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

<b>let </b><font color="Maroon">c<sub>1</sub></font> be  non <a href="struct_0.html#V3">empty</a>  <a href="vectsp_1.html#L3">doubleLoopStr</a> ;<br/><b>let </b><font color="Maroon">c<sub>2</sub></font>, <font color="Maroon">c<sub>3</sub></font> be  non <a href="xboole_0.html#V1">empty</a> <a href="struct_0.html#NM2">Subset</a> of <font color="Maroon">c<sub>1</sub></font>;<br/>



<b>assume </b><a NAME="E1:87"/><i><font color="Green">E43</font></i>: 
<font color="Maroon">c<sub>2</sub></font> <a href="tarski.html#R1">c=</a> <font color="Maroon">c<sub>3</sub></font>
 ;<br/>

<a NAME="E2:87"/>
<font color="Maroon">c<sub>3</sub></font> <a href="tarski.html#R1">c=</a> <font color="Maroon">c<sub>3</sub></font> <a href="ideal_1.html#K8" target="_self">-LeftIdeal</a> 
 
<b>by </b><i><a class="ref" href="ideal_1.html#D16" target="_self">Def16</a></i>;<br/>
<a NAME="E3:87"/><b>then </b>
<font color="Maroon">c<sub>2</sub></font> <a href="tarski.html#R1">c=</a> <font color="Maroon">c<sub>3</sub></font> <a href="ideal_1.html#K8" target="_self">-LeftIdeal</a> 
 
<b>by </b><i><a class="txt" href="ideal_1.html#E1:87"><i><font color="Green">E43</font></i></a>, <a class="ref" href="xboole_1.html#T1">XBOOLE_1:1</a></i>;<br/>
<b>hence </b><a NAME="E4:87"/>
<font color="Maroon">c<sub>2</sub></font> <a href="ideal_1.html#K8" target="_self">-LeftIdeal</a>  <a href="tarski.html#R1">c=</a> <font color="Maroon">c<sub>3</sub></font> <a href="ideal_1.html#K8" target="_self">-LeftIdeal</a> 
 <b>by </b><i><a class="ref" href="ideal_1.html#D16" target="_self">Def16</a></i>;<br/>


</div>
