| Entry |
Value |
|
Name |
FORALL_IN_IMAGE |
|
Conclusion |
!p f s. (!y. y IN IMAGE f s ==> p y) <=> (!x. x IN s ==> p (f x)) |
|
Constructive Proof |
Yes |
|
Axiom |
N|A |
|
Classical Lemmas |
N|A |
|
Constructive Lemmas |
T!x. x = x!y s f. y IN IMAGE f s <=> (?x. y = f x /\ x IN s)!t1 t2. t1 /\ t2 <=> t2 /\ t1!t. (!x. 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!f y. (\x. f x) y = f y!f s. IMAGE f s = {y | ?x. x IN s /\ y = f x}!p a. (?x. a = x /\ p x) <=> p a!p x. x IN GSPEC p <=> p x!p x. x IN {y | p y} <=> p xF <=> (!p. p)T <=> (\p. p) = (\p. p)(~) = (\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 |
set-thm |
|
Comment |
Standard HOL library retrieved from OpenTheory |
