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Theorem limit-unique
⊦ converges(f, r0) → (converges(f, r1) ↔ r0 = r1)
Type: A user defined theorem
Validity: The proof is valid.
Features:
Comment: justifies definition of limit
Used by:
limit-neg-limit
,
monle-limit-sup
,
Used by units in proved state:
Proof exists?: Yes
View
the proof
Infos about the proof
Proved?: Yes
Interactions: 28
Proof steps: 48
Used lemmas:
convergesto-def
,
Used spec theorems:
real-multdiv
/
abs-ite
real-abs
/
lels
real-abs
/
lsls-add-notge
real-multdiv
/
mult-com
Used simplifier rules:
real-abs
/
sub-def
nat
/
ge
real-abs
/
gr-def
real-multdiv
/
mult-com
real-multdiv
/
mult-ass
real-multdiv
/
invmult-gr-pos
real-basic
/
ls-num
real-basic
/
add-comm
real-basic
/
add-assoc
real-basic
/
add-zero
real-basic
/
sub-eq
real-abs
/
abs-06
real-multdiv
/
mult-zero
nat
/
ler
real-multdiv
/
mult-one
real-multdiv
/
inv-def
real-multdiv
/
add-mult-two
real-basic
/
neg-add
real-basic
/
double-neg
real-basic
/
negladd-ls
real-basic
/
neg-08
real-abs
/
lels
real-abs
/
forward-lels
real-basic
/
trans
real-basic
/
negradd-ls
real-basic
/
sub-eq-01
real-basic
/
irref
real-multdiv
/
minus-left
real-basic
/
less-add-cancel-l
real-basic
/
negadd
real-multdiv
/
ls-posint
real-basic
/
bls-01
real-basic
/
sub-ls-02
real-basic
/
blst-01
real-abs
/
lenls
nat-basic
/
f
nat
/
le-def
nat
/
lels-03
nat
/
fle
real-abs
/
lels-03
real-abs
/
sub-le
real-abs
/
abssub-02