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<div class="add">

<b>let </b><font color="Maroon" title="c2">R</font> be    <a href="pre_topc.html#M1" title="PRE_TOPC:mode.1">SubSpace</a> of <font color="Maroon" title="c1">T</font>;<br/>

<a NAME="E1:17_1_1"/>
the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c2">R</font> is <a href="membered.html#V3" title="MEMBERED:attr.3">real-membered</a>
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="17_1_1_1"><b>proof </b></a><div class="add">

<b>let </b><font color="Maroon" title="c3">x</font> be    <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a> ; <i><font color="Red">:: according to </font></i><a class="ref" href="membered.html#D3" title="MEMBERED:def.3">MEMBERED:def 3</a><br/>

<b>assume </b><a NAME="E1:17_1_1_1"/><i><font color="Green" title="E15">A1</font></i>: 
<font color="Maroon" title="c3">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="c2">R</font>
 ;<br/>

<a NAME="E2:17_1_1_1"/>
the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c2">R</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c1">T</font>
 
<b>by </b><i><a class="ref" href="borsuk_1.html#T35" title="BORSUK_1:th.35">BORSUK_1:35</a></i>;<br/>
<a NAME="E3:17_1_1_1"/><b>then </b>
<font color="Maroon" title="c3">x</font> is   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Maroon" title="c1">T</font>
 
<b>by </b><i><a class="txt" href="borsuk_6.html#E1:17_1_1_1"><i><font color="Green" title="E15">A1</font></i></a></i>;<br/>
<b>hence </b><a NAME="E4:17_1_1_1"/>
<font color="Maroon" title="c3">x</font> is <a href="xreal_0.html#V1" title="XREAL_0:attr.1">real</a>
 ;<br/>


</div><b>end;</b></div>
<b>hence </b><a NAME="E2:17_1_1"/>
<font color="Maroon" title="c2">R</font> is <a href="borsuk_4.html#V1" title="BORSUK_4:attr.1">real-membered</a>
 <b>by </b><i><a class="ref" href="borsuk_4.html#D2" title="BORSUK_4:def.2">BORSUK_4:def 2</a></i>;<br/>


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