Package list-quant-thm: list-quant-thm

Information

namelist-quant-thm
version1.0
descriptionlist-quant-thm
authorJoe Hurd <joe@gilith.com>
licenseHOLLight
provenanceHOL Light theory extracted on 2011-03-15
showData.Bool

Files

Theorems

l. Data.List.all (λx. T) l

P l. ¬Data.List.exists P l Data.List.all (λx. ¬P x) l

P l. ¬Data.List.all P l Data.List.exists (λx. ¬P x) l

P f l.
    Data.List.all P (Data.List.map f l) Data.List.all (Function.o P f) l

P f l.
    Data.List.exists P (Data.List.map f l)
    Data.List.exists (Function.o P f) l

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

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

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

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

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

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

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

Input Type Operators

Input Constants

Assumptions

T

x. Function.id x = x

a. x. x = a

t. (x. t) t

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)

(¬T F) (¬F T)

f y. (λx. f x) y = f y

() = 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.o 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. 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

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

(t. ¬¬t t) (¬T F) (¬F T)

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

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

t1 t2. (¬(t1 t2) ¬t1 ¬t2) (¬(t1 t2) ¬t1 ¬t2)

(P. Data.List.all P Data.List.[] T)
  h P t. Data.List.all P (Data.List.:: h t) P h Data.List.all P t

(P. Data.List.exists P Data.List.[] F)
  h P t.
    Data.List.exists P (Data.List.:: h t) P h Data.List.exists P t

(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)

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)

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)