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<b>let </b><font color="Maroon" title="c1">T</font> be   <a href="t_0topsp.html#NM1" title="T_0TOPSP:NM.1">T_0-TopSpace</a>;<br/>

<b>assume </b><a NAME="E1:58_1_1"/>
<font color="Maroon" title="c1">T</font> is <a href="struct_0.html#V7" title="STRUCT_0:attr.7">trivial</a>
 ;<br/>

<b>then consider </b><font color="Maroon" title="c2">d</font> being   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Maroon" title="c1">T</font><b> such that </b><br/><a NAME="E3:58_1_1"/><i><font color="Green" title="E33">A1</font></i>: 
the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c1">T</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1"><a href="domain_1.html#K6" title="DOMAIN_1:func.6">{</a><span class="default"><font color="Maroon" title="c2">d</font></span><a href="domain_1.html#K6" title="DOMAIN_1:func.6">}</a></span>
 <b>by </b><i><a class="ref" href="tex_1.html#D1" title="TEX_1:def.1">TEX_1:def 1</a></i>;<br/>
<b>let </b><font color="Maroon" title="c3">D</font> be  non <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a> <a href="waybel_0.html#V1" title="WAYBEL_0:attr.1">directed</a> <a href="struct_0.html#NM2" title="STRUCT_0:NM.2">Subset</a> of <span class="p1">(<span class="default"><a href="waybel25.html#K1" title="WAYBEL25:func.1">Omega</a> <font color="Maroon" title="c1">T</font></span>)</span>; <i><font color="Red">:: according to </font></i><a class="ref" href="waybel25.html#D4" target="_self" title="WAYBEL25:def.4">WAYBEL25:def 4</a><br/>

<a NAME="E4:58_1_1"/><i><font color="Green" title="E34">A2</font></i>: 
the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c1">T</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</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> <font color="Maroon" title="c1">T</font></span>)</span>
 
<b>by </b><i><a class="txt" href="waybel25.html#E15"><i><font color="Green" title="E10">Lm1</font></i></a></i>;<br/>
<b>reconsider </b><font color="Maroon" title="c4">d</font> = <font color="Maroon" title="c2">d</font> as   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <span class="p1">(<span class="default"><a href="waybel25.html#K1" title="WAYBEL25:func.1">Omega</a> <font color="Maroon" title="c1">T</font></span>)</span> <b>by </b><i><a class="txt" href="waybel25.html#E15"><i><font color="Green" title="E10">Lm1</font></i></a></i>;<br/>
<a NAME="E6:58_1_1"/>
<font color="Maroon" title="c3">D</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1"><a href="domain_1.html#K6" title="DOMAIN_1:func.6">{</a><span class="default"><font color="Maroon" title="c4">d</font></span><a href="domain_1.html#K6" title="DOMAIN_1:func.6">}</a></span>
 
<b>by </b><i><a class="txt" href="waybel25.html#E3:58_1_1"><i><font color="Green" title="E33">A1</font></i></a>, <a class="txt" href="waybel25.html#E4:58_1_1"><i><font color="Green" title="E34">A2</font></i></a>, <a class="txt" href="waybel25.html#E38"><i><font color="Green" title="E32">Lm7</font></i></a></i>;<br/>
<b>hence </b><a NAME="E7:58_1_1"/>
 <a href="yellow_0.html#R1" title="YELLOW_0:pred.1">ex_sup_of</a> <font color="Maroon" title="c3">D</font>, <a href="waybel25.html#K1" title="WAYBEL25:func.1">Omega</a> <font color="Maroon" title="c1">T</font>
 <b>by </b><i><a class="ref" href="yellow_0.html#T38" title="YELLOW_0:th.38">YELLOW_0:38</a></i>;<br/>

<b>let </b><font color="Maroon" title="c5">V</font> be  <a href="pre_topc.html#V3" title="PRE_TOPC:attr.3">open</a> <a href="struct_0.html#NM2" title="STRUCT_0:NM.2">Subset</a> of <font color="Maroon" title="c1">T</font>;<br/>

<b>assume </b><a NAME="E8:58_1_1"/>
 <a href="yellow_0.html#NK3" title="YELLOW_0:NK.3">sup</a> <font color="Maroon" title="c3">D</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c5">V</font>
 ;<br/>

<a NAME="E9:58_1_1"/><b>then </b><i><font color="Green" title="E35">A3</font></i>: 
<font color="Maroon" title="c5">V</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1"><a href="domain_1.html#K6" title="DOMAIN_1:func.6">{</a><span class="default"><font color="Maroon" title="c4">d</font></span><a href="domain_1.html#K6" title="DOMAIN_1:func.6">}</a></span>
 
<b>by </b><i><a class="txt" href="waybel25.html#E3:58_1_1"><i><font color="Green" title="E33">A1</font></i></a>, <a class="txt" href="waybel25.html#E38"><i><font color="Green" title="E32">Lm7</font></i></a></i>;<br/>
<a NAME="E10:58_1_1"/>
<span class="p1"><a href="domain_1.html#K6" title="DOMAIN_1:func.6">{</a><span class="default"><font color="Maroon" title="c4">d</font></span><a href="domain_1.html#K6" title="DOMAIN_1:func.6">}</a></span> <a href="subset_1.html#R2" title="SUBSET_1:pred.2">meets</a> <span class="p1"><a href="domain_1.html#K6" title="DOMAIN_1:func.6">{</a><span class="default"><font color="Maroon" title="c4">d</font></span><a href="domain_1.html#K6" title="DOMAIN_1:func.6">}</a></span>
 
;<br/>
<b>hence </b><a NAME="E11:58_1_1"/>
<font color="Maroon" title="c3">D</font> <a href="xboole_0.html#NR5" title="XBOOLE_0:NR.5">meets</a> <font color="Maroon" title="c5">V</font>
 <b>by </b><i><a class="txt" href="waybel25.html#E3:58_1_1"><i><font color="Green" title="E33">A1</font></i></a>, <a class="txt" href="waybel25.html#E4:58_1_1"><i><font color="Green" title="E34">A2</font></i></a>, <a class="txt" href="waybel25.html#E9:58_1_1"><i><font color="Green" title="E35">A3</font></i></a>, <a class="txt" href="waybel25.html#E38"><i><font color="Green" title="E32">Lm7</font></i></a></i>;<br/>


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