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Theorem countFun-dist
⊦ 0 ≤ i ∧ i ≤ j → Σ countFun(i, j, λ j0. intfun1(j0) + intfun2(j0)) = Σ countFun(i, j, λ j0. intfun1(j0)) + Σ countFun(i, j, λ j0. intfun2(j0))
Type: A user defined theorem
Validity: The proof is valid.
Features:
Comment:
Used by:
Used by units in proved state:
int-fac
,
Proof exists?: Yes
View
the proof
Infos about the proof
Proved?: Yes
Interactions: 6
Proof steps: 13
Used lemmas:
sum-empty
,
countFun-base-01
,
sum-rec
,
countFun-rec
,
countFun-base
,
Used spec theorems:
Used simplifier rules:
int-abs
/
elim-sub
int-abs
/
forward-le-01
int-abs
/
lels-01
int-basic2
/
ls
int-abs
/
lenls
int-abs
/
zero-gels-04
int-abs
/
lep
int-basic2
/
add-in
list
/intlista/
a
int-abs
/
numle-02
int-abs
/
numleledel-01
int-basic2
/
add-a
int-basic2
/
add-c
int-abs
/
le-add
int-abs
/
leone
int-abs
/
lels
int-abs
/
anti
int-basic2
/
add-zero
int-abs
/
sub-add-05
intnat
/
abs-pred