How to prove in a formal system (like HFOL) the following formula $\forall x\exists y(x = y)$?  Obviously, we would like to use the axiom $x = x$ and then use a rule for introducing $\exists$, but how do we get $x = y$?
Give a deduction of $\forall y \exists x (x=y)$  My thinking is I can prove $\exists x(x=y)$ then use generalization theorem， which is equivalent to prove $\neg \forall x \neg (x=y)$ but I got stuck proving this... thanks in advance  Sorry that I did not specify what deduction system that I want to use here, it is the deduction sequence  where ai is either Axiom or original hypothesis or obtained from MP
Do WALLS matter if I'm building the 6-inch brick defense from Corruption/Crimson for my city? Improve the user self-deletion process The current process for self-deletion of a user account has several problematic aspects, both in the process itself and in the end result. Some of these issues are:   The process requires manual intervention of a mod or SE employee, leading to delays and sometimes mistakes. It is more complicated than it has to be, which can lead to the impression that SE is imposing some rather arbitrary-looking restrictions and steps one has to take. This can give the impression that the user isn't really in control of his private data at SE. It is irreversible once the account is deleted, although an account can be partially reconstructed with a lot of manual effort from an SE developer. There is no real protection against mod/SE employee errors, if an account is deleted in error, there is no easy way to undo the damage. Because it is manual, it consumes the time of SE employees that have to deal with it  (unless  is used), removing useful voting information and annoying users that lose reputation that way.   I'm proposing an alternative way of handling self-deletion that would be automated, and also reversible to some extent, while still being pretty much a hard-delete (and not a soft-delete that would be problematic with respect to user privacy). The process would work roughly like this:   The user clicks a "delete profile" button in his profile. There should be a way to indicate if you want to delete all profiles on all SE sites, only on this site and a way to select multiple sites from a list where the profile should be deleted. It is verified that the user has true access to the account in some way (confirmation mail?) and not just someone that found the unlocked computer of the user. A countdown until deletion is started (I'd go with 48h, but that could be different). The timer shouldn't be too long, but long enough to correct mistakes and leave users a bit of time to reconsider. Alternative options would be to enable users to override the countdown if they really want to nuke their account immediately. Another option would be to soft-delete the account immediately, and make the countdown only for hard-deletion of the user data. Upon deletion, the posts of the user and his votes are transferred to a newly created blank account, the original account itself is hard-deleted with all the remaining data it contains. The dummy account that holds the user's data should be flagged in some way as deleted, so that the profile links will be disabled, the profile won't be accessible and it won't appear in any user lists.  The user receives a private code that can be used to claim ownership of the account. Other ways are not possible as all private information is removed about the account. This allows for an automatic way of reclaiming most of the important parts of a deleted account. The ability to restore a deleted account might have to be somewhat restricted to avoid misusing it to get rid of the account history. It is more meant as an additional safeguard so that account reconstruction is more easily possible in rare cases. Such additional safeguards might be necessary as the deletion itself would be automatic and without oversight from SE or moderators.   I personally think that the information which posts and votes were connected to a (now anonymized) account is not sensitive enough that it would have to be removed on account deletion. My idea is that this would be close enough to a hard-delete that it satisfies any privacy concerns, but still allow reassociation of posts with a recovered account. The partial reversibility would alleviate concerns about removing the manual oversight by mods and SE employees over the account deletion process. Suppose $z\neq -1$ is a complex number of norm 1m $(|z| =1)$. I know that $z= n + mi$, what is the most straightforward way of solving this problem? I was also given the following sketch for a possible approach. I have read several questions regarding how to fix an already enabled desktop cube or the problems it had in 11.04. But in 11.10, how can I correctly enable desktop cube in Unity 3D? System App Permissions I have an application that needs root permissions to run.  No biggie, all of my personal devices are rooted, so I am very comfortable with the process. The problem is that this application is to be used on company owned devices issued to certain employees and I don't want them to be able to uninstall the application nor do I want them having root access to the device.  I was thinking that the following process would accomplish my goals:   Root the device Install my app as a system app Launch the application and grant su rights to it Unroot the device   Since it would be a system app, and the device wouldn't be rooted, users would be prevented from removing the app.  What I am unsure of is whether or not that application would retain its root privileges once the device is unrooted?   Any feedback or insight would be greatly appreciated! Java string to date conversion Under Wild Shape it says "assume the shape of a beast" you have seen before. Does this mean they can only transform into creatures that have the beast type, such as bear, wolf, crocodile, etc.? Or can they turn into things with other types, like dragon, monstrosity, humanoid, fiend, etc.? How to make math font huge Using "answer your own question" to advertise completed open source project? Render semi-transparent volume with cycles I have the following ammeter:   The seller recommends 75mV 100A shunt be placed with it. I want to know what will happen if I change the voltage going through the shunt. Should I be changing the shunt as well to read amps correctly?   I want to build a 1-40V (or maybe 50V) adjustable DC power supply and use this ammeter to measure current. What the right value of shunt that I should use to get the right measurement? Changing shunts in a lab bench power supply is impractical, of course.  EDIT: I am planning to measure only up to 5A or so. Sorry I forgot to mention this previously. My grandparents bought a flight on United Airlines that departs on Feb 10 2019, as the one and same ticket, from Toronto, to ORD with 1 55-minute layover, then Maui. Please ping me if I ought post their return flight on Feb 24's details.   advises:     There should be no customs and immigrations formalities at ORD, as YYZ is a , and CBP matters will be handled in Toronto.    I'm assuming that  persists during their vacation to Maui.   reported some TSA agents' refusal to work.  Will  refuse to work, or any other federal workers pertinent to travelling to and from the US? Exporting video to .mov in Blender 2.79 In the past, Blender (at least the Mac version) has had the ability to encode video files as .mov, the format used by Quicktime Player. However, with Blender 2.79 this feature seems to have vanished, for both the Internal and Cycles render engines. The release log happens to have the entry "Video encoding settings have been simplified, along with the addition of a Constant Rate Factor (CRF) mode" which I suppose could be the cause.  Does anyone know what happened—whether it is the aformentioned reason or something else—and how to export videos as Quicktime .mov in Blender 2.79? SSL password on apache2 restart I setup wildcard SSL certificate from Godaddy on Apache2. Whenever the server restarts it asks for the passphrase for the SSL certificate's private key.    What's the best way to remove this obstacle to restarts, because when logfile rotation restart occurs in the middle of the night, the server doesn't come back up, and I get an unhappy client call in the morning, as it is a shared server. How can I get the list of available databases on a SQL Server instance? I'm planning to make a list of them in a combo box in VB.NET. Equivalent of "both" when referring to three or more items? What would be the correct word to use when referring to three or more items, in the same manner as the word both?  For example, using two words, with the word both:     "There are several recommendations I   have to further improve the sites —   both to improve their profit, and   decrease their cost."   Using three words, with a blank space in place of the correct word:     "There are several recommendations I   have to further improve the sites —   _ to improve their profit, decrease their cost and improve their   usability."   So, what would be the correct word to use in place of the __? Code coverage for wrapper class is 0% I have written below Wrapper class.  global class BI_VA_AutomationWrapper {      global class BI_VA_AutomationRequest {      webservice String userName;     webservice String emailId;     webservice String buinessUnit;     webservice String orgName;     webservice String country;     webservice String environment;     webservice String myShopNumber;     webservice String BidsId;//for testing     webservice String Type; //for testing  }  global class BI_VA_AutomationResponse {      webservice String responseStatus;     webservice String myShopNumber;     //webservice list&lt;Error&gt; errorMessages;     webservice String  errorMessages;//for testing   } global class BI_VA_Error {      webservice String type;     webservice String message;    }}   And test class is,  @isTest public class BI_VA_AutomationWrapperTestClass  { public static testMethod void unitTest(){      BI_VA_AutomationWrapper.BI_VA_AutomationRequest wrap= new BI_VA_AutomationWrapper.BI_VA_AutomationRequest();        wrap.userName='Test@test.com';     wrap.emailId='Test@test11.com';     wrap.buinessUnit='AH';     wrap.orgName='ORD';     wrap.country='US';     wrap.environment='QA';     wrap.myShopNumber='123456789';     wrap.BidsId='123';     wrap.Type='ResetPassword';              BI_VA_AutomationWrapper.BI_VA_AutomationResponse res= new BI_VA_AutomationWrapper.BI_VA_AutomationResponse();     res.responseStatus = 'Success';     res.myShopNumber = '987654321';     res.errorMessages = 'Test error';      BI_VA_AutomationWrapper.BI_VA_Error error = new BI_VA_AutomationWrapper.BI_VA_Error();     error.type = 'Test';     error.message = 'Test';  }}   Code coverage is 0% only. Read MIME data using PHP Distinct digits in a combination of 6 digits 3 Statements of axiom of choice are equivalent This winter I started to study much harder the set theory and especially the axiom of choice. Unfortunately, I have problems with solving the next exercise:  Prove that the 3 statements of the axiom of choice are equivalent :  1) For any non-empty collection $X$ of pairwise disjoint non-empty sets, there exists a choice set.  2) For any non-empty collection $X$ there is a choice function.  3) For any non-empty set $X$, there exists a function $f:P(X)\setminus\{\varnothing\}\to X$ so that for any non-empty set $A\subseteq X$, $f(A) \in A$.