| Entry |
Value |
|
Name |
wellfounded_irreflexive |
|
Conclusion |
!r. WF r ==> irreflexive r |
|
Constructive Proof |
Yes |
|
Axiom |
N|A |
|
Classical Lemmas |
N|A |
|
Constructive Lemmas |
T!x. x = x!p q. (!x. p ==> q x) <=> p ==> (!x. q x)!t. F ==> t <=> T!t. T ==> t <=> t!t. t ==> F <=> ~t!t. t ==> T <=> T!t. t ==> t!f y. (\x. f x) y = f y!r. WF r <=> (!p. (?x. p x) ==> (?x. p x /\ (!y. r y x ==> ~p y)))!r. irreflexive r <=> (!x. ~r x x)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. p = (\x. T))(?) = (\p. !q. (!x. p x ==> q) ==> q) |
|
Contained Package |
relation-well-founded-thm |
|
Comment |
Standard HOL library retrieved from OpenTheory |
