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

<span class="kw">let </span><font color="Maroon" title="c1">T</font> be   non  <a href="struct_0.html#V2" title="STRUCT_0:attr.2">empty</a>   <a href="struct_0.html#L1" title="STRUCT_0:struct.1">1-sorted</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"> ( <font color="Maroon" title="c1">T</font> is  <a href="topmetr.html#V3" title="TOPMETR:attr.3">real-membered</a>  iff  for <font color="Olive" title="b1">x</font> being   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Maroon" title="c1">T</font> holds  <font color="Olive" title="b1">x</font> is  <a href="xreal_0.html#V1" title="XREAL_0:attr.1">real</a>  )</span><br/>

<span class="kw">thus </span><a NAME="E1:14"/>
( <font color="Maroon" title="c1">T</font> is  <a href="topmetr.html#V3" title="TOPMETR:attr.3">real-membered</a>  implies  for <font color="Olive" title="b1">x</font> being   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Maroon" title="c1">T</font> holds  <font color="Olive" title="b1">x</font> is  <a href="xreal_0.html#V1" title="XREAL_0:attr.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"> ( (  for <font color="Olive" title="b1">x</font> being   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Maroon" title="c1">T</font> holds  <font color="Olive" title="b1">x</font> is  <a href="xreal_0.html#V1" title="XREAL_0:attr.1">real</a>  ) implies <font color="Maroon" title="c1">T</font> is  <a href="topmetr.html#V3" title="TOPMETR:attr.3">real-membered</a>  )</span><br/>

<span class="kw">assume </span><a NAME="E2:14"/>
 for <font color="Olive" title="b1">x</font> being   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Maroon" title="c1">T</font> holds  <font color="Olive" title="b1">x</font> is  <a href="xreal_0.html#V1" title="XREAL_0:attr.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"> <font color="Maroon" title="c1">T</font> is  <a href="topmetr.html#V3" title="TOPMETR:attr.3">real-membered</a> </span><br/>

<a NAME="E3:14"/><span class="kw">then </span>
 for <font color="Olive" title="b1">x</font> being    <a href="hidden.html#M1" title="HIDDEN:mode.1">object</a>   st <font color="Olive" title="b1">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c1">T</font> holds <br/><font color="Olive" title="b1">x</font> is  <a href="xreal_0.html#V1" title="XREAL_0:attr.1">real</a> 
 
;<br/>
<a NAME="E4:14"/><span class="kw">then </span>
 the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c1">T</font> is  <a href="membered.html#V3" title="MEMBERED:attr.3">real-membered</a> 
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="membered.html#D3" onmouseover="rs('membered/D3')" onmouseout="rh()">MEMBERED:def 3</a></span>;<br/>
<span class="kw">hence </span><a NAME="E5:14"/>
<font color="Maroon" title="c1">T</font> is  <a href="topmetr.html#V3" title="TOPMETR:attr.3">real-membered</a> 
 <span class="kw">by</span> <span class="lab"><a class="ref" href="topmetr.html#D8" onmouseover="rs('topmetr/D8')" onmouseout="rh()">TOPMETR:def 8</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/>


</div>
