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Theorem ordered-all-rev
⊦ ordered≤(rev(ar)) ↔ (∀ m, n. m ≤ n ∧ n < # ar → ¬ ar[m] < ar[n])
Type: A user defined theorem
Validity: The proof is valid.
Features:
Comment:
Used by:
next-proper-permutation
,
Used by units in proved state:
Proof exists?: Yes
View
the proof
Infos about the proof
Proved?: Yes
Interactions: 10
Proof steps: 24
Used lemmas:
Used spec theorems:
olist
/natarray-oarray-sort/
ole-last-01
list-del
/natarray-oarray-sort/
get-append-less
Used simplifier rules:
list-data
/natarray-oarray-sort/
size-nil
nat-basic
/
less-zero
list-last
/natarray-oarray-sort/
rev-e
olist
/natarray-oarray-sort/
le-e
list
/natarray-oarray-sort/
c
nat-basic
/
c
nat-basic
/
a
nat-basic
/
s-04
list
/natarray-oarray-sort/
a
nat-basic
/
succ
list
/natarray-oarray-sort/
len-05
list
/natarray-oarray-sort/
Last
list-last
/natarray-oarray-sort/
rev-r
nat-basic
/
zero
nat
/
lez-01
list
/natarray-oarray-sort/
app
list-del
/natarray-oarray-sort/
one-03
oelem
/natarray/
irreflexivity
list
/natarray-oarray-sort/
Nil
olist
/natarray-oarray-sort/
le-o
olist
/natarray-oarray-sort/
app
nat-basic
/
f
nat
/
let
nat
/
lels
list
/natarray-oarray-sort/
e-02
nat
/
le-sum
nat
/
ls-add-not-01
list-del
/natarray-oarray-sort/
get-succ
list-last
/natarray-oarray-sort/
last-def
nat-basic
/
one-01
list
/natarray-oarray-sort/
len-02
list-del
/natarray-oarray-sort/
get-append-grt
nat
/
elim-pred-c
nat
/
le-ls-simp
nat
/
fle
nat
/
succ-01
nat
/
lep-02
nat-basic
/
oz
nat
/
lez
nat
/
fle-01
list-del
/natarray-oarray-sort/
get-zero
nat-basic
/
nls-fst
list-del
/natarray-oarray-sort/
get-numrec