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<b>deffunc </b><font color="Maroon">H<sub>1</sub></font>(   <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a> ) <b>-&gt; </b>   <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of <a href="zfmisc_1.html#K1" title="ZFMISC_1:func.1">K18</a>(the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c1">T</font>) = <span class="p1">(<span class="default"><a href="relat_1.html#K11" title="RELAT_1:func.11">Im</a> the <a href="orders_2.html#U1" title="ORDERS_2:sel.1">InternalRel</a> of <font color="Maroon" title="c1">T</font>,$1</span>)</span> <a href="subset_1.html#K9" title="SUBSET_1:func.9">/\</a> <font color="Maroon" title="c2">P</font>;<br/>
<a NAME="E1:15_1_1"/><i><font color="Green" title="E11">A1</font></i>: 
for <font color="Olive" title="b1">x</font> being  <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Maroon" title="c1">T</font>  st <font color="Olive" title="b1">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c2">P</font> holds <br/><font color="Maroon">H<sub>1</sub></font>(<font color="Olive" title="b1">x</font>) <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <font color="Maroon" title="c2">P</font>
 
<b>by </b><i><a class="ref" href="xboole_1.html#T17" title="XBOOLE_1:th.17">XBOOLE_1:17</a></i>;<br/>
<b>consider </b><font color="Maroon" title="c3">G</font> being   <a href="relset_1.html#NM3" title="RELSET_1:NM.3">Relation</a> of <font color="Maroon" title="c2">P</font><b> such that </b><br/><a NAME="E3:15_1_1"/><i><font color="Green" title="E12">A2</font></i>: 
for <font color="Olive" title="b1">y</font> being  <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Maroon" title="c1">T</font>  st <font color="Olive" title="b1">y</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c2">P</font> holds <br/> <a href="relat_1.html#K11" title="RELAT_1:func.11">Im</a> <font color="Maroon" title="c3">G</font>,<font color="Olive" title="b1">y</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon">H<sub>1</sub></font>(<font color="Olive" title="b1">y</font>)
 <b>from </b><i><a class="ref" href="relset_1.html#S3" title="RELSET_1:sch.3">RELSET_1:sch 3</a>(<a class="txt" href="fintopo6.html#E1:15_1_1"><i><font color="Green" title="E11">A1</font></i></a>);<br/></i>
<b>set </b><font color="Maroon" title="c4">FS</font> =  <a href="orders_2.html#G1" title="ORDERS_2:aggr.1">RelStr</a>(# <font color="Maroon" title="c2">P</font>,<font color="Maroon" title="c3">G</font> #);<br/>
<a NAME="E4:15_1_1"/><i><font color="Green" title="E13">A3</font></i>: 
for <font color="Olive" title="b1">x</font> being  <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <a href="orders_2.html#G1" title="ORDERS_2:aggr.1">RelStr</a>(# <font color="Maroon" title="c2">P</font>,<font color="Maroon" title="c3">G</font> #)  st <font color="Olive" title="b1">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <a href="orders_2.html#G1" title="ORDERS_2:aggr.1">RelStr</a>(# <font color="Maroon" title="c2">P</font>,<font color="Maroon" title="c3">G</font> #) holds <br/> <a href="fin_topo.html#K1" title="FIN_TOPO:func.1">U_FT</a> <font color="Olive" title="b1">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="relat_1.html#K11" title="RELAT_1:func.11">Im</a> the <a href="orders_2.html#U1" title="ORDERS_2:sel.1">InternalRel</a> of <font color="Maroon" title="c1">T</font>,<font color="Olive" title="b1">x</font></span>)</span> <a href="xboole_0.html#K3" title="XBOOLE_0:func.3">/\</a> the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <a href="orders_2.html#G1" title="ORDERS_2:aggr.1">RelStr</a>(# <font color="Maroon" title="c2">P</font>,<font color="Maroon" title="c3">G</font> #)
 
<b>by </b><i><a class="txt" href="fintopo6.html#E3:15_1_1"><i><font color="Green" title="E12">A2</font></i></a></i>;<br/>
<a NAME="E5:15_1_1"/><i><font color="Green" title="E14">A4</font></i>: 
 <a href="struct_0.html#K2" title="STRUCT_0:func.2">[#]</a> <a href="orders_2.html#G1" title="ORDERS_2:aggr.1">RelStr</a>(# <font color="Maroon" title="c2">P</font>,<font color="Maroon" title="c3">G</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 <a href="orders_2.html#G1" title="ORDERS_2:aggr.1">RelStr</a>(# <font color="Maroon" title="c2">P</font>,<font color="Maroon" title="c3">G</font> #)
 
;<br/>
<a NAME="E6:15_1_1"/>
 <a href="orders_2.html#G1" title="ORDERS_2:aggr.1">RelStr</a>(# <font color="Maroon" title="c2">P</font>,<font color="Maroon" title="c3">G</font> #) is  non <a href="struct_0.html#V2" title="STRUCT_0:attr.2">empty</a> <a href="orders_2.html#V1" title="ORDERS_2:attr.1">strict</a>  <a href="fintopo6.html#M1" title="FINTOPO6:mode.1">SubSpace</a> of <font color="Maroon" title="c1">T</font>
 
<b>by </b><i><a class="ref" href="fintopo6.html#D2" target="_self" title="FINTOPO6:def.2">Def2</a>, <a class="txt" href="fintopo6.html#E4:15_1_1"><i><font color="Green" title="E13">A3</font></i></a>, <a class="ref" href="struct_0.html#D1" title="STRUCT_0:def.1">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#V2" title="STRUCT_0:attr.2">empty</a> <a href="orders_2.html#V1" title="ORDERS_2:attr.1">strict</a>  <a href="fintopo6.html#M1" title="FINTOPO6:mode.1">SubSpace</a> of <font color="Maroon" title="c1">T</font> st  <a href="struct_0.html#K2" title="STRUCT_0:func.2">[#]</a> <font color="Olive">b<sub>1</sub></font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c2">P</font>
 <b>by </b><i><a class="txt" href="fintopo6.html#E5:15_1_1"><i><font color="Green" title="E14">A4</font></i></a></i>;<br/>


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