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<div><a class="txt" onmouseover="tooltip.show('hs2',this)" onmouseout="tooltip.hide()" onclick="hs2(this)" href="javascript:()" title="26_1_1_1"><span class="kw">now </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">  not  <a href="field_5.html#K2" title="FIELD_5:func.2">KrRootP</a> <font color="Maroon" title="c2">p</font> <a href="tarski.html#R2" title="TARSKI:pred.2">in</a>  the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c1">F</font></span></a><div class="add"><span class="kw">assume </span><a NAME="E1:26_1_1_1"/>
 <a href="field_5.html#K2" title="FIELD_5:func.2">KrRootP</a> <font color="Maroon" title="c2">p</font> <a href="tarski.html#R2" title="TARSKI:pred.2">in</a>  the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</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"> contradiction</span><br/><span class="kw">then </span><span class="kw">reconsider </span><font color="Maroon" title="c3">o</font> =  <a href="field_5.html#K2" title="FIELD_5:func.2">KrRootP</a> <font color="Maroon" title="c2">p</font> as   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Maroon" title="c1">F</font> ;<br/> <a href="polynom4.html#K2" title="POLYNOM4:func.2">eval</a> (<font color="Maroon" title="c2">p</font>,<font color="Maroon" title="c3">o</font>) = 
 <a href="algnum_1.html#K1" title="ALGNUM_1:func.1">Ext_eval</a> (<font color="Maroon" title="c2">p</font>,<span class="p1">(<span class="default"><a href="field_5.html#K2" title="FIELD_5:func.2">KrRootP</a> <font color="Maroon" title="c2">p</font></span>)</span>)
<span class="kw">by</span> <span class="lab"><a class="ref" href="field_6.html#T10" onmouseover="rs('field_6/T10')" onmouseout="rh()">FIELD_6:10</a></span>
<br/>.= 
 <a href="struct_0.html#K4" title="STRUCT_0:func.4">0.</a> <font color="Maroon" title="c1">F</font>
<span class="kw">by</span> <span class="lab"><a class="ref" href="field_5.html#T17" onmouseover="rs('field_5/T17')" onmouseout="rh()">FIELD_5:17</a></span>
;<br/><a NAME="E4:26_1_1_1"/><span class="kw">then </span>
<font color="Maroon" title="c3">o</font> <a href="polynom5.html#R1" title="POLYNOM5:pred.1">is_a_root_of</a> <font color="Maroon" title="c2">p</font>
 ;<br/><a NAME="E5:26_1_1_1"/><span class="kw">then </span>
<font color="Maroon" title="c2">p</font> is  <a href="polynom5.html#V1" title="POLYNOM5:attr.1">with_roots</a> 
 ;<br/><span class="kw">hence </span><a NAME="E6:26_1_1_1"/>
contradiction
 ; <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><span class="kw">end;</span></div>
<span class="kw">hence </span><a NAME="E2:26_1_1"/>
(  not  <a href="field_5.html#K2" title="FIELD_5:func.2">KrRootP</a> <font color="Maroon" title="c2">p</font> is  <a href="struct_0.html#V9" title="STRUCT_0:attr.9">zero</a>  &amp;  not  <a href="field_5.html#K2" title="FIELD_5:func.2">KrRootP</a> <font color="Maroon" title="c2">p</font> is <font color="Maroon" title="c1">F</font> <a href="field_7.html#V1" title="FIELD_7:attr.1">-membered</a>  )
 <span class="kw">by</span> <span class="lab"><a class="ref" href="field_7.html#D5" onmouseover="rs('field_7/D5')" onmouseout="rh()">FIELD_7: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"> verum</span><br/>


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