# Question regarding proof environment with bigcap and bigcup

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}

-
but these aren't "regular" \cap and \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 \bigcap and \bigcup in 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

This is the default setting for inline mathmode (when using $...$). The math operators are larger in \displaystyle (when using $...$) than they are in \textstyle or inline math mode.
If you want the operators to expand to their full height, use \displaystyle\bigcup. Note, however, that the limits also be typeset over the top/bottom, rather than the sides.