one_Axiom

Entry	Value
Name	one_Axiom
Conclusion	!e. ?!fn. fn one = e
Constructive Proof	Yes
Axiom	(\a. a = (\b. (\c. c) = (\c. c))) (\d. (\e. d e) = d)
Classical Lemmas	N\|A
Constructive Lemmas	T !x y. x = y <=> y = x !x y. x = y ==> y = x !e. ?fn. fn one = e !x. x = x !v. v = one !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 !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 !f g. (!x. f x = g x) ==> f = g !t. (\x. t x) = t !p. (?!x. p x) <=> (?x. p x) /\ (!x x'. p x /\ p x' ==> x = 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 /\ (!x y. p x /\ p y ==> x = y))
Contained Package	unit-thm
Comment	Standard HOL library retrieved from OpenTheory