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<span class="kw">let </span><font color="Maroon" title="c1">X</font> be   <a href="csspace.html#NM1" title="CSSPACE:NM.1">ComplexUnitarySpace</a>; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" 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="xreal_0.html#NM1" title="XREAL_0:NM.1">Real</a> holds   <a href="clvect_2.html#K4" title="CLVECT_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="clvect_2.html#K5" title="CLVECT_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" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" 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="xreal_0.html#NM1" title="XREAL_0:NM.1">Real</a> holds   <a href="clvect_2.html#K4" title="CLVECT_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="clvect_2.html#K5" title="CLVECT_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="xreal_0.html#NM1" title="XREAL_0:NM.1">Real</a>; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide">  <a href="clvect_2.html#K4" title="CLVECT_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="clvect_2.html#K5" title="CLVECT_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="tarski.html#R2" title="TARSKI:pred.2">in</a>  <a href="clvect_2.html#K4" title="CLVECT_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="tarski.html#R2" title="TARSKI:pred.2">in</a>  <a href="clvect_2.html#K5" title="CLVECT_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="clvect_2.html#T50" target="_self" onmouseover="rs('clvect_2/T50')" onmouseout="rh()">Th50</a></span>;<br/>
<span class="kw">hence </span><a NAME="E2:60"/>
 <a href="clvect_2.html#K4" title="CLVECT_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="clvect_2.html#K5" title="CLVECT_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" onmouseover="rs('subset_1/T2')" onmouseout="rh()">SUBSET_1:2</a></span>; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> verum</span><br/>


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