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<b>let </b><font color="Maroon">L</font> be  non <a href="struct_0.html#V3">empty</a>  <a href="struct_0.html#L1">1-sorted</a> ;<br/><b>let </b><font color="Maroon">N</font> be  non <a href="struct_0.html#V3">empty</a>  <a href="waybel_0.html#L1">NetStr</a> of <font color="Maroon">L</font>;<br/><b>let </b><font color="Maroon">i</font> be   <a href="struct_0.html#NM1">Element</a> of <font color="Maroon">N</font>;<br/>





<a NAME="E1:44"/><i><font color="Green">E33</font></i>: 
the <a href="orders_2.html#U1">InternalRel</a> of <span class="p1">(<span class="default"><font color="Maroon">N</font> <a href="waybel_9.html#K5" target="_self">|</a> <font color="Maroon">i</font></span>)</span> <a href="hidden.html#R1">=</a> the <a href="orders_2.html#U1">InternalRel</a> of <font color="Maroon">N</font> <a href="toler_1.html#K1">|_2</a> the <a href="struct_0.html#U1">carrier</a> of <span class="p1">(<span class="default"><font color="Maroon">N</font> <a href="waybel_9.html#K5" target="_self">|</a> <font color="Maroon">i</font></span>)</span>
 
<b>by </b><i/>;<br/>
<a NAME="E2:44"/><i><font color="Green">E34</font></i>: 
<font color="Maroon">N</font> <a href="waybel_9.html#K5" target="_self">|</a> <font color="Maroon">i</font> is    <a href="yellow_0.html#M1">SubRelStr</a> of <font color="Maroon">N</font>
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="44_1"><b>proof </b></a><div class="add">

<b>thus </b><a NAME="E1:44_1"/>
the <a href="struct_0.html#U1">carrier</a> of <span class="p1">(<span class="default"><font color="Maroon">N</font> <a href="waybel_9.html#K5" target="_self">|</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">N</font>
 <b>by </b><i/>; <i><font color="Red">:: according to </font></i><a class="ref" href="yellow_0.html#D13">YELLOW_0:def 13</a><br/>

<b>thus </b><a NAME="E2:44_1"/>
the <a href="orders_2.html#U1">InternalRel</a> of <span class="p1">(<span class="default"><font color="Maroon">N</font> <a href="waybel_9.html#K5" target="_self">|</a> <font color="Maroon">i</font></span>)</span> <a href="tarski.html#R1">c=</a> the <a href="orders_2.html#U1">InternalRel</a> of <font color="Maroon">N</font>
 <b>by </b><i>, <a class="ref" href="xboole_1.html#T17">XBOOLE_1:17</a></i>;<br/>


</div><b>end;</b></div>
<a NAME="E3:44"/>
<font color="Maroon">N</font> <a href="waybel_9.html#K5" target="_self">|</a> <font color="Maroon">i</font> is    <a href="yellow_6.html#M1">SubNetStr</a> of <font color="Maroon">N</font>
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="44_2"><b>proof </b></a><div class="add">

<b>thus </b><a NAME="E1:44_2"/>
<font color="Maroon">N</font> <a href="waybel_9.html#K5" target="_self">|</a> <font color="Maroon">i</font> is    <a href="yellow_0.html#M1">SubRelStr</a> of <font color="Maroon">N</font>
 <b>by </b><i/>; <i><font color="Red">:: according to </font></i><a class="ref" href="yellow_6.html#D8">YELLOW_6:def 8</a><br/>

<b>thus </b><a NAME="E2:44_2"/>
the <a href="waybel_0.html#U1">mapping</a> of <span class="p1">(<span class="default"><font color="Maroon">N</font> <a href="waybel_9.html#K5" target="_self">|</a> <font color="Maroon">i</font></span>)</span> <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 <span class="p1">(<span class="default"><font color="Maroon">N</font> <a href="waybel_9.html#K5" target="_self">|</a> <font color="Maroon">i</font></span>)</span>
 <b>by </b><i/>;<br/>


</div><b>end;</b></div>
<b>then reconsider </b><font color="Maroon">K</font> = <font color="Maroon">N</font> <a href="waybel_9.html#K5" target="_self">|</a> <font color="Maroon">i</font> as    <a href="yellow_6.html#M1">SubNetStr</a> of <font color="Maroon">N</font> ;<br/>
<a NAME="E5:44"/>
<font color="Maroon">K</font> is <a href="yellow_6.html#V2">full</a>
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="44_3"><b>proof </b></a><div class="add">

<b>thus </b><a NAME="E1:44_3"/>
<font color="Maroon">K</font> is  <a href="yellow_0.html#V4">full</a>  <a href="yellow_0.html#M1">SubRelStr</a> of <font color="Maroon">N</font>
  <i><font color="Red">:: according to </font></i><a class="ref" href="yellow_6.html#D9">YELLOW_6:def 9</a><div><a class="txt" onclick="hs2(this)" href="javascript:()" title="44_3_1"><b>proof </b></a><div class="add">

<a NAME="E1:44_3_1"/>
the <a href="orders_2.html#U1">InternalRel</a> of <font color="Maroon">K</font> <a href="hidden.html#R1">=</a> the <a href="orders_2.html#U1">InternalRel</a> of <font color="Maroon">N</font> <a href="toler_1.html#K1">|_2</a> the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">K</font>
 
<b>by </b><i/>;<br/>
<b>hence </b><a NAME="E2:44_3_1"/>
<font color="Maroon">K</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_0.html#D14">YELLOW_0:def 14</a></i>;<br/>


</div><b>end;</b></div>


</div><b>end;</b></div>
<b>hence </b><a NAME="E6:44"/>
<font color="Maroon">N</font> <a href="waybel_9.html#K5" target="_self">|</a> <font color="Maroon">i</font> is  <a href="yellow_6.html#V2">full</a>  <a href="yellow_6.html#M1">SubNetStr</a> of <font color="Maroon">N</font>
 ;<br/>


</div>
