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<b>let </b><font color="Maroon">V</font> be   <a href="rlvect_1.html#NM2">RealLinearSpace</a>;<br/><b>let </b><font color="Maroon">M</font> be   <a href="struct_0.html#NM2">Subset</a> of <font color="Maroon">V</font>;<br/><b>let </b><font color="Maroon">u</font> be    <a href="hidden.html#M1">set</a> ; <i><font color="Red">:: according to </font></i><a class="ref" href="tarski.html#D3">TARSKI:def 3</a><br/>





<b>assume </b><a NAME="E1:17"/><i><font color="Green">E36</font></i>: 
<font color="Maroon">u</font> <a href="hidden.html#R2">in</a> <font color="Maroon">M</font>
 ;<br/>

<a NAME="E2:17"/>
for <font color="Olive">Y</font> being   <a href="hidden.html#M1">set</a>   st <font color="Olive">Y</font> <a href="hidden.html#R2">in</a>  <a href="circled1.html#K1" target="_self">Circled-Family</a> <font color="Maroon">M</font> holds <br/><font color="Maroon">u</font> <a href="hidden.html#R2">in</a> <font color="Olive">Y</font>
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="17_1"><b>proof </b></a><div class="add">

<b>let </b><font color="Maroon">Y</font> be    <a href="hidden.html#M1">set</a> ;<br/>

<b>assume </b><a NAME="E1:17_1"/><i><font color="Green">E37</font></i>: 
<font color="Maroon">Y</font> <a href="hidden.html#R2">in</a>  <a href="circled1.html#K1" target="_self">Circled-Family</a> <font color="Maroon">M</font>
 ;<br/>

<b>then reconsider </b><font color="Maroon">Y</font> = <font color="Maroon">Y</font> as   <a href="struct_0.html#NM2">Subset</a> of <font color="Maroon">V</font> ;<br/>
<a NAME="E3:17_1"/>
( <font color="Maroon">Y</font> is <a href="rltopsp1.html#V3">circled</a> &amp; <font color="Maroon">M</font> <a href="tarski.html#R1">c=</a> <font color="Maroon">Y</font> )
 
<b>by </b><i>, </i>;<br/>
<b>hence </b><a NAME="E4:17_1"/>
<font color="Maroon">u</font> <a href="hidden.html#R2">in</a> <font color="Maroon">Y</font>
 <b>by </b><i/>;<br/>


</div><b>end;</b></div>
<a NAME="E3:17"/><b>then </b>
<font color="Maroon">u</font> <a href="hidden.html#R2">in</a>  <a href="setfam_1.html#K6">meet</a> <span class="p1">(<span class="default"><a href="circled1.html#K1" target="_self">Circled-Family</a> <font color="Maroon">M</font></span>)</span>
 
<b>by </b><i><a class="ref" href="setfam_1.html#D1">SETFAM_1:def 1</a></i>;<br/>
<b>hence </b><a NAME="E4:17"/>
<font color="Maroon">u</font> <a href="hidden.html#R2">in</a>  <a href="circled1.html#K2" target="_self">Cir</a> <font color="Maroon">M</font>
 ;<br/>


</div>
