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<b>let </b><font color="Maroon">c<sub>1</sub></font> be  non <a href="struct_0.html#V3">empty</a> <a href="orders_2.html#V2">reflexive</a>  <a href="orders_2.html#L1">RelStr</a> ;<br/><b>let </b><font color="Maroon">c<sub>2</sub></font> be    <a href="hidden.html#M1">set</a> ;<br/>



<a NAME="E1:58"/>
( ( <font color="Maroon">c<sub>2</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> implies <font color="Maroon">c<sub>2</sub></font> is  <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> ) &amp; ( <font color="Maroon">c<sub>2</sub></font> is  <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> implies <font color="Maroon">c<sub>2</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> ) &amp; ( <font color="Maroon">c<sub>2</sub></font> is   <a href="struct_0.html#NM1">Element</a> of <span class="p1">(<span class="default"><a href="waybel10.html#K8" target="_self">DsupClOpers</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> implies <font color="Maroon">c<sub>2</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>, <a class="ref" href="yellow_0.html#T59">YELLOW_0:59</a></i>;<br/>
<b>hence </b><a NAME="E2:58"/>
( <font color="Maroon">c<sub>2</sub></font> is   <a href="struct_0.html#NM1">Element</a> of <span class="p1">(<span class="default"><a href="waybel10.html#K8" target="_self">DsupClOpers</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> iff <font color="Maroon">c<sub>2</sub></font> is  <a href="waybel_0.html#V22">directed-sups-preserving</a> <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#D7" target="_self">Def7</a></i>;<br/>


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