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Theorem remtau-equiv
¬ finp(ext !(⌜af⌝ )) ⊦ ext !(⌜af⌝ ) = ext !(⌜af0⌝ ) ↔ (∀ n. ∃ m. ext !(af.take(n)) = ext !(af0.take(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: 15
Proof steps: 29
Used lemmas:
remtau-append
,
not-lessto
,
remtau_of_to-to_of_rmtau
,
finremtau-def
,
to_of_remtau-remtau_of_to
,
Used spec theorems:
stream
/
extensionality-to
nat-inf
/
notinf-fin
stream
/
extensionality
stream
/
append-gr-to
Used simplifier rules:
stream-basic
/
elim-finp-suc
nat-inf
/
less-inf1
stream
/
size-inf
stream
/
to-inf
stream-basic
/
inj-rqui
nat-inf
/
less-inf2
nat-inf
/
add-comm
nat-inf
/
add-assoc
stream
/
size-succ
nat-basic
/
c
nat-basic
/
a
nat-inf
/
add-fin
stream
/
sel-inf
stream
/
size-fin
stream
/
size-inf-to
nat-inf
/
less-succ-leq
nat-inf
/
less-fin
nat-basic
/
refl-Nat
stream
/
elim-fromto-inf
stream
/
append-assoc
stream
/
appinf-selfun
nat-inf
/
addeqinf-cancel
stream
/
size-append
stream-basic
/
sel-rqui-dotl
nat
/
zero
stream
/
to-zero
list
/
app
list
/
a
stream
/
append-le-to
stream
/
to-fin
stream
/
to-to-eq-inf