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<span class="kw">let </span><font color="Maroon" title="c1">i1</font>, <font color="Maroon" title="c2">j1</font>, <font color="Maroon" title="c3">i2</font>, <font color="Maroon" title="c4">j2</font> be    <a href="subset_1.html#M2" title="SUBSET_1:mode.2">Element</a> of  <a href="numbers.html#K5" title="NUMBERS:func.5">NAT</a> ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide">  for <font color="Olive" title="b1">G</font> being   <a href="goboard1.html#NM1" title="GOBOARD1:NM.1">Go-board</a>  st <span class="p1"><a href="tarski.html#K4" title="TARSKI:func.4">[</a><span class="default"><font color="Maroon" title="c1">i1</font>,<font color="Maroon" title="c2">j1</font></span><a href="tarski.html#K4" title="TARSKI:func.4">]</a></span> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="matrix_1.html#K2" title="MATRIX_1:func.2">Indices</a> <font color="Olive" title="b1">G</font> &amp; <span class="p1"><a href="tarski.html#K4" title="TARSKI:func.4">[</a><span class="default"><font color="Maroon" title="c3">i2</font>,<font color="Maroon" title="c4">j2</font></span><a href="tarski.html#K4" title="TARSKI:func.4">]</a></span> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="matrix_1.html#K2" title="MATRIX_1:func.2">Indices</a> <font color="Olive" title="b1">G</font> &amp; <font color="Olive" title="b1">G</font> <a href="matrix_1.html#K3" title="MATRIX_1:func.3">*</a> (<font color="Maroon" title="c1">i1</font>,<font color="Maroon" title="c2">j1</font>) <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b1">G</font> <a href="matrix_1.html#K3" title="MATRIX_1:func.3">*</a> (<font color="Maroon" title="c3">i2</font>,<font color="Maroon" title="c4">j2</font>) holds <br/>( <font color="Maroon" title="c1">i1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c3">i2</font> &amp; <font color="Maroon" title="c2">j1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c4">j2</font> )</span><br/><span class="kw">let </span><font color="Maroon" title="c5">G</font> be   <a href="goboard1.html#NM1" title="GOBOARD1:NM.1">Go-board</a>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> ( <span class="p1"><a href="tarski.html#K4" title="TARSKI:func.4">[</a><span class="default"><font color="Maroon" title="c1">i1</font>,<font color="Maroon" title="c2">j1</font></span><a href="tarski.html#K4" title="TARSKI:func.4">]</a></span> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="matrix_1.html#K2" title="MATRIX_1:func.2">Indices</a> <font color="Maroon" title="c5">G</font> &amp; <span class="p1"><a href="tarski.html#K4" title="TARSKI:func.4">[</a><span class="default"><font color="Maroon" title="c3">i2</font>,<font color="Maroon" title="c4">j2</font></span><a href="tarski.html#K4" title="TARSKI:func.4">]</a></span> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="matrix_1.html#K2" title="MATRIX_1:func.2">Indices</a> <font color="Maroon" title="c5">G</font> &amp; <font color="Maroon" title="c5">G</font> <a href="matrix_1.html#K3" title="MATRIX_1:func.3">*</a> (<font color="Maroon" title="c1">i1</font>,<font color="Maroon" title="c2">j1</font>) <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c5">G</font> <a href="matrix_1.html#K3" title="MATRIX_1:func.3">*</a> (<font color="Maroon" title="c3">i2</font>,<font color="Maroon" title="c4">j2</font>) implies ( <font color="Maroon" title="c1">i1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c3">i2</font> &amp; <font color="Maroon" title="c2">j1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c4">j2</font> ) )</span><br/>



<span class="kw">assume </span><span class="kw">that </span><br/><a NAME="E1:37"/><span class="lab"><font color="Green" title="E26">A1</font></span>: 
<span class="p1"><a href="tarski.html#K4" title="TARSKI:func.4">[</a><span class="default"><font color="Maroon" title="c1">i1</font>,<font color="Maroon" title="c2">j1</font></span><a href="tarski.html#K4" title="TARSKI:func.4">]</a></span> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="matrix_1.html#K2" title="MATRIX_1:func.2">Indices</a> <font color="Maroon" title="c5">G</font>
 <span class="kw">and </span><br/><a NAME="E2:37"/><span class="lab"><font color="Green" title="E27">A2</font></span>: 
<span class="p1"><a href="tarski.html#K4" title="TARSKI:func.4">[</a><span class="default"><font color="Maroon" title="c3">i2</font>,<font color="Maroon" title="c4">j2</font></span><a href="tarski.html#K4" title="TARSKI:func.4">]</a></span> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="matrix_1.html#K2" title="MATRIX_1:func.2">Indices</a> <font color="Maroon" title="c5">G</font>
 <span class="kw">and </span><br/><a NAME="E3:37"/><span class="lab"><font color="Green" title="E28">A3</font></span>: 
<font color="Maroon" title="c5">G</font> <a href="matrix_1.html#K3" title="MATRIX_1:func.3">*</a> (<font color="Maroon" title="c1">i1</font>,<font color="Maroon" title="c2">j1</font>) <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c5">G</font> <a href="matrix_1.html#K3" title="MATRIX_1:func.3">*</a> (<font color="Maroon" title="c3">i2</font>,<font color="Maroon" title="c4">j2</font>)
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> ( <font color="Maroon" title="c1">i1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c3">i2</font> &amp; <font color="Maroon" title="c2">j1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c4">j2</font> )</span><br/>

<a NAME="E4:37"/><span class="lab"><font color="Green" title="E29">A4</font></span>: 
1 <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a> <font color="Maroon" title="c1">i1</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:37"><span class="lab"><font color="Green" title="E26">A1</font></span></a>, <a class="ref" href="matrix_1.html#T38" title="MATRIX_1:th.38">MATRIX_1:38</a></span>;<br/>
<a NAME="E5:37"/><span class="lab"><font color="Green" title="E30">A5</font></span>: 
<font color="Maroon" title="c2">j1</font> <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a>  <a href="matrix_1.html#K1" title="MATRIX_1:func.1">width</a> <font color="Maroon" title="c5">G</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:37"><span class="lab"><font color="Green" title="E26">A1</font></span></a>, <a class="ref" href="matrix_1.html#T38" title="MATRIX_1:th.38">MATRIX_1:38</a></span>;<br/>
<a NAME="E6:37"/><span class="lab"><font color="Green" title="E31">A6</font></span>: 
1 <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a> <font color="Maroon" title="c2">j1</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:37"><span class="lab"><font color="Green" title="E26">A1</font></span></a>, <a class="ref" href="matrix_1.html#T38" title="MATRIX_1:th.38">MATRIX_1:38</a></span>;<br/>
<a NAME="E7:37"/><span class="lab"><font color="Green" title="E32">A7</font></span>: 
1 <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a> <font color="Maroon" title="c3">i2</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:37"><span class="lab"><font color="Green" title="E27">A2</font></span></a>, <a class="ref" href="matrix_1.html#T38" title="MATRIX_1:th.38">MATRIX_1:38</a></span>;<br/>
<a NAME="E8:37"/><span class="lab"><font color="Green" title="E33">A8</font></span>: 
<font color="Maroon" title="c1">i1</font> <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a>  <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Maroon" title="c5">G</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:37"><span class="lab"><font color="Green" title="E26">A1</font></span></a>, <a class="ref" href="matrix_1.html#T38" title="MATRIX_1:th.38">MATRIX_1:38</a></span>;<br/>
<a NAME="E9:37"/><span class="lab"><font color="Green" title="E34">A9</font></span>: 
<font color="Maroon" title="c3">i2</font> <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a>  <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Maroon" title="c5">G</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:37"><span class="lab"><font color="Green" title="E27">A2</font></span></a>, <a class="ref" href="matrix_1.html#T38" title="MATRIX_1:th.38">MATRIX_1:38</a></span>;<br/>
<a NAME="E10:37"/><span class="lab"><font color="Green" title="E35">A10</font></span>: 
<font color="Maroon" title="c4">j2</font> <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a>  <a href="matrix_1.html#K1" title="MATRIX_1:func.1">width</a> <font color="Maroon" title="c5">G</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:37"><span class="lab"><font color="Green" title="E27">A2</font></span></a>, <a class="ref" href="matrix_1.html#T38" title="MATRIX_1:th.38">MATRIX_1:38</a></span>;<br/>
<a NAME="E11:37"/><span class="lab"><font color="Green" title="E36">A11</font></span>: 
1 <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a> <font color="Maroon" title="c4">j2</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:37"><span class="lab"><font color="Green" title="E27">A2</font></span></a>, <a class="ref" href="matrix_1.html#T38" title="MATRIX_1:th.38">MATRIX_1:38</a></span>;<br/>
<span class="kw">then </span><span class="lab"><font color="Green" title="E37">A12</font></span>: <span class="p1">(<span class="default"><font color="Maroon" title="c5">G</font> <a href="matrix_1.html#K3" title="MATRIX_1:func.3">*</a> (<font color="Maroon" title="c1">i1</font>,<font color="Maroon" title="c4">j2</font>)</span>)</span> <a href="euclid.html#K18" title="EUCLID:func.18">`2</a>  = 
<span class="p1">(<span class="default"><font color="Maroon" title="c5">G</font> <a href="matrix_1.html#K3" title="MATRIX_1:func.3">*</a> (1,<font color="Maroon" title="c4">j2</font>)</span>)</span> <a href="euclid.html#K18" title="EUCLID:func.18">`2</a> 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E4:37"><span class="lab"><font color="Green" title="E29">A4</font></span></a>, <a class="txt" href="#E8:37"><span class="lab"><font color="Green" title="E33">A8</font></span></a>, <a class="txt" href="#E10:37"><span class="lab"><font color="Green" title="E35">A10</font></span></a>, <a class="ref" href="goboard5.html#T1" title="GOBOARD5:th.1">GOBOARD5:1</a></span>
<br/>.= 
<span class="p1">(<span class="default"><font color="Maroon" title="c5">G</font> <a href="matrix_1.html#K3" title="MATRIX_1:func.3">*</a> (<font color="Maroon" title="c1">i1</font>,<font color="Maroon" title="c2">j1</font>)</span>)</span> <a href="euclid.html#K18" title="EUCLID:func.18">`2</a> 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E3:37"><span class="lab"><font color="Green" title="E28">A3</font></span></a>, <a class="txt" href="#E7:37"><span class="lab"><font color="Green" title="E32">A7</font></span></a>, <a class="txt" href="#E9:37"><span class="lab"><font color="Green" title="E34">A9</font></span></a>, <a class="txt" href="#E11:37"><span class="lab"><font color="Green" title="E36">A11</font></span></a>, <a class="txt" href="#E10:37"><span class="lab"><font color="Green" title="E35">A10</font></span></a>, <a class="ref" href="goboard5.html#T1" title="GOBOARD5:th.1">GOBOARD5:1</a></span>
;<br/>
<span class="lab"><font color="Green" title="E38">A13</font></span>: <span class="p1">(<span class="default"><font color="Maroon" title="c5">G</font> <a href="matrix_1.html#K3" title="MATRIX_1:func.3">*</a> (<font color="Maroon" title="c1">i1</font>,<font color="Maroon" title="c4">j2</font>)</span>)</span> <a href="euclid.html#K17" title="EUCLID:func.17">`1</a>  = 
<span class="p1">(<span class="default"><font color="Maroon" title="c5">G</font> <a href="matrix_1.html#K3" title="MATRIX_1:func.3">*</a> (<font color="Maroon" title="c1">i1</font>,1)</span>)</span> <a href="euclid.html#K17" title="EUCLID:func.17">`1</a> 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E4:37"><span class="lab"><font color="Green" title="E29">A4</font></span></a>, <a class="txt" href="#E8:37"><span class="lab"><font color="Green" title="E33">A8</font></span></a>, <a class="txt" href="#E11:37"><span class="lab"><font color="Green" title="E36">A11</font></span></a>, <a class="txt" href="#E10:37"><span class="lab"><font color="Green" title="E35">A10</font></span></a>, <a class="ref" href="goboard5.html#T2" title="GOBOARD5:th.2">GOBOARD5:2</a></span>
<br/>.= 
<span class="p1">(<span class="default"><font color="Maroon" title="c5">G</font> <a href="matrix_1.html#K3" title="MATRIX_1:func.3">*</a> (<font color="Maroon" title="c1">i1</font>,<font color="Maroon" title="c2">j1</font>)</span>)</span> <a href="euclid.html#K17" title="EUCLID:func.17">`1</a> 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E4:37"><span class="lab"><font color="Green" title="E29">A4</font></span></a>, <a class="txt" href="#E8:37"><span class="lab"><font color="Green" title="E33">A8</font></span></a>, <a class="txt" href="#E6:37"><span class="lab"><font color="Green" title="E31">A6</font></span></a>, <a class="txt" href="#E5:37"><span class="lab"><font color="Green" title="E30">A5</font></span></a>, <a class="ref" href="goboard5.html#T2" title="GOBOARD5:th.2">GOBOARD5:2</a></span>
;<br/>
<span class="kw">assume </span><a NAME="E14:37"/><span class="lab"><font color="Green" title="E39">A14</font></span>: 
(  not <font color="Maroon" title="c1">i1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c3">i2</font> or  not <font color="Maroon" title="c2">j1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c4">j2</font> )
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> contradiction</span><br/>

<div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="37_3"><span class="kw">per </span></a><a class="txt" onclick="hs(this)" href="javascript:()"><span class="kw">cases </span></a><span class="hide"><a NAME="E1:37_3"/>
( <font color="Maroon" title="c1">i1</font> <a href="xxreal_0.html#NR3" title="XXREAL_0:NR.3">&lt;</a> <font color="Maroon" title="c3">i2</font> or <font color="Maroon" title="c1">i1</font> <a href="xxreal_0.html#NR4" title="XXREAL_0:NR.4">&gt;</a> <font color="Maroon" title="c3">i2</font> or <font color="Maroon" title="c2">j1</font> <a href="xxreal_0.html#NR3" title="XXREAL_0:NR.3">&lt;</a> <font color="Maroon" title="c4">j2</font> or <font color="Maroon" title="c2">j1</font> <a href="xxreal_0.html#NR4" title="XXREAL_0:NR.4">&gt;</a> <font color="Maroon" title="c4">j2</font> )
 </span><span class="kw">by</span> <span class="lab"><a class="txt" href="#E14:37"><span class="lab"><font color="Green" title="E39">A14</font></span></a>, <a class="ref" href="xxreal_0.html#T1" title="XXREAL_0:th.1">XXREAL_0:1</a></span>;<br/><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="37_3_1"><span class="kw">suppose </span></a><a NAME="E1:37_3_1"/>
<font color="Maroon" title="c1">i1</font> <a href="xxreal_0.html#NR3" title="XXREAL_0:NR.3">&lt;</a> <font color="Maroon" title="c3">i2</font>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> contradiction</span><br/><div class="add"><span class="kw">hence </span><a NAME="E2:37_3_1"/>
contradiction
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E3:37"><span class="lab"><font color="Green" title="E28">A3</font></span></a>, <a class="txt" href="#E4:37"><span class="lab"><font color="Green" title="E29">A4</font></span></a>, <a class="txt" href="#E9:37"><span class="lab"><font color="Green" title="E34">A9</font></span></a>, <a class="txt" href="#E11:37"><span class="lab"><font color="Green" title="E36">A11</font></span></a>, <a class="txt" href="#E10:37"><span class="lab"><font color="Green" title="E35">A10</font></span></a>, <a class="txt" href="#E13:37"><span class="lab"><font color="Green" title="E38">A13</font></span></a>, <a class="ref" href="goboard5.html#T3" title="GOBOARD5:th.3">GOBOARD5:3</a></span>; <a class="txt" 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><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="37_3_2"><span class="kw">suppose </span></a><a NAME="E1:37_3_2"/>
<font color="Maroon" title="c1">i1</font> <a href="xxreal_0.html#NR4" title="XXREAL_0:NR.4">&gt;</a> <font color="Maroon" title="c3">i2</font>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> contradiction</span><br/><div class="add"><span class="kw">hence </span><a NAME="E2:37_3_2"/>
contradiction
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E3:37"><span class="lab"><font color="Green" title="E28">A3</font></span></a>, <a class="txt" href="#E8:37"><span class="lab"><font color="Green" title="E33">A8</font></span></a>, <a class="txt" href="#E7:37"><span class="lab"><font color="Green" title="E32">A7</font></span></a>, <a class="txt" href="#E11:37"><span class="lab"><font color="Green" title="E36">A11</font></span></a>, <a class="txt" href="#E10:37"><span class="lab"><font color="Green" title="E35">A10</font></span></a>, <a class="txt" href="#E13:37"><span class="lab"><font color="Green" title="E38">A13</font></span></a>, <a class="ref" href="goboard5.html#T3" title="GOBOARD5:th.3">GOBOARD5:3</a></span>; <a class="txt" 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><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="37_3_3"><span class="kw">suppose </span></a><a NAME="E1:37_3_3"/>
<font color="Maroon" title="c2">j1</font> <a href="xxreal_0.html#NR3" title="XXREAL_0:NR.3">&lt;</a> <font color="Maroon" title="c4">j2</font>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> contradiction</span><br/><div class="add"><span class="kw">hence </span><a NAME="E2:37_3_3"/>
contradiction
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E4:37"><span class="lab"><font color="Green" title="E29">A4</font></span></a>, <a class="txt" href="#E8:37"><span class="lab"><font color="Green" title="E33">A8</font></span></a>, <a class="txt" href="#E6:37"><span class="lab"><font color="Green" title="E31">A6</font></span></a>, <a class="txt" href="#E10:37"><span class="lab"><font color="Green" title="E35">A10</font></span></a>, <a class="txt" href="#E12:37"><span class="lab"><font color="Green" title="E37">A12</font></span></a>, <a class="ref" href="goboard5.html#T4" title="GOBOARD5:th.4">GOBOARD5:4</a></span>; <a class="txt" 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><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="37_3_4"><span class="kw">suppose </span></a><a NAME="E1:37_3_4"/>
<font color="Maroon" title="c2">j1</font> <a href="xxreal_0.html#NR4" title="XXREAL_0:NR.4">&gt;</a> <font color="Maroon" title="c4">j2</font>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> contradiction</span><br/><div class="add"><span class="kw">hence </span><a NAME="E2:37_3_4"/>
contradiction
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E4:37"><span class="lab"><font color="Green" title="E29">A4</font></span></a>, <a class="txt" href="#E8:37"><span class="lab"><font color="Green" title="E33">A8</font></span></a>, <a class="txt" href="#E5:37"><span class="lab"><font color="Green" title="E30">A5</font></span></a>, <a class="txt" href="#E11:37"><span class="lab"><font color="Green" title="E36">A11</font></span></a>, <a class="txt" href="#E12:37"><span class="lab"><font color="Green" title="E37">A12</font></span></a>, <a class="ref" href="goboard5.html#T4" title="GOBOARD5:th.4">GOBOARD5:4</a></span>; <a class="txt" 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></div><span class="kw">end;</span></div>

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