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<b>let </b><font color="Maroon">M</font> be  <a href="lattice3.html#V3">complete</a> <a href="waybel_0.html#NM8">LATTICE</a>, <font color="Maroon">N</font> be  <a href="lattice3.html#V3">complete</a> <a href="waybel_0.html#NM8">LATTICE</a>;<br/><b>let </b><font color="Maroon">P</font> be  <a href="pre_topc.html#V2">correct</a> <a href="waybel19.html#V2">Lawson</a>  <a href="yellow_9.html#M1">TopAugmentation</a> of <span class="p1"><a href="yellow_3.html#K3">[:</a><span class="default"><font color="Maroon">M</font>,<font color="Maroon">N</font></span><a href="yellow_3.html#K3">:]</a></span>;<br/><b>let </b><font color="Maroon">Q</font> be  <a href="pre_topc.html#V2">correct</a> <a href="waybel19.html#V2">Lawson</a>  <a href="yellow_9.html#M1">TopAugmentation</a> of <font color="Maroon">M</font>;<br/><b>let </b><font color="Maroon">R</font> be  <a href="pre_topc.html#V2">correct</a> <a href="waybel19.html#V2">Lawson</a>  <a href="yellow_9.html#M1">TopAugmentation</a> of <font color="Maroon">N</font>;<br/>







<b>assume </b><a NAME="E1:34"/><i><font color="Green">E32</font></i>: 
 <a href="yellow_1.html#K2">InclPoset</a> <span class="p1">(<span class="default"><a href="waybel11.html#K5">sigma</a> <font color="Maroon">N</font></span>)</span> is <a href="waybel_3.html#V3">continuous</a>
 ;<br/>

<a NAME="E2:34"/><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">P</font>,the <a href="orders_2.html#U1">InternalRel</a> of <font color="Maroon">P</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 <span class="p1"><a href="yellow_3.html#K3">[:</a><span class="default"><font color="Maroon">M</font>,<font color="Maroon">N</font></span><a href="yellow_3.html#K3">:]</a></span>,the <a href="orders_2.html#U1">InternalRel</a> of <span class="p1"><a href="yellow_3.html#K3">[:</a><span class="default"><font color="Maroon">M</font>,<font color="Maroon">N</font></span><a href="yellow_3.html#K3">:]</a></span> #) &amp;  <a href="orders_2.html#G1">RelStr</a>(# the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">Q</font>,the <a href="orders_2.html#U1">InternalRel</a> of <font color="Maroon">Q</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">M</font>,the <a href="orders_2.html#U1">InternalRel</a> of <font color="Maroon">M</font> #) &amp;  <a href="orders_2.html#G1">RelStr</a>(# the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">R</font>,the <a href="orders_2.html#U1">InternalRel</a> of <font color="Maroon">R</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> #) )
 
<b>by </b><i><a class="ref" href="yellow_9.html#D4">YELLOW_9:def 4</a></i>;<br/>
<b>then </b><i><font color="Green">E35</font></i>: the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">P</font> = 
<span class="p1"><a href="zfmisc_1.html#K2">[:</a><span class="default">the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">Q</font>,the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">N</font></span><a href="zfmisc_1.html#K2">:]</a></span>
<b>by </b><i><a class="ref" href="yellow_3.html#D2">YELLOW_3:def 2</a></i>
<br/>.= 
the <a href="struct_0.html#U1">carrier</a> of <span class="p1"><a href="borsuk_1.html#K5">[:</a><span class="default"><font color="Maroon">Q</font>,<font color="Maroon">R</font></span><a href="borsuk_1.html#K5">:]</a></span>
<b>by </b><i>, <a class="ref" href="borsuk_1.html#D5">BORSUK_1:def 5</a></i>
;<br/>
the <a href="pre_topc.html#U1">topology</a> of <font color="Maroon">P</font> = 
 <a href="waybel19.html#K2">lambda</a> <span class="p1"><a href="yellow_3.html#K3">[:</a><span class="default"><font color="Maroon">M</font>,<font color="Maroon">N</font></span><a href="yellow_3.html#K3">:]</a></span>
<b>by </b><i><a class="ref" href="waybel19.html#D4">WAYBEL19:def 4</a></i>
<br/>.= 
the <a href="pre_topc.html#U1">topology</a> of <span class="p1"><a href="borsuk_1.html#K5">[:</a><span class="default"><font color="Maroon">Q</font>,<font color="Maroon">R</font></span><a href="borsuk_1.html#K5">:]</a></span>
<b>by </b><i>, </i>
;<br/>
<b>hence </b><a NAME="E5:34"/>
 <a href="pre_topc.html#G1">TopStruct</a>(# the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">P</font>,the <a href="pre_topc.html#U1">topology</a> of <font color="Maroon">P</font> #) <a href="hidden.html#R1">=</a> <span class="p1"><a href="borsuk_1.html#K5">[:</a><span class="default"><font color="Maroon">Q</font>,<font color="Maroon">R</font></span><a href="borsuk_1.html#K5">:]</a></span>
 <b>by </b><i/>;<br/>


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