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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>assume </b><b>that </b><br/><a NAME="E1:51"/><i><font color="Green">E36</font></i>: 
<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="E2:51"/><i><font color="Green">E37</font></i>: 
<font color="Maroon">c<sub>1</sub></font> is <a href="dickson.html#V4" target="_self">Dickson</a>
 ;<br/>

<a NAME="E3:51"/><i><font color="Green">E38</font></i>: 
for <font color="Olive">b<sub>1</sub></font> being  <a href="normsp_1.html#NM2">sequence</a> of <font color="Maroon">c<sub>1</sub></font>ex <font color="Olive">b<sub>2</sub></font>, <font color="Olive">b<sub>3</sub></font> being  <a href="nat_1.html#NM1">Nat</a> st <br/>( <font color="Olive">b<sub>2</sub></font> <a href="xxreal_0.html#NR3" target="_self">&lt;</a> <font color="Olive">b<sub>3</sub></font> &amp; <font color="Olive">b<sub>1</sub></font> <a href="normsp_1.html#K2">.</a> <font color="Olive">b<sub>2</sub></font> <a href="orders_2.html#R1">&lt;=</a> <font color="Olive">b<sub>1</sub></font> <a href="normsp_1.html#K2">.</a> <font color="Olive">b<sub>3</sub></font> )
 
<b>by </b><i><a class="txt" href="dickson.html#E1:51"><i><font color="Green">E36</font></i></a>, <a class="txt" href="dickson.html#E2:51"><i><font color="Green">E37</font></i></a>, <a class="ref" href="dickson.html#T30" target="_self">Th30</a></i>;<br/>
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="51_1"><b>now </b></a><div class="add"><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>assume </b><a NAME="E1:51_1"/><i><font color="Green">E39</font></i>: 
<font color="Maroon">c<sub>2</sub></font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a>  <a href="xboole_0.html#K1">{}</a> 
 ;<br/><a NAME="E2:51_1"/>
not  <a href="dickson.html#K6" target="_self">min-classes</a> <font color="Maroon">c<sub>2</sub></font> is <a href="xboole_0.html#V1">empty</a>
 <b>by </b><i><a class="txt" href="dickson.html#E1:51"><i><font color="Green">E36</font></i></a>, <a class="txt" href="dickson.html#E3:51"><i><font color="Green">E38</font></i></a>, <a class="txt" href="dickson.html#E1:51_1"><i><font color="Green">E39</font></i></a>, <a class="ref" href="dickson.html#T32" target="_self">Th32</a></i>;<br/><b>hence </b><a NAME="E3:51_1"/>
ex <font color="Olive">b<sub>1</sub></font> being   <a href="hidden.html#M1">set</a>  st <font color="Olive">b<sub>1</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>
 <b>by </b><i><a class="ref" href="xboole_0.html#D1">XBOOLE_0:def 1</a></i>;<br/></div><b>end;</b></div>
<b>hence </b><a NAME="E5:51"/>
<font color="Maroon">c<sub>1</sub></font> <a href="dickson.html#K5" target="_self">\~</a>  is <a href="wellfnd1.html#V1">well_founded</a>
 <b>by </b><i><a class="ref" href="dickson.html#T21" target="_self">Th21</a></i>;<br/>


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