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<b>let </b><font color="Maroon">IT1</font> be  non <a href="xboole_0.html#V1">empty</a> <a href="struct_0.html#NM3">Subset-Family</a> of <font color="Maroon">R</font>, <font color="Maroon">IT2</font> be  non <a href="xboole_0.html#V1">empty</a> <a href="struct_0.html#NM3">Subset-Family</a> of <font color="Maroon">R</font>;<br/>

<b>assume </b><b>that </b><br/><a NAME="E1:53_1_2"/><i><font color="Green">E35</font></i>: 
for <font color="Olive">B</font> being   <a href="hidden.html#M1">set</a>  holds <br/> ( <font color="Olive">B</font> <a href="hidden.html#R2">in</a> <font color="Maroon">IT1</font> iff <font color="Olive">B</font> <a href="dickson.html#R1" target="_self">is_Dickson-basis_of</a> <font color="Maroon">N</font>,<font color="Maroon">R</font> )
 <b>and </b><br/><a NAME="E2:53_1_2"/><i><font color="Green">E68</font></i>: 
for <font color="Olive">B</font> being   <a href="hidden.html#M1">set</a>  holds <br/> ( <font color="Olive">B</font> <a href="hidden.html#R2">in</a> <font color="Maroon">IT2</font> iff <font color="Olive">B</font> <a href="dickson.html#R1" target="_self">is_Dickson-basis_of</a> <font color="Maroon">N</font>,<font color="Maroon">R</font> )
 ;<br/>

<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="53_1_2_1"><b>now </b></a><div class="add"><b>let </b><font color="Maroon">x</font> be    <a href="hidden.html#M1">set</a> ;<br/><div><b>hereby </b>
<div class="add"><b>assume </b><a NAME="E1:53_1_2_1_1"/>
<font color="Maroon">x</font> <a href="hidden.html#R2">in</a> <font color="Maroon">IT1</font>
 ;<br/><a NAME="E2:53_1_2_1_1"/><b>then </b>
<font color="Maroon">x</font> <a href="dickson.html#R1" target="_self">is_Dickson-basis_of</a> <font color="Maroon">N</font>,<font color="Maroon">R</font>
 <b>by </b><i/>;<br/><b>hence </b><a NAME="E3:53_1_2_1_1"/>
<font color="Maroon">x</font> <a href="hidden.html#R2">in</a> <font color="Maroon">IT2</font>
 <b>by </b><i/>;<br/></div>
<b>end;</b></div><b>assume </b><a NAME="E2:53_1_2_1"/>
<font color="Maroon">x</font> <a href="hidden.html#R2">in</a> <font color="Maroon">IT2</font>
 ;<br/><a NAME="E3:53_1_2_1"/><b>then </b>
<font color="Maroon">x</font> <a href="dickson.html#R1" target="_self">is_Dickson-basis_of</a> <font color="Maroon">N</font>,<font color="Maroon">R</font>
 <b>by </b><i/>;<br/><b>hence </b><a NAME="E4:53_1_2_1"/>
<font color="Maroon">x</font> <a href="hidden.html#R2">in</a> <font color="Maroon">IT1</font>
 <b>by </b><i/>;<br/></div><b>end;</b></div>
<b>hence </b><a NAME="E4:53_1_2"/>
<font color="Maroon">IT1</font> <a href="hidden.html#R1">=</a> <font color="Maroon">IT2</font>
 <b>by </b><i><a class="ref" href="tarski.html#T2">TARSKI:2</a></i>;<br/>


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