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In proving general facts like inequalities and polynomial equations, what's the difference between importing Reals and things like Coq.Reals.{Rineq, R_sqrt, ...}?

I started from searching specific facts/theorems and ended up in using the latter, but I've seen others using just Reals. Is it easier or more comprehensive to just use Reals?

Suspecting it's a legacy thing, I tried to import just Coq.Reals but it does not seem to exist (Coq 8.5 beta 3).

thor
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  • Note that `Require RIneq` works too (for backwards compatibility, I suppose). However using unambiguous (extended) paths allows you to define your own `MyProject.RIneq` if you find that there are some derived facts you use a lot but are lacking in the standard library. A few years ago, we used to have this problem and [resorted to awful names](https://github.com/coqtail/coqtail/blob/master/src/mytheories/myReals/MyRIneq.v) but we could have a nicer naming convention now that the stdlib has been refactored. :) – gallais Dec 22 '15 at 17:50
  • The fact that the modules in `Coq.Reals.*` always feature an `R` (`Raxioms`, `Rdefinitions`, `Rbase`, `RIneq`, etc.) is also an artefact of these olden days where they were not in `Coq.Reals.*` but rather "at the top-level". – gallais Dec 22 '15 at 17:53

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