Entry Value
Name WF_EQ
Conclusion !r. WF r <=> (!p. (?x. p x) <=> (?x. p x /\ (!y. r y x ==> ~p y)))
Constructive Proof No
Axiom 
!t. t \/ ~t
Classical Lemmas
  • !t1 t2. ~t1 ==> ~t2 <=> t2 ==> t1
  • !t. (t <=> T) \/ (t <=> F)
    		•
    Constructive Lemmas
  • T
  • !x. x = x
  • !t1 t2. ~t1 ==> ~t2 <=> t2 ==> t1
  • !t. (F <=> t) <=> ~t
  • !t. (T <=> t) <=> t
  • !t. (t <=> F) <=> ~t
  • !t. (t <=> T) <=> t
  • !t. F ==> t <=> T
  • !t. T ==> t <=> t
  • !t. t ==> F <=> ~t
  • !t. t ==> T <=> T
  • !t. F \/ t <=> t
  • !t. T \/ t <=> T
  • !t. t \/ F <=> t
  • !t. t \/ T <=> T
  • !t. t \/ t <=> t
  • !t. t ==> t
  • !t. (t <=> T) \/ (t <=> F)
  • !r. WF r <=> (!p. (?x. p x) ==> (?x. p x /\ (!y. r y x ==> ~p y)))
  • F <=> (!p. p)
  • T <=> (\p. p) = (\p. p)
  • ~F <=> T
  • ~T <=> F
  • (~) = (\p. p ==> F)
  • (/\) = (\p q. (\f. f p q) = (\f. f T T))
  • (==>) = (\p q. p /\ q <=> p)
  • (\/) = (\p q. !r. (p ==> r) ==> (q ==> r) ==> r)
  • (!) = (\p. p = (\x. T))
  • (?) = (\p. !q. (!x. p x ==> q) ==> q)
    		•
    Contained Package relation-well-founded-thm
    Comment Standard HOL library retrieved from OpenTheory
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