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<b>let </b><font color="Maroon">L</font> be  non <a href="struct_0.html#V3">empty</a> <a href="rlvect_1.html#V4">add-associative</a> <a href="rlvect_1.html#V5">right_zeroed</a> <a href="rlvect_1.html#V6">right_complementable</a> <a href="group_1.html#V2">unital</a> <a href="vectsp_1.html#V7">distributive</a>  <a href="vectsp_1.html#L3">doubleLoopStr</a> ;<br/><b>let </b><font color="Maroon">I</font> be  non <a href="xboole_0.html#V1">empty</a> <a href="struct_0.html#NM2">Subset</a> of <span class="p1">(<span class="default"><a href="polynom3.html#K16">Polynom-Ring</a> <font color="Maroon">L</font></span>)</span>;<br/><b>let </b><font color="Maroon">i1</font> be   <a href="polynom3.html#NM1">Polynomial</a> of <font color="Maroon">L</font>, <font color="Maroon">i2</font> be   <a href="polynom3.html#NM1">Polynomial</a> of <font color="Maroon">L</font>;<br/>





<b>assume </b><a NAME="E1:22"/><i><font color="Green">E44</font></i>: 
( <font color="Maroon">i1</font> <a href="hidden.html#R2">in</a>  <a href="hilbasis.html#K4" target="_self">minlen</a> <font color="Maroon">I</font> &amp; <font color="Maroon">i2</font> <a href="hidden.html#R2">in</a> <font color="Maroon">I</font> )
 ;<br/>

<a NAME="E2:22"/><b>then </b>
<font color="Maroon">i1</font> <a href="hidden.html#R2">in</a> <span class="p1">{<span class="default"> <font color="Olive">x</font> where <font color="Olive">x</font> is    <a href="subset_1.html#M2">Element</a> of <font color="Maroon">I</font> : for <font color="Olive">x'</font>, <font color="Olive">y'</font> being  <a href="polynom3.html#NM1">Polynomial</a> of <font color="Maroon">L</font>  st <font color="Olive">x'</font> <a href="hidden.html#R1">=</a> <font color="Olive">x</font> &amp; <font color="Olive">y'</font> <a href="hidden.html#R2">in</a> <font color="Maroon">I</font> holds <br/> <a href="algseq_1.html#K3">len</a> <font color="Olive">x'</font> <a href="xxreal_0.html#R1">&lt;=</a>  <a href="algseq_1.html#K3">len</a> <font color="Olive">y'</font> </span>}</span> 
 
;<br/>
<b>then consider </b><font color="Maroon">i1'</font> being    <a href="subset_1.html#M2">Element</a> of <font color="Maroon">I</font><b> such that </b><br/><a NAME="E4:22"/><i><font color="Green">E45</font></i>: 
( <font color="Maroon">i1'</font> <a href="hidden.html#R1">=</a> <font color="Maroon">i1</font> &amp; ( for <font color="Olive">x'</font>, <font color="Olive">y'</font> being  <a href="polynom3.html#NM1">Polynomial</a> of <font color="Maroon">L</font>  st <font color="Olive">x'</font> <a href="hidden.html#R1">=</a> <font color="Maroon">i1'</font> &amp; <font color="Olive">y'</font> <a href="hidden.html#R2">in</a> <font color="Maroon">I</font> holds <br/> <a href="algseq_1.html#K3">len</a> <font color="Olive">x'</font> <a href="xxreal_0.html#R1">&lt;=</a>  <a href="algseq_1.html#K3">len</a> <font color="Olive">y'</font> ) )
 ;<br/>
<b>thus </b><a NAME="E5:22"/>
( <font color="Maroon">i1</font> <a href="hidden.html#R2">in</a> <font color="Maroon">I</font> &amp;  <a href="algseq_1.html#K3">len</a> <font color="Maroon">i1</font> <a href="xxreal_0.html#R1">&lt;=</a>  <a href="algseq_1.html#K3">len</a> <font color="Maroon">i2</font> )
 <b>by </b><i>, </i>;<br/>


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