Trivial

A list of things to say when you can’t be bothered to write a proof.
Text file can be found here.
(Credits)

1. Obviously
2. Clearly
3. Anyone can see that
4. Trivially
5. Indubitably
6. It follows that
7. Evidently
8. By basic applications of previously proven lemmas,
9. The proof is left to the reader that
10. It goes without saying that
11. Consequently
12. By immediate consequence,
13. Of course
14. But then again
15. By symmetry
16. Without loss of generality,
17. Anyone with a fifth grade education can see that
18. I would wager 5 dollars that
19. By the contrapositive
20. We need not waste ink in proving that
21. By Euler
22. By Fermat
23. By a simple diagonalization argument,
24. We all agree that
25. It would be absurd to deny that
26. Unquestionably,
27. Indisputably,
28. It is plain to see that
29. It would be embarrassing to miss the fact that
30. It would be an insult to my time and yours to prove that
31. Any cretin with half a brain could see that
32. By Fermat’s Last Theorem,
33. By the Axiom of Choice,
34. It is equivalent to the Riemann Hypothesis that
35. By a simple counting argument,
36. Simply put,
37. One’s mind immediately leaps to the conclusion that
38. By contradiction,
39. I shudder to think of the poor soul who denies that
40. It is readily apparent to the casual observer that
41. With p < 5% we conclude that
42. It follows from the Zermelo-Fraenkel axioms that
43. Set theory tells us that
44. Divine inspiration reveals to us that
45. Patently,
46. Needless to say,
47. By logic
48. By the Laws of Mathematics
49. By all means,
50. With probability 1,
51. Who could deny that
52. Assuming the Continuum Hypothesis,
53. Galois died in order to show us that
54. There is a marvellous proof (which is too long to write here) that
55. We proved in class that
56. Our friends over at Harvard recently discovered that
57. It is straightforward to show that
58. By definition,
59. By a simple assumption,
60. It is easy to see that
61. Even you would be able to see that
62. Everybody knows that
63. I don’t know why anybody would ask, but
64. Between you and me,
65. Unless you accept Gödel’s Incompleteness Theorem,
66. A reliable source has told me
67. It is a matter of simple arithmetic to show that
68. Beyond a shadow of a doubt,
69. When we view this problem as an undecidable residue class whose elements are universal DAGs, we see that
70. You and I both know that
71. And there you have it,
72. And as easy as ABC,
73. And then as quick as a wink,
74. If you’ve been paying attention you’d realize that
75. By the Pigeonhole Principle
76. By circular reasoning we see that
77. When we make the necessary and sufficient assumptions,
78. It is beyond the scope of this course to prove that
79. Only idealogues and sycophants would debate whether
80. It is an unfortunately common misconception to doubt that
81. By petitio principii, we assert that
82. We may take for granted that
83. For legal reasons I am required to disclose that
84. It is elementary to show that
85. I don’t remember why, but you’ll have to trust me that
86. Following the logical steps, we might conclude
87. We are all but forced to see that
88. By the same logic,
89. I’m not even going to bother to prove that
90. By Kant’s Categorical imperative,
91. Everyone and their mother can see that
92. A child could tell you that
93. It baffles me that you haven’t already realized that
94. Notice then that
95. Just this once I will admit to you that
96. Using the proper mindset one sees that
97. Remember the basic laws of common sense:
98. There is a lovely little argument that shows that
99. Figure 2 (not shown here) makes it clear that
100. Alas, would that it were not true that
101. If I’m being honest with you,
102. According to the pointy-headed theorists sitting in their Ivory Towers in academia,
103. We will take as an axiom that
104. Accept for the moment that
105. These are your words, not mine, but
106. A little birdie told me that
107. I heard through the grapevine that
108. In the realm of constructive mathematics,
109. It is a theorem from classical analysis that
110. Life is too short to prove that
111. A consequence of IUT is that
112. As practitioners are generally aware,
113. It is commonly understood that
114. As the reader is no doubt cognizant,
115. As an exercise for the reader, show that
116. All the cool kids know that
117. It is not difficult to see that
118. Terry Tao told me in a personal email that
119. Behold,
120. Verify that
121. In particular,
122. Moreover,
123. Yea verily
124. By inspection,
125. A trivial but tedious calculation shows that
126. Suppose by way of contradiction that
127. By a known theorem,
128. Henceforth
129. Recall that
130. Wherefore said He unto them,
131. It is the will of the Gods that
132. It transpires that
133. We find
134. As must be obvious to the meanest intellect,
135. It pleases the symmetry of the world that
136. Accordingly,
137. If there be any justice in the world,
138. It is a matter of fact that
139. It can be shown that
140. Implicitly, then
141. Ipso facto
142. Which leads us to the conclusion that
143. Which is to say
144. That is,
145. The force of deductive logic then drives one to the conclusion that
146. Whereafter we find
147. Assuming the reader’s intellect approaches that of the writer, it should be obvious that
148. Ergo
149. With God as my witness,
150. As a great man once told me,
151. One would be hard-pressed to disprove that
152. Even an applied mathematician would concede that
153. One sees in a trice that
154. You can convince yourself that
155. Mama always told me
156. I know it, you know it, everybody knows that
157. Even the most incompetent T.A. could see,
158. This won’t be on the test, but
159. Take it from me,
160. Axiomatically,
161. Naturally,
162. A cursory glance reveals that
163. As luck would have it,
164. Through the careful use of common sense,
165. By the standard argument,
166. I hope I don’t need to explain that
167. According to prophecy,
168. Only a fool would deny that
169. It is almost obvious that
170. By method of thinking,
171. Through sheer force of will,
172. Intuitively,
173. I’m sure I don’t need to tell you that
174. You of all people should realize that
175. The Math Gods demand that
176. The clever student will notice
177. An astute reader will have noticed that
178. It was once revealed to me in a dream that
179. Even my grandma knows that
180. Unless something is horribly wrong,
181. And now we have all we need to show that
182. If you use math, you can see that
183. It holds vacuously that
184. Now check this out:
185. Barring causality breakdown, clearly
186. We don’t want to deprive the reader of the joy of discovering for themselves why
187. One of the Bernoullis probably showed that
188. Somebody once told me
189. By extrapolation,
190. Categorically,
191. If the reader is sufficiently alert, they will notice that
192. It’s hard not to prove that
193. The sophisticated reader will realize that
194. In this context,
195. It was Lebesque who first asked whether
196. As is tradition,
197. According to local folklore,
198. We hold these truths to be self-evident that
199. By simple induction,
200. In case you weren’t paying attention,
201. A poor student or a particularly clever dog will realize immediately that
202. Every student brought up in the American education system is told that
203. Most experts agree that
204. Sober readers see that
205. And would you look at that:
206. And lo!
207. By abstract nonsense,
208. I leave the proof to the suspicious reader that
209. When one stares at the equations they immediately rearrange themselves to show that
210. This behooves you to state that
211. Therefore
212. The heralds shall sing for generations hence that
213. If I’ve said it once I’ve said it a thousand times,
214. Our forefathers built this country on the proposition that
215. My father told me, and his father before that, and his before that, that
216. As sure as the sun will rise again tomorrow morning,
217. The burden of proof is on my opponents to disprove that
218. If you ask me,
219. I didn’t think I would have to spell this out, but
220. For all we know,
221. Promise me you won’t tell mom, but
222. It would be a disservice to human intelligence to deny that
223. Proof of the following has been intentionally omitted:
224. here isn’t enough space in the footnote section to prove that
225. Someone of your status would understand that
226. It would stand to reason that
227. Ostensibly,
228. The hatred of 10,000 years ensures that
229. There isn’t enough space in the footnote section to prove that
230. Simple deduction from peano’s axioms shows
231. By a careful change of basis we see that
232. Using Conway’s notation we see that
233. The TL;DR is that
234. Certainly,
235. Surely
236. An early theorem of Gauss shows that
237. An engineer could deduce that
238. And Jesus said to his Apostles,
239. This fact may follow obviously from a theorem, but it’s not obvious which theorem you’re using:
240. Word on the streets is that
241. Assuming an arbitrary alignment of planets, astrology tells us
242. The voices insist that
243. Someone whispered to me on the subway yesterday that
244. For surely all cases,
245. Indeed,
246. Legend says that
247. As if by design,
248. Come to think of it,
249. And as if that weren’t enough,
250. Without further ado,

You may submit a line of your own here.

Your submissions

1. This is the choice of Steins;Gate,
   - Wrath
2. As is mentioned in the vedas,
   - A well-wisher
3. As found out by Newton/Galileo/some great scientists n-hundred years ago,
   - Sharl Eclair/Sharley Claire
4. By the blessing of Elves and Men and all Free Folk,
   - Gandalf
5. As Jesus sometimes says,
   - Ram (no, not the goat)