# Thread: How to write a lazy proof (in mathematics)

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## How to write a lazy proof (in mathematics)

You too can write a lazy proof! Just use at least one of the following phrases in a key point of your proof.
For an ultra-lazy proof use one of the phrases with an asterisk.

1) It is easy to see that...
2) Obviously...
3) Immediate. *
4) ...and the result follows.
5) As a result, we find that...
6) One easily verifies that...
7) The proof is left to the reader. *
8) The proof is left as an exercise.*
9) ....and the X theorem completes the proof.
10) Clearly...
11) It can be shown that...
12) Trivially...
13) The proof is standard.
14) ...the rest of the proof follows the same line.
15) ...by a trivial argument...

(but you have to have actually seen the phrase used in a book or a lecturer's notes)

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Originally Posted by TruDog
Is that the jocular version of "quod erat demonstrandum".

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Originally Posted by TruDog
Sounds good and I think that some of my lecturers use it often but I have not seen it written (yet).

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Originally Posted by asianeconomist
Is that the jocular version of "quod erat demonstrandum".
nope. quod erat demonstrandum stands for "which was to be shown" and concludes a proof without making it less clear.

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We can also "assume without loss of generality" or "to exclude trivial cases assume"... That's only a little lazy, though, I guess.

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I thought of another half-lazy one: "For specificity assume..." (e.g., if proving something about a monotonic function, assume that it is increasing)

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4 & 5 are my favorites, along with "WLOG, take ... . All other cases are trivial/analogous."
You also have to love the technique, especially common in Rudin, of citing 10+ numbered theorems in a sentence or two, writing one or two expressions, and stating that the desired consequence follows easily.

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A good one that i hate is "...and with some simple algebraic manipulations we have..." , it usually means that you have to write half proof by yourself...

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10) Clearly ....(whatever they wanted to prove)
11) It can be shown that ....(yes, but not by me)