| Entry |
Value |
|
Name |
NOT_EX_NOT |
|
Conclusion |
!p l. ~EX (\x. ~p x) l <=> ALL p l |
|
Constructive Proof |
No |
|
Axiom |
!t. t \/ ~t
(\a. a = (\b. (\c. c) = (\c. c))) (\d. (\e. d e) = d) |
|
Classical Lemmas |
!t1 t2. ~(t1 /\ t2) <=> ~t1 \/ ~t2!t1 t2. ~(t1 \/ t2) <=> ~t1 /\ ~t2!t. ~ ~t <=> t!t. (t <=> T) \/ (t <=> F)!p l. ~ALL p l <=> EX (\x. ~p x) l!p l. ~ALL (\x. ~p x) l <=> EX p l!p l. ~EX p l <=> ALL (\x. ~p x) l |
|
Constructive Lemmas |
T!x. x = x!p1 p2 q1 q2. (p1 ==> p2) /\ (q1 ==> q2) ==> p1 /\ q1 ==> p2 /\ q2!p1 p2 q1 q2. (p1 ==> p2) /\ (q1 ==> q2) ==> p1 \/ q1 ==> p2 \/ q2!t1 t2. ~(t1 /\ t2) <=> ~t1 \/ ~t2!t1 t2. ~(t1 \/ t2) <=> ~t1 /\ ~t2!t. (!x. t) <=> t!t. ~ ~t <=> t!t. F /\ t <=> F!t. T /\ t <=> t!t. t /\ F <=> F!t. t /\ T <=> 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 <=> F)!f y. (\x. f x) y = f y!t. (\x. t x) = t!p h t. ALL p (CONS h t) <=> p h /\ ALL p t!p h t. EX p (CONS h t) <=> p h \/ EX p t!p q. (!x. p x ==> q x) ==> (?x. p x) ==> (?x. q x)!p l. ~ALL p l <=> EX (\x. ~p x) l!p l. ~ALL (\x. ~p x) l <=> EX p l!p l. ~EX p l <=> ALL (\x. ~p x) l!p. ~EX p []!p. ALL p []!p. p [] /\ (!h t. p t ==> p (CONS h t)) ==> (!l. p l)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 |
list-set-thm |
|
Comment |
Standard HOL library retrieved from OpenTheory |
