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<b>let </b><font color="Maroon">c<sub>1</sub></font> be  non <a href="struct_0.html#V3">empty</a>  <a href="orders_2.html#L1">RelStr</a> ;<br/><b>let </b><font color="Maroon">c<sub>2</sub></font> be   <a href="struct_0.html#NM2">Subset</a> of <font color="Maroon">c<sub>1</sub></font>;<br/><b>let </b><font color="Maroon">c<sub>3</sub></font> be    <a href="hidden.html#M1">set</a> ;<br/>





<b>assume </b><b>that </b><br/><a NAME="E1:36"/>
<font color="Maroon">c<sub>1</sub></font> is <a href="dickson.html#V3" target="_self">quasi_ordered</a>
 <b>and </b><br/><a NAME="E2:36"/><i><font color="Green">E22</font></i>: 
<font color="Maroon">c<sub>3</sub></font> <a href="hidden.html#R2">in</a>  <a href="dickson.html#K6" target="_self">min-classes</a> <font color="Maroon">c<sub>2</sub></font>
 ;<br/>

<b>consider </b><font color="Maroon">c<sub>4</sub></font> being   <a href="struct_0.html#NM1">Element</a> of <span class="p1">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="dickson.html#K5" target="_self">\~</a> </span>)</span><b> such that </b><br/><a NAME="E4:36"/><i><font color="Green">E23</font></i>: 
<font color="Maroon">c<sub>4</sub></font> <a href="waybel_4.html#R4">is_minimal_wrt</a> <font color="Maroon">c<sub>2</sub></font>,the <a href="orders_2.html#U1">InternalRel</a> of <span class="p1">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="dickson.html#K5" target="_self">\~</a> </span>)</span>
 <b>and </b><br/><a NAME="E5:36"/><i><font color="Green">E24</font></i>: 
<font color="Maroon">c<sub>3</sub></font> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><a href="eqrel_1.html#K7">Class</a> <span class="p2">(<span class="default"><a href="dickson.html#K1" target="_self">EqRel</a> <font color="Maroon">c<sub>1</sub></font></span>)</span>,<font color="Maroon">c<sub>4</sub></font></span>)</span> <a href="subset_1.html#K9">/\</a> <font color="Maroon">c<sub>2</sub></font>
 <b>by </b><i><a class="txt" href="dickson.html#E2:36"><i><font color="Green">E22</font></i></a>, <a class="ref" href="dickson.html#D8" target="_self">Def8</a></i>;<br/>
<a NAME="E6:36"/><i><font color="Green">E25</font></i>: 
<font color="Maroon">c<sub>4</sub></font> <a href="hidden.html#R2">in</a> <font color="Maroon">c<sub>2</sub></font>
 
<b>by </b><i><a class="txt" href="dickson.html#E4:36"><i><font color="Green">E23</font></i></a>, <a class="ref" href="waybel_4.html#D26">WAYBEL_4:def 26</a></i>;<br/>
<a NAME="E7:36"/>
<font color="Maroon">c<sub>4</sub></font> <a href="hidden.html#R2">in</a>  <a href="eqrel_1.html#K7">Class</a> <span class="p1">(<span class="default"><a href="dickson.html#K1" target="_self">EqRel</a> <font color="Maroon">c<sub>1</sub></font></span>)</span>,<font color="Maroon">c<sub>4</sub></font>
 
<b>by </b><i><a class="ref" href="eqrel_1.html#T28">EQREL_1:28</a></i>;<br/>
<b>hence </b><a NAME="E8:36"/>
not <font color="Maroon">c<sub>3</sub></font> is <a href="xboole_0.html#V1">empty</a>
 <b>by </b><i><a class="txt" href="dickson.html#E5:36"><i><font color="Green">E24</font></i></a>, <a class="txt" href="dickson.html#E6:36"><i><font color="Green">E25</font></i></a>, <a class="ref" href="xboole_0.html#D3">XBOOLE_0:def 3</a></i>;<br/>


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