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<b>let </b><font color="Maroon">S</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">D</font> be  non <a href="xboole_0.html#V1">empty</a> <a href="waybel_0.html#V1">directed</a> <a href="struct_0.html#NM2">Subset</a> of <font color="Maroon">S</font>;<br/>



<a NAME="E1:43"/>
(  <a href="relset_1.html#K4">dom</a> <span class="p1">(<span class="default"><a href="partfun1.html#K6">id</a> <font color="Maroon">D</font></span>)</span> <a href="hidden.html#R1">=</a> <font color="Maroon">D</font> &amp;  <a href="relset_1.html#K5">rng</a> <span class="p1">(<span class="default"><a href="partfun1.html#K6">id</a> <font color="Maroon">D</font></span>)</span> <a href="hidden.html#R1">=</a> <font color="Maroon">D</font> )
 
<b>by </b><i><a class="ref" href="relat_1.html#T71">RELAT_1:71</a></i>;<br/>
<b>then reconsider </b><font color="Maroon">g</font> =  <a href="partfun1.html#K6">id</a> <font color="Maroon">D</font> as   <a href="funct_2.html#NM1">Function</a> of <font color="Maroon">D</font>,the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">S</font> <b>by </b><i><a class="ref" href="funct_2.html#D1">FUNCT_2:def 1</a>, <a class="ref" href="relset_1.html#T11">RELSET_1:11</a></i>;<br/>
<a NAME="E3:43"/>
<span class="p1">(<span class="default"><a href="partfun1.html#K6">id</a> the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">S</font></span>)</span> <a href="partfun1.html#K2">|</a> <font color="Maroon">D</font> <a href="hidden.html#R1">=</a>  <a href="partfun1.html#K6">id</a> <font color="Maroon">D</font>
 
<b>by </b><i><a class="ref" href="funct_3.html#T1">FUNCT_3:1</a></i>;<br/>
<a NAME="E4:43"/><b>then </b>
 <a href="waybel17.html#K4">Net-Str</a> <font color="Maroon">D</font> <a href="hidden.html#R1">=</a>  <a href="waybel11.html#K3">Net-Str</a> <font color="Maroon">D</font>,<font color="Maroon">g</font>
 
<b>by </b><i><a class="ref" href="waybel17.html#T9">WAYBEL17:9</a></i>;<br/>
<b>hence </b><a NAME="E5:43"/>
for <font color="Olive">i</font>, <font color="Olive">j</font> being  <a href="struct_0.html#NM1">Element</a> of <span class="p1">(<span class="default"><a href="waybel17.html#K4">Net-Str</a> <font color="Maroon">D</font></span>)</span> holds <br/> ( <font color="Olive">i</font> <a href="orders_2.html#R3">&lt;=</a> <font color="Olive">j</font> iff <span class="p1">(<span class="default"><a href="waybel17.html#K4">Net-Str</a> <font color="Maroon">D</font></span>)</span> <a href="waybel_0.html#K2">.</a> <font color="Olive">i</font> <a href="orders_2.html#R3">&lt;=</a> <span class="p1">(<span class="default"><a href="waybel17.html#K4">Net-Str</a> <font color="Maroon">D</font></span>)</span> <a href="waybel_0.html#K2">.</a> <font color="Olive">j</font> )
 <b>by </b><i><a class="ref" href="waybel11.html#D10">WAYBEL11:def 10</a></i>;<br/>


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