Entry Value
Name EX_CONS
Conclusion !p h t. EX p (CONS h t) <=> p h \/ EX p t
Constructive Proof Yes
Axiom
N|A
Classical Lemmas N|A
Constructive Lemmas
  • T
  • !t. (F <=> t) <=> ~t
  • !t. (T <=> t) <=> t
  • !t. (t <=> F) <=> ~t
  • !t. (t <=> T) <=> t
  • 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))
  • Contained Package list-set-def
    Comment Standard HOL library retrieved from OpenTheory
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