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

<a NAME="E1:100"/><span class="lab"><font color="Green" title="E49">J</font></span>: 
 <a href="ring_3.html#K3" title="RING_3:func.3">Char</a> <span class="p1">(<span class="default"><a href="ring_3.html#NK1" title="RING_3:NK.1">Z/</a> 2</span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 2
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="ring_3.html#D6" onmouseover="rs('ring_3/D6')" onmouseout="rh()">RING_3:def 6</a></span>;<br/>
<a NAME="E2:100"/>
 <a href="ring_3.html#NK1" title="RING_3:NK.1">Z/</a> 2 is    <a href="c0sp1.html#M1" title="C0SP1:mode.1">Subring</a> of  <a href="field_2.html#K7" title="FIELD_2:func.7">embField</a> <span class="p1">(<span class="default"><a href="field_5.html#K1" title="FIELD_5:func.1">canHomP</a> <a href="field_9.html#K11" title="FIELD_9:func.11">X^2+X+1</a></span>)</span>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="field_4.html#D1" onmouseover="rs('field_4/D1')" onmouseout="rh()">FIELD_4:def 1</a></span>;<br/>
<a NAME="E3:100"/><span class="kw">then </span><span class="lab"><font color="Green" title="E50">I</font></span>: 
 <a href="ring_3.html#K3" title="RING_3:func.3">Char</a> <span class="p1">(<span class="default"><a href="field_2.html#K7" title="FIELD_2:func.7">embField</a> <span class="p2">(<span class="default"><a href="field_5.html#K1" title="FIELD_5:func.1">canHomP</a> <a href="field_9.html#K11" title="FIELD_9:func.11">X^2+X+1</a></span>)</span></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 2
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:100"><span class="lab"><font color="Green" title="E49">J</font></span></a>, <a class="ref" href="ring_3.html#T89" onmouseover="rs('ring_3/T89')" onmouseout="rh()">RING_3:89</a></span>;<br/>
<span class="lab"><font color="Green" title="E51">H</font></span>: 2 <a href="ring_3.html#K1" title="RING_3:func.1">'*'</a> <a href="field_9.html#K14" title="FIELD_9:func.14">alpha</a> = 
2 <a href="ring_3.html#K1" title="RING_3:func.1">'*'</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="struct_0.html#K5" title="STRUCT_0:func.5">1.</a> <span class="p3">(<span class="default"><a href="field_2.html#K7" title="FIELD_2:func.7">embField</a> <span class="p4">(<span class="default"><a href="field_5.html#K1" title="FIELD_5:func.1">canHomP</a> <a href="field_9.html#K11" title="FIELD_9:func.11">X^2+X+1</a></span>)</span></span>)</span></span>)</span> <a href="algstr_0.html#K6" title="ALGSTR_0:func.6">*</a> <a href="field_9.html#K14" title="FIELD_9:func.14">alpha</a></span>)</span>

<br/>.= 
<span class="p1">(<span class="default">2 <a href="ring_3.html#K1" title="RING_3:func.1">'*'</a> <span class="p2">(<span class="default"><a href="struct_0.html#K5" title="STRUCT_0:func.5">1.</a> <span class="p3">(<span class="default"><a href="field_2.html#K7" title="FIELD_2:func.7">embField</a> <span class="p4">(<span class="default"><a href="field_5.html#K1" title="FIELD_5:func.1">canHomP</a> <a href="field_9.html#K11" title="FIELD_9:func.11">X^2+X+1</a></span>)</span></span>)</span></span>)</span></span>)</span> <a href="algstr_0.html#K6" title="ALGSTR_0:func.6">*</a> <a href="field_9.html#K14" title="FIELD_9:func.14">alpha</a>
<span class="kw">by</span> <span class="lab"><a class="ref" href="realalg2.html#T5" onmouseover="rs('realalg2/T5')" onmouseout="rh()">REALALG2:5</a></span>
<br/>.= 
<span class="p1">(<span class="default"><a href="struct_0.html#K4" title="STRUCT_0:func.4">0.</a> <span class="p2">(<span class="default"><a href="field_2.html#K7" title="FIELD_2:func.7">embField</a> <span class="p3">(<span class="default"><a href="field_5.html#K1" title="FIELD_5:func.1">canHomP</a> <a href="field_9.html#K11" title="FIELD_9:func.11">X^2+X+1</a></span>)</span></span>)</span></span>)</span> <a href="algstr_0.html#K6" title="ALGSTR_0:func.6">*</a> <a href="field_9.html#K14" title="FIELD_9:func.14">alpha</a>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E3:100"><span class="lab"><font color="Green" title="E50">I</font></span></a>, <a class="ref" href="realalg2.html#T24" onmouseover="rs('realalg2/T24')" onmouseout="rh()">REALALG2:24</a></span>
;<br/>
<a NAME="E5:100"/><span class="kw">then </span>
<a href="field_9.html#K14" title="FIELD_9:func.14">alpha</a> <a href="rlvect_1.html#K3" title="RLVECT_1:func.3">+</a> <a href="field_9.html#K14" title="FIELD_9:func.14">alpha</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="field_2.html#K7" title="FIELD_2:func.7">embField</a> <span class="p2">(<span class="default"><a href="field_5.html#K1" title="FIELD_5:func.1">canHomP</a> <a href="field_9.html#K11" title="FIELD_9:func.11">X^2+X+1</a></span>)</span></span>)</span>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="ring_5.html#T2" onmouseover="rs('ring_5/T2')" onmouseout="rh()">RING_5:2</a></span>;<br/>
<span class="kw">then </span><span class="p1">(<span class="default"><a href="struct_0.html#K4" title="STRUCT_0:func.4">0.</a> <span class="p2">(<span class="default"><a href="field_2.html#K7" title="FIELD_2:func.7">embField</a> <span class="p3">(<span class="default"><a href="field_5.html#K1" title="FIELD_5:func.1">canHomP</a> <a href="field_9.html#K11" title="FIELD_9:func.11">X^2+X+1</a></span>)</span></span>)</span></span>)</span> <a href="algstr_0.html#K5" title="ALGSTR_0:func.5">-</a> <a href="field_9.html#K14" title="FIELD_9:func.14">alpha</a> = 
<a href="field_9.html#K14" title="FIELD_9:func.14">alpha</a> <a href="rlvect_1.html#K3" title="RLVECT_1:func.3">+</a> <span class="p1">(<span class="default"><a href="field_9.html#K14" title="FIELD_9:func.14">alpha</a> <a href="algstr_0.html#K5" title="ALGSTR_0:func.5">-</a> <a href="field_9.html#K14" title="FIELD_9:func.14">alpha</a></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="ref" href="rlvect_1.html#D3" onmouseover="rs('rlvect_1/D3')" onmouseout="rh()">RLVECT_1:def 3</a></span>
<br/>.= 
<a href="field_9.html#K14" title="FIELD_9:func.14">alpha</a> <a href="rlvect_1.html#K3" title="RLVECT_1:func.3">+</a> <span class="p1">(<span class="default"><a href="struct_0.html#K4" title="STRUCT_0:func.4">0.</a> <span class="p2">(<span class="default"><a href="field_2.html#K7" title="FIELD_2:func.7">embField</a> <span class="p3">(<span class="default"><a href="field_5.html#K1" title="FIELD_5:func.1">canHomP</a> <a href="field_9.html#K11" title="FIELD_9:func.11">X^2+X+1</a></span>)</span></span>)</span></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="ref" href="rlvect_1.html#T15" onmouseover="rs('rlvect_1/T15')" onmouseout="rh()">RLVECT_1:15</a></span>
;<br/>
<span class="kw">hence </span><a NAME="E7:100"/><span class="lab"><font color="Green" title="E52">H3</font></span>: 
 <a href="algstr_0.html#K4" title="ALGSTR_0:func.4">-</a> <a href="field_9.html#K14" title="FIELD_9:func.14">alpha</a> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="field_9.html#K14" title="FIELD_9:func.14">alpha</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"> ( <a href="field_9.html#K14" title="FIELD_9:func.14">alpha</a> <a href="algstr_0.html#K9" title="ALGSTR_0:func.9">"</a>  <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="field_9.html#K15" title="FIELD_9:func.15">alpha-1</a>  &amp; <a href="field_9.html#K14" title="FIELD_9:func.14">alpha</a> <a href="algstr_0.html#K9" title="ALGSTR_0:func.9">"</a>  <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a>  <a href="field_9.html#K14" title="FIELD_9:func.14">alpha</a>  )</span><br/>

<span class="kw">thus </span><a NAME="E8:100"/>
<a href="field_9.html#K14" title="FIELD_9:func.14">alpha</a> <a href="algstr_0.html#K9" title="ALGSTR_0:func.9">"</a>  <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="field_9.html#K15" title="FIELD_9:func.15">alpha-1</a> 
 <span class="kw">by</span> <span class="lab"><a class="txt" href="field_9.html#E73"><span class="lab"><font color="Green" title="E47">lemZ2</font></span></a>, <a class="txt" href="#E7:100"><span class="lab"><font color="Green" title="E52">H3</font></span></a>, <a class="ref" href="rlvect_1.html#T31" onmouseover="rs('rlvect_1/T31')" onmouseout="rh()">RLVECT_1:31</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"> <a href="field_9.html#K14" title="FIELD_9:func.14">alpha</a> <a href="algstr_0.html#K9" title="ALGSTR_0:func.9">"</a>  <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a>  <a href="field_9.html#K14" title="FIELD_9:func.14">alpha</a> </span><br/>

<div><a class="txt" onmouseover="tooltip.show('hs2',this)" onmouseout="tooltip.hide()" onclick="hs2(this)" href="javascript:()" title="100_3"><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_9.html#K14" title="FIELD_9:func.14">alpha</a> <a href="algstr_0.html#K9" title="ALGSTR_0:func.9">"</a>  <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="field_9.html#K14" title="FIELD_9:func.14">alpha</a> </span></a><div class="add"><span class="kw">assume </span><a NAME="E1:100_3"/>
<a href="field_9.html#K14" title="FIELD_9:func.14">alpha</a> <a href="algstr_0.html#K9" title="ALGSTR_0:func.9">"</a>  <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="field_9.html#K14" title="FIELD_9:func.14">alpha</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"> contradiction</span><br/><a NAME="E2:100_3"/><span class="kw">then </span>
 <a href="field_9.html#K14" title="FIELD_9:func.14">alpha</a>  <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="algstr_0.html#K4" title="ALGSTR_0:func.4">-</a> <a href="field_9.html#K14" title="FIELD_9:func.14">alpha</a></span>)</span> <a href="rlvect_1.html#K3" title="RLVECT_1:func.3">+</a> <span class="p1">(<span class="default"><a href="algstr_0.html#K4" title="ALGSTR_0:func.4">-</a> <span class="p2">(<span class="default"><a href="struct_0.html#K5" title="STRUCT_0:func.5">1.</a> <span class="p3">(<span class="default"><a href="field_2.html#K7" title="FIELD_2:func.7">embField</a> <span class="p4">(<span class="default"><a href="field_5.html#K1" title="FIELD_5:func.1">canHomP</a> <a href="field_9.html#K11" title="FIELD_9:func.11">X^2+X+1</a></span>)</span></span>)</span></span>)</span></span>)</span>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="rlvect_1.html#T31" onmouseover="rs('rlvect_1/T31')" onmouseout="rh()">RLVECT_1:31</a>, <a class="txt" href="field_9.html#E73"><span class="lab"><font color="Green" title="E47">lemZ2</font></span></a></span>;<br/><span class="kw">then </span><a href="field_9.html#K14" title="FIELD_9:func.14">alpha</a> <a href="rlvect_1.html#K3" title="RLVECT_1:func.3">+</a> <a href="field_9.html#K14" title="FIELD_9:func.14">alpha</a> = 
<span class="p1">(<span class="default"><a href="field_9.html#K14" title="FIELD_9:func.14">alpha</a> <a href="rlvect_1.html#K3" title="RLVECT_1:func.3">+</a> <span class="p2">(<span class="default"><a href="algstr_0.html#K4" title="ALGSTR_0:func.4">-</a> <a href="field_9.html#K14" title="FIELD_9:func.14">alpha</a></span>)</span></span>)</span> <a href="rlvect_1.html#K3" title="RLVECT_1:func.3">+</a> <span class="p1">(<span class="default"><a href="algstr_0.html#K4" title="ALGSTR_0:func.4">-</a> <span class="p2">(<span class="default"><a href="struct_0.html#K5" title="STRUCT_0:func.5">1.</a> <span class="p3">(<span class="default"><a href="field_2.html#K7" title="FIELD_2:func.7">embField</a> <span class="p4">(<span class="default"><a href="field_5.html#K1" title="FIELD_5:func.1">canHomP</a> <a href="field_9.html#K11" title="FIELD_9:func.11">X^2+X+1</a></span>)</span></span>)</span></span>)</span></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="ref" href="rlvect_1.html#D3" onmouseover="rs('rlvect_1/D3')" onmouseout="rh()">RLVECT_1:def 3</a></span>
<br/>.= 
<span class="p1">(<span class="default"><a href="struct_0.html#K4" title="STRUCT_0:func.4">0.</a> <span class="p2">(<span class="default"><a href="field_2.html#K7" title="FIELD_2:func.7">embField</a> <span class="p3">(<span class="default"><a href="field_5.html#K1" title="FIELD_5:func.1">canHomP</a> <a href="field_9.html#K11" title="FIELD_9:func.11">X^2+X+1</a></span>)</span></span>)</span></span>)</span> <a href="rlvect_1.html#K3" title="RLVECT_1:func.3">+</a> <span class="p1">(<span class="default"><a href="algstr_0.html#K4" title="ALGSTR_0:func.4">-</a> <span class="p2">(<span class="default"><a href="struct_0.html#K5" title="STRUCT_0:func.5">1.</a> <span class="p3">(<span class="default"><a href="field_2.html#K7" title="FIELD_2:func.7">embField</a> <span class="p4">(<span class="default"><a href="field_5.html#K1" title="FIELD_5:func.1">canHomP</a> <a href="field_9.html#K11" title="FIELD_9:func.11">X^2+X+1</a></span>)</span></span>)</span></span>)</span></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="ref" href="rlvect_1.html#T5" onmouseover="rs('rlvect_1/T5')" onmouseout="rh()">RLVECT_1:5</a></span>
;<br/><a NAME="E4:100_3"/><span class="kw">then </span>
 <a href="algstr_0.html#K4" title="ALGSTR_0:func.4">-</a> <span class="p1">(<span class="default"><a href="struct_0.html#K4" title="STRUCT_0:func.4">0.</a> <span class="p2">(<span class="default"><a href="field_2.html#K7" title="FIELD_2:func.7">embField</a> <span class="p3">(<span class="default"><a href="field_5.html#K1" title="FIELD_5:func.1">canHomP</a> <a href="field_9.html#K11" title="FIELD_9:func.11">X^2+X+1</a></span>)</span></span>)</span></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="algstr_0.html#K4" title="ALGSTR_0:func.4">-</a> <span class="p1">(<span class="default"><a href="algstr_0.html#K4" title="ALGSTR_0:func.4">-</a> <span class="p2">(<span class="default"><a href="struct_0.html#K5" title="STRUCT_0:func.5">1.</a> <span class="p3">(<span class="default"><a href="field_2.html#K7" title="FIELD_2:func.7">embField</a> <span class="p4">(<span class="default"><a href="field_5.html#K1" title="FIELD_5:func.1">canHomP</a> <a href="field_9.html#K11" title="FIELD_9:func.11">X^2+X+1</a></span>)</span></span>)</span></span>)</span></span>)</span>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E4:100"><span class="lab"><font color="Green" title="E51">H</font></span></a>, <a class="ref" href="ring_5.html#T2" onmouseover="rs('ring_5/T2')" onmouseout="rh()">RING_5:2</a></span>;<br/><span class="kw">hence </span><a NAME="E5:100_3"/>
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="E10:100"/>
<a href="field_9.html#K14" title="FIELD_9:func.14">alpha</a> <a href="algstr_0.html#K9" title="ALGSTR_0:func.9">"</a>  <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a>  <a href="field_9.html#K14" title="FIELD_9:func.14">alpha</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/>


</div>
