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<b>let </b><font color="Maroon" title="c1">M</font> be  non <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a>  <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a> ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> for <font color="Olive" title="b1">L</font> being <a href="lattice3.html#V3" title="LATTICE3:attr.3">complete</a> <a href="waybel_3.html#V3" title="WAYBEL_3:attr.3">continuous</a> <a href="waybel_0.html#NM8" title="WAYBEL_0:NM.8">LATTICE</a> holds   <a href="waybel25.html#K1" title="WAYBEL25:func.1">Omega</a> <span class="p1">(<span class="default"><font color="Maroon" title="c1">M</font> <a href="waybel26.html#NK2" title="WAYBEL26:NK.2">-TOP_prod</a> <span class="p2">(<span class="default"><font color="Maroon" title="c1">M</font> <a href="waybel_5.html#K7" title="WAYBEL_5:func.7">=&gt;</a> <span class="p3">(<span class="default"><a href="waybel29.html#K1" title="WAYBEL29:func.1">Sigma</a> <font color="Olive" title="b1">L</font></span>)</span></span>)</span></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="waybel29.html#K1" title="WAYBEL29:func.1">Sigma</a> <span class="p1">(<span class="default"><font color="Maroon" title="c1">M</font> <a href="waybel26.html#NK1" title="WAYBEL26:NK.1">-POS_prod</a> <span class="p2">(<span class="default"><font color="Maroon" title="c1">M</font> <a href="waybel_5.html#K7" title="WAYBEL_5:func.7">=&gt;</a> <font color="Olive" title="b1">L</font></span>)</span></span>)</span></span><br/><b>let </b><font color="Maroon" title="c2">L</font> be  <a href="lattice3.html#V3" title="LATTICE3:attr.3">complete</a> <a href="waybel_3.html#V3" title="WAYBEL_3:attr.3">continuous</a> <a href="waybel_0.html#NM8" title="WAYBEL_0:NM.8">LATTICE</a>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide">  <a href="waybel25.html#K1" title="WAYBEL25:func.1">Omega</a> <span class="p1">(<span class="default"><font color="Maroon" title="c1">M</font> <a href="waybel26.html#NK2" title="WAYBEL26:NK.2">-TOP_prod</a> <span class="p2">(<span class="default"><font color="Maroon" title="c1">M</font> <a href="waybel_5.html#K7" title="WAYBEL_5:func.7">=&gt;</a> <span class="p3">(<span class="default"><a href="waybel29.html#K1" title="WAYBEL29:func.1">Sigma</a> <font color="Maroon" title="c2">L</font></span>)</span></span>)</span></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="waybel29.html#K1" title="WAYBEL29:func.1">Sigma</a> <span class="p1">(<span class="default"><font color="Maroon" title="c1">M</font> <a href="waybel26.html#NK1" title="WAYBEL26:NK.1">-POS_prod</a> <span class="p2">(<span class="default"><font color="Maroon" title="c1">M</font> <a href="waybel_5.html#K7" title="WAYBEL_5:func.7">=&gt;</a> <font color="Maroon" title="c2">L</font></span>)</span></span>)</span></span><br/>



<a NAME="E1:39"/><i><font color="Green" title="E19">A1</font></i>: 
 <a href="orders_2.html#G1" title="ORDERS_2:aggr.1">RelStr</a>(# the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <span class="p1">(<span class="default"><a href="waybel29.html#K1" title="WAYBEL29:func.1">Sigma</a> <font color="Maroon" title="c2">L</font></span>)</span>,the <a href="orders_2.html#U1" title="ORDERS_2:sel.1">InternalRel</a> of <span class="p1">(<span class="default"><a href="waybel29.html#K1" title="WAYBEL29:func.1">Sigma</a> <font color="Maroon" title="c2">L</font></span>)</span> #) <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="orders_2.html#G1" title="ORDERS_2:aggr.1">RelStr</a>(# the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c2">L</font>,the <a href="orders_2.html#U1" title="ORDERS_2:sel.1">InternalRel</a> of <font color="Maroon" title="c2">L</font> #)
 
<b>by </b><i><a class="ref" href="yellow_9.html#D4" title="YELLOW_9:def.4">YELLOW_9:def 4</a></i>;<br/>
<b>reconsider </b><font color="Maroon" title="c3">S</font> =  <a href="waybel29.html#K1" title="WAYBEL29:func.1">Sigma</a> <font color="Maroon" title="c2">L</font> as  <a href="waybel18.html#V2" title="WAYBEL18:attr.2">injective</a> <a href="t_0topsp.html#NM1" title="T_0TOPSP:NM.1">T_0-TopSpace</a> ;<br/>
<a NAME="E3:39"/>
 <a href="waybel25.html#K1" title="WAYBEL25:func.1">Omega</a> <span class="p1">(<span class="default"><a href="waybel29.html#K1" title="WAYBEL29:func.1">Sigma</a> <font color="Maroon" title="c2">L</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="waybel29.html#K1" title="WAYBEL29:func.1">Sigma</a> <font color="Maroon" title="c2">L</font>
 
<b>by </b><i><a class="ref" href="waybel25.html#T15" title="WAYBEL25:th.15">WAYBEL25:15</a></i>;<br/>
<b>then </b> <a href="orders_2.html#G1" title="ORDERS_2:aggr.1">RelStr</a>(# the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <span class="p1">(<span class="default"><a href="waybel25.html#K1" title="WAYBEL25:func.1">Omega</a> <span class="p2">(<span class="default"><font color="Maroon" title="c1">M</font> <a href="waybel26.html#NK2" title="WAYBEL26:NK.2">-TOP_prod</a> <span class="p3">(<span class="default"><font color="Maroon" title="c1">M</font> <a href="waybel_5.html#K7" title="WAYBEL_5:func.7">=&gt;</a> <span class="p4">(<span class="default"><a href="waybel29.html#K1" title="WAYBEL29:func.1">Sigma</a> <font color="Maroon" title="c2">L</font></span>)</span></span>)</span></span>)</span></span>)</span>,the <a href="orders_2.html#U1" title="ORDERS_2:sel.1">InternalRel</a> of <span class="p1">(<span class="default"><a href="waybel25.html#K1" title="WAYBEL25:func.1">Omega</a> <span class="p2">(<span class="default"><font color="Maroon" title="c1">M</font> <a href="waybel26.html#NK2" title="WAYBEL26:NK.2">-TOP_prod</a> <span class="p3">(<span class="default"><font color="Maroon" title="c1">M</font> <a href="waybel_5.html#K7" title="WAYBEL_5:func.7">=&gt;</a> <span class="p4">(<span class="default"><a href="waybel29.html#K1" title="WAYBEL29:func.1">Sigma</a> <font color="Maroon" title="c2">L</font></span>)</span></span>)</span></span>)</span></span>)</span> #) = 
<font color="Maroon" title="c1">M</font> <a href="waybel26.html#NK1" title="WAYBEL26:NK.1">-POS_prod</a> <span class="p1">(<span class="default"><font color="Maroon" title="c1">M</font> <a href="waybel_5.html#K7" title="WAYBEL_5:func.7">=&gt;</a> <span class="p2">(<span class="default"><a href="waybel29.html#K1" title="WAYBEL29:func.1">Sigma</a> <font color="Maroon" title="c2">L</font></span>)</span></span>)</span>
<b>by </b><i><a class="ref" href="waybel25.html#T14" title="WAYBEL25:th.14">WAYBEL25:14</a></i>
<br/>.= 
<span class="p1">(<span class="default"><a href="waybel29.html#K1" title="WAYBEL29:func.1">Sigma</a> <font color="Maroon" title="c2">L</font></span>)</span> <a href="yellow_1.html#K6" title="YELLOW_1:func.6">|^</a> <font color="Maroon" title="c1">M</font>
<b>by </b><i><a class="ref" href="yellow_1.html#D5" title="YELLOW_1:def.5">YELLOW_1:def 5</a></i>
<br/>.= 
<font color="Maroon" title="c2">L</font> <a href="yellow_1.html#K6" title="YELLOW_1:func.6">|^</a> <font color="Maroon" title="c1">M</font>
<b>by </b><i><a class="txt" href="waybel29.html#E1:39"><i><font color="Green" title="E19">A1</font></i></a>, <a class="ref" href="waybel27.html#T15" title="WAYBEL27:th.15">WAYBEL27:15</a></i>
;<br/>
<b>then </b> <a href="waybel29.html#K1" title="WAYBEL29:func.1">Sigma</a> <span class="p1">(<span class="default"><font color="Maroon" title="c2">L</font> <a href="yellow_1.html#K6" title="YELLOW_1:func.6">|^</a> <font color="Maroon" title="c1">M</font></span>)</span> = 
 <a href="waybel29.html#K1" title="WAYBEL29:func.1">Sigma</a> <span class="p1">(<span class="default"><a href="waybel25.html#K1" title="WAYBEL25:func.1">Omega</a> <span class="p2">(<span class="default"><font color="Maroon" title="c1">M</font> <a href="waybel26.html#NK2" title="WAYBEL26:NK.2">-TOP_prod</a> <span class="p3">(<span class="default"><font color="Maroon" title="c1">M</font> <a href="waybel_5.html#K7" title="WAYBEL_5:func.7">=&gt;</a> <font color="Maroon" title="c3">S</font></span>)</span></span>)</span></span>)</span>
<b>by </b><i><a class="ref" href="waybel29.html#T20" target="_self" title="WAYBEL29:th.20">Th20</a></i>
<br/>.= 
 <a href="waybel25.html#K1" title="WAYBEL25:func.1">Omega</a> <span class="p1">(<span class="default"><font color="Maroon" title="c1">M</font> <a href="waybel26.html#NK2" title="WAYBEL26:NK.2">-TOP_prod</a> <span class="p2">(<span class="default"><font color="Maroon" title="c1">M</font> <a href="waybel_5.html#K7" title="WAYBEL_5:func.7">=&gt;</a> <span class="p3">(<span class="default"><a href="waybel29.html#K1" title="WAYBEL29:func.1">Sigma</a> <font color="Maroon" title="c2">L</font></span>)</span></span>)</span></span>)</span>
<b>by </b><i><a class="ref" href="waybel29.html#T19" target="_self" title="WAYBEL29:th.19">Th19</a></i>
;<br/>
<b>hence </b><a NAME="E6:39"/>
 <a href="waybel25.html#K1" title="WAYBEL25:func.1">Omega</a> <span class="p1">(<span class="default"><font color="Maroon" title="c1">M</font> <a href="waybel26.html#NK2" title="WAYBEL26:NK.2">-TOP_prod</a> <span class="p2">(<span class="default"><font color="Maroon" title="c1">M</font> <a href="waybel_5.html#K7" title="WAYBEL_5:func.7">=&gt;</a> <span class="p3">(<span class="default"><a href="waybel29.html#K1" title="WAYBEL29:func.1">Sigma</a> <font color="Maroon" title="c2">L</font></span>)</span></span>)</span></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="waybel29.html#K1" title="WAYBEL29:func.1">Sigma</a> <span class="p1">(<span class="default"><font color="Maroon" title="c1">M</font> <a href="waybel26.html#NK1" title="WAYBEL26:NK.1">-POS_prod</a> <span class="p2">(<span class="default"><font color="Maroon" title="c1">M</font> <a href="waybel_5.html#K7" title="WAYBEL_5:func.7">=&gt;</a> <font color="Maroon" title="c2">L</font></span>)</span></span>)</span>
 <b>by </b><i><a class="ref" href="yellow_1.html#D5" title="YELLOW_1:def.5">YELLOW_1:def 5</a></i>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> verum</span><br/>


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