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Theorem rem-preserves-monls
⊦ mon<(nσ) → (mon<(rem(nσ, np)) ↔ true)
Type: A user defined theorem
Validity: The proof is valid.
Features: ss, lss,
Comment:
Used by:
Used by units in proved state:
Proof exists?: Yes
View
the proof
Infos about the proof
Proved?: Yes
Interactions: 16
Proof steps: 31
Used lemmas:
monls-to
,
monls-mon-implies-monls
,
monls-ls
,
monls-def
,
monls-append1
,
Used spec theorems:
list
/
lastdiv-rew
stream
/
get-append-ls
mon-lim-filter-count
/
rem-member1-fin
mon-lim-filter-count
/
rem-inf
mon-lim-filter-count
/
mon-remfun
Used simplifier rules:
stream
/
empty
mon-lim-filter-count
/
rem-base
stream
/
append-assoc
mon-lim-filter-count
/
rem-rec
list
/
a
stream
/
append-finfin
stream
/
append-empty
list
/
len
list
/
len-02
nat-basic
/
s-04
nat-basic
/
refl-nat
nat-basic
/
a
nat-basic
/
c
nat
/
lels
stream
/
get-append-ls
nat-inf
/
add-comm
nat-inf
/
add-assoc
nat-inf
/
add-ls-cancel-01
stream
/
size-fin
stream
/
size-append
list-del
/
one-03
nat
/
zero
nat
/
cancel-01
nat-inf
/
sel-rqui-dotn
nat-inf
/
prime-add-fin
nat-inf
/
disj-rqui-infty
nat-inf
/
less-fin
nat-inf
/
eqls-succ
nat-inf
/
less-less-leftsucc
nat-inf
/
add-fin
stream
/
sel-fin
stream
/
get-append-notls
list-data
/
l
nat-basic
/
f
nat-inf
/
less-succ-leq
list-del
/
get-append-less
stream
/
get-append2-fin
list-del
/
get-last-03
nat
/
le-ls-simp