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<b>let </b><font color="Maroon">G1</font> be   <a href="group_1.html#NM1">Group</a>, <font color="Maroon">G2</font> be   <a href="group_1.html#NM1">Group</a>;<br/><b>let </b><font color="Maroon">f</font> be   <a href="group_6.html#NM2">Homomorphism</a> of <font color="Maroon">G1</font>,<font color="Maroon">G2</font>;<br/>



<b>assume </b><a NAME="E1:35"/>
<font color="Maroon">f</font> is <a href="funct_1.html#V2">one-to-one</a>
 ;<br/>

<a NAME="E2:35"/><b>then </b>
(  <a href="latsubgr.html#K3" target="_self">FuncLatt</a> <font color="Maroon">f</font> is    <a href="vectsp_8.html#M3">Semilattice-Homomorphism</a> of  <a href="group_4.html#K11">lattice</a> <font color="Maroon">G1</font>, <a href="group_4.html#K11">lattice</a> <font color="Maroon">G2</font> &amp;  <a href="latsubgr.html#K3" target="_self">FuncLatt</a> <font color="Maroon">f</font> is    <a href="vectsp_8.html#M4">sup-Semilattice-Homomorphism</a> of  <a href="group_4.html#K11">lattice</a> <font color="Maroon">G1</font>, <a href="group_4.html#K11">lattice</a> <font color="Maroon">G2</font> )
 
<b>by </b><i>, </i>;<br/>
<b>hence </b><a NAME="E3:35"/>
 <a href="latsubgr.html#K3" target="_self">FuncLatt</a> <font color="Maroon">f</font> is    <a href="lattice4.html#M1">Homomorphism</a> of  <a href="group_4.html#K11">lattice</a> <font color="Maroon">G1</font>, <a href="group_4.html#K11">lattice</a> <font color="Maroon">G2</font>
 <b>by </b><i><a class="ref" href="vectsp_8.html#T11">VECTSP_8:11</a></i>;<br/>


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