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Theorem countFun-at
⊦ n→i(n) ≤ j - i ∧ 0 ≤ i ∧ i ≤ j → countFun(i, j, intfun)[n] = intfun(i + n→i(n))
Type: A user defined theorem
Validity: The proof is valid.
Features: simp, localsimp,
Comment:
Used by:
Used by units in proved state:
int-mod
,
int-fac
,
Proof exists?: Yes
View
the proof
Infos about the proof
Proved?: Yes
Interactions: 16
Proof steps: 29
Used lemmas:
countFun-base-03
,
countFun-base-02
,
countFun-length
,
countFun-last
,
Used spec theorems:
list-del
/intlista/
get-last
list-del
/intlista/
get-butlast
int-abs
/
sub-le-01
int-abs
/
Abs-pos
intnat
/
abs-succ-02
Used simplifier rules:
nat-basic1
/
neq-01
list
/intlista/
a
list-del
/intlista/
get-append-grt
nat
/
sub-base
int-abs
/
lep-01
intnat
/
nat2int-10
intnat
/
inni-ls
nat
/
lels
nat
/
ls
int-abs
/
lenls
nat
/
elim-sub
int-abs
/
forward-lsle
int-abs
/
lels-01
int-abs
/
sub-ls
int-abs
/
succ-02
int-abs
/
ler
int-abs
/
bet-01
int-abs
/
abs-03
int-abs
/
absle
intnat
/
labs-01
nat-basic2
/
z-01
nat
/
not-zero
int-abs
/
forward-le-01
nat
/
lez
int-abs
/
numleledel
nat-basic2
/
add-base
int-abs
/
abs-16
int-abs
/
abs-09
nat
/
pred-03
intnat
/
abs-zero
nat-basic2
/
a
nat-basic2
/
c
nat
/
eq
oelem
/intlista/
lel
nat
/
elim-pred-c
int-abs
/
forward-le-04
list-data
/intlista/
l
int-abs
/
forward-le-05
nat-basic1
/
f
nat
/
ler
intnat
/
le
int-basic2
/
ls-02
intnat
/
nat2int-02
int-basic2
/
eq
int-abs
/
lels-02
int-abs
/
sub-add
intnat
/
n2n
int-abs
/
le-add
int-abs
/
leone
intnat
/
num-n2i-ls-02
nat-basic1
/
zero
int-abs
/
Sub-def
int-basic2
/
add-a
int-basic2
/
add-c
intnat
/
ini2-abs
int-abs
/
abssub
int-abs
/
zero-gels-04
int-abs
/
sub-le-01
int-abs
/
succ-01
int-abs
/
lels
int-abs
/
anti
list-data
/intlista/
size-01
int-basic2
/
add-zero