Entry Value
Name IN_IMAGE
Conclusion !y s f. y IN IMAGE f s <=> (?x. y = f x /\ x IN s)
Constructive Proof Yes
Axiom
N|A
Classical Lemmas N|A
Constructive Lemmas
  • T
  • !x. x = x
  • !t1 t2. t1 /\ t2 <=> t2 /\ t1
  • !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
  • !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 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)
  • Contained Package set-thm
    Comment Standard HOL library retrieved from OpenTheory
    Back to main package pageBack to contained package page