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Theorem ordered-step-down
⊦ # ar0 = (n0 + 1) + m ∧ ordered≤(rev(subarray(ar0, m + 1, n0))) ∧ ar0[m + 1] ≤ ar0[m] → ordered≤(rev(subarray(ar0, m, n0 + 1)))
Type: A user defined theorem
Validity: The proof is valid.
Features: ss, lss,
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: 4
Proof steps: 8
Used lemmas:
rev-mkarray-empty
,
subarray-inc-offset0
,
Used spec theorems:
olist
/natarray-oarray-sort/
ole-last-01
array-listops
/natarray/
nil
Used simplifier rules:
nat
/
succ-01
nat-basic
/
oz
nat-basic
/
a
nat-basic
/
c
nat
/
lels
nat
/
eq
oelem
/natarray/
irreflexivity
nat-basic
/
s-04
nat-basic
/
l
nat
/
ler
list-data
/natarray-oarray-sort/
l
nat-basic
/
lf-01
nat-basic
/
f
nat
/
eqle-one
list
/natarray-oarray-sort/
a
list
/natarray-oarray-sort/
Last
list-last
/natarray-oarray-sort/
rev-r
list
/natarray-oarray-sort/
c
nat-basic
/
add-base
nat
/
add-01
list-last
/natarray-oarray-sort/
rev-empty
olist
/natarray-oarray-sort/
le-e
list-last
/natarray-oarray-sort/
rev-e
list
/natarray-oarray-sort/
Nil
olist
/natarray-oarray-sort/
le-o
nat
/
fle-01
list
/natarray-oarray-sort/
e-01
list-last
/natarray-oarray-sort/
last-def
nat
/
lep-02
nat
/
les
array-copy
/natarray/
subarray-zero