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<b>let </b><font color="Maroon" title="c1">a</font>, <font color="Maroon" title="c2">b</font>, <font color="Maroon" title="c3">c</font> be    <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a> ;<br/>

<a NAME="E1:8"/><i><font color="Green" title="E5">A1</font></i>: 
(  <a href="relat_1.html#K1" title="RELAT_1:func.1">dom</a> <span class="p1">(<span class="default"><a href="numbers.html#K5" title="NUMBERS:func.5">NAT</a>  <a href="funcop_1.html#K2" title="FUNCOP_1:func.2">--&gt;</a> <font color="Maroon" title="c3">c</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="numbers.html#K5" title="NUMBERS:func.5">NAT</a>  &amp;  <a href="relat_1.html#K2" title="RELAT_1:func.2">rng</a> <span class="p1">(<span class="default"><a href="numbers.html#K5" title="NUMBERS:func.5">NAT</a>  <a href="funcop_1.html#K2" title="FUNCOP_1:func.2">--&gt;</a> <font color="Maroon" title="c3">c</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1"><a href="tarski.html#K1" title="TARSKI:func.1">{</a><span class="default"><font color="Maroon" title="c3">c</font></span><a href="tarski.html#K1" title="TARSKI:func.1">}</a></span> &amp;  <a href="relat_1.html#K1" title="RELAT_1:func.1">dom</a> <span class="p1">(<span class="default">0,1 <a href="funct_4.html#K4" title="FUNCT_4:func.4">--&gt;</a> <font color="Maroon" title="c1">a</font>,<font color="Maroon" title="c2">b</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1"><a href="tarski.html#K2" title="TARSKI:func.2">{</a><span class="default">0,1</span><a href="tarski.html#K2" title="TARSKI:func.2">}</a></span> &amp;  <a href="relat_1.html#K2" title="RELAT_1:func.2">rng</a> <span class="p1">(<span class="default">0,1 <a href="funct_4.html#K4" title="FUNCT_4:func.4">--&gt;</a> <font color="Maroon" title="c1">a</font>,<font color="Maroon" title="c2">b</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1"><a href="tarski.html#K2" title="TARSKI:func.2">{</a><span class="default"><font color="Maroon" title="c1">a</font>,<font color="Maroon" title="c2">b</font></span><a href="tarski.html#K2" title="TARSKI:func.2">}</a></span> )
 
<b>by </b><i><a class="ref" href="funcop_1.html#T14" title="FUNCOP_1:th.14">FUNCOP_1:14</a>, <a class="ref" href="funcop_1.html#T19" title="FUNCOP_1:th.19">FUNCOP_1:19</a>, <a class="ref" href="funct_4.html#T65" title="FUNCT_4:th.65">FUNCT_4:65</a>, <a class="ref" href="funct_4.html#T67" title="FUNCT_4:th.67">FUNCT_4:67</a></i>;<br/>
<a NAME="E2:8"/><i><font color="Green" title="E6">A2</font></i>: 
( <span class="p1">(<span class="default">0,1 <a href="funct_4.html#K4" title="FUNCT_4:func.4">--&gt;</a> <font color="Maroon" title="c1">a</font>,<font color="Maroon" title="c2">b</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> 0 <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c1">a</font> &amp; <span class="p1">(<span class="default">0,1 <a href="funct_4.html#K4" title="FUNCT_4:func.4">--&gt;</a> <font color="Maroon" title="c1">a</font>,<font color="Maroon" title="c2">b</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> 1 <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c2">b</font> )
 
<b>by </b><i><a class="ref" href="funct_4.html#T66" title="FUNCT_4:th.66">FUNCT_4:66</a></i>;<br/>
<a NAME="E3:8"/>
( 0 <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <span class="p1"><a href="tarski.html#K2" title="TARSKI:func.2">{</a><span class="default">0,1</span><a href="tarski.html#K2" title="TARSKI:func.2">}</a></span> &amp; 1 <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <span class="p1"><a href="tarski.html#K2" title="TARSKI:func.2">{</a><span class="default">0,1</span><a href="tarski.html#K2" title="TARSKI:func.2">}</a></span> )
 
<b>by </b><i><a class="ref" href="tarski.html#D2" title="TARSKI:def.2">TARSKI:def 2</a></i>;<br/>
<a NAME="E4:8"/><b>then </b>
( <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="numbers.html#K5" title="NUMBERS:func.5">NAT</a>  <a href="funcop_1.html#K2" title="FUNCOP_1:func.2">--&gt;</a> <font color="Maroon" title="c3">c</font></span>)</span> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p2">(<span class="default">0,1 <a href="funct_4.html#K4" title="FUNCT_4:func.4">--&gt;</a> <font color="Maroon" title="c1">a</font>,<font color="Maroon" title="c2">b</font></span>)</span></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> 0 <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c1">a</font> &amp; <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="numbers.html#K5" title="NUMBERS:func.5">NAT</a>  <a href="funcop_1.html#K2" title="FUNCOP_1:func.2">--&gt;</a> <font color="Maroon" title="c3">c</font></span>)</span> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p2">(<span class="default">0,1 <a href="funct_4.html#K4" title="FUNCT_4:func.4">--&gt;</a> <font color="Maroon" title="c1">a</font>,<font color="Maroon" title="c2">b</font></span>)</span></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> 1 <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c2">b</font> )
 
<b>by </b><i><a class="txt" href="dynkin.html#E1:8"><i><font color="Green" title="E5">A1</font></i></a>, <a class="txt" href="dynkin.html#E2:8"><i><font color="Green" title="E6">A2</font></i></a>, <a class="ref" href="funct_4.html#T14" title="FUNCT_4:th.14">FUNCT_4:14</a></i>;<br/>
<b>hence </b><a NAME="E5:8"/>
( <span class="p1">(<span class="default"><font color="Maroon" title="c1">a</font>,<font color="Maroon" title="c2">b</font> <a href="dynkin.html#K1" title="DYNKIN:func.1">followed_by</a> <font color="Maroon" title="c3">c</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> 0 <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c1">a</font> &amp; <span class="p1">(<span class="default"><font color="Maroon" title="c1">a</font>,<font color="Maroon" title="c2">b</font> <a href="dynkin.html#K1" title="DYNKIN:func.1">followed_by</a> <font color="Maroon" title="c3">c</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> 1 <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c2">b</font> )
 ;<br/>

<b>let </b><font color="Maroon" title="c4">n</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> ;<br/>

<b>assume </b><a NAME="E6:8"/><i><font color="Green" title="E7">A3</font></i>: 
( <font color="Maroon" title="c4">n</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> 0 &amp; <font color="Maroon" title="c4">n</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> 1 )
 ;<br/>

<a NAME="E7:8"/><i><font color="Green" title="E8">A4</font></i>: 
not <font color="Maroon" title="c4">n</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="relat_1.html#K1" title="RELAT_1:func.1">dom</a> <span class="p1">(<span class="default">0,1 <a href="funct_4.html#K4" title="FUNCT_4:func.4">--&gt;</a> <font color="Maroon" title="c1">a</font>,<font color="Maroon" title="c2">b</font></span>)</span>
 
<b>by </b><i><a class="txt" href="dynkin.html#E1:8"><i><font color="Green" title="E5">A1</font></i></a>, <a class="txt" href="dynkin.html#E6:8"><i><font color="Green" title="E7">A3</font></i></a>, <a class="ref" href="tarski.html#D2" title="TARSKI:def.2">TARSKI:def 2</a></i>;<br/>
<b>thus </b><span class="p1">(<span class="default"><font color="Maroon" title="c1">a</font>,<font color="Maroon" title="c2">b</font> <a href="dynkin.html#K1" title="DYNKIN:func.1">followed_by</a> <font color="Maroon" title="c3">c</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c4">n</font> = 
<span class="p1">(<span class="default"><a href="numbers.html#K5" title="NUMBERS:func.5">NAT</a>  <a href="funcop_1.html#K2" title="FUNCOP_1:func.2">--&gt;</a> <font color="Maroon" title="c3">c</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c4">n</font>
<b>by </b><i><a class="txt" href="dynkin.html#E7:8"><i><font color="Green" title="E8">A4</font></i></a>, <a class="ref" href="funct_4.html#T12" title="FUNCT_4:th.12">FUNCT_4:12</a></i>
<br/>.= 
<font color="Maroon" title="c3">c</font>
<b>by </b><i><a class="ref" href="funcop_1.html#T13" title="FUNCOP_1:th.13">FUNCOP_1:13</a></i>
;<br/>


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