| Entry |
Value |
|
Name |
INFINITE_NONEMPTY |
|
Conclusion |
!s. INFINITE s ==> ~(s = {}) |
|
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!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 <=> 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)!p q. (!x. p x ==> q x) ==> (?x. p x) ==> (?x. q x)!s. INFINITE s <=> ~FINITE sFINITE {}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 |
set-finite-thm |
|
Comment |
Standard HOL library retrieved from OpenTheory |
