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<div><span class="kw">theorem </span><span class="lab"><font color="Green" title="E15">Th31</font></span>: <a NAME="T31"><span class="comment"><font color="firebrick">:: LATSUBGR:31</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">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>  st <font color="Olive" title="b3">f</font> is  <a href="funct_1.html#V2" title="FUNCT_1:attr.2">one-to-one</a>  holds <br/> <a href="latsubgr.html#K3" title="LATSUBGR:func.3">FuncLatt</a> <font color="Olive" title="b3">f</font> is   <a href="vectsp_8.html#NM3" title="VECTSP_8:NM.3">Semilattice-Homomorphism</a> of <span class="p1">(<span class="default"><a href="group_4.html#K11" title="GROUP_4:func.11">lattice</a> <font color="Olive" title="b1">G1</font></span>)</span>,<span class="p1">(<span class="default"><a href="group_4.html#K11" title="GROUP_4:func.11">lattice</a> <font color="Olive" title="b2">G2</font></span>)</span></div></div>
