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Theorem get-split-take-drop
n < # x ⊦ x = x.take(n) + (x[n] + x.drop(n + 1))
Type: A user defined theorem
Validity: The proof is valid.
Features:
Comment:
Used by:
Used by units in proved state:
Proof exists?: Yes
View
the proof
Infos about the proof
Proved?: Yes
Interactions: 1
Proof steps: 9
Used lemmas:
firstN-len
,
firstN-rec
,
firstN-zero
,
get-last-04
,
elim-firstn-restn
,
restN-rec
,
Used spec theorems:
Used simplifier rules:
list-data
/
l
nat-basic
/
f
list
/
a
list
/
c
nat-basic
/
c
nat-basic
/
a
list-data
/
elim-add
nat
/
lels
nat-basic
/
s-04
nat-basic
/
succ
list
/
len-05
list
/
e
list
/
app-02
nat
/
lep
list
/
len
list
/
len-06
list-data
/
size-nil
list
/
app
list-last
/
last-one
list
/
Nil
list
/
c-04
list-last
/
l-02
list
/
len-02
list
/
c-08
list
/
c-07
list
/
len-01
list-last
/
last-elim