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<div><span class="kw">theorem </span><span class="lab"><font color="Green" title="E40">Th36</font></span>: <a NAME="T34"><span class="comment"><font color="firebrick">:: GROUP_22:34</font></span><br/></a><div class="add"> for <font color="Olive" title="b1">G1</font>, <font color="Olive" title="b2">G2</font> being   <a href="group_1.html#NM1" title="GROUP_1:NM.1">Group</a><br/>  for <font color="Olive" title="b3">H1</font> being    <a href="group_2.html#M1" title="GROUP_2:mode.1">Subgroup</a> of <font color="Olive" title="b1">G1</font><br/>  for <font color="Olive" title="b4">K</font> being    <a href="group_6.html#M1" title="GROUP_6:mode.1">Subgroup</a> of <font color="Olive" title="b3">H1</font><br/>  for <font color="Olive" title="b5">H2</font> being    <a href="group_2.html#M1" title="GROUP_2:mode.1">Subgroup</a> of <font color="Olive" title="b2">G2</font><br/>  for <font color="Olive" title="b6">f</font> being   <a href="group_6.html#NM2" title="GROUP_6:NM.2">Homomorphism</a> of <font color="Olive" title="b1">G1</font>,<font color="Olive" title="b2">G2</font><br/>  for <font color="Olive" title="b7">g</font> being   <a href="group_6.html#NM2" title="GROUP_6:NM.2">Homomorphism</a> of <font color="Olive" title="b3">H1</font>,<font color="Olive" title="b5">H2</font>  st (  for <font color="Olive" title="b8">k</font> being   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Olive" title="b1">G1</font>  st <font color="Olive" title="b8">k</font> <a href="struct_0.html#R1" title="STRUCT_0:pred.1">in</a> <font color="Olive" title="b4">K</font> holds <br/><font color="Olive" title="b6">f</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Olive" title="b8">k</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b7">g</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Olive" title="b8">k</font> ) holds <br/> <a href="group_6.html#K10" title="GROUP_6:func.10">Image</a> <span class="p1">(<span class="default"><font color="Olive" title="b6">f</font> <a href="grsolv_1.html#K1" title="GRSOLV_1:func.1">|</a> <font color="Olive" title="b4">K</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="group_6.html#K10" title="GROUP_6:func.10">Image</a> <span class="p1">(<span class="default"><font color="Olive" title="b7">g</font> <a href="grsolv_1.html#K1" title="GRSOLV_1:func.1">|</a> <font color="Olive" title="b4">K</font></span>)</span></div></div>
