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

<b>assume </b><a NAME="E1:17_1_2"/><i><font color="Green">E52</font></i>: 
( the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">S1</font> <a href="hidden.html#R1">=</a> <font color="Maroon">A</font> &amp; the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">S2</font> <a href="hidden.html#R1">=</a> <font color="Maroon">A</font> )
 ;<br/>

<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="17_1_2_1"><b>now </b></a><div class="add"><b>let </b><font color="Maroon">a</font> be    <a href="subset_1.html#M2">Element</a> of <font color="Maroon">A</font>, <font color="Maroon">b</font> be    <a href="subset_1.html#M2">Element</a> of <font color="Maroon">A</font>;<br/><b>thus </b>the <a href="metric_1.html#U1">distance</a> of <font color="Maroon">S1</font> <a href="binop_1.html#K1">.</a> <font color="Maroon">a</font>,<font color="Maroon">b</font> = 
the <a href="metric_1.html#U1">distance</a> of <font color="Maroon">M</font> <a href="metric_1.html#K1">.</a> <font color="Maroon">a</font>,<font color="Maroon">b</font>
<b>by </b><i>, </i>
<br/>.= 
the <a href="metric_1.html#U1">distance</a> of <font color="Maroon">S2</font> <a href="binop_1.html#K1">.</a> <font color="Maroon">a</font>,<font color="Maroon">b</font>
<b>by </b><i>, </i>
;<br/></div><b>end;</b></div>
<b>hence </b><a NAME="E3:17_1_2"/>
<font color="Maroon">S1</font> <a href="hidden.html#R1">=</a> <font color="Maroon">S2</font>
 <b>by </b><i>, <a class="ref" href="binop_1.html#T2">BINOP_1:2</a></i>;<br/>


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