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<span class="kw">let </span><font color="Maroon" title="c2">p</font> be   <a href="polynom3.html#NM1" title="POLYNOM3:NM.1">Polynomial</a> of <font color="Maroon" title="c1">F</font>; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> ( <font color="Maroon" title="c2">p</font> is  <a href="field_5.html#V1" title="FIELD_5:attr.1">linear</a>  implies <font color="Maroon" title="c2">p</font> is  <a href="polynom5.html#V1" title="POLYNOM5:attr.1">with_roots</a>  )</span><br/>

<span class="kw">assume </span><a NAME="E1:23_1_1"/>
<font color="Maroon" title="c2">p</font> is  <a href="field_5.html#V1" title="FIELD_5:attr.1">linear</a> 
 ; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> <font color="Maroon" title="c2">p</font> is  <a href="polynom5.html#V1" title="POLYNOM5:attr.1">with_roots</a> </span><br/>

<span class="kw">then </span><span class="kw">consider </span><font color="Maroon" title="c3">x</font>, <font color="Maroon" title="c4">z</font> being   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Maroon" title="c1">F</font><span class="kw"> such that </span><br/><a NAME="E3:23_1_1"/><span class="lab"><font color="Green" title="E14">A</font></span>: 
( <font color="Maroon" title="c3">x</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="c1">F</font> &amp; <font color="Maroon" title="c2">p</font> <a href="funct_2.html#R2" title="FUNCT_2:pred.2">=</a> <font color="Maroon" title="c3">x</font> <a href="polynom5.html#K4" title="POLYNOM5:func.4">*</a> <span class="p1">(<span class="default"><a href="hurwitz.html#K3" title="HURWITZ:func.3">rpoly</a> (1,<font color="Maroon" title="c4">z</font>)</span>)</span> )
 <span class="kw">by</span> <span class="lab"><a class="ref" href="hurwitz.html#T28" onmouseover="rs('hurwitz/T28')" onmouseout="rh()">HURWITZ:28</a></span>;<br/>
<span class="kw">thus </span><a NAME="E4:23_1_1"/>
<font color="Maroon" title="c2">p</font> is  <a href="polynom5.html#V1" title="POLYNOM5:attr.1">with_roots</a> 
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E3:23_1_1"><span class="lab"><font color="Green" title="E14">A</font></span></a></span>; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> verum</span><br/>


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