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<b>deffunc </b><font color="Maroon">H<sub>1</sub></font>(   <a href="hidden.html#M1">set</a> ) <b>-&gt; </b>   <a href="subset_1.html#M1">Element</a> of <a href="zfmisc_1.html#K1">K18</a>(the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">T</font>) = <span class="p1">(<span class="default">the <a href="orders_2.html#U1">InternalRel</a> of <font color="Maroon">T</font> <a href="relset_1.html#K10">.:</a> <span class="p2"><a href="tarski.html#K1">{</a><span class="default"><font color="Maroon">a<sub>1</sub></font></span><a href="tarski.html#K1">}</a></span></span>)</span> <a href="subset_1.html#K9">/\</a> <font color="Maroon">P</font>;<br/>
<a NAME="E1:15_1_1"/><i><font color="Green">E27</font></i>: 
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="Maroon">P</font> holds <br/><font color="Maroon">H<sub>1</sub></font>(<font color="Olive">x</font>) <a href="tarski.html#R1">c=</a> <font color="Maroon">P</font>
 
<b>by </b><i><a class="ref" href="xboole_1.html#T17">XBOOLE_1:17</a></i>;<br/>
<b>consider </b><font color="Maroon">G</font> being   <a href="relset_1.html#NM3">Relation</a> of <font color="Maroon">P</font><b> such that </b><br/><a NAME="E3:15_1_1"/><i><font color="Green">E31</font></i>: 
for <font color="Olive">y</font> being  <a href="struct_0.html#NM1">Element</a> of <font color="Maroon">T</font>  st <font color="Olive">y</font> <a href="hidden.html#R2">in</a> <font color="Maroon">P</font> holds <br/><font color="Maroon">G</font> <a href="relset_1.html#K10">.:</a> <span class="p1"><a href="domain_1.html#K6">{</a><span class="default"><font color="Olive">y</font></span><a href="domain_1.html#K6">}</a></span> <a href="hidden.html#R1">=</a> <font color="Maroon">H<sub>1</sub></font>(<font color="Olive">y</font>)
 <b>from </b><i><a class="ref" href="relset_1.html#S3">RELSET_1:sch 3</a>();<br/></i>
<b>set </b><font color="Maroon">FS</font> =  <a href="orders_2.html#G1">RelStr</a>(# <font color="Maroon">P</font>,<font color="Maroon">G</font> #);<br/>
<a NAME="E4:15_1_1"/><i><font color="Green">E33</font></i>: 
for <font color="Olive">x</font> being  <a href="struct_0.html#NM1">Element</a> of <a href="orders_2.html#G1">RelStr</a>(# <font color="Maroon">P</font>,<font color="Maroon">G</font> #)  st <font color="Olive">x</font> <a href="hidden.html#R2">in</a> the <a href="struct_0.html#U1">carrier</a> of <a href="orders_2.html#G1">RelStr</a>(# <font color="Maroon">P</font>,<font color="Maroon">G</font> #) holds <br/> <a href="fin_topo.html#K1">U_FT</a> <font color="Olive">x</font> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default">the <a href="orders_2.html#U1">InternalRel</a> of <font color="Maroon">T</font> <a href="relset_1.html#K10">.:</a> <span class="p2"><a href="tarski.html#K1">{</a><span class="default"><font color="Olive">x</font></span><a href="tarski.html#K1">}</a></span></span>)</span> <a href="subset_1.html#K8">/\</a> the <a href="struct_0.html#U1">carrier</a> of <a href="orders_2.html#G1">RelStr</a>(# <font color="Maroon">P</font>,<font color="Maroon">G</font> #)
 
<b>by </b><i/>;<br/>
<a NAME="E5:15_1_1"/><i><font color="Green">E41</font></i>: 
 <a href="pre_topc.html#K2">[#]</a> <a href="orders_2.html#G1">RelStr</a>(# <font color="Maroon">P</font>,<font color="Maroon">G</font> #) <a href="hidden.html#R1">=</a> the <a href="struct_0.html#U1">carrier</a> of <a href="orders_2.html#G1">RelStr</a>(# <font color="Maroon">P</font>,<font color="Maroon">G</font> #)
 
;<br/>
<a NAME="E6:15_1_1"/>
 <a href="orders_2.html#G1">RelStr</a>(# <font color="Maroon">P</font>,<font color="Maroon">G</font> #) is  non <a href="struct_0.html#V3">empty</a> <a href="orders_2.html#V1">strict</a>  <a href="fintopo6.html#M1" target="_self">SubSpace</a> of <font color="Maroon">T</font>
 
<b>by </b><i>, , <a class="ref" href="struct_0.html#D1">STRUCT_0:def 1</a></i>;<br/>
<b>hence </b><a NAME="E7:15_1_1"/>
 ex <font color="Olive">b<sub>1</sub></font> being non <a href="struct_0.html#V3">empty</a> <a href="orders_2.html#V1">strict</a>  <a href="fintopo6.html#M1" target="_self">SubSpace</a> of <font color="Maroon">T</font> st  <a href="pre_topc.html#K2">[#]</a> <font color="Olive">b<sub>1</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">P</font>
 <b>by </b><i/>;<br/>


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