How to remove this space in proof environment?
You should never (in the sense of never ever) use $$...$$
in LaTeX. For no reason whatsoever. See Why is \[ ... \] preferable to $$ ... $$?
For proofs that end with a display there is \qedhere
.
\documentclass[10pt,a4paper]{article}
\usepackage[latin1]{inputenc}
\usepackage{amsmath}
\usepackage{amsfonts}
\usepackage{amssymb}
\usepackage{amsthm}
\theoremstyle{plain}
\newtheorem{theorem}{Theorem}[section]
\begin{document}
\begin{theorem}
...
\end{theorem}
\begin{proof}
...
\begin{align*}
A & \Longrightarrow B\\
& \Longrightarrow C\qedhere
\end{align*}
\end{proof}
\begin{theorem}
...
\end{theorem}
\end{document}
Depending on the nature of the alignment, you can also use
\begin{proof}
...
\begin{equation*}
\begin{split}
A & \Longrightarrow B\\
& \Longrightarrow C\qedhere
\end{split}
\end{equation*}
\end{proof}
At a minimum, you should (a) insert the directive \qedhere
immediately after "C
" and (b) change \begin{array}{ccc}
to \begin{array}[b]{ccc}
. The [b]
("bottom") positioning specifier informs LaTeX that the QED symbol should be aligned at the bottom rather than at the center of the array
.
Incidentally, you should not use $$
to initiate and terminate displaymath-mode in a LaTeX document. It's badly deprecated. Instead, use \[
and \]
. See Why is \[ ... \]
preferable to $$ ... $$
? for a longer discussion.
I would like to point that ntheorem
has an automatic placement of the end-of-proof symbol, without having to ask it (thmmarks
option). In addition, we can use its amsthm
compatibility option:
\documentclass[10pt, a4paper]{article}
\usepackage[utf8]{inputenc}
\usepackage{amsmath}
\usepackage{amsfonts}
\usepackage{amssymb}
\usepackage[thmmarks, amsmath, thref, amsthm]{ntheorem}%
\theoremstyle{plain}
\newtheorem{theorem}{Theorem}[section]
\begin{document}
\begin{theorem}
...
\end{theorem}
\begin{proof}
...
\begin{align*}
A & \Longrightarrow B\\
& \Longrightarrow C
\end{align*} %
\end{proof}
\begin{theorem}
...
\end{theorem}
\end{document}