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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> ] means ex <font color="Olive">b<sub>1</sub></font> being <a href="waybel_1.html#V7">closure</a> <a href="struct_0.html#NM7">Function</a> of <font color="Maroon">c<sub>1</sub></font>,<font color="Maroon">c<sub>1</sub></font> st <br/>( <font color="Olive">b<sub>1</sub></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">b<sub>1</sub></font> );<br/>
<div><i><font color="Green">E21</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">c<sub>2</sub></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">c<sub>1</sub></font></span>)</span>;<br/><b>reconsider </b><font color="Maroon">c<sub>3</sub></font> = <font color="Maroon">c<sub>2</sub></font> as  <a href="waybel_1.html#V7">closure</a> <a href="struct_0.html#NM7">Function</a> of <font color="Maroon">c<sub>1</sub></font>,<font color="Maroon">c<sub>1</sub></font> <b>by </b><i><a class="ref" href="waybel10.html#T11" target="_self">Th11</a></i>;<br/><b>reconsider </b><font color="Maroon">c<sub>4</sub></font> =  <a href="yellow_2.html#K1">Image</a> <font color="Maroon">c<sub>3</sub></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">c<sub>1</sub></font></span>)</span> <b>by </b><i><a class="ref" href="waybel10.html#T17" target="_self">Th17</a></i>;<br/><b>take </b><font color="Maroon">c<sub>5</sub></font> = <font color="Maroon">c<sub>4</sub></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">c<sub>2</sub></font>,<font color="Maroon">c<sub>5</sub></font>]
 ;<br/></div><b>end;</b></div>
<b>consider </b><font color="Maroon">c<sub>2</sub></font> being   <a href="struct_0.html#NM7">Function</a> of <span class="p1">(<span class="default"><a href="waybel10.html#K3" target="_self">ClOpers</a> <font color="Maroon">c<sub>1</sub></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">c<sub>1</sub></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">E22</font></i>: 
for <font color="Olive">b<sub>1</sub></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">c<sub>1</sub></font></span>)</span> holds <font color="Maroon">S<sub>1</sub></font>[<font color="Olive">b<sub>1</sub></font>,<font color="Maroon">c<sub>2</sub></font> <a href="funct_2.html#K3">.</a> <font color="Olive">b<sub>1</sub></font>]
 <b>from </b><i><a class="ref" href="funct_2.html#S10">FUNCT_2:sch 10</a>(<a class="txt" href="waybel10.html#E1:42_1_1"><i><font color="Green">E21</font></i></a>);<br/></i>
<b>take </b>
<font color="Maroon">c<sub>2</sub></font>
;<br/>

<b>let </b><font color="Maroon">c<sub>3</sub></font> be  <a href="waybel_1.html#V7">closure</a> <a href="struct_0.html#NM7">Function</a> of <font color="Maroon">c<sub>1</sub></font>,<font color="Maroon">c<sub>1</sub></font>;<br/>

<a NAME="E4:42_1_1"/>
<font color="Maroon">c<sub>3</sub></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">c<sub>1</sub></font></span>)</span>
 
<b>by </b><i><a class="ref" href="waybel10.html#T11" target="_self">Th11</a></i>;<br/>
<a NAME="E5:42_1_1"/><b>then </b>
ex <font color="Olive">b<sub>1</sub></font> being <a href="waybel_1.html#V7">closure</a> <a href="struct_0.html#NM7">Function</a> of <font color="Maroon">c<sub>1</sub></font>,<font color="Maroon">c<sub>1</sub></font> st <br/>( <font color="Olive">b<sub>1</sub></font> <a href="funct_2.html#R2">=</a> <font color="Maroon">c<sub>3</sub></font> &amp; <font color="Maroon">c<sub>2</sub></font> <a href="funct_1.html#K1">.</a> <font color="Maroon">c<sub>3</sub></font> <a href="hidden.html#R1">=</a>  <a href="yellow_2.html#K1">Image</a> <font color="Olive">b<sub>1</sub></font> )
 
<b>by </b><i><a class="txt" href="waybel10.html#E3:42_1_1"><i><font color="Green">E22</font></i></a></i>;<br/>
<b>hence </b><a NAME="E6:42_1_1"/>
<font color="Maroon">c<sub>2</sub></font> <a href="funct_1.html#K1">.</a> <font color="Maroon">c<sub>3</sub></font> <a href="hidden.html#R1">=</a>  <a href="yellow_2.html#K1">Image</a> <font color="Maroon">c<sub>3</sub></font>
 ;<br/>


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