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<b>let </b><font color="Maroon">M</font> be  non <a href="xboole_0.html#V1">empty</a>  <a href="hidden.html#M1">set</a> ;<br/><b>let </b><font color="Maroon">L</font> be  <a href="lattice3.html#V3">complete</a> <a href="waybel_3.html#V3">continuous</a> <a href="waybel_0.html#NM8">LATTICE</a>;<br/>



<a NAME="E1:39"/><i><font color="Green">E46</font></i>: 
 <a href="orders_2.html#G1">RelStr</a>(# the <a href="struct_0.html#U1">carrier</a> of <span class="p1">(<span class="default"><a href="waybel29.html#K1" target="_self">Sigma</a> <font color="Maroon">L</font></span>)</span>,the <a href="orders_2.html#U1">InternalRel</a> of <span class="p1">(<span class="default"><a href="waybel29.html#K1" target="_self">Sigma</a> <font color="Maroon">L</font></span>)</span> #) <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">L</font>,the <a href="orders_2.html#U1">InternalRel</a> of <font color="Maroon">L</font> #)
 
<b>by </b><i><a class="ref" href="yellow_9.html#D4">YELLOW_9:def 4</a></i>;<br/>
<b>reconsider </b><font color="Maroon">S</font> =  <a href="waybel29.html#K1" target="_self">Sigma</a> <font color="Maroon">L</font> as  <a href="waybel18.html#V2">injective</a> <a href="t_0topsp.html#NM1">T_0-TopSpace</a> ;<br/>
<a NAME="E3:39"/>
 <a href="waybel25.html#K1">Omega</a> <span class="p1">(<span class="default"><a href="waybel29.html#K1" target="_self">Sigma</a> <font color="Maroon">L</font></span>)</span> <a href="hidden.html#R1">=</a>  <a href="waybel29.html#K1" target="_self">Sigma</a> <font color="Maroon">L</font>
 
<b>by </b><i><a class="ref" href="waybel25.html#T15">WAYBEL25:15</a></i>;<br/>
<b>then </b> <a href="orders_2.html#G1">RelStr</a>(# the <a href="struct_0.html#U1">carrier</a> of <span class="p1">(<span class="default"><a href="waybel25.html#K1">Omega</a> <span class="p2">(<span class="default"><font color="Maroon">M</font> <a href="waybel26.html#NK2" target="_self">-TOP_prod</a> <span class="p3">(<span class="default"><font color="Maroon">M</font> <a href="waybel_5.html#K7">=&gt;</a> <span class="p4">(<span class="default"><a href="waybel29.html#K1" target="_self">Sigma</a> <font color="Maroon">L</font></span>)</span></span>)</span></span>)</span></span>)</span>,the <a href="orders_2.html#U1">InternalRel</a> of <span class="p1">(<span class="default"><a href="waybel25.html#K1">Omega</a> <span class="p2">(<span class="default"><font color="Maroon">M</font> <a href="waybel26.html#NK2" target="_self">-TOP_prod</a> <span class="p3">(<span class="default"><font color="Maroon">M</font> <a href="waybel_5.html#K7">=&gt;</a> <span class="p4">(<span class="default"><a href="waybel29.html#K1" target="_self">Sigma</a> <font color="Maroon">L</font></span>)</span></span>)</span></span>)</span></span>)</span> #) = 
<font color="Maroon">M</font> <a href="waybel26.html#NK1" target="_self">-POS_prod</a> <span class="p1">(<span class="default"><font color="Maroon">M</font> <a href="waybel_5.html#K7">=&gt;</a> <span class="p2">(<span class="default"><a href="waybel29.html#K1" target="_self">Sigma</a> <font color="Maroon">L</font></span>)</span></span>)</span>
<b>by </b><i><a class="ref" href="waybel25.html#T14">WAYBEL25:14</a></i>
<br/>.= 
<span class="p1">(<span class="default"><a href="waybel29.html#K1" target="_self">Sigma</a> <font color="Maroon">L</font></span>)</span> <a href="yellow_1.html#K6">|^</a> <font color="Maroon">M</font>
<b>by </b><i><a class="ref" href="yellow_1.html#D5">YELLOW_1:def 5</a></i>
<br/>.= 
<font color="Maroon">L</font> <a href="yellow_1.html#K6">|^</a> <font color="Maroon">M</font>
<b>by </b><i>, <a class="ref" href="waybel27.html#T15">WAYBEL27:15</a></i>
;<br/>
<b>then </b> <a href="waybel29.html#K1" target="_self">Sigma</a> <span class="p1">(<span class="default"><font color="Maroon">L</font> <a href="yellow_1.html#K6">|^</a> <font color="Maroon">M</font></span>)</span> = 
 <a href="waybel29.html#K1" target="_self">Sigma</a> <span class="p1">(<span class="default"><a href="waybel25.html#K1">Omega</a> <span class="p2">(<span class="default"><font color="Maroon">M</font> <a href="waybel26.html#NK2" target="_self">-TOP_prod</a> <span class="p3">(<span class="default"><font color="Maroon">M</font> <a href="waybel_5.html#K7">=&gt;</a> <font color="Maroon">S</font></span>)</span></span>)</span></span>)</span>
<b>by </b><i/>
<br/>.= 
 <a href="waybel25.html#K1">Omega</a> <span class="p1">(<span class="default"><font color="Maroon">M</font> <a href="waybel26.html#NK2" target="_self">-TOP_prod</a> <span class="p2">(<span class="default"><font color="Maroon">M</font> <a href="waybel_5.html#K7">=&gt;</a> <span class="p3">(<span class="default"><a href="waybel29.html#K1" target="_self">Sigma</a> <font color="Maroon">L</font></span>)</span></span>)</span></span>)</span>
<b>by </b><i/>
;<br/>
<b>hence </b><a NAME="E6:39"/>
 <a href="waybel25.html#K1">Omega</a> <span class="p1">(<span class="default"><font color="Maroon">M</font> <a href="waybel26.html#NK2" target="_self">-TOP_prod</a> <span class="p2">(<span class="default"><font color="Maroon">M</font> <a href="waybel_5.html#K7">=&gt;</a> <span class="p3">(<span class="default"><a href="waybel29.html#K1" target="_self">Sigma</a> <font color="Maroon">L</font></span>)</span></span>)</span></span>)</span> <a href="hidden.html#R1">=</a>  <a href="waybel29.html#K1" target="_self">Sigma</a> <span class="p1">(<span class="default"><font color="Maroon">M</font> <a href="waybel26.html#NK1" target="_self">-POS_prod</a> <span class="p2">(<span class="default"><font color="Maroon">M</font> <a href="waybel_5.html#K7">=&gt;</a> <font color="Maroon">L</font></span>)</span></span>)</span>
 <b>by </b><i><a class="ref" href="yellow_1.html#D5">YELLOW_1:def 5</a></i>;<br/>


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