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Theorem nodups-interval-size
¬ dups(ints), ∀ i. i ∈ ints → j0 < i ∧ i ≤ j1, ints ≠ [] ⊦ n→i(# ints) ≤ j1 - 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: 12
Proof steps: 22
Used lemmas:
max-in-not-ls
,
max-in-01
,
Used spec theorems:
list-del
/intlista/
del1-in
list-data
/intlista/
le-one
list-del
/intlista/
l
intnat
/
n2i-sub
Used simplifier rules:
int-abs
/
lels-01
nat-basic1
/
zero
intnat
/
num-n2i-ls-02
int-basic2
/
ls-02
int-abs
/
forward-lsle
nat
/
lels
nat
/
ls-02
nat
/
le-add
nat
/
ler
list-del
/intlista/
dups
list-del
/intlista/
in-01-01
int-abs
/
ler
int-abs
/
forward-lels
int-abs
/
anti
int-abs
/
lels
int-abs
/
lels-02
list-del
/intlista/
dups-01
list-del
/intlista/
del1-empty
nat-basic1
/
one
list
/intlista/
e
list
/intlista/
len-02
nat-basic1
/
f
int-abs
/
succ-01
int-abs
/
sub-le-01
int-abs
/
sub-sub
list-del
/intlista/
in-02-01
intnat
/
nat2int-04
int-basic2
/
ls-01
oelem
/intlista/
transitivity
nat-basic2
/
c
nat-basic2
/
a
nat-basic1
/
ref-1
nat-basic2
/
s
nat
/
ls-01
nat
/
pred-03
int-abs
/
sub-add-01
int-basic2
/
add-a
int-basic2
/
add-c
int-abs
/
sub-ls
int-abs
/
succ-02
int-abs
/
lels-03
nat
/
lels-01
nat-basic1
/
one-01
list-data
/intlista/
l