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<div>:: <span class="kw">deftheorem </span><span class="lab"><font color="Green" title="E39">Def8</font></span>   defines <a href="group_19.html#M1" title="GROUP_19:mode.1">DirectSumComponents</a> <a onclick="hs(this)" href="javascript:()">GROUP_19:def 8 : <br/></a><span> 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">G</font> being   <a href="group_1.html#NM1" title="GROUP_1:NM.1">Group</a><br/>  for <font color="Olive">b<sub>3</sub></font> being   <a href="group_19.html#NM1" title="GROUP_19:NM.1">Group-Family</a> of <font color="Olive" title="b1">I</font> holds <br/> ( <font color="Olive">b<sub>3</sub></font> is    <a href="group_19.html#M1" title="GROUP_19:mode.1">DirectSumComponents</a> of <font color="Olive" title="b2">G</font>,<font color="Olive" title="b1">I</font> iff  ex <font color="Olive" title="b4">h</font> being   <a href="group_6.html#NM2" title="GROUP_6:NM.2">Homomorphism</a> of <span class="p1">(<span class="default"><a href="group_7.html#K3" title="GROUP_7:func.3">sum</a> <font color="Olive">b<sub>3</sub></font></span>)</span>,<font color="Olive" title="b2">G</font> st <font color="Olive" title="b4">h</font> is  <a href="funct_2.html#V3" title="FUNCT_2:attr.3">bijective</a>  );<br/></span></div>
