Package list-map-thm: list-map-thm

Information

namelist-map-thm
version1.12
descriptionlist-map-thm
authorJoe Hurd <joe@gilith.com>
licenseHOLLight
provenanceHOL Light theory extracted on 2011-09-21
showData.Bool

Files

Theorems

Data.List.map Function.id = Function.id

l. Data.List.map (λx. x) l = l

l f. Data.List.length (Data.List.map f l) = Data.List.length l

f l.
    Data.List.toSet (Data.List.map f l) = Set.image f (Data.List.toSet l)

f l. Data.List.map f l = Data.List.[] l = Data.List.[]

f g l.
    Data.List.map (Function.∘ g f) l = Data.List.map g (Data.List.map f l)

f l1 l2.
    Data.List.map f (Data.List.@ l1 l2) =
    Data.List.@ (Data.List.map f l1) (Data.List.map f l2)

f. (m. l. Data.List.map f l = m) y. x. f x = y

f.
    (l m. Data.List.map f l = Data.List.map f m l = m)
    x y. f x = f y x = y

Input Type Operators

Input Constants

Assumptions

T

Function.id = λx. x

F p. p

x. Function.id x = x

t. t ¬t

(¬) = λp. p F

t. (x. t) t

t. (λx. t x) = t

() = λp. p = λx. T

x. x = x T

() = λp q. p q p

t. (t T) (t F)

h t. ¬(Data.List.:: h t = Data.List.[])

(¬T F) (¬F T)

() = 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

f g x. Function.∘ f g x = f (g x)

f g. f = g x. f x = g x

() = λp q. r. (p r) (q r) r

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

Data.List.length Data.List.[] = 0
  h t.
    Data.List.length (Data.List.:: h t) =
    Number.Natural.suc (Data.List.length t)

(t. ¬¬t t) (¬T F) (¬F T)

Data.List.toSet Data.List.[] = Set.∅
  h t.
    Data.List.toSet (Data.List.:: h t) = Set.insert h (Data.List.toSet t)

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

h1 h2 t1 t2. Data.List.:: h1 t1 = Data.List.:: h2 t2 h1 = h2 t1 = t2

(l. Data.List.@ Data.List.[] l = l)
  l h t.
    Data.List.@ (Data.List.:: h t) l = Data.List.:: h (Data.List.@ t l)

(f. Data.List.map f Data.List.[] = Data.List.[])
  f h t.
    Data.List.map f (Data.List.:: h t) =
    Data.List.:: (f h) (Data.List.map f t)

(f. Set.image f Set.∅ = Set.∅)
  f x s. Set.image f (Set.insert x s) = Set.insert (f x) (Set.image f s)

t. ((T t) t) ((t T) t) ((F t) ¬t) ((t F) ¬t)

t. (T t t) (t T t) (F t F) (t F F) (t t t)

t. (T t T) (t T T) (F t t) (t F t) (t t t)

t. (T t t) (t T T) (F t T) (t t T) (t F ¬t)

p q r.
    (p q q p) ((p q) r p q r) (p q r q p r)
    (p p p) (p p q p q)