Package list-nub-thm: Properties of the list nub function

Information

namelist-nub-thm
version1.49
descriptionProperties of the list nub function
authorJoe Hurd <joe@gilith.com>
licenseMIT
provenanceHOL Light theory extracted on 2012-08-06
requiresbool
list-def
list-length
list-nub-def
list-reverse
list-set
natural
set
showData.Bool
Data.List
Number.Natural
Set

Files

Theorems

l. nub (nub l) = nub l

l. nubReverse (nubReverse l) = nubReverse l

l. toSet (nub l) = toSet l

l. toSet (nubReverse l) = toSet l

l. length (nub l) length l

l. length (nubReverse l) length l

l x. member x (nub l) member x l

l x. member x (nubReverse l) member x l

Input Type Operators

Input Constants

Assumptions

¬

length [] = 0

nubReverse [] = []

n. n n

p. p

x. ¬member x []

t. t ¬t

(¬) = λp. p

t. (x. t) t

() = λp. p = λx.

t. (t ) t

t. t t

t. t

t. t

l. reverse (reverse l) = l

t. ( t) ¬t

l. length (reverse l) = length l

() = λp q. p q p

t. (t ) (t )

l. nub l = reverse (nubReverse (reverse l))

t1 t2. (if then t1 else t2) = t2

t1 t2. (if then t1 else t2) = t1

x y. x = y y = x

h t. length (h :: t) = suc (length t)

l x. member x l x toSet l

l x. member x (reverse l) member x l

() = λp q. (λf. f p q) = λf. f

m n. suc m suc n m n

() = λp q. r. (p r) (q r) r

s t. (x. x s x t) s = t

m n. m suc n m = suc n m n

x h t. member x (h :: t) x = h member x t

h t.
    nubReverse (h :: t) =
    if member h t then nubReverse t else h :: nubReverse t

p. p [] (h t. p t p (h :: t)) l. p l