Proving Predicate Logic using Coq - Beginner Syntax

Posted by Alan on Stack Overflow See other posts from Stack Overflow or by Alan
Published on 2010-05-04T16:53:15Z Indexed on 2010/05/04 16:58 UTC
Read the original article Hit count: 243

Filed under:

coq

|

predicate

I'm trying to prove the following in Coq:

Goal (forall x:X, P(x) /\ Q(x)) -> ((forall x:X, P (x)) /\ (forall x:X, Q (x))).

Can someone please help? I'm not sure whether to split, make an assumption etc.

My apologies for being a complete noob

© Stack Overflow or respective owner

Related posts about coq

Proving Predicate Logic using Coq - Beginner Syntax

as seen on Stack Overflow - Search for 'Stack Overflow'
I'm trying to prove the following in Coq: Goal (forall x:X, P(x) /\ Q(x)) - ((forall x:X, P (x)) /\ (forall x:X, Q (x))). Can someone please help? I'm not sure whether to split, make an assumption etc. My apologies for being a complete noob >>> More
using an already proved lema/theorem/corollary in coq

as seen on Stack Overflow - Search for 'Stack Overflow'
I am trying to make a proof in Coq, and I would like to use a lemma already definded and proved by me. Is it possible for the following code? Lemma conj_comm: forall A B : Prop, A /\ B -> B /\ A. Proof. intros. destruct H. split. exact H0. exact H. Qed. Lemma not_conj_comm: forall A B : Prop… >>> More
How do I target a div without a class or id but with all these specific style-attributes

as seen on Stack Overflow - Search for 'Stack Overflow'
I'm restyling a certain page where I don't have access to all the source-HTML. So I'm left over with some hard to target elements within a page I need removed. For example the page is swamped with <div style="float: left; width: 10.25px; height: 284px;"></div>. To get rid of them I… >>> More
Proving f (f bool) = bool

as seen on Stack Overflow - Search for 'Stack Overflow'
How can I in coq, prove that a function f that accepts a bool true|false and returns a bool true|false (shown below), when applied twice to a single bool true|false would always return that same value true|false: (f:bool -> bool) For example the function f can only do 4 things, lets call the… >>> More
Good application for taking notes on 12.04?

as seen on Ask Ubuntu - Search for 'Ask Ubuntu'
Is there a good note taking application in ubuntu like Evernote exists for windows and Mac users. Requirements for good applications:- A thumbnail/list preview for all the created notes. An integration with the email address so that we can view the notes anywhere anytime. Any easy way to input… >>> More

Related posts about predicate

Try a sample: Using the counter predicate for event sampling

as seen on SQL Blog - Search for 'SQL Blog'
Extended Events offers a rich filtering mechanism, called predicates, that allows you to reduce the number of events you collect by specifying criteria that will be applied during event collection. (You can find more information about predicates in Using SQL Server 2008 Extended Events (by Jonathan… >>> More
What is the proper way to remove elements from a scala mutable map using a predicate

as seen on Stack Overflow - Search for 'Stack Overflow'
How to do that without creating any new collections? Is there something better than this? val m = scala.collection.mutable.Map[String, Long]("1" -> 1, "2" -> 2, "3" -> 3, "4" -> 4) m.foreach(t => if (t._2 % 2 == 0) m.remove(t._1)) println(m) >>> More
Predicate problem in ToSelectList

as seen on Stack Overflow - Search for 'Stack Overflow'
the ToSelectList method I have: public static IList<SelectListItem> ToSelectList<T>(this IEnumerable<T> itemsToMap, Func<T, string> textProperty, Func<T, string> valueProperty, Predicate<T> isSelected) { var result = new List<SelectListItem>(); foreach… >>> More
Basics of Join Predicate Pushdown in Oracle

as seen on Oracle Blogs - Search for 'Oracle Blogs'
Happy New Year to all of our readers! We hope you all had a great holiday season. We start the new year by continuing our series on Optimizer transformations. This time it is the turn of Predicate Pushdown. I would like to thank Rafi Ahmed for the content of this blog.Normally, a view cannot be joined… >>> More
How to use PredicateBuilder with nested OR conditionals in Linq

as seen on Stack Overflow - Search for 'Stack Overflow'
I've been very happily using PredicateBuilder but until now have only used it for queries with only either concatenated AND statements or OR statements. Now for the first time I need a pair of OR statements nested along with a some AND statements like this: select x from Table1 where a = 1 AND b… >>> More