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<a NAME="E1:17_1_1"/>
for <font color="Olive">D</font> being non <a href="xboole_0.html#V1">empty</a> <a href="waybel_0.html#V1">directed</a> <a href="struct_0.html#NM2">Subset</a> of <font color="Maroon">T</font>  st  <a href="yellow_0.html#NK3" target="_self">sup</a> <font color="Olive">D</font> <a href="hidden.html#R2">in</a>  <a href="pre_topc.html#K1">{}</a> <font color="Maroon">T</font> holds <br/> ex <font color="Olive">y</font> being  <a href="struct_0.html#NM1">Element</a> of <font color="Maroon">T</font> st <br/>( <font color="Olive">y</font> <a href="hidden.html#R2">in</a> <font color="Olive">D</font> &amp; ( for <font color="Olive">x</font> being  <a href="struct_0.html#NM1">Element</a> of <font color="Maroon">T</font>  st <font color="Olive">x</font> <a href="hidden.html#R2">in</a> <font color="Olive">D</font> &amp; <font color="Olive">x</font> <a href="orders_2.html#NR2" target="_self">&gt;=</a> <font color="Olive">y</font> holds <br/><font color="Olive">x</font> <a href="hidden.html#R2">in</a>  <a href="pre_topc.html#K1">{}</a> <font color="Maroon">T</font> ) )
 
;<br/>
<b>hence </b><a NAME="E2:17_1_1"/>
 <a href="pre_topc.html#K1">{}</a> <font color="Maroon">T</font> is <a href="waybel11.html#V3" target="_self">property(S)</a>
 <b>by </b><i/>;<br/>

<b>thus </b><a NAME="E3:17_1_1"/>
for <font color="Olive">D</font> being non <a href="xboole_0.html#V1">empty</a> <a href="waybel_0.html#V1">directed</a> <a href="struct_0.html#NM2">Subset</a> of <font color="Maroon">T</font>  st <font color="Olive">D</font> <a href="tarski.html#R1">c=</a>  <a href="pre_topc.html#K1">{}</a> <font color="Maroon">T</font> holds <br/> <a href="yellow_0.html#NK3" target="_self">sup</a> <font color="Olive">D</font> <a href="hidden.html#R2">in</a>  <a href="pre_topc.html#K1">{}</a> <font color="Maroon">T</font>
 <b>by </b><i><a class="ref" href="xboole_1.html#T3">XBOOLE_1:3</a></i>; <i><font color="Red">:: according to </font></i><a class="ref" href="waybel11.html#D2" target="_self">WAYBEL11:def 2</a><br/>


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