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<b>let </b><font color="Maroon" title="c3">S1</font>, <font color="Maroon" title="c4">S2</font> be  non <a href="struct_0.html#V2" title="STRUCT_0:attr.2">empty</a> <a href="metric_1.html#V1" title="METRIC_1:attr.1">strict</a>  <a href="topmetr.html#M1" title="TOPMETR:mode.1">SubSpace</a> of  <a href="metric_1.html#K8" title="METRIC_1:func.8">RealSpace</a> ;<br/>

<b>assume </b><b>that </b><br/><a NAME="E1:19_1_2"/><i><font color="Green" title="E11">A2</font></i>: 
for <font color="Olive" title="b1">P</font> being non <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a> <a href="struct_0.html#NM2" title="STRUCT_0:NM.2">Subset</a> of <a href="metric_1.html#K8" title="METRIC_1:func.8">RealSpace</a>   st <font color="Olive" title="b1">P</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1"><a href="rcomp_1.html#K1" title="RCOMP_1:func.1">[.</a><span class="default"><font color="Maroon" title="c1">a</font>,<font color="Maroon" title="c2">b</font></span><a href="rcomp_1.html#K1" title="RCOMP_1:func.1">.]</a></span> holds <br/><font color="Maroon" title="c3">S1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <a href="metric_1.html#K8" title="METRIC_1:func.8">RealSpace</a>  <a href="topmetr.html#K1" title="TOPMETR:func.1">|</a> <font color="Olive" title="b1">P</font>
 <b>and </b><br/><a NAME="E2:19_1_2"/><i><font color="Green" title="E12">A3</font></i>: 
for <font color="Olive" title="b1">P</font> being non <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a> <a href="struct_0.html#NM2" title="STRUCT_0:NM.2">Subset</a> of <a href="metric_1.html#K8" title="METRIC_1:func.8">RealSpace</a>   st <font color="Olive" title="b1">P</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1"><a href="rcomp_1.html#K1" title="RCOMP_1:func.1">[.</a><span class="default"><font color="Maroon" title="c1">a</font>,<font color="Maroon" title="c2">b</font></span><a href="rcomp_1.html#K1" title="RCOMP_1:func.1">.]</a></span> holds <br/><font color="Maroon" title="c4">S2</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <a href="metric_1.html#K8" title="METRIC_1:func.8">RealSpace</a>  <a href="topmetr.html#K1" title="TOPMETR:func.1">|</a> <font color="Olive" title="b1">P</font>
 ;<br/>

<b>reconsider </b><font color="Maroon" title="c5">P</font> = <span class="p1"><a href="rcomp_1.html#K1" title="RCOMP_1:func.1">[.</a><span class="default"><font color="Maroon" title="c1">a</font>,<font color="Maroon" title="c2">b</font></span><a href="rcomp_1.html#K1" title="RCOMP_1:func.1">.]</a></span> as   <a href="struct_0.html#NM2" title="STRUCT_0:NM.2">Subset</a> of <a href="metric_1.html#K8" title="METRIC_1:func.8">RealSpace</a>  <b>by </b><i><a class="ref" href="metric_1.html#D14" title="METRIC_1:def.14">METRIC_1:def 14</a></i>;<br/>
<b>reconsider </b><font color="Maroon" title="c6">P</font> = <font color="Maroon" title="c5">P</font> as  non <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a> <a href="struct_0.html#NM2" title="STRUCT_0:NM.2">Subset</a> of <a href="metric_1.html#K8" title="METRIC_1:func.8">RealSpace</a>  <b>by </b><i><a class="txt" href="topmetr.html#E1:19"><i><font color="Green" title="E10">A1</font></i></a>, <a class="ref" href="rcomp_1.html#T15" title="RCOMP_1:th.15">RCOMP_1:15</a></i>;<br/>
<b>thus </b><font color="Maroon" title="c3">S1</font> = 
<a href="metric_1.html#K8" title="METRIC_1:func.8">RealSpace</a>  <a href="topmetr.html#K1" title="TOPMETR:func.1">|</a> <font color="Maroon" title="c6">P</font>
<b>by </b><i><a class="txt" href="topmetr.html#E1:19_1_2"><i><font color="Green" title="E11">A2</font></i></a></i>
<br/>.= 
<font color="Maroon" title="c4">S2</font>
<b>by </b><i><a class="txt" href="topmetr.html#E2:19_1_2"><i><font color="Green" title="E12">A3</font></i></a></i>
;<br/>


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