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

<a NAME="E1:14_1_1"/><i><font color="Green" title="E8">A1</font></i>: 
 <a href="rusub_4.html#K3" title="RUSUB_4:func.3">Up</a> <span class="p1">(<span class="default"><a href="rlsub_1.html#K2" title="RLSUB_1:func.2">(Omega).</a> <font color="Maroon" title="c1">V</font></span>)</span> is <a href="rltopsp1.html#V3" title="RLTOPSP1:attr.3">circled</a>
 
<b>by </b><i><a class="ref" href="circled1.html#T6" target="_self" title="CIRCLED1:th.6">Th6</a></i>;<br/>
<a NAME="E2:14_1_1"/>
<font color="Maroon" title="c2">M</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a>  <a href="rusub_4.html#K3" title="RUSUB_4:func.3">Up</a> <span class="p1">(<span class="default"><a href="rlsub_1.html#K2" title="RLSUB_1:func.2">(Omega).</a> <font color="Maroon" title="c1">V</font></span>)</span>
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="14_1_1_1"><b>proof </b></a><div class="add">

<b>let </b><font color="Maroon" title="c3">u</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="tarski.html#D3" title="TARSKI:def.3">TARSKI:def 3</a><br/>

<b>assume </b><a NAME="E1:14_1_1_1"/>
<font color="Maroon" title="c3">u</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c2">M</font>
 ;<br/>

<b>then reconsider </b><font color="Maroon" title="c4">u</font> = <font color="Maroon" title="c3">u</font> as   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Maroon" title="c1">V</font> ;<br/>
<a NAME="E3:14_1_1_1"/>
<font color="Maroon" title="c4">u</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 <a href="rlvect_1.html#G1" title="RLVECT_1:aggr.1">RLSStruct</a>(# the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c1">V</font>,the <a href="struct_0.html#U2" title="STRUCT_0:sel.2">U2</a> of <font color="Maroon" title="c1">V</font>,the <a href="algstr_0.html#U1" title="ALGSTR_0:sel.1">U5</a> of <font color="Maroon" title="c1">V</font>,the <a href="rlvect_1.html#U1" title="RLVECT_1:sel.1">Mult</a> of <font color="Maroon" title="c1">V</font> #)
 
;<br/>
<a NAME="E4:14_1_1_1"/><b>then </b>
<font color="Maroon" title="c4">u</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 <span class="p1">(<span class="default"><a href="rlsub_1.html#K2" title="RLSUB_1:func.2">(Omega).</a> <font color="Maroon" title="c1">V</font></span>)</span>
 
<b>by </b><i><a class="ref" href="rlsub_1.html#D4" title="RLSUB_1:def.4">RLSUB_1:def 4</a></i>;<br/>
<b>hence </b><a NAME="E5:14_1_1_1"/>
<font color="Maroon" title="c3">u</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="rusub_4.html#K3" title="RUSUB_4:func.3">Up</a> <span class="p1">(<span class="default"><a href="rlsub_1.html#K2" title="RLSUB_1:func.2">(Omega).</a> <font color="Maroon" title="c1">V</font></span>)</span>
 <b>by </b><i><a class="ref" href="rusub_4.html#D6" title="RUSUB_4:def.6">RUSUB_4:def 6</a></i>;<br/>


</div><b>end;</b></div>
<b>hence </b><a NAME="E3:14_1_1"/>
not  <a href="circled1.html#K1" title="CIRCLED1:func.1">Circled-Family</a> <font color="Maroon" title="c2">M</font> is <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a>
 <b>by </b><i><a class="txt" href="circled1.html#E1:14_1_1"><i><font color="Green" title="E8">A1</font></i></a>, <a class="ref" href="circled1.html#D2" target="_self" title="CIRCLED1:def.2">Def2</a></i>;<br/>


</div>
