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Theorem sum-constant-countFun
∀ i1. i ≤ i1 ∧ i1 ≤ j → intfun(i1) = i0, i ≤ j, 0 ≤ i ⊦ Σ countFun(i, j, intfun) = (1 + j - i) * i0
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: 10
Proof steps: 22
Used lemmas:
countFun-base-02
,
countFun-base-03
,
sum-empty
,
countFun-base
,
sum-one
,
sum-app
,
countFun-last
,
Used spec theorems:
intnat
/
abs-succ-02
int-mult
/
numsucc
Used simplifier rules:
int-abs
/
forward-lele
list
/intlista/
a
nat
/
lels
nat
/
ls
int-abs
/
lels
nat
/
lez
nat
/
not-zero
int-abs
/
bet
nat-basic2
/
oz
int-abs
/
leone
int-abs
/
lenls
intnat
/
num-i2n-le
int-basic1
/
lst-01
nat
/
eq-02
nat
/
pred-03
oelem
/intlista/
lel
nat
/
elim-pred-c
nat
/
succ-01
nat
/
lep
nat-basic2
/
a
nat-basic2
/
c
nat-basic2
/
l
intnat
/
labs
int-abs
/
absle
oelem
/intlista/
irreflexivity
nat
/
lels-01
nat
/
eqle-one
nat-basic1
/
f
intnat
/
abs-zero
intnat
/
labs-01
int-abs
/
abs-16
nat
/
elim-sub
int-abs
/
succ-01
int-abs
/
sub-le-01
int-basic2
/
add-zero
int-abs
/
sub-add
int-mult
/
one
int-mult
/
associativity
int-mult
/
commutativity
int-abs
/
zero-gels-04
int-abs
/
anti
int-abs
/
forward-le-05
int-abs
/
forward-le-01
int-abs
/
forward-lels
int-abs
/
lels-02
int-abs
/
lels-01
int-basic1
/
ls-01
int-abs
/
Sub-def
int-abs
/
ler
int-abs
/
sub-add-01
int-basic2
/
add-a
int-basic2
/
add-c