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<b>let </b><font color="Maroon">S1</font> be  non <a href="struct_0.html#V3">empty</a> <a href="metric_1.html#V1">strict</a>  <a href="topmetr.html#M1" target="_self">SubSpace</a> of  <a href="metric_1.html#K8">RealSpace</a> , <font color="Maroon">S2</font> be  non <a href="struct_0.html#V3">empty</a> <a href="metric_1.html#V1">strict</a>  <a href="topmetr.html#M1" target="_self">SubSpace</a> of  <a href="metric_1.html#K8">RealSpace</a> ;<br/>

<b>assume </b><b>that </b><br/><a NAME="E1:19_1_2"/><i><font color="Green">E32</font></i>: 
for <font color="Olive">P</font> being non <a href="xboole_0.html#V1">empty</a> <a href="struct_0.html#NM2">Subset</a> of <a href="metric_1.html#K8">RealSpace</a>   st <font color="Olive">P</font> <a href="hidden.html#R1">=</a> <span class="p1"><a href="rcomp_1.html#K1">[.</a><span class="default"><font color="Maroon">a</font>,<font color="Maroon">b</font></span><a href="rcomp_1.html#K1">.]</a></span> holds <br/><font color="Maroon">S1</font> <a href="hidden.html#R1">=</a> <a href="metric_1.html#K8">RealSpace</a>  <a href="topmetr.html#K1" target="_self">|</a> <font color="Olive">P</font>
 <b>and </b><br/><a NAME="E2:19_1_2"/><i><font color="Green">E35</font></i>: 
for <font color="Olive">P</font> being non <a href="xboole_0.html#V1">empty</a> <a href="struct_0.html#NM2">Subset</a> of <a href="metric_1.html#K8">RealSpace</a>   st <font color="Olive">P</font> <a href="hidden.html#R1">=</a> <span class="p1"><a href="rcomp_1.html#K1">[.</a><span class="default"><font color="Maroon">a</font>,<font color="Maroon">b</font></span><a href="rcomp_1.html#K1">.]</a></span> holds <br/><font color="Maroon">S2</font> <a href="hidden.html#R1">=</a> <a href="metric_1.html#K8">RealSpace</a>  <a href="topmetr.html#K1" target="_self">|</a> <font color="Olive">P</font>
 ;<br/>

<b>reconsider </b><font color="Maroon">P</font> = <span class="p1"><a href="rcomp_1.html#K1">[.</a><span class="default"><font color="Maroon">a</font>,<font color="Maroon">b</font></span><a href="rcomp_1.html#K1">.]</a></span> as   <a href="struct_0.html#NM2">Subset</a> of <a href="metric_1.html#K8">RealSpace</a>  <b>by </b><i><a class="ref" href="metric_1.html#D14">METRIC_1:def 14</a></i>;<br/>
<b>reconsider </b><font color="Maroon">P</font> = <font color="Maroon">P</font> as  non <a href="xboole_0.html#V1">empty</a> <a href="struct_0.html#NM2">Subset</a> of <a href="metric_1.html#K8">RealSpace</a>  <b>by </b><i>, <a class="ref" href="rcomp_1.html#T15">RCOMP_1:15</a></i>;<br/>
<b>thus </b><font color="Maroon">S1</font> = 
<a href="metric_1.html#K8">RealSpace</a>  <a href="topmetr.html#K1" target="_self">|</a> <font color="Maroon">P</font>
<b>by </b><i/>
<br/>.= 
<font color="Maroon">S2</font>
<b>by </b><i/>
;<br/>


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