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<b>let </b><font color="Maroon">L1</font> be   <a href="lattices.html#NM1">Lattice</a>;<br/><b>let </b><font color="Maroon">L2</font> be   <a href="lattices.html#NM1">Lattice</a>;<br/><b>let </b><font color="Maroon">f</font> be   <a href="funct_2.html#NM1">Function</a> of the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">L1</font>,the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">L2</font>;<br/>





<b>assume </b><a NAME="E1:9"/><i><font color="Green">E25</font></i>: 
<font color="Maroon">f</font> is <a href="lattice4.html#V2" target="_self">epimorphism</a>
 ;<br/>

<b>reconsider </b><font color="Maroon">g</font> = <font color="Maroon">f</font> as   <a href="funct_2.html#NM1">Function</a> of the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">L1</font>,the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">L2</font> ;<br/>
<a NAME="E3:9"/><i><font color="Green">E26</font></i>: 
 <a href="relat_1.html#K2">rng</a> <font color="Maroon">g</font> <a href="hidden.html#R1">=</a> the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">L2</font>
 
<b>by </b><i>, </i>;<br/>
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="9_1"><b>now </b></a><div class="add"><b>let </b><font color="Maroon">a2</font> be   <a href="struct_0.html#NM1">Element</a> of <font color="Maroon">L2</font>;<br/><b>consider </b><font color="Maroon">x</font> being    <a href="hidden.html#M1">set</a> <b> such that </b><br/><a NAME="E2:9_1"/><i><font color="Green">E27</font></i>: 
( <font color="Maroon">x</font> <a href="hidden.html#R2">in</a> the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">L1</font> &amp; <font color="Maroon">g</font> <a href="funct_1.html#K1">.</a> <font color="Maroon">x</font> <a href="hidden.html#R1">=</a> <font color="Maroon">a2</font> )
 <b>by </b><i>, <a class="ref" href="funct_2.html#T17">FUNCT_2:17</a></i>;<br/><b>thus </b><a NAME="E3:9_1"/>
 ex <font color="Olive">a1</font> being  <a href="struct_0.html#NM1">Element</a> of <font color="Maroon">L1</font> st <font color="Maroon">g</font> <a href="funct_2.html#K3">.</a> <font color="Olive">a1</font> <a href="hidden.html#R1">=</a> <font color="Maroon">a2</font>
 <b>by </b><i/>;<br/></div><b>end;</b></div>
<b>hence </b><a NAME="E5:9"/>
for <font color="Olive">a2</font> being  <a href="struct_0.html#NM1">Element</a> of <font color="Maroon">L2</font>  ex <font color="Olive">a1</font> being  <a href="struct_0.html#NM1">Element</a> of <font color="Maroon">L1</font> st <font color="Olive">a2</font> <a href="hidden.html#R1">=</a> <font color="Maroon">f</font> <a href="funct_2.html#K3">.</a> <font color="Olive">a1</font>
 ;<br/>


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