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<a NAME="E1:48_1_1"/>
the <a href="struct_0.html#U1">carrier</a> of <span class="p1">(<span class="default"><a href="polynom3.html#K16">Polynom-Ring</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="tarski.html#R1">c=</a> the <a href="struct_0.html#U1">carrier</a> of <span class="p1">(<span class="default"><a href="polyalg1.html#K1" target="_self">Formal-Series</a> <font color="Maroon">c<sub>1</sub></font></span>)</span>
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="48_1_1_1"><b>proof </b></a><div class="add">

<b>let </b><font color="Maroon">c<sub>2</sub></font> be    <a href="hidden.html#M1">set</a> ; <i><font color="Red">:: according to </font></i><a class="ref" href="tarski.html#D3">TARSKI:def 3</a><br/>

<b>assume </b><a NAME="E1:48_1_1_1"/>
<font color="Maroon">c<sub>2</sub></font> <a href="hidden.html#R2">in</a> the <a href="struct_0.html#U1">carrier</a> of <span class="p1">(<span class="default"><a href="polynom3.html#K16">Polynom-Ring</a> <font color="Maroon">c<sub>1</sub></font></span>)</span>
 ;<br/>

<a NAME="E2:48_1_1_1"/><b>then </b>
<font color="Maroon">c<sub>2</sub></font> is   <a href="algseq_1.html#NM1">AlgSequence</a> of <font color="Maroon">c<sub>1</sub></font>
 
<b>by </b><i><a class="ref" href="polynom3.html#D12">POLYNOM3:def 12</a></i>;<br/>
<b>hence </b><a NAME="E3:48_1_1_1"/>
<font color="Maroon">c<sub>2</sub></font> <a href="hidden.html#R2">in</a> the <a href="struct_0.html#U1">carrier</a> of <span class="p1">(<span class="default"><a href="polyalg1.html#K1" target="_self">Formal-Series</a> <font color="Maroon">c<sub>1</sub></font></span>)</span>
 <b>by </b><i><a class="ref" href="polyalg1.html#D2" target="_self">Def2</a></i>;<br/>


</div><b>end;</b></div>
<b>then reconsider </b><font color="Maroon">c<sub>2</sub></font> = the <a href="struct_0.html#U1">carrier</a> of <span class="p1">(<span class="default"><a href="polynom3.html#K16">Polynom-Ring</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> as  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="polyalg1.html#K1" target="_self">Formal-Series</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> ;<br/>
<b>take </b>
 <a href="polyalg1.html#K2" target="_self">GenAlg</a> <font color="Maroon">c<sub>2</sub></font>
;<br/>

<b>thus </b><a NAME="E3:48_1_1"/>
ex <font color="Olive">b<sub>1</sub></font> being 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="polyalg1.html#K1" target="_self">Formal-Series</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> st <br/>( <font color="Olive">b<sub>1</sub></font> <a href="hidden.html#R1">=</a> the <a href="struct_0.html#U1">carrier</a> of <span class="p1">(<span class="default"><a href="polynom3.html#K16">Polynom-Ring</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> &amp;  <a href="polyalg1.html#K2" target="_self">GenAlg</a> <font color="Maroon">c<sub>2</sub></font> <a href="hidden.html#R1">=</a>  <a href="polyalg1.html#K2" target="_self">GenAlg</a> <font color="Olive">b<sub>1</sub></font> )
 ;<br/>


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