| Entry |
Value |
|
Name |
LEFT_IMP_FORALL_THM |
|
Conclusion |
!p q. (!x. p x) ==> q <=> (?x. p x ==> q) |
|
Constructive Proof |
No |
|
Axiom |
!t. t \/ ~t |
|
Classical Lemmas |
!t1 t2. ~(t1 ==> t2) <=> t1 /\ ~t2!t. ~ ~t <=> t!t. (t <=> T) \/ (t <=> F)!p. ~(?x. p x) <=> (!x. ~p x) |
|
Constructive Lemmas |
T!x. x = x!t1 t2. ~(t1 ==> t2) <=> t1 /\ ~t2!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. 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. p x /\ q)!p. ~(?x. p x) <=> (!x. ~p 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 q. !r. (p ==> r) ==> (q ==> r) ==> r)(!) = (\p. p = (\x. T))(?) = (\p. !q. (!x. p x ==> q) ==> q) |
|
Contained Package |
bool-class |
|
Comment |
Standard HOL library retrieved from OpenTheory |
