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Theorem monge-limit-inf
mon≥(f), bounded≥(f, r) ⊦ limit(f) = inf(λ r. ∃ n. r = f(n))
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: 11
Proof steps: 15
Used lemmas:
boundedle-def
,
monle-boundedle-converges
,
converges-neg-converges
,
limit-neg-limit
,
monle-limit-sup
,
monge-neg-monle
,
boundedge-neg-boundedle
,
Used spec theorems:
real-supinf
/
inf-neg-sup
real-supinf
/
boundedge-neg-boundedle
real-supinf
/
boundedle-def
real-supinf
/
upperbound-def
Used simplifier rules:
real-basic
/
add-zero
real-basic
/
add-assoc
real-basic
/
add-comm
real-basic
/
negeq
real-basic
/
neg-12
real-abs
/
sub-le-01
real-abs
/
negle-13
real-basic
/
less-add-cancel-l
real-basic
/
lf-03
real-abs
/
le-def
real-abs
/
negle-07
real-abs
/
lels-03