Entry
Value
Name
IN_UNIONS
Conclusion
!s x. x IN UNIONS s <=> (?t. t IN s /\ x IN t)
Constructive Proof
Yes
Axiom
N|A
Classical Lemmas
N|A
Constructive Lemmas
T
!x. x = x
!t. (!x. 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
!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 x
!s. UNIONS s = {x | ?u. u IN s /\ x IN u}
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)
Contained Package
set-thm
Comment
Standard HOL library retrieved from OpenTheory
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