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<b>let </b><font color="Maroon" title="c1">X</font> be   <a href="bhsp_1.html#NM1" title="BHSP_1:NM.1">RealUnitarySpace</a>;<br/><b>let </b><font color="Maroon" title="c2">y</font>, <font color="Maroon" title="c3">x</font>, <font color="Maroon" title="c4">z</font> be   <a href="pre_topc.html#NM2" title="PRE_TOPC:NM.2">Point</a> of <font color="Maroon" title="c1">X</font>;<br/><b>let </b><font color="Maroon" title="c5">r</font> be   <a href="real_1.html#NM1" title="REAL_1:NM.1">Real</a>;<br/>









<b>assume </b><a NAME="E1:50"/>
<font color="Maroon" title="c2">y</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="bhsp_2.html#K4" title="BHSP_2:func.4">Ball</a> <font color="Maroon" title="c3">x</font>,<font color="Maroon" title="c5">r</font>
 ;<br/>

<a NAME="E2:50"/><b>then </b><i><font color="Green" title="E30">A1</font></i>: 
 <a href="bhsp_1.html#K5" title="BHSP_1:func.5">dist</a> <font color="Maroon" title="c3">x</font>,<font color="Maroon" title="c2">y</font> <a href="xxreal_0.html#NR3" title="XXREAL_0:NR.3">&lt;</a> <font color="Maroon" title="c5">r</font>
 
<b>by </b><i><a class="ref" href="bhsp_2.html#T41" target="_self" title="BHSP_2:th.41">Th41</a></i>;<br/>
<a NAME="E3:50"/>
 <a href="bhsp_1.html#K5" title="BHSP_1:func.5">dist</a> <span class="p1">(<span class="default"><font color="Maroon" title="c3">x</font> <a href="rlvect_1.html#K5" title="RLVECT_1:func.5">-</a> <font color="Maroon" title="c4">z</font></span>)</span>,<span class="p1">(<span class="default"><font color="Maroon" title="c2">y</font> <a href="rlvect_1.html#K5" title="RLVECT_1:func.5">-</a> <font color="Maroon" title="c4">z</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="bhsp_1.html#K5" title="BHSP_1:func.5">dist</a> <font color="Maroon" title="c3">x</font>,<font color="Maroon" title="c2">y</font>
 
<b>by </b><i><a class="ref" href="bhsp_1.html#T49" title="BHSP_1:th.49">BHSP_1:49</a></i>;<br/>
<b>hence </b><a NAME="E4:50"/>
<font color="Maroon" title="c2">y</font> <a href="rlvect_1.html#K5" title="RLVECT_1:func.5">-</a> <font color="Maroon" title="c4">z</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="bhsp_2.html#K4" title="BHSP_2:func.4">Ball</a> <span class="p1">(<span class="default"><font color="Maroon" title="c3">x</font> <a href="rlvect_1.html#K5" title="RLVECT_1:func.5">-</a> <font color="Maroon" title="c4">z</font></span>)</span>,<font color="Maroon" title="c5">r</font>
 <b>by </b><i><a class="txt" href="bhsp_2.html#E2:50"><i><font color="Green" title="E30">A1</font></i></a>, <a class="ref" href="bhsp_2.html#T41" target="_self" title="BHSP_2:th.41">Th41</a></i>;<br/>


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