Package relation-measure: Definitions and theorems about natural number measures

Information

namerelation-measure
version1.0
description Definitions and theorems about natural number measures
authorJoe Hurd <joe@gilith.com>
licenseMIT
showData.Bool
Number.Natural
Relation

Files

Defined Constant

Theorems

m. wellFounded (measure m)

m. measure m = λx y. m x < m y

m a b. (y. measure m y a measure m y b) m a m b

Input Type Operators

Input Constants

Assumptions

T

wellFounded (<)

n. ¬(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 n. ¬(m n) 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. wellFounded << 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. m < n n p 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)