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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="rltopsp1.html#V3">circled</a> <a href="struct_0.html#NM2">Subset</a> of <font color="Maroon">V</font>, <font color="Maroon">N</font> be  <a href="rltopsp1.html#V3">circled</a> <a href="struct_0.html#NM2">Subset</a> of <font color="Maroon">V</font>;<br/><b>let </b><font color="Maroon">x</font> be   <a href="rlvect_1.html#NM1">VECTOR</a> of <font color="Maroon">V</font>; <i><font color="Red">:: according to </font></i><a class="ref" href="circled1.html#D1" target="_self">CIRCLED1:def 1</a><br/><b>let </b><font color="Maroon">r</font> be   <a href="real_1.html#NM1">Real</a>;<br/>







<b>assume </b><a NAME="E1:11"/><i><font color="Green">E36</font></i>: 
(  <a href="complex1.html#K18">abs</a> <font color="Maroon">r</font> <a href="xxreal_0.html#R1">&lt;=</a> 1 &amp; <font color="Maroon">x</font> <a href="hidden.html#R2">in</a> <font color="Maroon">M</font> <a href="subset_1.html#K4">\/</a> <font color="Maroon">N</font> )
 ;<br/>

<a NAME="E2:11"/><b>then </b>
( <font color="Maroon">x</font> <a href="hidden.html#R2">in</a> <font color="Maroon">M</font> or <font color="Maroon">x</font> <a href="hidden.html#R2">in</a> <font color="Maroon">N</font> )
 
<b>by </b><i><a class="ref" href="xboole_0.html#D2">XBOOLE_0:def 2</a></i>;<br/>
<a NAME="E3:11"/><b>then </b>
( <font color="Maroon">r</font> <a href="rlvect_1.html#K3">*</a> <font color="Maroon">x</font> <a href="hidden.html#R2">in</a> <font color="Maroon">M</font> or <font color="Maroon">r</font> <a href="rlvect_1.html#K3">*</a> <font color="Maroon">x</font> <a href="hidden.html#R2">in</a> <font color="Maroon">N</font> )
 
<b>by </b><i>, </i>;<br/>
<b>hence </b><a NAME="E4:11"/>
<font color="Maroon">r</font> <a href="rlvect_1.html#K3">*</a> <font color="Maroon">x</font> <a href="hidden.html#R2">in</a> <font color="Maroon">M</font> <a href="subset_1.html#K4">\/</a> <font color="Maroon">N</font>
 <b>by </b><i><a class="ref" href="xboole_0.html#D2">XBOOLE_0:def 2</a></i>;<br/>


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