How to create a proof environment with a different typeset name in addition to the original proof environment?

Question

Picking up on this comment, how can I define a proof environment with a different typeset name than "Proof" (say, "Explanation") in such a way that the new environment coexists rather than supplants the original proof environment?

I currently use the amsthm package to generate proof environments, but if it helps, I don't mind loading another package.

Answer 1

You could define a new LaTeX environment called, say, explanation. Entering a LaTeX environment automatically starts a new TeX group. This environment first redefines the macro \proofname and then opens a proof environment. At the end of the explanation environment, the proof environment is closed. This approach "works" because the scope of the redefinition of the \proofname is confined to the current TeX group and is therefore "forgotten" when the explanation environment ends.

\documentclass{article}
\usepackage{amsthm}
\newcommand\explanationname{Explanation} % could be made language-dependent
\newenvironment{explanation}%
   {\renewcommand\proofname\explanationname%
    \begin{proof}}%
   {\end{proof}}
\begin{document}
\begin{explanation} bla bla bla \end{explanation}
\begin{proof} ble ble ble \end{proof}
\begin{explanation} bli bli bli \end{explanation}
\end{document}