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<b>consider </b><font color="Maroon">S</font> being  <a href="pre_topc.html#V2">correct</a> <a href="waybel19.html#V2" target="_self">Lawson</a>  <a href="yellow_9.html#M1">TopAugmentation</a> of <font color="Maroon">T</font>;<br/>
<a NAME="E2:47_1_2"/><i><font color="Green">E34</font></i>: 
 <a href="orders_2.html#G1">RelStr</a>(# the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">S</font>,the <a href="orders_2.html#U1">InternalRel</a> of <font color="Maroon">S</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">T</font>,the <a href="orders_2.html#U1">InternalRel</a> of <font color="Maroon">T</font> #)
 
<b>by </b><i><a class="ref" href="yellow_9.html#D4">YELLOW_9:def 4</a></i>;<br/>
<b>then reconsider </b><font color="Maroon">t</font> = the <a href="pre_topc.html#U1">topology</a> of <font color="Maroon">S</font> as   <a href="struct_0.html#NM3">Subset-Family</a> of <font color="Maroon">T</font> ;<br/>
<b>take </b>
<font color="Maroon">t</font>
;<br/>

<b>let </b><font color="Maroon">S'</font> be  <a href="pre_topc.html#V2">correct</a> <a href="waybel19.html#V2" target="_self">Lawson</a>  <a href="yellow_9.html#M1">TopAugmentation</a> of <font color="Maroon">T</font>;<br/>

<a NAME="E4:47_1_2"/><i><font color="Green">E36</font></i>: 
 <a href="orders_2.html#G1">RelStr</a>(# the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">S'</font>,the <a href="orders_2.html#U1">InternalRel</a> of <font color="Maroon">S'</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">T</font>,the <a href="orders_2.html#U1">InternalRel</a> of <font color="Maroon">T</font> #)
 
<b>by </b><i><a class="ref" href="yellow_9.html#D4">YELLOW_9:def 4</a></i>;<br/>
<a NAME="E5:47_1_2"/><b>then </b><i><font color="Green">E38</font></i>: 
(  <a href="waybel19.html#K1" target="_self">omega</a> <font color="Maroon">S'</font> <a href="hidden.html#R1">=</a>  <a href="waybel19.html#K1" target="_self">omega</a> <font color="Maroon">S</font> &amp;  <a href="waybel11.html#K5">sigma</a> <font color="Maroon">S'</font> <a href="hidden.html#R1">=</a>  <a href="waybel11.html#K5">sigma</a> <font color="Maroon">S</font> )
 
<b>by </b><i>, , <a class="ref" href="yellow_9.html#T52">YELLOW_9:52</a></i>;<br/>
<a NAME="E6:47_1_2"/>
( <span class="p1">(<span class="default"><a href="waybel19.html#K1" target="_self">omega</a> <font color="Maroon">S'</font></span>)</span> <a href="subset_1.html#K4">\/</a> <span class="p1">(<span class="default"><a href="waybel11.html#K5">sigma</a> <font color="Maroon">S'</font></span>)</span> is    <a href="cantor_1.html#M2">prebasis</a> of <font color="Maroon">S'</font> &amp; <span class="p1">(<span class="default"><a href="waybel19.html#K1" target="_self">omega</a> <font color="Maroon">S</font></span>)</span> <a href="subset_1.html#K4">\/</a> <span class="p1">(<span class="default"><a href="waybel11.html#K5">sigma</a> <font color="Maroon">S</font></span>)</span> is    <a href="cantor_1.html#M2">prebasis</a> of <font color="Maroon">S</font> )
 
<b>by </b><i/>;<br/>
<a NAME="E7:47_1_2"/><b>then </b><i><font color="Green">E40</font></i>: 
(  <a href="cantor_1.html#K2">FinMeetCl</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="waybel19.html#K1" target="_self">omega</a> <font color="Maroon">S'</font></span>)</span> <a href="subset_1.html#K4">\/</a> <span class="p2">(<span class="default"><a href="waybel11.html#K5">sigma</a> <font color="Maroon">S'</font></span>)</span></span>)</span> is    <a href="cantor_1.html#M1">Basis</a> of <font color="Maroon">S'</font> &amp;  <a href="cantor_1.html#K2">FinMeetCl</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="waybel19.html#K1" target="_self">omega</a> <font color="Maroon">S</font></span>)</span> <a href="subset_1.html#K4">\/</a> <span class="p2">(<span class="default"><a href="waybel11.html#K5">sigma</a> <font color="Maroon">S</font></span>)</span></span>)</span> is    <a href="cantor_1.html#M1">Basis</a> of <font color="Maroon">S</font> )
 
<b>by </b><i><a class="ref" href="yellow_9.html#T23">YELLOW_9:23</a></i>;<br/>
<b>hence </b><font color="Maroon">t</font> = 
 <a href="cantor_1.html#K1">UniCl</a> <span class="p1">(<span class="default"><a href="cantor_1.html#K2">FinMeetCl</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="waybel19.html#K1" target="_self">omega</a> <font color="Maroon">S</font></span>)</span> <a href="subset_1.html#K4">\/</a> <span class="p3">(<span class="default"><a href="waybel11.html#K5">sigma</a> <font color="Maroon">S</font></span>)</span></span>)</span></span>)</span>
<b>by </b><i><a class="ref" href="yellow_9.html#T22">YELLOW_9:22</a></i>
<br/>.= 
the <a href="pre_topc.html#U1">topology</a> of <font color="Maroon">S'</font>
<b>by </b><i>, , , , <a class="ref" href="yellow_9.html#T22">YELLOW_9:22</a></i>
;<br/><br/>


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