf
/
less-fin
stream
/
size-fin
nat-inf
/
ls-natinf-to-nat-2-1
nat-inf
/
eq-natinf-to-nat-2-1
stream
/
fin-finlen-tolen
nat-basic
/
refl-Nat
list-last
/
prefix-size-eq
stream
/
prefix-bothfin-listprefix
stream
/
leq-symm-2
stream
/
leq-trans
stream
/
append-two-is-fin
stream-basic
/
elim-finp-ant
nat-inf
/
add-fin
list
/
len
stream
/
eq-stream-to-list-2-1
list
/
app-04
stream
/
append-assoc
stream-basic
/
sel-rqui-dotl
stream
/
append-finfin
list
/
a
nat-basic
/
eq-02
list-data
/
l
nat-basic
/
a
nat-basic
/
c
nat-inf
/
less-inf1
stream
/
to-inf
nat-inf
/
add-inf2
stream-basic
/
inj-rqui
list-last
/
prefix-eq
nat-basic
/
f
nat
/
le-def
nat
/
lels-03
nat-inf
/
inj-rqui
nat-inf
/
add-all-zero
nat-inf
/
add-cancel-num-03
stream
/
inf-size-to
stream-basic
/
disj-rqui-rqui0
stream
/
not-prefix-inf-fin
stream
/
size-inf-to
nat-basic
/
z-01
stream-basic
/
inj-rqui0
stream
/
prefix-inf-inf-equal
stream-basic
/
sel-rqui0-dotf
stream
/
infapp-embed
stream-basic
/
elim-finp-suc
stream
/
append-fin-is-inf
stream
/
leq-append-right
nat-basic
/
s-04
stream
/
get-infto