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Theorem convergesto-neg-convergesto
⊦ converges(f, r) ↔ converges(λ n. ~ f(n), ~ r)
Type: A user defined theorem
Validity: The proof is valid.
Features:
Comment:
Used by:
converges-neg-converges
,
limit-neg-limit
,
Used by units in proved state:
Proof exists?: Yes
View
the proof
Infos about the proof
Proved?: Yes
Interactions: 12
Proof steps: 28
Used lemmas:
convergesto-def
,
Used spec theorems:
real-abs
/
Abs-pos
real-abs
/
Abs-neg
Used simplifier rules:
real-abs
/
sub-def
nat
/
ge
real-abs
/
gr-def
real-basic
/
double-neg
real-basic
/
add-comm
real-basic
/
add-assoc
real-basic
/
add-zero
real-basic
/
sub-eq
real-abs
/
abs-06
real-abs
/
forward-le
real-abs
/
lels
real-abs
/
forward-lsle
real-basic
/
negradd-ls
real-abs
/
abssub-02
real-abs
/
sub-le-01
real-basic
/
neg-08
real-basic
/
neg-add
real-basic
/
negladd-ls
real-abs
/
lenls
real-abs
/
Abs-pos
real-multdiv
/
add-mult-two
real-multdiv
/
ls-posint
real-multdiv
/
mult-ass
real-multdiv
/
mult-com
real-abs
/
lels-03
real-basic
/
add-less
real-basic
/
ls-02
real-basic
/
trans
real-abs
/
lels-02
real-basic
/
bls-01