I state a theorem first, and want to write the proof in the later section. And I want to restate the theorem when I am going to prove it. So in the whole paper, I write the theorem for two times, but I want them have the same number. How can i do this?
Often in my papers I want to mention theorems in the introduction that are introduced in more detail and proved in a later section.  I'd like to include the statement of these theorems twice over, each time numbered as the theorem would naturally appear in its later section.  My current solution (using amsthm) is, e.g.  %(in the introduction) \newtheorem*{thm:associativity}{Theorem \ref{thm:associativity}} \begin{thm:associativity} Lorem ipsum ... \end{thm:associativity}  %(in a later section) \begin{thm} \label{thm:associativity} Lorem ipsum ... \end{thm}      Can anyone think of a cleaner solution?
I just came over this syntax in some of the questions in this forum, but Google and any other searchengine tends to block out anything but letters and number in the search so it is impossible to search out "=>".  So can anyone tell me what it is and how it is used? Can anybody please suggest how I can compute the moment generating function of the inner product of two Gaussian random vectors, each distributed as $\mathcal N(0,\sigma^2)$, independent of each other? Is there some standard result available for this? Any pointer is highly appreciated. Questions about right ideals Toggle Switch to swap the connections of two buttons Adding values to a C# array $\|h(x)-h(y)\|\geq 3\|x-y\|$ prove that image of open is open A disabled module has a schema version of -1, how can I enable the module and then run DB updates using hook_update_N? I have to submit a manuscript to a journal, and I just realized that they want every single part of the paper to be in 12 pt font. This includes tables text, footnotes, acknowledgements etc. Is there a way to force all text to be the same size? My girlfriend is Russian. Last night we tried to fly her to the US on a valid tourist visa. She was stopped at DME and told she would be required to have $2700 USD to get back home immediately even though she had a return ticket. She said this was an "unwritten" rule because of the nonsense i keep seeing on CNN , Anybody else know anything? She is literally trapped and scared to death. Unable to change privacy settings upon install of Ubuntu 18.04 LTS Is it correct to use Bernoulli's theorem to explain that a disk floats in the air? Should the correct explanation be based on Boyle's law? In this video, a device is introduced from 1 minute to 18 seconds. After entering the air, the disc at the bottom of the device will be suspended in the air. The video explains that this is because of the Bernoulli effect, but I think this explanation is incorrect, because the disc gap, the radial volume is increasing. Therefore, the reason why the disk is suspended is that the air volume becomes larger, so the pressure decreases (according to Boyle's law). If the air moves along the radial direction at a constant speed, the volume of the air must be constantly increasing, right? So the pressure is decreasing, right? I have 3 folders with large amount of data in each which has to be maintained seperately. Can I create a sym link or shortcut.in windows which should show me the merged contents of the 3 folders. I am not looking for library conf in Win7.   Any suggestion is highly appreciated. I'm reading . Then I'm not able to figure out the difference between hard voting and soft voting in context to ensemble based methods.  I quote descriptions of them from the book. The first two images from the top are description for hard voting, and last one is for soft voting.        In my view hard voting is majority decision, but I don't understand soft voting and the reason why soft voting is better than hard voting. Would anyone teach me these? How can I disassociate an account? I want to disassociate an account from the rest of my associated accounts. How can I do that?  The information in  doesn't seem to be relevant anymore, since I can't find this thing     Click the "Clear All Associations" button on the bottom of the Accounts page on your profile.   Every time I add or remove an email or OpenID from one site it propagates to the entire network. Convert .sdf database to .mdf database how to get the current chapter name, section name, subsection name, etc? How can one get the current name of the following: Chapter, Section, Subsection(s), frame, label, mdframed? How to install Oracle 18c (Enterprise Edition) on Ubuntu 18.04? This question is unanswered since Oracle 18c has been released. Except Ubuntu Linux platform, most of the other Linux platform supports Oracle 18c installation. I, myself, tested this on CentOS 7 and oracle 18c got installed without any glitch!  It is unfortunate that Oracle Corporation has not documented the installation procedure particularly for Ubuntu Linux platform, nevertheless one good thing is that the image file db_home.zip is a generic one, installable across all Linux platforms.    So how can I install Oracle 18c (Enterprise Edition) on Ubuntu 18.04? Prove that if $a$ and $b$ are relatively prime, then $\gcd(a+b, a-b) = 1$ or $2$ Prove that if $a$ and $b$ are relatively prime, then $\gcd(a+b, a-b) = 1$ or $2$.  I started off by putting $\gcd(a+b, a-b) = d$. This implies that there are two relatively prime integers $x_1, x_2$, such that   $dx_1 = a+b$   $dx_2 = a -b$  Adding the first equation to the second gives us: $d(x_1 + x_2) = 2a$, and subtracting the second from the first gives us $d(x_1 - x_2) = 2b$. This implies that $d\mid2a, d\mid2b \implies \gcd(2a, 2b) = d \implies d = 2\cdot \gcd(a,b) \implies d = 2$.   This is based on the fact that $\gcd(x_1 + x_2, x_1 - x_2) = 1$, which is in fact the statement of the problem. How do I prove this? Can I somehow use the Euclidean Algorithm for this. I'm unable to get Atom text editor from the Software Center. When I try I get this error:  Package does not exist. Check the spelling of the package name, and that the appropriate repository is enabled. Intellisense in IntelliJ no longer working