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<a NAME="E1:85"/><span class="lab"><font color="Green" title="E41">H1</font></span>: 
( <a href="field_9.html#K8" title="FIELD_9:func.8">X^2</a> <a href="nat_1.html#K8" title="NAT_1:func.8">.</a> <a href="numbers.html#K5" title="NUMBERS:func.5">0</a> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="struct_0.html#K4" title="STRUCT_0:func.4">0.</a> <span class="p1">(<span class="default"><a href="ring_3.html#NK1" title="RING_3:NK.1">Z/</a> 2</span>)</span> &amp; <a href="field_9.html#K8" title="FIELD_9:func.8">X^2</a> <a href="nat_1.html#K8" title="NAT_1:func.8">.</a> 1 <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="struct_0.html#K4" title="STRUCT_0:func.4">0.</a> <span class="p1">(<span class="default"><a href="ring_3.html#NK1" title="RING_3:NK.1">Z/</a> 2</span>)</span> )
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="field_9.html#E22"><span class="lab"><font color="Green" title="E15">qua1</font></span></a></span>;<br/>
<a NAME="E2:85"/><span class="lab"><font color="Green" title="E42">H2</font></span>: 
( <a href="field_9.html#K9" title="FIELD_9:func.9">X^2+1</a> <a href="nat_1.html#K8" title="NAT_1:func.8">.</a> <a href="numbers.html#K5" title="NUMBERS:func.5">0</a> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="struct_0.html#K5" title="STRUCT_0:func.5">1.</a> <span class="p1">(<span class="default"><a href="ring_3.html#NK1" title="RING_3:NK.1">Z/</a> 2</span>)</span> &amp; <a href="field_9.html#K9" title="FIELD_9:func.9">X^2+1</a> <a href="nat_1.html#K8" title="NAT_1:func.8">.</a> 1 <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="struct_0.html#K4" title="STRUCT_0:func.4">0.</a> <span class="p1">(<span class="default"><a href="ring_3.html#NK1" title="RING_3:NK.1">Z/</a> 2</span>)</span> )
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="field_9.html#E22"><span class="lab"><font color="Green" title="E15">qua1</font></span></a></span>;<br/>
<a NAME="E3:85"/><span class="lab"><font color="Green" title="E43">H3</font></span>: 
( <a href="field_9.html#K10" title="FIELD_9:func.10">X^2+X</a> <a href="nat_1.html#K8" title="NAT_1:func.8">.</a> <a href="numbers.html#K5" title="NUMBERS:func.5">0</a> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="struct_0.html#K4" title="STRUCT_0:func.4">0.</a> <span class="p1">(<span class="default"><a href="ring_3.html#NK1" title="RING_3:NK.1">Z/</a> 2</span>)</span> &amp; <a href="field_9.html#K10" title="FIELD_9:func.10">X^2+X</a> <a href="nat_1.html#K8" title="NAT_1:func.8">.</a> 1 <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="struct_0.html#K5" title="STRUCT_0:func.5">1.</a> <span class="p1">(<span class="default"><a href="ring_3.html#NK1" title="RING_3:NK.1">Z/</a> 2</span>)</span> )
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="field_9.html#E22"><span class="lab"><font color="Green" title="E15">qua1</font></span></a></span>;<br/>
<a NAME="E4:85"/><span class="lab"><font color="Green" title="E44">A1</font></span>: 
 <a href="field_9.html#K8" title="FIELD_9:func.8">X^2</a>  <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a>  <a href="field_9.html#K9" title="FIELD_9:func.9">X^2+1</a> 
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:85"><span class="lab"><font color="Green" title="E41">H1</font></span></a>, <a class="txt" href="field_9.html#E22"><span class="lab"><font color="Green" title="E15">qua1</font></span></a></span>;<br/>
<a NAME="E5:85"/><span class="lab"><font color="Green" title="E45">A2</font></span>: 
 <a href="field_9.html#K8" title="FIELD_9:func.8">X^2</a>  <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a>  <a href="field_9.html#K10" title="FIELD_9:func.10">X^2+X</a> 
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:85"><span class="lab"><font color="Green" title="E41">H1</font></span></a>, <a class="txt" href="field_9.html#E22"><span class="lab"><font color="Green" title="E15">qua1</font></span></a></span>;<br/>
<a NAME="E6:85"/><span class="lab"><font color="Green" title="E46">A3</font></span>: 
 <a href="field_9.html#K8" title="FIELD_9:func.8">X^2</a>  <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a>  <a href="field_9.html#K11" title="FIELD_9:func.11">X^2+X+1</a> 
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:85"><span class="lab"><font color="Green" title="E41">H1</font></span></a>, <a class="txt" href="field_9.html#E22"><span class="lab"><font color="Green" title="E15">qua1</font></span></a></span>;<br/>
<a NAME="E7:85"/><span class="lab"><font color="Green" title="E47">A4</font></span>: 
 <a href="field_9.html#K9" title="FIELD_9:func.9">X^2+1</a>  <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a>  <a href="field_9.html#K10" title="FIELD_9:func.10">X^2+X</a> 
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:85"><span class="lab"><font color="Green" title="E42">H2</font></span></a>, <a class="txt" href="field_9.html#E22"><span class="lab"><font color="Green" title="E15">qua1</font></span></a></span>;<br/>
<a NAME="E8:85"/><span class="lab"><font color="Green" title="E48">A5</font></span>: 
 <a href="field_9.html#K9" title="FIELD_9:func.9">X^2+1</a>  <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a>  <a href="field_9.html#K11" title="FIELD_9:func.11">X^2+X+1</a> 
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:85"><span class="lab"><font color="Green" title="E42">H2</font></span></a>, <a class="txt" href="field_9.html#E22"><span class="lab"><font color="Green" title="E15">qua1</font></span></a></span>;<br/>
<a NAME="E9:85"/>
 <a href="field_9.html#K10" title="FIELD_9:func.10">X^2+X</a>  <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a>  <a href="field_9.html#K11" title="FIELD_9:func.11">X^2+X+1</a> 
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E3:85"><span class="lab"><font color="Green" title="E43">H3</font></span></a>, <a class="txt" href="field_9.html#E22"><span class="lab"><font color="Green" title="E15">qua1</font></span></a></span>;<br/>
<span class="kw">hence </span><a NAME="E10:85"/>
 <a href="card_1.html#K1" title="CARD_1:func.1">card</a> <span class="p1"> { <span class="default"> <font color="Olive" title="b1">p</font> where <font color="Olive" title="b1">p</font> is   <a href="field_9.html#V1" title="FIELD_9:attr.1">quadratic</a>  <a href="polynom3.html#NM1" title="POLYNOM3:NM.1">Polynomial</a> of <span class="p1">(<span class="default"><a href="ring_3.html#NK1" title="RING_3:NK.1">Z/</a> 2</span>)</span> : verum </span> } </span>  <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 4
 <span class="kw">by</span> <span class="lab"><a class="ref" href="field_9.html#T36" target="_self" onmouseover="rs('field_9/T36')" onmouseout="rh()">pz2</a>, <a class="txt" href="#E4:85"><span class="lab"><font color="Green" title="E44">A1</font></span></a>, <a class="txt" href="#E5:85"><span class="lab"><font color="Green" title="E45">A2</font></span></a>, <a class="txt" href="#E6:85"><span class="lab"><font color="Green" title="E46">A3</font></span></a>, <a class="txt" href="#E7:85"><span class="lab"><font color="Green" title="E47">A4</font></span></a>, <a class="txt" href="#E8:85"><span class="lab"><font color="Green" title="E48">A5</font></span></a>, <a class="ref" href="card_2.html#T59" onmouseover="rs('card_2/T59')" onmouseout="rh()">CARD_2:59</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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