Entry
Value
Name
case_option_id
Conclusion
!x. case_option NONE SOME x = x
Constructive Proof
Yes
Axiom
N|A
Classical Lemmas
N|A
Constructive Lemmas
T
!x. x = x
!b f a. case_option b f (SOME a) = f a
!b f. case_option b f NONE = b
!f y. (\x. f x) y = f y
!p. p NONE /\ (!a. p (SOME a)) ==> (!x. p x)
!x. x = NONE \/ (?a. x = SOME a)
T <=> (\p. p) = (\p. p)
(/\) = (\p q. (\f. f p q) = (\f. f T T))
(==>) = (\p q. p /\ q <=> p)
(\/) = (\p q. !r. (p ==> r) ==> (q ==> r) ==> r)
(!) = (\p. p = (\x. T))
(?) = (\p. !q. (!x. p x ==> q) ==> q)
Contained Package
option-dest-thm
Comment
Standard HOL library retrieved from OpenTheory
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