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<b>set </b><font color="Maroon">S</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>,the <a href="waybel_0.html#U1">mapping</a> of <font color="Maroon">N</font> #);<br/>
<a NAME="E1:45_1_1"/><i><font color="Green">E31</font></i>: 
( <font color="Maroon">N</font> is    <a href="yellow_6.html#M1">SubNetStr</a> of <font color="Maroon">N</font> &amp;  <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> #) <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;  <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>,the <a href="waybel_0.html#U1">mapping</a> of <font color="Maroon">N</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>,the <a href="waybel_0.html#U1">mapping</a> of <font color="Maroon">N</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 <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>,the <a href="waybel_0.html#U1">mapping</a> of <font color="Maroon">N</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>,the <a href="waybel_0.html#U1">mapping</a> of <font color="Maroon">N</font> #) #) &amp; <font color="Maroon">N</font> is  <a href="yellow_0.html#V4">full</a>  <a href="yellow_0.html#M1">SubRelStr</a> of <font color="Maroon">N</font> )
 
<b>by </b><i><a class="ref" href="yellow_6.html#T15">YELLOW_6:15</a>, <a class="ref" href="yellow_6.html#T17">YELLOW_6:17</a></i>;<br/>
<a NAME="E2:45_1_1"/><b>then </b>
( the <a href="waybel_0.html#U1">mapping</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>,the <a href="waybel_0.html#U1">mapping</a> of <font color="Maroon">N</font> #) <a href="hidden.html#R1">=</a> the <a href="waybel_0.html#U1">mapping</a> of <font color="Maroon">N</font> <a href="partfun1.html#K2">|</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>,the <a href="waybel_0.html#U1">mapping</a> of <font color="Maroon">N</font> #) &amp;  <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>,the <a href="waybel_0.html#U1">mapping</a> of <font color="Maroon">N</font> #) is  <a href="yellow_0.html#V4">full</a>  <a href="yellow_0.html#M1">SubRelStr</a> of <font color="Maroon">N</font> )
 
<b>by </b><i><a class="ref" href="waybel21.html#T12">WAYBEL21:12</a>, <a class="ref" href="yellow_6.html#D8">YELLOW_6:def 8</a></i>;<br/>
<b>then reconsider </b><font color="Maroon">S</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>,the <a href="waybel_0.html#U1">mapping</a> of <font color="Maroon">N</font> #) as  non <a href="struct_0.html#V3">empty</a> <a href="waybel_0.html#V6">strict</a> <a href="yellow_6.html#V2">full</a>  <a href="yellow_6.html#M1">SubNetStr</a> of <font color="Maroon">N</font> <b>by </b><i><a class="ref" href="yellow_6.html#D8">YELLOW_6:def 8</a>, <a class="ref" href="yellow_6.html#D9">YELLOW_6:def 9</a></i>;<br/>
<a NAME="E4:45_1_1"/>
<font color="Maroon">S</font> is <a href="waybel_0.html#V7">directed</a>
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="45_1_1_1"><b>proof </b></a><div class="add">

<a NAME="E1:45_1_1_1"/>
(  <a href="pre_topc.html#K2">[#]</a> <font color="Maroon">N</font> <a href="hidden.html#R1">=</a> the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">N</font> &amp;  <a href="pre_topc.html#K2">[#]</a> <font color="Maroon">S</font> <a href="hidden.html#R1">=</a> the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">S</font> &amp;  <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="pre_topc.html#T12">PRE_TOPC:12</a>, <a class="ref" href="waybel_0.html#D6">WAYBEL_0:def 6</a></i>;<br/>
<b>hence </b><a NAME="E2:45_1_1_1"/>
 <a href="pre_topc.html#K2">[#]</a> <font color="Maroon">S</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>hence </b><a NAME="E5:45_1_1"/>
 ex <font color="Olive">b<sub>1</sub></font> being   <a href="yellow_6.html#M1">SubNetStr</a> of <font color="Maroon">N</font> st <br/>( <font color="Olive">b<sub>1</sub></font> is <a href="waybel_0.html#V6">strict</a> &amp; not <font color="Olive">b<sub>1</sub></font> is <a href="struct_0.html#V3">empty</a> &amp; <font color="Olive">b<sub>1</sub></font> is <a href="waybel_0.html#V7">directed</a> &amp; <font color="Olive">b<sub>1</sub></font> is <a href="yellow_6.html#V2">full</a> )
 ;<br/>


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