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Theorem twomon-limsize
mon(⌜σf⌝ ), mon(⌜αf⌝ ), ∀ n. # σf(n) = # αf(n) + ⌜m⌝ ⊦ # lim(⌜σf⌝ ) = # lim(⌜αf⌝ ) + ⌜m⌝
Type: A user defined theorem
Validity: The proof is valid.
Features:
Comment:
Used by:
conttr-relative-thm
,
conttr-thm
,
Used by units in proved state:
Proof exists?: Yes
View
the proof
Infos about the proof
Proved?: Yes
Interactions: 30
Proof steps: 54
Used lemmas:
Used spec theorems:
streamseq-mon-lim
/
lim-def
stream
/
prefix-def
stream
/
extensionality
Used simplifier rules:
stream
/
sel-inf
nat-inf
/
less-inf2
stream
/
size-inf
stream
/
fun-nonempty
stream
/
to-fin
nat-inf
/
less-fin
stream
/
size-fin
nat-inf
/
add-comm
nat-inf
/
add-assoc
nat-inf
/
eq-natinf-to-nat-2-1
list-data
/
l
nat-basic
/
f
stream
/
fin-finlen-tolen
nat-basic
/
refl-Nat
list-last
/
prefix-size-eq
stream
/
prefix-bothfin-listprefix
stream
/
leq-symm-2
stream
/
append-two-is-fin
stream
/
append-assoc
stream-basic
/
elim-finp-ant
stream
/
append-finfin
list
/
len
list
/
a
stream-basic
/
sel-rqui-dotl
nat-basic
/
lf-01
nat-basic
/
l
nat-basic
/
l-02
nat-basic
/
a
nat-basic
/
c
nat-basic
/
neq-01
nat-basic
/
eq-02
stream
/
to-inf
nat-inf
/
less-inf1
nat-inf
/
disj-rqui-infty
nat-inf
/
addeqinf-cancel
nat-inf
/
inf-inseq-reduce
nat-inf
/
add-fin
stream
/
inf-size-to
stream
/
size-append
nat-inf
/
add-cancel-01
nat-inf
/
add-cancel-03
nat-inf
/
sum-zero-fin
nat-inf
/
add-cancel-num-02
nat-inf
/
add-inf2