| Entry |
Value |
|
Name |
INJECTIVE_ON_LEFT_INVERSE |
|
Conclusion |
!f s.
(!x y. x IN s /\ y IN s /\ f x = f y ==> x = y) <=>
(?g. !x. x IN s ==> g (f x) = x) |
|
Constructive Proof |
Yes |
|
Axiom |
(\a. a = (\b. (\c. c) = (\c. c))) (\d. (\e. d e) = d)
(\a. a = (\b. (\c. c) = (\c. c)))
(\d. (\e. e = (\f. (\c. c) = (\c. c)))
(\g. (\h i.
(\j k.
(\l. l j k) =
(\m. m ((\c. c) = (\c. c)) ((\c. c) = (\c. c))))
h
i <=>
h)
(d g)
(d ((@) d)))) |
|
Classical Lemmas |
N|A |
|
Constructive Lemmas |
T!x. x = x!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. t ==> t!f y. (\x. f x) y = f y!f g. (!x. f x = g x) ==> f = g!t. (\x. t x) = t!p x. p x ==> p ((@) p)!r. (!x. ?y. r x y) <=> (?f. !x. r x (f x))F <=> (!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)(?) = (\p. p ((@) p)) |
|
Contained Package |
set-thm |
|
Comment |
Standard HOL library retrieved from OpenTheory |
