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<span class="kw">let </span><font color="Maroon" title="c1">a</font>, <font color="Maroon" title="c2">b</font>, <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="topreal9.html#K1" title="TOPREAL9:func.1">Ball</a> (<span class="p1"><a href="euclid.html#K19" title="EUCLID:func.19">|[</a><span class="default"><font color="Maroon" title="c1">a</font>,<font color="Maroon" title="c2">b</font></span><a href="euclid.html#K19" title="EUCLID:func.19">]|</a></span>,<font color="Maroon" title="c3">r</font>) <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="jgraph_6.html#K6" title="JGRAPH_6:func.6">inside_of_circle</a> (<font color="Maroon" title="c1">a</font>,<font color="Maroon" title="c2">b</font>,<font color="Maroon" title="c3">r</font>)</span><br/>





<span class="kw">reconsider </span><font color="Maroon" title="c4">e</font> = <span class="p1"><a href="euclid.html#K19" title="EUCLID:func.19">|[</a><span class="default"><font color="Maroon" title="c1">a</font>,<font color="Maroon" title="c2">b</font></span><a href="euclid.html#K19" title="EUCLID:func.19">]|</a></span> as   <a href="pre_topc.html#NM2" title="PRE_TOPC:NM.2">Point</a> of <span class="p1">(<span class="default"><a href="euclid.html#K14" title="EUCLID:func.14">Euclid</a> 2</span>)</span> <span class="kw">by</span> <span class="lab"><a class="ref" href="topreal3.html#T8" onmouseover="rs('topreal3/T8')" onmouseout="rh()">TOPREAL3:8</a></span>;<br/>
<span class="kw">thus </span> <a href="topreal9.html#K1" title="TOPREAL9:func.1">Ball</a> (<span class="p1"><a href="euclid.html#K19" title="EUCLID:func.19">|[</a><span class="default"><font color="Maroon" title="c1">a</font>,<font color="Maroon" title="c2">b</font></span><a href="euclid.html#K19" title="EUCLID:func.19">]|</a></span>,<font color="Maroon" title="c3">r</font>) = 
 <a href="metric_1.html#K8" title="METRIC_1:func.8">Ball</a> (<font color="Maroon" title="c4">e</font>,<font color="Maroon" title="c3">r</font>)
<span class="kw">by</span> <span class="lab"><a class="ref" href="topreal9.html#T13" target="_self" onmouseover="rs('topreal9/T13')" onmouseout="rh()">Th11</a></span>
<br/>.= 
 <a href="jgraph_6.html#K6" title="JGRAPH_6:func.6">inside_of_circle</a> (<font color="Maroon" title="c1">a</font>,<font color="Maroon" title="c2">b</font>,<font color="Maroon" title="c3">r</font>)
<span class="kw">by</span> <span class="lab"><a class="ref" href="topreal9.html#T48" target="_self" onmouseover="rs('topreal9/T48')" onmouseout="rh()">Th46</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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