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<span class="kw">set </span><font color="Maroon" title="c4">f</font> =  <a href="polynom1.html#K7" title="POLYNOM1:func.7">-</a> <font color="Maroon" title="c3">p</font>;<br/>
<a NAME="E1:111_1_1"/><span class="lab"><font color="Green" title="E32">A1</font></span>: 
 <a href="polynom1.html#K3" title="POLYNOM1:func.3">Support</a> <span class="p1">(<span class="default"><a href="polynom1.html#K7" title="POLYNOM1:func.7">-</a> <font color="Maroon" title="c3">p</font></span>)</span> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a>  <a href="polynom1.html#K3" title="POLYNOM1:func.3">Support</a> <font color="Maroon" title="c3">p</font>
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="111_1_1_1"><span class="kw">proof </span></a><div class="add">

<span class="kw">let </span><font color="Maroon" title="c5">x</font> be    <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a> ; <span class="comment"><font color="Red">:: according to </font></span><a class="ref" href="tarski.html#D3" title="TARSKI:def.3">TARSKI:def 3</a> <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> (  not <font color="Maroon" title="c5">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="polynom1.html#K3" title="POLYNOM1:func.3">Support</a> <span class="p1">(<span class="default"><a href="polynom1.html#K7" title="POLYNOM1:func.7">-</a> <font color="Maroon" title="c3">p</font></span>)</span> or <font color="Maroon" title="c5">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="polynom1.html#K3" title="POLYNOM1:func.3">Support</a> <font color="Maroon" title="c3">p</font> )</span><br/>

<span class="kw">assume </span><a NAME="E1:111_1_1_1"/><span class="lab"><font color="Green" title="E33">A2</font></span>: 
<font color="Maroon" title="c5">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="polynom1.html#K3" title="POLYNOM1:func.3">Support</a> <span class="p1">(<span class="default"><a href="polynom1.html#K7" title="POLYNOM1:func.7">-</a> <font color="Maroon" title="c3">p</font></span>)</span>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> <font color="Maroon" title="c5">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="polynom1.html#K3" title="POLYNOM1:func.3">Support</a> <font color="Maroon" title="c3">p</font></span><br/>

<span class="kw">then </span><span class="kw">reconsider </span><font color="Maroon" title="c6">x9</font> = <font color="Maroon" title="c5">x</font> as    <a href="pre_poly.html#M2" title="PRE_POLY:mode.2">Element</a> of  <a href="pre_poly.html#K16" title="PRE_POLY:func.16">Bags</a> <font color="Maroon" title="c1">n</font> ;<br/>
<a NAME="E3:111_1_1_1"/>
<span class="p1">(<span class="default"><a href="polynom1.html#K7" title="POLYNOM1:func.7">-</a> <font color="Maroon" title="c3">p</font></span>)</span> <a href="polynom1.html#K4" title="POLYNOM1:func.4">.</a> <font color="Maroon" title="c6">x9</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a>  <a href="struct_0.html#K4" title="STRUCT_0:func.4">0.</a> <font color="Maroon" title="c2">L</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:111_1_1_1"><span class="lab"><font color="Green" title="E33">A2</font></span></a>, <a class="ref" href="polynom1.html#D9" target="_self" title="POLYNOM1:def.9">Def9</a></span>;<br/>
<a NAME="E4:111_1_1_1"/><span class="kw">then </span>
 <a href="algstr_0.html#K4" title="ALGSTR_0:func.4">-</a> <span class="p1">(<span class="default"><font color="Maroon" title="c3">p</font> <a href="polynom1.html#K4" title="POLYNOM1:func.4">.</a> <font color="Maroon" title="c6">x9</font></span>)</span> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a>  <a href="struct_0.html#K4" title="STRUCT_0:func.4">0.</a> <font color="Maroon" title="c2">L</font>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="polynom1.html#D22" target="_self" title="POLYNOM1:def.22">Def22</a></span>;<br/>
<a NAME="E5:111_1_1_1"/><span class="kw">then </span>
<font color="Maroon" title="c3">p</font> <a href="polynom1.html#K4" title="POLYNOM1:func.4">.</a> <font color="Maroon" title="c6">x9</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a>  <a href="struct_0.html#K4" title="STRUCT_0:func.4">0.</a> <font color="Maroon" title="c2">L</font>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="rlvect_1.html#T25" title="RLVECT_1:th.25">RLVECT_1:25</a></span>;<br/>
<span class="kw">hence </span><a NAME="E6:111_1_1_1"/>
<font color="Maroon" title="c5">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="polynom1.html#K3" title="POLYNOM1:func.3">Support</a> <font color="Maroon" title="c3">p</font>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="polynom1.html#D9" target="_self" title="POLYNOM1:def.9">Def9</a></span>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> verum</span><br/>


</div><span class="kw">end;</span></div>
<a NAME="E2:111_1_1"/>
 <a href="polynom1.html#K3" title="POLYNOM1:func.3">Support</a> <font color="Maroon" title="c3">p</font> is  <a href="finset_1.html#V1" title="FINSET_1:attr.1">finite</a> 
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="polynom1.html#D10" target="_self" title="POLYNOM1:def.10">Def10</a></span>;<br/>
<span class="kw">hence </span><a NAME="E3:111_1_1"/>
 <a href="polynom1.html#K7" title="POLYNOM1:func.7">-</a> <font color="Maroon" title="c3">p</font> is  <a href="polynom1.html#V1" title="POLYNOM1:attr.1">finite-Support</a> 
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:111_1_1"><span class="lab"><font color="Green" title="E32">A1</font></span></a>, <a class="ref" href="polynom1.html#D10" target="_self" title="POLYNOM1:def.10">Def10</a></span>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> verum</span><br/>


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