When I use proof environment, the \bigcap and \bigcup become regular \cap and \cup. I wonder is this a bug? and how can I work around this issue? Thank you.
Minimal Example
\documentclass[10pt,letterpaper]{article}
\usepackage{amsmath}
\usepackage{amsfonts}
\usepackage{amssymb}
\usepackage{amsthm}
\begin{document}
Give a careful proof of the second DeMorgan's laws, given on page 26
$$\bigg(\bigcap_{i=1}^{n}E_{i}\bigg)^{c} = \bigcup_{i=1}^{n}E_{i}^c$$
for sets $\{E_i\}_{i=1}^{n} \subseteq S$.
\begin{proof}
Assume $x \in \bigg(\bigcap_{i=1}^{n}E_{i}\bigg)^{c} \implies x \not\in \bigcap_{i=1}^{n}E_{i}
\implies x \not\in E_i, \forall i, 1 \leq i \leq n \implies x \in E_i^c, \forall i, 1 \leq i \leq n$
$\implies x \in \bigcup_{i=1}^{n}E_{i}^c$. Therefore $\bigg(\bigcap_{i=1}^{n}E_{i}\bigg)^{c} =
\bigcup_{i=1}^{n}E_{i}^c$.
\end{proof}
\end{document}
\capand\cup. you would see the difference if you input, say$\bigcap_{i-1}^n E_i \cap x$. the reason for the smaller versions of\bigcapand\bigcupin text is to avoid unevenly spaced baselines, which make a page look un-beautiful, and could make the text less readable. – barbara beeton Sep 12 '11 at 13:32