Package relation-measure-thm: relation-measure-thm

Information

namerelation-measure-thm
version1.9
descriptionrelation-measure-thm
authorJoe Hurd <joe@gilith.com>
licenseHOLLight
provenanceHOL Light theory extracted on 2011-09-21
showData.Bool

Files

Theorems

m. Relation.wellFounded (Relation.measure m)

m a b.
    (y. Relation.measure m y a Relation.measure m y b)
    Number.Natural.≤ (m a) (m b)

Input Type Operators

Input Constants

Assumptions

T

Relation.wellFounded Number.Natural.<

n. ¬Number.Natural.< n n

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)

m. Relation.measure m = λx y. Number.Natural.< (m x) (m y)

m n. ¬Number.Natural.≤ m n Number.Natural.< n m

() = λp q. (λf. f p q) = λf. f T T

P. ¬(x. P x) x. ¬P x

() = λP. q. (x. P x q) q

<< m.
    Relation.wellFounded << Relation.wellFounded (λx x'. << (m x) (m 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

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

m n p.
    Number.Natural.< m n Number.Natural.≤ n p Number.Natural.< m p

(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

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)