Package bool-int: Intuitionistic boolean theorems

Information

namebool-int
version1.3
descriptionIntuitionistic boolean theorems
authorJoe Hurd <joe@gilith.com>
licenseMIT
provenanceHOL Light theory extracted on 2011-07-18
showData.Bool

Files

Theorems

T

x. x = x

a. x. x = a

a. ∃!x. x = a

t. (x. t) t

t. (x. t) t

x. x = x T

t1 t2. (let xt2t1) = t1

(¬T F) (¬F T)

f y. (let xyf x) = f y

x y. x = y y = x

x y. x = y y = x

t1 t2. t1 t2 t2 t1

t1 t2. t1 t2 t2 t1

a b. (a b) a b

A B. (B A) ¬A ¬B

P a. (x. a = x P x) P a

P a. (x. x = a P x) P a

P a. (x. a = x P x) P a

P a. (x. x = a P x) P a

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

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

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

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

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

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

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

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

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

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

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

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

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

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

P. (∃!x. P x) x. y. P y x = y

x y z. x = y y = z x = z

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

p q r. p q r p q r

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

p q r. p q r p q r

p q r. p q r q p r

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

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

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

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

P. (∃!x. P x) x. P x y. P y y = x

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

A B C D. (A B) (C D) A C B D

A B C D. (A B) (C D) A C B D

A B C D. (B A) (C D) (A C) B D

P. (∃!x. P x) (x. P x) x x'. P x P x' x = 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)

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)

Input Type Operators

Input Constants

Assumptions

F p. p

(~) = λp. p F

T (λp. p) = λp. p

() = λp. p = λx. T

() = λp q. p q p

() = λp q. (λf. f p q) = λf. f T T

() = λP. q. (x. P x q) q

() = λp q. r. (p r) (q r) r

(∃!) = λP. () P x y. P x P y x = y