Package pair-def: pair-def

Information

namepair-def
version1.0
descriptionpair-def
authorJoe Hurd <joe@gilith.com>
licenseHOLLight
provenanceHOL Light theory extracted on 2011-02-19
showData.Bool

Files

Defined Type Operator

Defined Constants

Theorems

x y. Data.Pair.fst (Data.Pair., x y) = x

x y. Data.Pair.snd (Data.Pair., x y) = y

p. x y. p = Data.Pair., x y

x y a b. Data.Pair., x y = Data.Pair., a b x = a y = b

Input Type Operators

Input Constants

Assumptions

T

() = λP. P ((select) P)

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)

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

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

P x. (y. P y y = x) (select) P = x

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

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)