Package list-quant-thm: Properties of list quantifiers

Information

namelist-quant-thm
version1.25
descriptionProperties of list quantifiers
authorJoe Hurd <joe@gilith.com>
licenseHOLLight
provenanceHOL Light theory extracted on 2011-11-27
requiresbool
function
set
list-def
list-set
list-append
list-map
list-quant-def
showData.Bool
Data.List
Function
Set

Files

Theorems

l. all (λx. T) l

P l. ¬all P l exists (λx. ¬P x) l

P l. ¬exists P l all (λx. ¬P x) l

P l. all P l x. x toSet l P x

P l. exists P l x. x toSet l P x

P f l. all P (map f l) all (P f) l

P f l. exists P (map f l) exists (P f) l

P l. (x. all (P x) l) all (λs. x. P x s) l

P l. (x. exists (P x) l) exists (λs. x. P x s) l

P l1 l2. all P (l1 @ l2) all P l1 all P l2

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

f g l. all (λx. f x = g x) l map f l = map g l

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

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

Input Type Operators

Input Constants

Assumptions

T

¬F T

¬T F

toSet [] =

p. all p []

F p. p

x. ¬(x )

x. id x = x

p. ¬exists p []

(¬) = λp. p F

a. x. x = a

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 T t

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

l. [] @ l = l

f. map f [] = []

t. (F t) ¬t

t. t F ¬t

() = λp q. p q p

t. (t T) (t F)

f y. (let x y in f x) = f y

x y. x = y y = x

t1 t2. t1 t2 t2 t1

t1 t2. t1 t2 t2 t1

() = 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)

f g x. (f g) x = f (g x)

t1 t2. ¬(t1 t2) ¬t1 ¬t2

t1 t2. ¬(t1 t2) ¬t1 ¬t2

f g. (x. f x = g x) f = g

() = λp q. r. (p r) (q r) r

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

P Q. (x. P x) Q x. P x Q

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

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

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

P Q. (x. P x Q x) (x. P x) x. Q x

P Q. (x. P x Q x) (x. P x) x. Q x

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