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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:
nat-basic1
/
less-1
list
/
app-02-ant
list
/
e
list-data
/
size-01
list
/
app
nat-basic1
/
z
list-del
/
one-03
list
/
c-08
list
/
c-07
list-data
/
elim-list-c
list
/
e-01
list
/
len-02
list
/
len
list
/
c
nat
/
lez-01
oelem
/
irreflexivity
nat
/
elim-pred-c
nat
/
lez
list-data
/
l
nat-basic1
/
f
nat
/
succ-01
list-del
/
get-in
oelem
/
nll
oelem
/
nnn
nat
/
pred-03
nat
/
lep-02
nat-basic2
/
oz
nat
/
let
nat
/
lels
nat-basic2
/
s
nat-basic2
/
succ
nat
/
le-sum
nat-basic2
/
l
nat
/
le-ls-simp
list-del
/
get-succ
nat-basic2
/
l-02
nat-basic2
/
a
nat-basic2
/
c
list-del
/
get-numrec
list-del
/
get-zero-01
list
/
a