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<b>consider </b><font color="Maroon">b</font> being   <a href="struct_0.html#NM1">Element</a> of <font color="Maroon">L2</font>;<br/>
<b>defpred </b><font color="Maroon">S<sub>1</sub></font>[   <a href="hidden.html#M1">set</a> ,   <a href="hidden.html#M1">set</a> ] <b>means </b>for <font color="Olive">a1</font> being  <a href="struct_0.html#NM1">Element</a> of <font color="Maroon">L1</font>  st <font color="Maroon">a<sub>1</sub></font> <a href="hidden.html#R1">=</a> <font color="Olive">a1</font> holds <br/><font color="Maroon">a<sub>2</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">b</font>;<br/>
<div><i><font color="Green">E25</font></i>: <a class="txt" onclick="hs2(this)" href="javascript:()" title="5_1_1_1"><b>now </b></a><div class="add"><b>let </b><font color="Maroon">x</font> be   <a href="struct_0.html#NM1">Element</a> of <font color="Maroon">L1</font>;<br/><b>take </b><font color="Maroon">b</font> = <font color="Maroon">b</font>;<br/><b>thus </b><a NAME="E1:5_1_1_1"/>
<font color="Maroon">S<sub>1</sub></font>[<font color="Maroon">x</font>,<font color="Maroon">b</font>]
 ;<br/></div><b>end;</b></div>
<b>consider </b><font color="Maroon">f</font> being   <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><b> such that </b><br/><a NAME="E4:5_1_1"/><i><font color="Green">E26</font></i>: 
for <font color="Olive">x</font> being  <a href="struct_0.html#NM1">Element</a> of <font color="Maroon">L1</font> holds  <font color="Maroon">S<sub>1</sub></font>[<font color="Olive">x</font>,<font color="Maroon">f</font> <a href="funct_2.html#K3">.</a> <font color="Olive">x</font>]
 <b>from </b><i><a class="ref" href="funct_2.html#S3">FUNCT_2:sch 3</a>();<br/></i>
<b>take </b>
<font color="Maroon">f</font>
;<br/>

<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="5_1_1_2"><b>now </b></a><div class="add"><b>let </b><font color="Maroon">a1</font> be   <a href="struct_0.html#NM1">Element</a> of <font color="Maroon">L1</font>;<br/><b>let </b><font color="Maroon">b1</font> be   <a href="struct_0.html#NM1">Element</a> of <font color="Maroon">L1</font>;<br/><b>thus </b><font color="Maroon">f</font> <a href="funct_2.html#K3">.</a> <span class="p1">(<span class="default"><font color="Maroon">a1</font> <a href="lattices.html#K3">"\/"</a> <font color="Maroon">b1</font></span>)</span> = 
<font color="Maroon">b</font>
<b>by </b><i/>
<br/>.= 
<font color="Maroon">b</font> <a href="lattices.html#K3">"\/"</a> <font color="Maroon">b</font>
<b>by </b><i><a class="ref" href="lattices.html#T17">LATTICES:17</a></i>
<br/>.= 
<span class="p1">(<span class="default"><font color="Maroon">f</font> <a href="funct_2.html#K3">.</a> <font color="Maroon">a1</font></span>)</span> <a href="lattices.html#K3">"\/"</a> <font color="Maroon">b</font>
<b>by </b><i/>
<br/>.= 
<span class="p1">(<span class="default"><font color="Maroon">f</font> <a href="funct_2.html#K3">.</a> <font color="Maroon">a1</font></span>)</span> <a href="lattices.html#K3">"\/"</a> <span class="p1">(<span class="default"><font color="Maroon">f</font> <a href="funct_2.html#K3">.</a> <font color="Maroon">b1</font></span>)</span>
<b>by </b><i/>
;<br/><b>thus </b><font color="Maroon">f</font> <a href="funct_2.html#K3">.</a> <span class="p1">(<span class="default"><font color="Maroon">a1</font> <a href="lattices.html#K4">"/\"</a> <font color="Maroon">b1</font></span>)</span> = 
<font color="Maroon">b</font>
<b>by </b><i/>
<br/>.= 
<font color="Maroon">b</font> <a href="lattices.html#K4">"/\"</a> <font color="Maroon">b</font>
<b>by </b><i><a class="ref" href="lattices.html#T18">LATTICES:18</a></i>
<br/>.= 
<span class="p1">(<span class="default"><font color="Maroon">f</font> <a href="funct_2.html#K3">.</a> <font color="Maroon">a1</font></span>)</span> <a href="lattices.html#K4">"/\"</a> <font color="Maroon">b</font>
<b>by </b><i/>
<br/>.= 
<span class="p1">(<span class="default"><font color="Maroon">f</font> <a href="funct_2.html#K3">.</a> <font color="Maroon">a1</font></span>)</span> <a href="lattices.html#K4">"/\"</a> <span class="p1">(<span class="default"><font color="Maroon">f</font> <a href="funct_2.html#K3">.</a> <font color="Maroon">b1</font></span>)</span>
<b>by </b><i/>
;<br/></div><b>end;</b></div>
<b>hence </b><a NAME="E6:5_1_1"/>
for <font color="Olive">a1</font>, <font color="Olive">b1</font> being  <a href="struct_0.html#NM1">Element</a> of <font color="Maroon">L1</font> holds <br/> ( <font color="Maroon">f</font> <a href="funct_2.html#K3">.</a> <span class="p1">(<span class="default"><font color="Olive">a1</font> <a href="lattices.html#K3">"\/"</a> <font color="Olive">b1</font></span>)</span> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><font color="Maroon">f</font> <a href="funct_2.html#K3">.</a> <font color="Olive">a1</font></span>)</span> <a href="lattices.html#K3">"\/"</a> <span class="p1">(<span class="default"><font color="Maroon">f</font> <a href="funct_2.html#K3">.</a> <font color="Olive">b1</font></span>)</span> &amp; <font color="Maroon">f</font> <a href="funct_2.html#K3">.</a> <span class="p1">(<span class="default"><font color="Olive">a1</font> <a href="lattices.html#K4">"/\"</a> <font color="Olive">b1</font></span>)</span> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><font color="Maroon">f</font> <a href="funct_2.html#K3">.</a> <font color="Olive">a1</font></span>)</span> <a href="lattices.html#K4">"/\"</a> <span class="p1">(<span class="default"><font color="Maroon">f</font> <a href="funct_2.html#K3">.</a> <font color="Olive">b1</font></span>)</span> )
 ;<br/>


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