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<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> ex <font color="Olive">c</font> being <a href="waybel_1.html#V7">closure</a> <a href="struct_0.html#NM6">Function</a> of <font color="Maroon">L</font>,<font color="Maroon">L</font> st <br/>( <font color="Olive">c</font> <a href="hidden.html#R1">=</a> <font color="Maroon">a<sub>1</sub></font> &amp; <font color="Maroon">a<sub>2</sub></font> <a href="hidden.html#R1">=</a>  <a href="yellow_2.html#K1">Image</a> <font color="Olive">c</font> );<br/>
<div><i><font color="Green">E31</font></i>: <a class="txt" onclick="hs2(this)" href="javascript:()" title="42_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 <span class="p1">(<span class="default"><a href="waybel10.html#K3" target="_self">ClOpers</a> <font color="Maroon">L</font></span>)</span>;<br/><b>reconsider </b><font color="Maroon">c</font> = <font color="Maroon">x</font> as  <a href="waybel_1.html#V7">closure</a> <a href="struct_0.html#NM6">Function</a> of <font color="Maroon">L</font>,<font color="Maroon">L</font> <b>by </b><i/>;<br/><b>reconsider </b><font color="Maroon">a</font> =  <a href="yellow_2.html#K1">Image</a> <font color="Maroon">c</font> as   <a href="struct_0.html#NM1">Element</a> of <span class="p1">(<span class="default"><a href="waybel10.html#K5" target="_self">ClosureSystems</a> <font color="Maroon">L</font></span>)</span> <b>by </b><i/>;<br/><b>take </b><font color="Maroon">b</font> = <font color="Maroon">a</font> <a href="lattice3.html#K8">~</a> ;<br/><b>thus </b><a NAME="E3:42_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="struct_0.html#NM6">Function</a> of <span class="p1">(<span class="default"><a href="waybel10.html#K3" target="_self">ClOpers</a> <font color="Maroon">L</font></span>)</span>,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="waybel10.html#K5" target="_self">ClosureSystems</a> <font color="Maroon">L</font></span>)</span> <a href="waybel10.html#K1" target="_self">opp</a> </span>)</span><b> such that </b><br/><a NAME="E3:42_1_1"/><i><font color="Green">E32</font></i>: 
for <font color="Olive">x</font> being  <a href="struct_0.html#NM1">Element</a> of <span class="p1">(<span class="default"><a href="waybel10.html#K3" target="_self">ClOpers</a> <font color="Maroon">L</font></span>)</span> 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#S10">FUNCT_2:sch 10</a>();<br/></i>
<b>take </b>
<font color="Maroon">f</font>
;<br/>

<b>let </b><font color="Maroon">c</font> be  <a href="waybel_1.html#V7">closure</a> <a href="struct_0.html#NM6">Function</a> of <font color="Maroon">L</font>,<font color="Maroon">L</font>;<br/>

<a NAME="E4:42_1_1"/>
<font color="Maroon">c</font> is   <a href="struct_0.html#NM1">Element</a> of <span class="p1">(<span class="default"><a href="waybel10.html#K3" target="_self">ClOpers</a> <font color="Maroon">L</font></span>)</span>
 
<b>by </b><i/>;<br/>
<a NAME="E5:42_1_1"/><b>then </b>
 ex <font color="Olive">c1</font> being <a href="waybel_1.html#V7">closure</a> <a href="struct_0.html#NM6">Function</a> of <font color="Maroon">L</font>,<font color="Maroon">L</font> st <br/>( <font color="Olive">c1</font> <a href="funct_2.html#R2">=</a> <font color="Maroon">c</font> &amp; <font color="Maroon">f</font> <a href="funct_1.html#K1">.</a> <font color="Maroon">c</font> <a href="hidden.html#R1">=</a>  <a href="yellow_2.html#K1">Image</a> <font color="Olive">c1</font> )
 
<b>by </b><i/>;<br/>
<b>hence </b><a NAME="E6:42_1_1"/>
<font color="Maroon">f</font> <a href="funct_1.html#K1">.</a> <font color="Maroon">c</font> <a href="hidden.html#R1">=</a>  <a href="yellow_2.html#K1">Image</a> <font color="Maroon">c</font>
 ;<br/>


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