<?xml version="1.0"?>
<div><span class="kw">theorem </span><a NAME="T31"><span class="comment"><font color="firebrick">:: GROUP_23:31</font></span><br/></a><div class="add"> for <font color="Olive" title="b1">I</font> being   non  <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a>   <a href="hidden.html#M2" title="HIDDEN:mode.2">set</a> <br/>  for <font color="Olive" title="b2">A</font>, <font color="Olive" title="b3">B</font> being   <a href="group_19.html#NM1" title="GROUP_19:NM.1">Group-Family</a> of <font color="Olive" title="b1">I</font><br/>  for <font color="Olive" title="b4">f</font> being   <a href="pboole.html#NM1" title="PBOOLE:NM.1">ManySortedSet</a> of <font color="Olive" title="b1">I</font> holds <br/> ( <font color="Olive" title="b4">f</font> is    <a href="group_23.html#M2" title="GROUP_23:mode.2">Homomorphism-Family</a> of <font color="Olive" title="b2">A</font>,<font color="Olive" title="b3">B</font> iff  for <font color="Olive" title="b5">i</font> being    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of <font color="Olive" title="b1">I</font> holds  <font color="Olive" title="b4">f</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Olive" title="b5">i</font> is   <a href="group_6.html#NM2" title="GROUP_6:NM.2">Homomorphism</a> of <span class="p1">(<span class="default"><font color="Olive" title="b2">A</font> <a href="group_7.html#K1" title="GROUP_7:func.1">.</a> <font color="Olive" title="b5">i</font></span>)</span>,<span class="p1">(<span class="default"><font color="Olive" title="b3">B</font> <a href="group_7.html#K1" title="GROUP_7:func.1">.</a> <font color="Olive" title="b5">i</font></span>)</span> )</div></div>
