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<b>let </b><font color="Maroon">L</font> be  non <a href="struct_0.html#V3">empty</a>  <a href="vectsp_1.html#L1">multLoopStr</a> ;<br/><b>let </b><font color="Maroon">P</font> be  non <a href="xboole_0.html#V1">empty</a> <a href="struct_0.html#NM2">Subset</a> of <font color="Maroon">L</font>, <font color="Maroon">Q</font> be  non <a href="xboole_0.html#V1">empty</a> <a href="struct_0.html#NM2">Subset</a> of <font color="Maroon">L</font>;<br/><b>let </b><font color="Maroon">A</font> be    <a href="ideal_1.html#M2">LeftLinearCombination</a> of <font color="Maroon">P</font>;<br/>





<b>assume </b><a NAME="E1:44"/><i><font color="Green">E31</font></i>: 
<font color="Maroon">P</font> <a href="tarski.html#R1">c=</a> <font color="Maroon">Q</font>
 ;<br/>

<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="44_1"><b>now </b></a><div class="add"><b>let </b><font color="Maroon">i</font> be    <a href="hidden.html#M1">set</a> ;<br/><b>assume </b><a NAME="E1:44_1"/>
<font color="Maroon">i</font> <a href="hidden.html#R2">in</a>  <a href="finseq_1.html#K4">dom</a> <font color="Maroon">A</font>
 ;<br/><b>then consider </b><font color="Maroon">u</font> being   <a href="struct_0.html#NM1">Element</a> of <font color="Maroon">L</font>, <font color="Maroon">a</font> being    <a href="subset_1.html#M2">Element</a> of <font color="Maroon">P</font><b> such that </b><br/><a NAME="E3:44_1"/><i><font color="Green">E33</font></i>: 
<font color="Maroon">A</font> <a href="finseq_4.html#K4">/.</a> <font color="Maroon">i</font> <a href="hidden.html#R1">=</a> <font color="Maroon">u</font> <a href="group_1.html#K1">*</a> <font color="Maroon">a</font>
 <b>by </b><i><a class="ref" href="ideal_1.html#D10">IDEAL_1:def 10</a></i>;<br/><a NAME="E4:44_1"/>
<font color="Maroon">a</font> <a href="hidden.html#R2">in</a> <font color="Maroon">P</font>
 ;<br/><b>hence </b><a NAME="E5:44_1"/>
 ex <font color="Olive">u</font> being  <a href="struct_0.html#NM1">Element</a> of <font color="Maroon">L</font> ex <font color="Olive">a</font> being   <a href="subset_1.html#M2">Element</a> of <font color="Maroon">Q</font> st <font color="Maroon">A</font> <a href="finseq_4.html#K4">/.</a> <font color="Maroon">i</font> <a href="hidden.html#R1">=</a> <font color="Olive">u</font> <a href="group_1.html#K1">*</a> <font color="Olive">a</font>
 <b>by </b><i>, </i>;<br/></div><b>end;</b></div>
<b>hence </b><a NAME="E3:44"/>
<font color="Maroon">A</font> is    <a href="ideal_1.html#M2">LeftLinearCombination</a> of <font color="Maroon">Q</font>
 <b>by </b><i><a class="ref" href="ideal_1.html#D10">IDEAL_1:def 10</a></i>;<br/>


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