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Theorem array-le-one-diffrent-position
⊦ ar1[m] < ar2[m] ∧ m < # ar2 ∧ m < # ar1 ∧ subarray(ar1, 0, m) = subarray(ar2, 0, m) → ar1 ≤ ar2
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: 12
Proof steps: 35
Used lemmas:
subarray-inc-offset0
,
lexicographic-rec1
,
Used spec theorems:
array
/natarray/
Extension
Used simplifier rules:
list-data
/natarray-oarray-sort/
l
nat-basic
/
f
nat
/
lels
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/
e-01
nat
/
lels-02
list-data
/natarray-oarray-sort/
size-nil
nat
/
lez-01
list
/natarray-oarray-sort/
app
array-copy
/natarray/
subarray-zero
list-del
/natarray-oarray-sort/
get-zero
list-del
/natarray-oarray-sort/
one-03
nat
/
lez
oelem
/natarray/
lel
nat-basic
/
lf-01
nat-basic
/
ls-02
nat
/
le-ls-simp
nat-basic
/
add-base
nat
/
le-def
nat
/
fle
nat-basic
/
l-02
list
/natarray-oarray-sort/
in-14
nat
/
elim-pred-c
list-del
/natarray-oarray-sort/
get-succ
nat
/
lels-03
nat
/
lep-02
nat
/
succ-01
nat-basic
/
oz
nat
/
ler
list
/natarray-oarray-sort/
in-rec
nat
/
add-01
list
/natarray-oarray-sort/
c-06
list-del
/natarray-oarray-sort/
get-zero-01
nat-basic
/
zero
nat-basic
/
lf
oelem
/natarray/
transitivity
array-copy
/natarray/
subarray-at
array-copy
/natarray/
size-subarray