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<div class="add">

<span class="kw">let </span><font color="Maroon" title="c1">n</font> be   <a href="nat_1.html#NM1" title="NAT_1:NM.1">Nat</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">A</font> being   <a href="struct_0.html#NM2" title="STRUCT_0:NM.2">Subset</a> of <span class="p1">(<span class="default"><a href="euclid.html#K15" title="EUCLID:func.15">TOP-REAL</a> <font color="Maroon" title="c1">n</font></span>)</span><br/>  for <font color="Olive" title="b2">a</font> being   <a href="tbsp_1.html#V6" title="TBSP_1:attr.6">bounded</a>  <a href="struct_0.html#NM2" title="STRUCT_0:NM.2">Subset</a> of <span class="p1">(<span class="default"><a href="euclid.html#K14" title="EUCLID:func.14">Euclid</a> <font color="Maroon" title="c1">n</font></span>)</span>  st <font color="Olive" title="b2">a</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b1">A</font> holds <br/> for <font color="Olive" title="b3">p</font> being   <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> <font color="Maroon" title="c1">n</font></span>)</span>  st <font color="Olive" title="b3">p</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="convex1.html#K3" title="CONVEX1:func.3">conv</a> <font color="Olive" title="b1">A</font> holds <br/> <a href="convex1.html#K3" title="CONVEX1:func.3">conv</a> <font color="Olive" title="b1">A</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a>  <a href="metric_1.html#K10" title="METRIC_1:func.10">cl_Ball</a> (<font color="Olive" title="b3">p</font>,<span class="p1">(<span class="default"><a href="tbsp_1.html#K3" title="TBSP_1:func.3">diameter</a> <font color="Olive" title="b2">a</font></span>)</span>)</span><br/><span class="kw">let </span><font color="Maroon" title="c2">A</font> be   <a href="struct_0.html#NM2" title="STRUCT_0:NM.2">Subset</a> of <span class="p1">(<span class="default"><a href="euclid.html#K15" title="EUCLID:func.15">TOP-REAL</a> <font color="Maroon" title="c1">n</font></span>)</span>; <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">a</font> being   <a href="tbsp_1.html#V6" title="TBSP_1:attr.6">bounded</a>  <a href="struct_0.html#NM2" title="STRUCT_0:NM.2">Subset</a> of <span class="p1">(<span class="default"><a href="euclid.html#K14" title="EUCLID:func.14">Euclid</a> <font color="Maroon" title="c1">n</font></span>)</span>  st <font color="Olive" title="b1">a</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c2">A</font> holds <br/> for <font color="Olive" title="b2">p</font> being   <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> <font color="Maroon" title="c1">n</font></span>)</span>  st <font color="Olive" title="b2">p</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="convex1.html#K3" title="CONVEX1:func.3">conv</a> <font color="Maroon" title="c2">A</font> holds <br/> <a href="convex1.html#K3" title="CONVEX1:func.3">conv</a> <font color="Maroon" title="c2">A</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a>  <a href="metric_1.html#K10" title="METRIC_1:func.10">cl_Ball</a> (<font color="Olive" title="b2">p</font>,<span class="p1">(<span class="default"><a href="tbsp_1.html#K3" title="TBSP_1:func.3">diameter</a> <font color="Olive" title="b1">a</font></span>)</span>)</span><br/>



<a NAME="E1:26"/><span class="lab"><font color="Green" title="E15">A1</font></span>: 
<font color="Maroon" title="c1">n</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="numbers.html#K5" title="NUMBERS:func.5">NAT</a> 
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="ordinal1.html#D12" title="ORDINAL1:def.12">ORDINAL1:def 12</a></span>;<br/>
<a NAME="E2:26"/><span class="lab"><font color="Green" title="E16">A2</font></span>: 
 <a href="pre_topc.html#G1" title="PRE_TOPC:aggr.1">TopStruct</a>(#  the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <span class="p1">(<span class="default"><a href="euclid.html#K15" title="EUCLID:func.15">TOP-REAL</a> <font color="Maroon" title="c1">n</font></span>)</span>, the <a href="pre_topc.html#U1" title="PRE_TOPC:sel.1">topology</a> of <span class="p1">(<span class="default"><a href="euclid.html#K15" title="EUCLID:func.15">TOP-REAL</a> <font color="Maroon" title="c1">n</font></span>)</span> #) <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="pcomps_1.html#K3" title="PCOMPS_1:func.3">TopSpaceMetr</a> <span class="p1">(<span class="default"><a href="euclid.html#K14" title="EUCLID:func.14">Euclid</a> <font color="Maroon" title="c1">n</font></span>)</span>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="euclid.html#D8" title="EUCLID:def.8">EUCLID:def 8</a></span>;<br/>
<span class="kw">let </span><font color="Maroon" title="c3">a</font> be   <a href="tbsp_1.html#V6" title="TBSP_1:attr.6">bounded</a>  <a href="struct_0.html#NM2" title="STRUCT_0:NM.2">Subset</a> of <span class="p1">(<span class="default"><a href="euclid.html#K14" title="EUCLID:func.14">Euclid</a> <font color="Maroon" title="c1">n</font></span>)</span>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> ( <font color="Maroon" title="c3">a</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c2">A</font> implies  for <font color="Olive" title="b1">p</font> being   <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> <font color="Maroon" title="c1">n</font></span>)</span>  st <font color="Olive" title="b1">p</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="convex1.html#K3" title="CONVEX1:func.3">conv</a> <font color="Maroon" title="c2">A</font> holds <br/> <a href="convex1.html#K3" title="CONVEX1:func.3">conv</a> <font color="Maroon" title="c2">A</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a>  <a href="metric_1.html#K10" title="METRIC_1:func.10">cl_Ball</a> (<font color="Olive" title="b1">p</font>,<span class="p1">(<span class="default"><a href="tbsp_1.html#K3" title="TBSP_1:func.3">diameter</a> <font color="Maroon" title="c3">a</font></span>)</span>) )</span><br/>

<span class="kw">assume </span><a NAME="E3:26"/><span class="lab"><font color="Green" title="E17">A3</font></span>: 
<font color="Maroon" title="c2">A</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c3">a</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">p</font> being   <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> <font color="Maroon" title="c1">n</font></span>)</span>  st <font color="Olive" title="b1">p</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="convex1.html#K3" title="CONVEX1:func.3">conv</a> <font color="Maroon" title="c2">A</font> holds <br/> <a href="convex1.html#K3" title="CONVEX1:func.3">conv</a> <font color="Maroon" title="c2">A</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a>  <a href="metric_1.html#K10" title="METRIC_1:func.10">cl_Ball</a> (<font color="Olive" title="b1">p</font>,<span class="p1">(<span class="default"><a href="tbsp_1.html#K3" title="TBSP_1:func.3">diameter</a> <font color="Maroon" title="c3">a</font></span>)</span>)</span><br/>

<span class="kw">let </span><font color="Maroon" title="c4">x</font> be   <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> <font color="Maroon" title="c1">n</font></span>)</span>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> ( <font color="Maroon" title="c4">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="convex1.html#K3" title="CONVEX1:func.3">conv</a> <font color="Maroon" title="c2">A</font> implies  <a href="convex1.html#K3" title="CONVEX1:func.3">conv</a> <font color="Maroon" title="c2">A</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a>  <a href="metric_1.html#K10" title="METRIC_1:func.10">cl_Ball</a> (<font color="Maroon" title="c4">x</font>,<span class="p1">(<span class="default"><a href="tbsp_1.html#K3" title="TBSP_1:func.3">diameter</a> <font color="Maroon" title="c3">a</font></span>)</span>) )</span><br/>

<span class="kw">assume </span><a NAME="E4:26"/><span class="lab"><font color="Green" title="E18">A4</font></span>: 
<font color="Maroon" title="c4">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="convex1.html#K3" title="CONVEX1:func.3">conv</a> <font color="Maroon" title="c2">A</font>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide">  <a href="convex1.html#K3" title="CONVEX1:func.3">conv</a> <font color="Maroon" title="c2">A</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a>  <a href="metric_1.html#K10" title="METRIC_1:func.10">cl_Ball</a> (<font color="Maroon" title="c4">x</font>,<span class="p1">(<span class="default"><a href="tbsp_1.html#K3" title="TBSP_1:func.3">diameter</a> <font color="Maroon" title="c3">a</font></span>)</span>)</span><br/>

<a NAME="E5:26"/><span class="lab"><font color="Green" title="E19">A5</font></span>: 
<font color="Maroon" title="c2">A</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a>  <a href="metric_1.html#K10" title="METRIC_1:func.10">cl_Ball</a> (<font color="Maroon" title="c4">x</font>,<span class="p1">(<span class="default"><a href="tbsp_1.html#K3" title="TBSP_1:func.3">diameter</a> <font color="Maroon" title="c3">a</font></span>)</span>)
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="26_1"><span class="kw">proof </span></a><div class="add">

<span class="kw">let </span><font color="Maroon" title="c5">p</font> be    <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a> ; <span class="comment"><font color="firebrick">:: according to </font></span><a class="ref" href="tarski.html#D3" title="TARSKI:def.3">TARSKI:def 3</a> <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> (  not <font color="Maroon" title="c5">p</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c2">A</font> or <font color="Maroon" title="c5">p</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="metric_1.html#K10" title="METRIC_1:func.10">cl_Ball</a> (<font color="Maroon" title="c4">x</font>,<span class="p1">(<span class="default"><a href="tbsp_1.html#K3" title="TBSP_1:func.3">diameter</a> <font color="Maroon" title="c3">a</font></span>)</span>) )</span><br/>

<span class="kw">assume </span><a NAME="E1:26_1"/><span class="lab"><font color="Green" title="E20">A6</font></span>: 
<font color="Maroon" title="c5">p</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c2">A</font>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> <font color="Maroon" title="c5">p</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="metric_1.html#K10" title="METRIC_1:func.10">cl_Ball</a> (<font color="Maroon" title="c4">x</font>,<span class="p1">(<span class="default"><a href="tbsp_1.html#K3" title="TBSP_1:func.3">diameter</a> <font color="Maroon" title="c3">a</font></span>)</span>)</span><br/>

<span class="kw">then </span><span class="kw">reconsider </span><font color="Maroon" title="c6">p</font> = <font color="Maroon" title="c5">p</font> 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> <font color="Maroon" title="c1">n</font></span>)</span> <span class="kw">by</span> <span class="lab"><a class="txt" href="#E3:26"><span class="lab"><font color="Green" title="E17">A3</font></span></a></span>;<br/>
<span class="kw">reconsider </span><font color="Maroon" title="c7">pp</font> = <font color="Maroon" title="c6">p</font> 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#K15" title="EUCLID:func.15">TOP-REAL</a> <font color="Maroon" title="c1">n</font></span>)</span> <span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:26"><span class="lab"><font color="Green" title="E16">A2</font></span></a></span>;<br/>
<a NAME="E4:26_1"/><span class="lab"><font color="Green" title="E21">A7</font></span>: 
 <a href="metric_1.html#K10" title="METRIC_1:func.10">cl_Ball</a> (<font color="Maroon" title="c6">p</font>,<span class="p1">(<span class="default"><a href="tbsp_1.html#K3" title="TBSP_1:func.3">diameter</a> <font color="Maroon" title="c3">a</font></span>)</span>) <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="topreal9.html#K2" title="TOPREAL9:func.2">cl_Ball</a> (<font color="Maroon" title="c7">pp</font>,<span class="p1">(<span class="default"><a href="tbsp_1.html#K3" title="TBSP_1:func.3">diameter</a> <font color="Maroon" title="c3">a</font></span>)</span>)
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:26"><span class="lab"><font color="Green" title="E15">A1</font></span></a>, <a class="ref" href="topreal9.html#T14" title="TOPREAL9:th.14">TOPREAL9:14</a></span>;<br/>
<a NAME="E5:26_1"/>
<font color="Maroon" title="c2">A</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a>  <a href="metric_1.html#K10" title="METRIC_1:func.10">cl_Ball</a> (<font color="Maroon" title="c6">p</font>,<span class="p1">(<span class="default"><a href="tbsp_1.html#K3" title="TBSP_1:func.3">diameter</a> <font color="Maroon" title="c3">a</font></span>)</span>)
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="26_1_1"><span class="kw">proof </span></a><div class="add">

<span class="kw">let </span><font color="Maroon" title="c8">y</font> be    <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a> ; <span class="comment"><font color="firebrick">:: according to </font></span><a class="ref" href="tarski.html#D3" title="TARSKI:def.3">TARSKI:def 3</a> <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> (  not <font color="Maroon" title="c8">y</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c2">A</font> or <font color="Maroon" title="c8">y</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="metric_1.html#K10" title="METRIC_1:func.10">cl_Ball</a> (<font color="Maroon" title="c6">p</font>,<span class="p1">(<span class="default"><a href="tbsp_1.html#K3" title="TBSP_1:func.3">diameter</a> <font color="Maroon" title="c3">a</font></span>)</span>) )</span><br/>

<span class="kw">assume </span><a NAME="E1:26_1_1"/><span class="lab"><font color="Green" title="E22">A8</font></span>: 
<font color="Maroon" title="c8">y</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c2">A</font>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> <font color="Maroon" title="c8">y</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="metric_1.html#K10" title="METRIC_1:func.10">cl_Ball</a> (<font color="Maroon" title="c6">p</font>,<span class="p1">(<span class="default"><a href="tbsp_1.html#K3" title="TBSP_1:func.3">diameter</a> <font color="Maroon" title="c3">a</font></span>)</span>)</span><br/>

<span class="kw">then </span><span class="kw">reconsider </span><font color="Maroon" title="c9">q</font> = <font color="Maroon" title="c8">y</font> 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> <font color="Maroon" title="c1">n</font></span>)</span> <span class="kw">by</span> <span class="lab"><a class="txt" href="#E3:26"><span class="lab"><font color="Green" title="E17">A3</font></span></a></span>;<br/>
<a NAME="E3:26_1_1"/>
 <a href="metric_1.html#K4" title="METRIC_1:func.4">dist</a> (<font color="Maroon" title="c6">p</font>,<font color="Maroon" title="c9">q</font>) <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a>  <a href="tbsp_1.html#K3" title="TBSP_1:func.3">diameter</a> <font color="Maroon" title="c3">a</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E3:26"><span class="lab"><font color="Green" title="E17">A3</font></span></a>, <a class="txt" href="#E1:26_1"><span class="lab"><font color="Green" title="E20">A6</font></span></a>, <a class="txt" href="#E1:26_1_1"><span class="lab"><font color="Green" title="E22">A8</font></span></a>, <a class="ref" href="tbsp_1.html#D8" title="TBSP_1:def.8">TBSP_1:def 8</a></span>;<br/>
<span class="kw">hence </span><a NAME="E4:26_1_1"/>
<font color="Maroon" title="c8">y</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="metric_1.html#K10" title="METRIC_1:func.10">cl_Ball</a> (<font color="Maroon" title="c6">p</font>,<span class="p1">(<span class="default"><a href="tbsp_1.html#K3" title="TBSP_1:func.3">diameter</a> <font color="Maroon" title="c3">a</font></span>)</span>)
 <span class="kw">by</span> <span class="lab"><a class="ref" href="metric_1.html#T12" title="METRIC_1:th.12">METRIC_1:12</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><span class="kw">end;</span></div>
<a NAME="E6:26_1"/><span class="kw">then </span>
 <a href="convex1.html#K3" title="CONVEX1:func.3">conv</a> <font color="Maroon" title="c2">A</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a>  <a href="topreal9.html#K2" title="TOPREAL9:func.2">cl_Ball</a> (<font color="Maroon" title="c7">pp</font>,<span class="p1">(<span class="default"><a href="tbsp_1.html#K3" title="TBSP_1:func.3">diameter</a> <font color="Maroon" title="c3">a</font></span>)</span>)
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E4:26_1"><span class="lab"><font color="Green" title="E21">A7</font></span></a>, <a class="ref" href="convex1.html#T30" title="CONVEX1:th.30">CONVEX1:30</a></span>;<br/>
<a NAME="E7:26_1"/><span class="kw">then </span>
 <a href="metric_1.html#K4" title="METRIC_1:func.4">dist</a> (<font color="Maroon" title="c6">p</font>,<font color="Maroon" title="c4">x</font>) <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a>  <a href="tbsp_1.html#K3" title="TBSP_1:func.3">diameter</a> <font color="Maroon" title="c3">a</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E4:26"><span class="lab"><font color="Green" title="E18">A4</font></span></a>, <a class="txt" href="#E4:26_1"><span class="lab"><font color="Green" title="E21">A7</font></span></a>, <a class="ref" href="metric_1.html#T12" title="METRIC_1:th.12">METRIC_1:12</a></span>;<br/>
<span class="kw">hence </span><a NAME="E8:26_1"/>
<font color="Maroon" title="c5">p</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="metric_1.html#K10" title="METRIC_1:func.10">cl_Ball</a> (<font color="Maroon" title="c4">x</font>,<span class="p1">(<span class="default"><a href="tbsp_1.html#K3" title="TBSP_1:func.3">diameter</a> <font color="Maroon" title="c3">a</font></span>)</span>)
 <span class="kw">by</span> <span class="lab"><a class="ref" href="metric_1.html#T12" title="METRIC_1:th.12">METRIC_1:12</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><span class="kw">end;</span></div>
<span class="kw">reconsider </span><font color="Maroon" title="c5">xx</font> = <font color="Maroon" title="c4">x</font> 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#K15" title="EUCLID:func.15">TOP-REAL</a> <font color="Maroon" title="c1">n</font></span>)</span> <span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:26"><span class="lab"><font color="Green" title="E16">A2</font></span></a></span>;<br/>
<a NAME="E7:26"/>
 <a href="metric_1.html#K10" title="METRIC_1:func.10">cl_Ball</a> (<font color="Maroon" title="c4">x</font>,<span class="p1">(<span class="default"><a href="tbsp_1.html#K3" title="TBSP_1:func.3">diameter</a> <font color="Maroon" title="c3">a</font></span>)</span>) <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="topreal9.html#K2" title="TOPREAL9:func.2">cl_Ball</a> (<font color="Maroon" title="c5">xx</font>,<span class="p1">(<span class="default"><a href="tbsp_1.html#K3" title="TBSP_1:func.3">diameter</a> <font color="Maroon" title="c3">a</font></span>)</span>)
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:26"><span class="lab"><font color="Green" title="E15">A1</font></span></a>, <a class="ref" href="topreal9.html#T14" title="TOPREAL9:th.14">TOPREAL9:14</a></span>;<br/>
<span class="kw">hence </span><a NAME="E8:26"/>
 <a href="convex1.html#K3" title="CONVEX1:func.3">conv</a> <font color="Maroon" title="c2">A</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a>  <a href="metric_1.html#K10" title="METRIC_1:func.10">cl_Ball</a> (<font color="Maroon" title="c4">x</font>,<span class="p1">(<span class="default"><a href="tbsp_1.html#K3" title="TBSP_1:func.3">diameter</a> <font color="Maroon" title="c3">a</font></span>)</span>)
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E5:26"><span class="lab"><font color="Green" title="E19">A5</font></span></a>, <a class="ref" href="convex1.html#T30" title="CONVEX1:th.30">CONVEX1:30</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>
