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<a NAME="E1:47_1_1"/><i><font color="Green">E43</font></i>: 
the <a href="waybel_0.html#U1">mapping</a> of <font color="Maroon">N</font> <a href="hidden.html#R2">in</a>  <a href="funct_2.html#K1">Funcs</a> the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">N</font>,the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">T</font>
 
<b>by </b><i><a class="ref" href="funct_2.html#T11">FUNCT_2:11</a></i>;<br/>
<a NAME="E2:47_1_1"/>
the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">T</font> <a href="tarski.html#R1">c=</a>  <a href="funct_2.html#K1">Funcs</a> <font color="Maroon">I</font>,the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">S</font>
 
<b>by </b><i>, <a class="ref" href="yellow_1.html#T28">YELLOW_1:28</a></i>;<br/>
<a NAME="E3:47_1_1"/><b>then </b>
 <a href="funct_2.html#K1">Funcs</a> the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">N</font>,the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">T</font> <a href="tarski.html#R1">c=</a>  <a href="funct_2.html#K1">Funcs</a> the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">N</font>,<span class="p1">(<span class="default"><a href="funct_2.html#K1">Funcs</a> <font color="Maroon">I</font>,the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">S</font></span>)</span>
 
<b>by </b><i><a class="ref" href="funct_5.html#T63">FUNCT_5:63</a></i>;<br/>
<a NAME="E4:47_1_1"/><b>then </b>
(  <a href="relat_1.html#K1">dom</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="funct_6.html#K10">commute</a> the <a href="waybel_0.html#U1">mapping</a> of <font color="Maroon">N</font></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">i</font></span>)</span> <a href="hidden.html#R1">=</a> the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">N</font> &amp;  <a href="relat_1.html#K2">rng</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="funct_6.html#K10">commute</a> the <a href="waybel_0.html#U1">mapping</a> of <font color="Maroon">N</font></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">i</font></span>)</span> <a href="tarski.html#R1">c=</a> the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">S</font> )
 
<b>by </b><i>, <a class="ref" href="equation.html#T3">EQUATION:3</a></i>;<br/>
<b>then reconsider </b><font color="Maroon">f</font> = <span class="p1">(<span class="default"><a href="funct_6.html#K10">commute</a> the <a href="waybel_0.html#U1">mapping</a> of <font color="Maroon">N</font></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">i</font> as   <a href="funct_2.html#NM1">Function</a> of the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">N</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/>
<b>set </b><font color="Maroon">A</font> =  <a href="waybel_0.html#G1">NetStr</a>(# the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">N</font>,the <a href="orders_2.html#U1">InternalRel</a> of <font color="Maroon">N</font>,<font color="Maroon">f</font> #);<br/>
<a NAME="E6:47_1_1"/><i><font color="Green">E44</font></i>: 
 <a href="orders_2.html#G1">RelStr</a>(# the <a href="struct_0.html#U1">carrier</a> of <a href="waybel_0.html#G1">NetStr</a>(# the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">N</font>,the <a href="orders_2.html#U1">InternalRel</a> of <font color="Maroon">N</font>,<font color="Maroon">f</font> #),the <a href="orders_2.html#U1">InternalRel</a> of <a href="waybel_0.html#G1">NetStr</a>(# the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">N</font>,the <a href="orders_2.html#U1">InternalRel</a> of <font color="Maroon">N</font>,<font color="Maroon">f</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">N</font>,the <a href="orders_2.html#U1">InternalRel</a> of <font color="Maroon">N</font> #)
 
;<br/>
<a NAME="E7:47_1_1"/>
 <a href="waybel_0.html#G1">NetStr</a>(# the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">N</font>,the <a href="orders_2.html#U1">InternalRel</a> of <font color="Maroon">N</font>,<font color="Maroon">f</font> #) is <a href="waybel_0.html#V7">directed</a>
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="47_1_1_1"><b>proof </b></a><div class="add">

<a NAME="E1:47_1_1_1"/><i><font color="Green">E47</font></i>: 
 <a href="pre_topc.html#K2">[#]</a> <font color="Maroon">N</font> is <a href="waybel_0.html#V1">directed</a>
 
<b>by </b><i><a class="ref" href="waybel_0.html#D6">WAYBEL_0:def 6</a></i>;<br/>
<b>thus </b><a NAME="E2:47_1_1_1"/>
 <a href="pre_topc.html#K2">[#]</a> <a href="waybel_0.html#G1">NetStr</a>(# the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">N</font>,the <a href="orders_2.html#U1">InternalRel</a> of <font color="Maroon">N</font>,<font color="Maroon">f</font> #) is <a href="waybel_0.html#V1">directed</a>
 <b>by </b><i>, , <a class="ref" href="waybel_0.html#T3">WAYBEL_0:3</a></i>; <i><font color="Red">:: according to </font></i><a class="ref" href="waybel_0.html#D6">WAYBEL_0:def 6</a><br/>


</div><b>end;</b></div>
<b>then reconsider </b><font color="Maroon">A</font> =  <a href="waybel_0.html#G1">NetStr</a>(# the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">N</font>,the <a href="orders_2.html#U1">InternalRel</a> of <font color="Maroon">N</font>,<font color="Maroon">f</font> #) as  <a href="waybel_0.html#V6">strict</a> <a href="waybel_0.html#NM2">net</a> of <font color="Maroon">S</font> <b>by </b><i>, <a class="ref" href="waybel_8.html#T13">WAYBEL_8:13</a></i>;<br/>
<b>take </b>
<font color="Maroon">A</font>
;<br/>

<b>thus </b><a NAME="E9:47_1_1"/>
(  <a href="orders_2.html#G1">RelStr</a>(# the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">A</font>,the <a href="orders_2.html#U1">InternalRel</a> of <font color="Maroon">A</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">N</font>,the <a href="orders_2.html#U1">InternalRel</a> of <font color="Maroon">N</font> #) &amp; the <a href="waybel_0.html#U1">mapping</a> of <font color="Maroon">A</font> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><a href="funct_6.html#K10">commute</a> the <a href="waybel_0.html#U1">mapping</a> of <font color="Maroon">N</font></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">i</font> )
 ;<br/>


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