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<span class="kw">consider </span><font color="Maroon" title="c3">a</font> being    <a href="subset_1.html#M2" title="SUBSET_1:mode.2">Element</a> of  <a href="struct_0.html#K8" title="STRUCT_0:func.8">NonZero</a> <font color="Maroon" title="c2">R</font>;<br/>
<span class="kw">reconsider </span><font color="Maroon" title="c4">a</font> = <font color="Maroon" title="c3">a</font> as   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Maroon" title="c2">R</font> ;<br/>
<span class="kw">take </span><font color="Maroon" title="c5">q</font> = <font color="Maroon" title="c4">a</font> <a href="polynom7.html#K4" title="POLYNOM7:func.4">|</a> <font color="Maroon" title="c1">n</font>,<font color="Maroon" title="c2">R</font>; <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">q</font> is  <a href="polynom7.html#V1" title="POLYNOM7:attr.1">non-zero</a> </span><br/>

<a NAME="E3:1_1_1"/><span class="lab"><font color="Green" title="E1">A1</font></span>: 
( <font color="Maroon" title="c4">a</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">R</font> &amp;  <a href="polynom1.html#K9" title="POLYNOM1:func.9">0_</a> <font color="Maroon" title="c1">n</font>,<font color="Maroon" title="c2">R</font> <a href="funct_2.html#R2" title="FUNCT_2:pred.2">=</a> <span class="p1">(<span class="default"><a href="struct_0.html#K4" title="STRUCT_0:func.4">0.</a> <font color="Maroon" title="c2">R</font></span>)</span> <a href="polynom7.html#K4" title="POLYNOM7:func.4">|</a> <font color="Maroon" title="c1">n</font>,<font color="Maroon" title="c2">R</font> )
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="polynom7.html#T19" title="POLYNOM7:th.19">POLYNOM7:19</a>, <a class="ref" href="zfmisc_1.html#T64" title="ZFMISC_1:th.64">ZFMISC_1:64</a></span>;<br/>
<span class="kw">assume </span><a NAME="E4:1_1_1"/>
<font color="Maroon" title="c5">q</font> <a href="funct_2.html#R2" title="FUNCT_2:pred.2">=</a>  <a href="polynom1.html#K9" title="POLYNOM1:func.9">0_</a> <font color="Maroon" title="c1">n</font>,<font color="Maroon" title="c2">R</font>
 ; <span class="comment"><font color="Red">:: according to </font></span><a class="ref" href="polynom7.html#D2" title="POLYNOM7:def.2">POLYNOM7:def 2</a> <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> contradiction</span><br/>

<span class="kw">hence </span><a NAME="E5:1_1_1"/>
contradiction
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E3:1_1_1"><span class="lab"><font color="Green" title="E1">A1</font></span></a>, <a class="ref" href="polynom7.html#T21" title="POLYNOM7:th.21">POLYNOM7:21</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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