<?xml version="1.0"?>
<div><span class="kw">theorem </span><span class="lab"><font color="Green" title="E32">Th37</font></span>: <a NAME="T37"><span class="comment"><font color="firebrick">:: GROUP_19:37</font></span><br/></a><div class="add"> for <font color="Olive" title="b1">F</font>, <font color="Olive" title="b2">G</font> being   <a href="relat_1.html#V2" title="RELAT_1:attr.2">non-empty</a>   non  <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a>  <a href="funct_1.html#NM1" title="FUNCT_1:NM.1">Function</a><br/>  for <font color="Olive" title="b3">h</font> being   non  <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a>  <a href="funct_1.html#NM1" title="FUNCT_1:NM.1">Function</a>  st  <a href="relat_1.html#NK1" title="RELAT_1:NK.1">dom</a> <font color="Olive" title="b1">F</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="relat_1.html#NK1" title="RELAT_1:NK.1">dom</a> <font color="Olive" title="b2">G</font> &amp;  <a href="relat_1.html#NK1" title="RELAT_1:NK.1">dom</a> <font color="Olive" title="b2">G</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="relat_1.html#NK1" title="RELAT_1:NK.1">dom</a> <font color="Olive" title="b3">h</font> &amp; (  for <font color="Olive" title="b4">i</font> being    <a href="hidden.html#M1" title="HIDDEN:mode.1">object</a>   st <font color="Olive" title="b4">i</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="relat_1.html#NK1" title="RELAT_1:NK.1">dom</a> <font color="Olive" title="b3">h</font> holds <br/> ex <font color="Olive" title="b5">hi</font> being   <a href="funct_2.html#NM1" title="FUNCT_2:NM.1">Function</a> of <span class="p1">(<span class="default"><font color="Olive" title="b1">F</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Olive" title="b4">i</font></span>)</span>,<span class="p1">(<span class="default"><font color="Olive" title="b2">G</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Olive" title="b4">i</font></span>)</span> st <br/>( <font color="Olive" title="b5">hi</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b3">h</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Olive" title="b4">i</font> &amp; <font color="Olive" title="b5">hi</font> is  <a href="funct_2.html#V3" title="FUNCT_2:attr.3">bijective</a>  ) ) holds <br/> <a href="group_19.html#K6" title="GROUP_19:func.6">ProductMap</a> (<font color="Olive" title="b1">F</font>,<font color="Olive" title="b2">G</font>,<font color="Olive" title="b3">h</font>) is  <a href="funct_2.html#V3" title="FUNCT_2:attr.3">bijective</a> </div></div>
