# Is there a compact notation for indicating the reasons for an implication?

Is there a compact, commonly used notation for indicating the reasons for an implication? For example, suppose I have previously established or been given $P$, and can use it to show that $B$ follows from $A$ because of $P$. I'd like to be able to write something like

$$A \underset{P}\Rightarrow B,$$

but feel like I'm making up notation that will not be understood. Is something like this common practice, and if so are there LaTeX conventions for generating it?

You can use the super useful mathtools package (for bunch of other stuff too!). Use it with \xRightarrow[below]{above}. There is also extarrows package with similar usage \xlongequal[below]{above}.

My humble advice is not to exploit this, rather keep the text at max from (2) and (5) or via Fubini Thm. or something similar to draw attention to known results, previous relations, elsewhere in the text.

When people write mathematics on a blackboard, they have many idiosyncratic ways of abbreviating arguments to save space. But when we write mathematics in print, we typically use prose. So there is no common way in LaTeX to do what you ask, because we generally just explain the argument in words.

• Exactly! Why do some people tend to obsess about notation? The main goal is to communicate the mathematics and, yes, a good notation that everyone understands is great for that, but not obscure, complicated notation. – lhf Dec 1 '11 at 21:50
• I've seen people use $\because$ \because and $\therefore$ \therefore on blackboards. I find this utterly confusing because I can't remember which one is which. $p \mid a \implies p^2 \mid a \because a \text{ is a } \Box$... This would give $P \therefore A \implies B$ or $A \implies B \because P$. – t.b. Dec 1 '11 at 21:55
• @lhf: Actually, my purpose was not to obscure or merely save space, but to take advantage of compact notation to make it easier to grasp the structure of an argument without having to refer to surrounding text. One of the things I find hardest as a (slightly dyslexic) beginner is assessing the precise meaning of natural language in the context of mathematical arguments, and (to me, at least) a well-defined notation helps with that. – orome Dec 1 '11 at 21:58
• @raxacoricofallapatorius, I didn't mean you personally (and hence the comment to this answer and not your question). No offense meant. – lhf Dec 1 '11 at 22:07
• @lhf: Yes, sorry, that came off wrong. A further note: Another goal is to have a way of putting $P$ in as close a proximity as possible to the step that uses it. I often find, for example, that when I see "from P" followed by some notation, it is not always clear precisely what elements of the notation are related through $P$. – orome Dec 1 '11 at 22:16

If you want to enphasize that you are using P, together with A, to deduce B

you could write

P & A ⟹ B

that is: if P and A then B

This is standard logic notation and it draws attention to P. It might also come useful if you or your readers want to use some proof-assistant or automatic-theorem-prover