<?xml version="1.0"?>
<div class="add">

<span class="kw">let </span><font color="Maroon" title="c2">a</font> be    <a href="ring_4.html#M1" title="RING_4:mode.1">Element</a> of  the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <span class="p1">(<span class="default"><a href="polynom3.html#K13" title="POLYNOM3:func.13">Polynom-Ring</a> <font color="Maroon" title="c1">F</font></span>)</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"> ( <font color="Maroon" title="c2">a</font> is  <a href="gcd_1.html#V1" title="GCD_1:attr.1">unital</a>  implies (  not <font color="Maroon" title="c2">a</font> is  <a href="ratfunc1.html#NV1" title="RATFUNC1:NV.1">zero</a>  &amp; <font color="Maroon" title="c2">a</font> is  <a href="ring_4.html#V3" title="RING_4:attr.3">constant</a>  ) )</span><br/>

<span class="kw">reconsider </span><font color="Maroon" title="c3">p</font> = <font color="Maroon" title="c2">a</font> as   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <span class="p1">(<span class="default"><a href="polynom3.html#K13" title="POLYNOM3:func.13">Polynom-Ring</a> <font color="Maroon" title="c1">F</font></span>)</span> ;<br/>
<span class="kw">assume </span><a NAME="E2:89_2_1"/><span class="lab"><font color="Green" title="E42">AS</font></span>: 
<font color="Maroon" title="c2">a</font> is  <a href="gcd_1.html#V1" title="GCD_1:attr.1">unital</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"> (  not <font color="Maroon" title="c2">a</font> is  <a href="ratfunc1.html#NV1" title="RATFUNC1:NV.1">zero</a>  &amp; <font color="Maroon" title="c2">a</font> is  <a href="ring_4.html#V3" title="RING_4:attr.3">constant</a>  )</span><br/>

<a NAME="E3:89_2_1"/><span class="kw">then </span>
 <a href="hurwitz.html#NK3" title="HURWITZ:NK.3">deg</a> <font color="Maroon" title="c2">a</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="numbers.html#K5" title="NUMBERS:func.5">0</a> 
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="ring_4.html#T36" target="_self" onmouseover="rs('ring_4/T36')" onmouseout="rh()">T88</a></span>;<br/>
<a NAME="E4:89_2_1"/><span class="kw">then </span>
<font color="Maroon" title="c2">a</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a>  <a href="polynom3.html#K9" title="POLYNOM3:func.9">0_.</a> <font color="Maroon" title="c1">F</font>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="hurwitz.html#T20" onmouseover="rs('hurwitz/T20')" onmouseout="rh()">HURWITZ:20</a></span>;<br/>
<span class="kw">hence </span><a NAME="E5:89_2_1"/>
 not <font color="Maroon" title="c2">a</font> is  <a href="ratfunc1.html#NV1" title="RATFUNC1:NV.1">zero</a> 
 <span class="kw">by</span> <span class="lab"><a class="ref" href="uproots.html#D5" onmouseover="rs('uproots/D5')" onmouseout="rh()">UPROOTS:def 5</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"> <font color="Maroon" title="c2">a</font> is  <a href="ring_4.html#V3" title="RING_4:attr.3">constant</a> </span><br/>

<span class="kw">thus </span><a NAME="E6:89_2_1"/>
<font color="Maroon" title="c2">a</font> is  <a href="ring_4.html#V3" title="RING_4:attr.3">constant</a> 
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:89_2_1"><span class="lab"><font color="Green" title="E42">AS</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/>


</div>
