<?xml version="1.0"?>
<div class="add">

<span class="kw">let </span><font color="Maroon" title="c1">X</font> be   <a href="bhsp_1.html#NM1" title="BHSP_1:NM.1">RealUnitarySpace</a>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide">  for <font color="Olive" title="b1">x</font> being   <a href="pre_topc.html#NM2" title="PRE_TOPC:NM.2">Point</a> of <font color="Maroon" title="c1">X</font><br/>  for <font color="Olive" title="b2">r</font> being   <a href="real_1.html#NM1" title="REAL_1:NM.1">Real</a> holds   <a href="bhsp_2.html#K4" title="BHSP_2:func.4">Ball</a> (<font color="Olive" title="b1">x</font>,<font color="Olive" title="b2">r</font>) <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a>  <a href="bhsp_2.html#K5" title="BHSP_2:func.5">cl_Ball</a> (<font color="Olive" title="b1">x</font>,<font color="Olive" title="b2">r</font>)</span><br/><span class="kw">let </span><font color="Maroon" title="c2">x</font> be   <a href="pre_topc.html#NM2" title="PRE_TOPC:NM.2">Point</a> of <font color="Maroon" title="c1">X</font>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide">  for <font color="Olive" title="b1">r</font> being   <a href="real_1.html#NM1" title="REAL_1:NM.1">Real</a> holds   <a href="bhsp_2.html#K4" title="BHSP_2:func.4">Ball</a> (<font color="Maroon" title="c2">x</font>,<font color="Olive" title="b1">r</font>) <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a>  <a href="bhsp_2.html#K5" title="BHSP_2:func.5">cl_Ball</a> (<font color="Maroon" title="c2">x</font>,<font color="Olive" title="b1">r</font>)</span><br/><span class="kw">let </span><font color="Maroon" title="c3">r</font> be   <a href="real_1.html#NM1" title="REAL_1:NM.1">Real</a>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide">  <a href="bhsp_2.html#K4" title="BHSP_2:func.4">Ball</a> (<font color="Maroon" title="c2">x</font>,<font color="Maroon" title="c3">r</font>) <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a>  <a href="bhsp_2.html#K5" title="BHSP_2:func.5">cl_Ball</a> (<font color="Maroon" title="c2">x</font>,<font color="Maroon" title="c3">r</font>)</span><br/>





<a NAME="E1:60"/>
 for <font color="Olive" title="b1">y</font> being   <a href="pre_topc.html#NM2" title="PRE_TOPC:NM.2">Point</a> of <font color="Maroon" title="c1">X</font>  st <font color="Olive" title="b1">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="c2">x</font>,<font color="Maroon" title="c3">r</font>) holds <br/><font color="Olive" title="b1">y</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="bhsp_2.html#K5" title="BHSP_2:func.5">cl_Ball</a> (<font color="Maroon" title="c2">x</font>,<font color="Maroon" title="c3">r</font>)
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="bhsp_2.html#T50" target="_self" title="BHSP_2:th.50">Th50</a></span>;<br/>
<span class="kw">hence </span><a NAME="E2:60"/>
 <a href="bhsp_2.html#K4" title="BHSP_2:func.4">Ball</a> (<font color="Maroon" title="c2">x</font>,<font color="Maroon" title="c3">r</font>) <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a>  <a href="bhsp_2.html#K5" title="BHSP_2:func.5">cl_Ball</a> (<font color="Maroon" title="c2">x</font>,<font color="Maroon" title="c3">r</font>)
 <span class="kw">by</span> <span class="lab"><a class="ref" href="subset_1.html#T2" title="SUBSET_1:th.2">SUBSET_1:2</a></span>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> verum</span><br/>


</div>
