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<b>let </b><font color="Maroon">S1</font> be  non <a href="struct_0.html#V3">empty</a> <a href="orders_2.html#V1">strict</a> <a href="yellow_0.html#V4">full</a>  <a href="yellow_0.html#M1">SubRelStr</a> of  <a href="waybel10.html#K3" target="_self">ClOpers</a> <font color="Maroon">L</font>, <font color="Maroon">S2</font> be  non <a href="struct_0.html#V3">empty</a> <a href="orders_2.html#V1">strict</a> <a href="yellow_0.html#V4">full</a>  <a href="yellow_0.html#M1">SubRelStr</a> of  <a href="waybel10.html#K3" target="_self">ClOpers</a> <font color="Maroon">L</font>;<br/>

<b>assume </b><b>that </b><br/><a NAME="E1:57_1_2"/><i><font color="Green">E45</font></i>: 
for <font color="Olive">f</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> holds <br/> ( <font color="Olive">f</font> is   <a href="struct_0.html#NM1">Element</a> of <font color="Maroon">S1</font> iff <font color="Olive">f</font> is <a href="waybel_0.html#V22">directed-sups-preserving</a> )
 <b>and </b><br/><a NAME="E2:57_1_2"/><i><font color="Green">E50</font></i>: 
for <font color="Olive">f</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> holds <br/> ( <font color="Olive">f</font> is   <a href="struct_0.html#NM1">Element</a> of <font color="Maroon">S2</font> iff <font color="Olive">f</font> is <a href="waybel_0.html#V22">directed-sups-preserving</a> )
 ;<br/>

<b>defpred </b><font color="Maroon">S<sub>1</sub></font>[   <a href="hidden.html#M1">set</a> ] <b>means </b><font color="Maroon">a<sub>1</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#NM6">Function</a> of <font color="Maroon">L</font>,<font color="Maroon">L</font>;<br/>
<div><i><font color="Green">E69</font></i>: <a class="txt" onclick="hs2(this)" href="javascript:()" title="57_1_2_1"><b>now </b></a><div class="add"><b>let </b><font color="Maroon">f</font> be    <a href="hidden.html#M1">set</a> ;<br/><a NAME="E1:57_1_2_1"/>
( <font color="Maroon">f</font> is   <a href="struct_0.html#NM1">Element</a> of <font color="Maroon">S1</font> implies <font color="Maroon">f</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><a class="ref" href="yellow_0.html#T59">YELLOW_0:59</a></i>;<br/><a NAME="E2:57_1_2_1"/><b>then </b>
( <font color="Maroon">f</font> is   <a href="struct_0.html#NM1">Element</a> of <font color="Maroon">S1</font> implies <font color="Maroon">f</font> is  <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>hence </b><a NAME="E3:57_1_2_1"/>
( <font color="Maroon">f</font> is   <a href="struct_0.html#NM1">Element</a> of <font color="Maroon">S1</font> iff <font color="Maroon">S<sub>1</sub></font>[<font color="Maroon">f</font>] )
 <b>by </b><i/>;<br/></div><b>end;</b></div>
<div><i><font color="Green">E70</font></i>: <a class="txt" onclick="hs2(this)" href="javascript:()" title="57_1_2_2"><b>now </b></a><div class="add"><b>let </b><font color="Maroon">f</font> be    <a href="hidden.html#M1">set</a> ;<br/><a NAME="E1:57_1_2_2"/>
( <font color="Maroon">f</font> is   <a href="struct_0.html#NM1">Element</a> of <font color="Maroon">S2</font> implies <font color="Maroon">f</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><a class="ref" href="yellow_0.html#T59">YELLOW_0:59</a></i>;<br/><a NAME="E2:57_1_2_2"/><b>then </b>
( <font color="Maroon">f</font> is   <a href="struct_0.html#NM1">Element</a> of <font color="Maroon">S2</font> implies <font color="Maroon">f</font> is  <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>hence </b><a NAME="E3:57_1_2_2"/>
( <font color="Maroon">f</font> is   <a href="struct_0.html#NM1">Element</a> of <font color="Maroon">S2</font> iff <font color="Maroon">S<sub>1</sub></font>[<font color="Maroon">f</font>] )
 <b>by </b><i/>;<br/></div><b>end;</b></div>
<a NAME="E5:57_1_2"/>
 <a href="orders_2.html#G1">RelStr</a>(# the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">S1</font>,the <a href="orders_2.html#U1">InternalRel</a> of <font color="Maroon">S1</font> #) <a href="hidden.html#R1">=</a>  <a href="orders_2.html#G1">RelStr</a>(# the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">S2</font>,the <a href="orders_2.html#U1">InternalRel</a> of <font color="Maroon">S2</font> #)
 
<b>from </b><i><a class="ref" href="waybel10.html#S3" target="_self">WAYBEL10:sch 3</a>(, );<br/></i>
<b>hence </b><a NAME="E6:57_1_2"/>
<font color="Maroon">S1</font> <a href="hidden.html#R1">=</a> <font color="Maroon">S2</font>
 ;<br/>


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