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

Information

namelist-append-thm
version1.13
descriptionProperties of the list append function
authorJoe Hurd <joe@gilith.com>
licenseHOLLight
provenanceHOL Light theory extracted on 2011-11-15
requiresbool
natural
set
list-def
list-thm
list-dest
list-length
list-set
list-append-def
showData.Bool
Data.List
Number.Natural
Set

Files

Theorems

l. l @ [] = l

l m. null (l @ m) null l null m

l m. length (l @ m) = length l + length m

l1 l2. toSet (l1 @ l2) = toSet l1 toSet l2

l m n. l @ m @ n = (l @ m) @ n

l m. head (l @ m) = if l = [] then head m else head l

l m. l @ m = [] l = [] m = []

Input Type Operators

Input Constants

Assumptions

T

¬F T

length [] = 0

toSet [] =

F p. p

(¬) = λp. p F

t. (x. t) t

() = λp. p = λx. T

t. (T t) t

t. F t F

t. T t t

t. t t t

n. 0 + n = n

l. [] @ l = l

t. (F t) ¬t

l. null l l = []

() = λp q. p q p

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

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

h t. ¬(h :: t = [])

h t. head (h :: t) = h

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

() = λp q. (λf. f p q) = λf. f T T

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

x s. insert x s = insert x s

m n. suc m + n = suc (m + n)

(s. s = s) s. s = s

P. (x y. P x y) y x. P x y

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

s t u. s t u = s (t u)

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