Entry Value
Name irreflexive_emptyr
Conclusion irreflexive emptyr
Constructive Proof Yes
Axiom
N|A
Classical Lemmas N|A
Constructive Lemmas
  • T
  • !x y. ~emptyr x y
  • !x. ~(x IN {})
  • !x. x = x
  • !t. (!x. t) <=> t
  • !t. (F <=> t) <=> ~t
  • !t. (T <=> t) <=> t
  • !t. (t <=> F) <=> ~t
  • !t. (t <=> T) <=> t
  • !f y. (\x. f x) y = f y
  • !p a. (?x. a = x /\ p x) <=> p a
  • !p x. x IN GSPEC p <=> p x
  • !p x. x IN {y | p y} <=> p x
  • !r. irreflexive r <=> (!x. ~r x x)
  • !s x y. set_to_relation s x y <=> x,y IN s
  • F <=> (!p. p)
  • T <=> (\p. p) = (\p. p)
  • ~F <=> T
  • ~T <=> F
  • emptyr = set_to_relation {}
  • (~) = (\p. p ==> F)
  • (/\) = (\p q. (\f. f p q) = (\f. f T T))
  • (==>) = (\p q. p /\ q <=> p)
  • (!) = (\p. p = (\x. T))
  • (?) = (\p. !q. (!x. p x ==> q) ==> q)
  • {} = {x | F}
  • Contained Package relation-thm
    Comment Standard HOL library retrieved from OpenTheory
    Back to main package pageBack to contained package page