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Theorem orderedle-all
⊦ ordered≤(x) ↔ (∀ m, n. m ≤ n ∧ n < # x → ¬ x[n] < x[m])
Type: A user defined theorem
Validity: The proof is valid.
Features:
Comment:
Used by:
Used by units in proved state:
olist-min-max
,
Proof exists?: Yes
View
the proof
Infos about the proof
Proved?: Yes
Interactions: 10
Proof steps: 29
Used lemmas:
orderedle-ls
,
app-01
,
cons-02
,
le-o
,
ole-rec
,
le-e
,
Used spec theorems:
list-del
/
get-numrec
Used simplifier rules:
list-data
/
size-nil
nat-basic
/
less-zero
list
/
c
nat-basic
/
c
nat-basic
/
a
nat-basic
/
s-04
list
/
a
nat-basic
/
succ
list
/
len-05
list
/
e-01
list
/
c-07
nat-basic
/
zero
nat
/
lez-01
list-del
/
one-03
weakord
/tord/
irreflexivity
list
/
app
list
/
c-08
list-data
/
elim-list-c
nat
/
let
nat
/
lels
nat
/
lez
list-del
/
get-zero
nat
/
pred-03
nat
/
elim-pred-c
nat
/
lep-02
nat-basic
/
oz
list-data
/
l
nat-basic
/
f
nat
/
succ-01
list-del
/
get-in
weakord
/tord/
nll
weakord
/tord/
leq-trans
nat
/
le-ls-simp
nat
/
le-sum
nat
/
ls-add-not-01
list-del
/
get-succ
nat-basic
/
nls-fst
list-del
/
get-numrec