Package list-member: The list member function

Information

namelist-member
version1.34
descriptionThe list member function
authorJoe Hurd <joe@gilith.com>
licenseMIT
requiresbool
function
natural
set
list-def
list-length
list-set
list-append
list-map
list-quant
list-filter
list-reverse
list-nth
showData.Bool
Data.List
Function
Number.Natural
Set

Files

Defined Constant

Theorems

x. ¬member x []

x l. member x l x toSet l

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

l n. n < length l member (nth n l) l

s. finite s x. member x (fromSet s) x s

P l. (x. member x l P x) all P l

P l. (x. P x member x l) exists P l

P l x. member x (filter P l) P x member x l

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

x l1 l2. member x (l1 @ l2) member x l1 member x l2

l x. member x l i. i < length l x = nth i l

f y l. member y (map f l) x. member x l y = f x

P Q l. (x. member x l P x Q x) all P l all Q l

P Q l. (x. member x l P x Q x) exists P l exists Q l

Input Type Operators

Input Constants

Assumptions

T

¬F T

¬T F

length [] = 0

reverse [] = []

toSet [] =

p. all p []

F p. p

x. ¬(x )

x. id x = x

n. 0 < suc n

p. ¬exists p []

(¬) = λp. p F

() = λp. p ((select) p)

t. (x. t) t

t. (x. t) t

t. (λx. t x) = t

() = λp. p = λx. T

t. ¬¬t t

t. (T t) t

t. F t F

t. T t t

t. t F F

t. F t T

t. T t t

t. t T T

t. F t t

t. T t T

t. t F t

t. t T T

m. m < 0 F

l. [] @ l = l

f. map f [] = []

P. filter P [] = []

t. (F t) ¬t

t. (t F) ¬t

t. t F ¬t

() = λp q. p q p

t. (t T) (t F)

s. finite s toSet (fromSet s) = s

x y. x = y y = x

h t. nth 0 (h :: t) = h

t1 t2. t1 t2 t2 t1

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

m. m = 0 n. m = suc n

() = λp q. (λf. f p q) = λf. f T T

p. ¬(x. p x) x. ¬p x

p. ¬(x. p x) x. ¬p x

() = λp. q. (x. p x q) q

h t. toSet (h :: t) = insert h (toSet t)

m n. suc m < suc n m < n

() = λp q. r. (p r) (q r) r

x l. reverse (x :: l) = reverse l @ x :: []

p q. p (x. q x) x. p q x

p q. p (x. q x) x. p q x

p q. (x. p x) q x. p x q

p q. (x. p x) q x. p x q

t1 t2 t3. (t1 t2) t3 t1 t2 t3

l h t. (h :: t) @ l = h :: t @ l

p. (x. y. p x y) y. x. p x (y x)

f h t. map f (h :: t) = f h :: map f t

p h t. all p (h :: t) p h all p t

p h t. exists p (h :: t) p h exists p t

P. P 0 (n. P n P (suc n)) n. P n

x y s. x insert y s x = y x s

p q. (x. p x) (x. q x) x. p x q x

P. P [] (a0 a1. P a1 P (a0 :: a1)) x. P x

h t n. n < length t nth (suc n) (h :: t) = nth n t

P h t. filter P (h :: t) = if P h then h :: filter P t else filter P t

p c x y. p (if c then x else y) (c p x) (¬c p y)

NIL' CONS'.
    fn. fn [] = NIL' a0 a1. fn (a0 :: a1) = CONS' a0 a1 (fn a1)