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Theorem monls-mon-implies-monls
⊦ (∀ n. mon<(nσf(n))) ∧ mon(nσf) → (¬ mon<(lim(λ n. nσf(n))) ↔ false)
Type: A user defined theorem
Validity: The proof is valid.
Features:
Comment:
Used by:
rem-preserves-monls
,
Used by units in proved state:
Proof exists?: Yes
View
the proof
Infos about the proof
Proved?: Yes
Interactions: 14
Proof steps: 23
Used lemmas:
monls-def
,
Used spec theorems:
mon-lim-filter-count
/natstream/
lim-def
mon-lim-filter-count
/natstream/
prefix-def
stream
/natstream/
get-append-ls
Used simplifier rules:
nat-inf
/
ls-trans
nat-inf
/
ls-natinf-to-nat-2-1
nat-basic1
/
lf
nat-basic1
/
trans-1
nat
/
add-num-03
nat-basic2
/
succ
nat-inf
/
less-inf1
nat-inf
/
lels-trans
stream
/natstream/
size-append
nat-inf
/
add-not-less
nat
/
cancel-01
nat
/
fle
nat-basic1
/
f
nat-basic2
/
l
nat-inf
/
less-fin
nat-inf
/
less-succ-leq
nat-inf
/
add-ls-cancel-num-04
nat-inf
/
add-fin
nat-basic2
/
a
nat-basic2
/
c
stream
/natstream/
size-to
nat-inf
/
ls-natinf-to-nat-1-2
nat-basic2
/
l-01
nat-inf
/
add-assoc
nat-inf
/
add-comm
stream
/natstream/
get-to
nat-basic1
/
ref-1
stream
/natstream/
get-append-notls
nat-inf-basic
/
disj
nat-inf
/
prime-add-fin
nat-inf-basic
/
sel
stream
/natstream/
append-assoc
nat
/
lels
nat
/
le-add