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<b>let </b><font color="Maroon">L1</font> be   <a href="lattices.html#NM1">Lattice</a>, <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="E1:19"/><i><font color="Green">E22</font></i>: 
for <font color="Olive">a</font>, <font color="Olive">b</font> being  <a href="struct_0.html#NM1">Element</a> of <font color="Maroon">L1</font>  st <font color="Maroon">f</font> <a href="funct_2.html#K3">.</a> <font color="Olive">a</font> <a href="lattices.html#R3">[=</a> <font color="Maroon">f</font> <a href="funct_2.html#K3">.</a> <font color="Olive">b</font> holds <br/><font color="Olive">a</font> <a href="lattices.html#R3">[=</a> <font color="Olive">b</font>
 ;<br/>

<b>let </b><font color="Maroon">x</font> be    <a href="hidden.html#M1">set</a> , <font color="Maroon">y</font> be    <a href="hidden.html#M1">set</a> ; <i><font color="Red">:: according to </font></i><a class="ref" href="funct_1.html#D8">FUNCT_1:def 8</a><br/>

<b>assume </b><a NAME="E2:19"/><i><font color="Green">E23</font></i>: 
( <font color="Maroon">x</font> <a href="hidden.html#R2">in</a>  <a href="relset_1.html#K4">dom</a> <font color="Maroon">f</font> &amp; <font color="Maroon">y</font> <a href="hidden.html#R2">in</a>  <a href="relset_1.html#K4">dom</a> <font color="Maroon">f</font> &amp; <font color="Maroon">f</font> <a href="funct_1.html#K1">.</a> <font color="Maroon">x</font> <a href="hidden.html#R1">=</a> <font color="Maroon">f</font> <a href="funct_1.html#K1">.</a> <font color="Maroon">y</font> )
 ;<br/>

<b>then reconsider </b><font color="Maroon">x</font> = <font color="Maroon">x</font> as   <a href="struct_0.html#NM1">Element</a> of <font color="Maroon">L1</font> ;<br/>
<b>reconsider </b><font color="Maroon">y</font> = <font color="Maroon">y</font> as   <a href="struct_0.html#NM1">Element</a> of <font color="Maroon">L1</font> <b>by </b><i/>;<br/>
<a NAME="E5:19"/>
( <font color="Maroon">x</font> <a href="lattices.html#R3">[=</a> <font color="Maroon">y</font> &amp; <font color="Maroon">y</font> <a href="lattices.html#R3">[=</a> <font color="Maroon">x</font> )
 
<b>by </b><i>, </i>;<br/>
<b>hence </b><a NAME="E6:19"/>
<font color="Maroon">x</font> <a href="hidden.html#R1">=</a> <font color="Maroon">y</font>
 <b>by </b><i><a class="ref" href="lattices.html#T26">LATTICES:26</a></i>;<br/>


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