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Theorem put-firstn-restn
⊦ n < # x → x[n := a] = firstn(n, x) + a ' + restn(n + 1, x)
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: 8
Proof steps: 20
Used lemmas:
first-all-01
,
put-one
,
firstN-len
,
put-last
,
put-app-right
,
put-app-left
,
first-append
,
put-succ
,
firstN-zero
,
put-zero
,
firstN-rec-01
,
elim-firstn-restn
,
restN-rec
,
Used spec theorems:
Used simplifier rules:
list-data
/
l
nat-basic
/
f
list
/
a
nat-basic
/
c
nat-basic
/
a
list-data
/
elim-list-c
nat
/
lels
nat-basic
/
s-04
nat-basic
/
succ
list
/
len-05
list
/
c
list
/
e
list
/
app-02
nat
/
lep
list
/
len
list-data
/
size-nil
list
/
Nil
list
/
len-01
nat
/
pred-03
nat
/
elim-pred-c
nat
/
le-def
nat-basic
/
lf-02
nat-basic
/
l-02
nat
/
eq
nat-basic
/
refl-nat
nat
/
les
nat-basic
/
oz
nat-basic
/
lf-01
nat
/
eqle-one
list
/
len-06
list-last
/
butlast-last
list
/
len-02
nat-basic
/
eq-01
nat
/
anti
nat
/
zero
nat-basic
/
add-base
nat
/
add-01
nat
/
ls-03
nat-basic
/
nls-fst
list-last
/
lb
nat
/
succ-01
nat
/
ls-02
nat-basic
/
z-01