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<a NAME="E1:28_1_1"/>
<font color="Maroon" title="c3">p</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a>  <a href="polynom3.html#K8" title="POLYNOM3:func.8">0_.</a> <font color="Maroon" title="c1">R</font>
 
;<br/>
<a NAME="E2:28_1_1"/><span class="kw">then </span><span class="lab"><font color="Green" title="E13">A</font></span>: 
<font color="Maroon" title="c3">p</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a>  <a href="polynom3.html#K8" title="POLYNOM3:func.8">0_.</a> <font color="Maroon" title="c2">S</font>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="field_4.html#T12" onmouseover="rs('field_4/T12')" onmouseout="rh()">FIELD_4:12</a></span>;<br/>
<a NAME="E3:28_1_1"/>
 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#K12" title="POLYNOM3:func.12">Polynom-Ring</a> <font color="Maroon" title="c1">R</font></span>)</span> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a>  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#K12" title="POLYNOM3:func.12">Polynom-Ring</a> <font color="Maroon" title="c2">S</font></span>)</span>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="field_4.html#T10" onmouseover="rs('field_4/T10')" onmouseout="rh()">FIELD_4:10</a></span>;<br/>
<span class="kw">then </span><span class="kw">reconsider </span><font color="Maroon" title="c4">p1</font> = <font color="Maroon" title="c3">p</font> as   non  <a href="ratfunc1.html#NV1" title="RATFUNC1:NV.1">zero</a>   <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#K12" title="POLYNOM3:func.12">Polynom-Ring</a> <font color="Maroon" title="c2">S</font></span>)</span> <span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:28_1_1"><span class="lab"><font color="Green" title="E13">A</font></span></a>, <a class="ref" href="uproots.html#D5" onmouseover="rs('uproots/D5')" onmouseout="rh()">UPROOTS:def 5</a></span>;<br/>
<a NAME="E5:28_1_1"/>
 <a href="field_4.html#K1" title="FIELD_4:func.1">Roots</a> (<font color="Maroon" title="c2">S</font>,<font color="Maroon" title="c3">p</font>) <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="polynom5.html#K7" title="POLYNOM5:func.7">Roots</a> <font color="Maroon" title="c4">p1</font>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="field_7.html#T13" target="_self" onmouseover="rs('field_7/T13')" onmouseout="rh()">m4</a></span>;<br/>
<span class="kw">hence </span><a NAME="E6:28_1_1"/>
 <a href="field_4.html#K1" title="FIELD_4:func.1">Roots</a> (<font color="Maroon" title="c2">S</font>,<font color="Maroon" title="c3">p</font>) is  <a href="finset_1.html#V1" title="FINSET_1:attr.1">finite</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"> verum</span><br/>


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