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<b>let </b><font color="Maroon">X</font> be   <a href="bhsp_1.html#NM1">RealUnitarySpace</a>;<br/><b>let </b><font color="Maroon">y</font> be   <a href="pre_topc.html#NM2">Point</a> of <font color="Maroon">X</font>;<br/><b>let </b><font color="Maroon">x</font> be   <a href="pre_topc.html#NM2">Point</a> of <font color="Maroon">X</font>;<br/><b>let </b><font color="Maroon">z</font> be   <a href="pre_topc.html#NM2">Point</a> of <font color="Maroon">X</font>;<br/><b>let </b><font color="Maroon">r</font> be   <a href="real_1.html#NM1">Real</a>;<br/>









<b>assume </b><a NAME="E1:50"/>
<font color="Maroon">y</font> <a href="hidden.html#R2">in</a>  <a href="bhsp_2.html#K4" target="_self">Ball</a> <font color="Maroon">x</font>,<font color="Maroon">r</font>
 ;<br/>

<a NAME="E2:50"/><b>then </b><i><font color="Green">E40</font></i>: 
 <a href="bhsp_1.html#K5">dist</a> <font color="Maroon">x</font>,<font color="Maroon">y</font> <a href="xxreal_0.html#NR3" target="_self">&lt;</a> <font color="Maroon">r</font>
 
<b>by </b><i/>;<br/>
<a NAME="E3:50"/>
 <a href="bhsp_1.html#K5">dist</a> <span class="p1">(<span class="default"><font color="Maroon">x</font> <a href="rlvect_1.html#K6">-</a> <font color="Maroon">z</font></span>)</span>,<span class="p1">(<span class="default"><font color="Maroon">y</font> <a href="rlvect_1.html#K6">-</a> <font color="Maroon">z</font></span>)</span> <a href="hidden.html#R1">=</a>  <a href="bhsp_1.html#K5">dist</a> <font color="Maroon">x</font>,<font color="Maroon">y</font>
 
<b>by </b><i><a class="ref" href="bhsp_1.html#T49">BHSP_1:49</a></i>;<br/>
<b>hence </b><a NAME="E4:50"/>
<font color="Maroon">y</font> <a href="rlvect_1.html#K6">-</a> <font color="Maroon">z</font> <a href="hidden.html#R2">in</a>  <a href="bhsp_2.html#K4" target="_self">Ball</a> <span class="p1">(<span class="default"><font color="Maroon">x</font> <a href="rlvect_1.html#K6">-</a> <font color="Maroon">z</font></span>)</span>,<font color="Maroon">r</font>
 <b>by </b><i>, </i>;<br/>


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