| Entry |
Value |
|
Name |
FORALL_BOOL_THM |
|
Conclusion |
!p. (!b. p b) <=> p T /\ p F |
|
Constructive Proof |
No |
|
Axiom |
!t. t \/ ~t |
|
Classical Lemmas |
!t. (t <=> T) \/ (t <=> F) |
|
Constructive Lemmas |
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 <=> (!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)) |
|
Contained Package |
bool-class |
|
Comment |
Standard HOL library retrieved from OpenTheory |
