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<b>let </b><font color="Maroon" title="c1">X</font> be   <a href="rltopsp1.html#NM1" title="RLTOPSP1:NM.1">LinearTopSpace</a>;<br/><b>let </b><font color="Maroon" title="c2">P</font> be  <a href="rltopsp1.html#V9" title="RLTOPSP1:attr.9">bounded</a> <a href="struct_0.html#NM2" title="STRUCT_0:NM.2">Subset</a> of <font color="Maroon" title="c1">X</font>;<br/><b>let </b><font color="Maroon" title="c3">Q</font> be   <a href="struct_0.html#NM2" title="STRUCT_0:NM.2">Subset</a> of <font color="Maroon" title="c1">X</font>;<br/>





<b>assume </b><a NAME="E1:88"/><i><font color="Green" title="E53">A1</font></i>: 
<font color="Maroon" title="c3">Q</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <font color="Maroon" title="c2">P</font>
 ;<br/>

<b>let </b><font color="Maroon" title="c4">V</font> be    <a href="connsp_2.html#M1" title="CONNSP_2:mode.1">a_neighborhood</a> of  <a href="struct_0.html#K4" title="STRUCT_0:func.4">0.</a> <font color="Maroon" title="c1">X</font>; <i><font color="Red">:: according to </font></i><a class="ref" href="rltopsp1.html#D12" target="_self" title="RLTOPSP1:def.12">RLTOPSP1:def 12</a><br/>

<b>consider </b><font color="Maroon" title="c5">s</font> being   <a href="real_1.html#NM1" title="REAL_1:NM.1">Real</a><b> such that </b><br/><a NAME="E3:88"/><i><font color="Green" title="E54">A2</font></i>: 
<font color="Maroon" title="c5">s</font> <a href="xxreal_0.html#NR4" title="XXREAL_0:NR.4">&gt;</a> 0
 <b>and </b><br/><a NAME="E4:88"/><i><font color="Green" title="E55">A3</font></i>: 
for <font color="Olive" title="b1">t</font> being  <a href="real_1.html#NM1" title="REAL_1:NM.1">Real</a>  st <font color="Olive" title="b1">t</font> <a href="xxreal_0.html#NR4" title="XXREAL_0:NR.4">&gt;</a> <font color="Maroon" title="c5">s</font> holds <br/><font color="Maroon" title="c2">P</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <font color="Olive" title="b1">t</font> <a href="convex1.html#K1" title="CONVEX1:func.1">*</a> <font color="Maroon" title="c4">V</font>
 <b>by </b><i><a class="ref" href="rltopsp1.html#D12" target="_self" title="RLTOPSP1:def.12">Def12</a></i>;<br/>
<b>take </b>
<font color="Maroon" title="c5">s</font>
;<br/>

<b>thus </b><a NAME="E5:88"/>
<font color="Maroon" title="c5">s</font> <a href="xxreal_0.html#NR4" title="XXREAL_0:NR.4">&gt;</a> 0
 <b>by </b><i><a class="txt" href="rltopsp1.html#E3:88"><i><font color="Green" title="E54">A2</font></i></a></i>;<br/>

<b>let </b><font color="Maroon" title="c6">t</font> be   <a href="real_1.html#NM1" title="REAL_1:NM.1">Real</a>;<br/>

<b>assume </b><a NAME="E6:88"/>
<font color="Maroon" title="c6">t</font> <a href="xxreal_0.html#NR4" title="XXREAL_0:NR.4">&gt;</a> <font color="Maroon" title="c5">s</font>
 ;<br/>

<a NAME="E7:88"/><b>then </b>
<font color="Maroon" title="c2">P</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <font color="Maroon" title="c6">t</font> <a href="convex1.html#K1" title="CONVEX1:func.1">*</a> <font color="Maroon" title="c4">V</font>
 
<b>by </b><i><a class="txt" href="rltopsp1.html#E4:88"><i><font color="Green" title="E55">A3</font></i></a></i>;<br/>
<b>hence </b><a NAME="E8:88"/>
<font color="Maroon" title="c3">Q</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <font color="Maroon" title="c6">t</font> <a href="convex1.html#K1" title="CONVEX1:func.1">*</a> <font color="Maroon" title="c4">V</font>
 <b>by </b><i><a class="txt" href="rltopsp1.html#E1:88"><i><font color="Green" title="E53">A1</font></i></a>, <a class="ref" href="xboole_1.html#T1" title="XBOOLE_1:th.1">XBOOLE_1:1</a></i>;<br/>


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