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

<b>let </b><font color="Maroon">x1</font> be   <a href="zf_lang.html#NM1">Variable</a>;<br/><b>let </b><font color="Maroon">x2</font> be   <a href="zf_lang.html#NM1">Variable</a>;<br/><b>let </b><font color="Maroon">y1</font> be   <a href="zf_lang.html#NM1">Variable</a>;<br/><b>let </b><font color="Maroon">y2</font> be   <a href="zf_lang.html#NM1">Variable</a>;<br/><b>let </b><font color="Maroon">z1</font> be   <a href="zf_lang.html#NM1">Variable</a>;<br/><b>let </b><font color="Maroon">z2</font> be   <a href="zf_lang.html#NM1">Variable</a>;<br/>











<b>set </b><font color="Maroon">H</font> = <font color="Maroon">x1</font> <a href="zf_lang.html#K4">'='</a> <font color="Maroon">x2</font>;<br/>
<b>set </b><font color="Maroon">Hz</font> = <font color="Maroon">z1</font> <a href="zf_lang.html#K4">'='</a> <font color="Maroon">z2</font>;<br/>
<b>set </b><font color="Maroon">f</font> = <span class="p1">(<span class="default"><font color="Maroon">x1</font> <a href="zf_lang.html#K4">'='</a> <font color="Maroon">x2</font></span>)</span> <a href="zf_lang1.html#K5" target="_self">/</a> <font color="Maroon">y1</font>,<font color="Maroon">y2</font>;<br/>
<a NAME="E1:149"/>
( <font color="Maroon">x1</font> <a href="zf_lang.html#K4">'='</a> <font color="Maroon">x2</font> <a href="zf_lang.html#NR1" target="_self">is_equality</a>  &amp; <font color="Maroon">z1</font> <a href="zf_lang.html#K4">'='</a> <font color="Maroon">z2</font> <a href="zf_lang.html#NR1" target="_self">is_equality</a>  )
 
<b>by </b><i><a class="ref" href="zf_lang.html#T16">ZF_LANG:16</a></i>;<br/>
<a NAME="E2:149"/><b>then </b><i><font color="Green">E46</font></i>: 
( <font color="Maroon">x1</font> <a href="zf_lang.html#K4">'='</a> <font color="Maroon">x2</font> is <a href="zf_lang.html#V7">atomic</a> &amp; <font color="Maroon">z1</font> <a href="zf_lang.html#K4">'='</a> <font color="Maroon">z2</font> is <a href="zf_lang.html#V7">atomic</a> )
 
<b>by </b><i><a class="ref" href="zf_lang.html#D15">ZF_LANG:def 15</a></i>;<br/>
<a NAME="E3:149"/><b>then </b><i><font color="Green">E48</font></i>: 
(  <a href="finseq_1.html#K3">len</a> <span class="p1">(<span class="default"><font color="Maroon">x1</font> <a href="zf_lang.html#K4">'='</a> <font color="Maroon">x2</font></span>)</span> <a href="hidden.html#R1">=</a> 3 &amp;  <a href="finseq_1.html#K3">len</a> <span class="p1">(<span class="default"><font color="Maroon">z1</font> <a href="zf_lang.html#K4">'='</a> <font color="Maroon">z2</font></span>)</span> <a href="hidden.html#R1">=</a> 3 )
 
<b>by </b><i><a class="ref" href="zf_lang.html#T27">ZF_LANG:27</a></i>;<br/>
<a NAME="E4:149"/><b>then </b><i><font color="Green">E51</font></i>: 
 <a href="finseq_1.html#K4">dom</a> <span class="p1">(<span class="default"><font color="Maroon">x1</font> <a href="zf_lang.html#K4">'='</a> <font color="Maroon">x2</font></span>)</span> <a href="hidden.html#R1">=</a> <span class="p1"><a href="enumset1.html#K1">{</a><span class="default">1,2,3</span><a href="enumset1.html#K1">}</a></span>
 
<b>by </b><i><a class="ref" href="finseq_1.html#D3">FINSEQ_1:def 3</a>, <a class="ref" href="finseq_3.html#T1">FINSEQ_3:1</a></i>;<br/>
<a NAME="E5:149"/><i><font color="Green">E52</font></i>: 
(  <a href="zf_lang.html#K18">Var1</a> <span class="p1">(<span class="default"><font color="Maroon">x1</font> <a href="zf_lang.html#K4">'='</a> <font color="Maroon">x2</font></span>)</span> <a href="hidden.html#R1">=</a> <font color="Maroon">x1</font> &amp;  <a href="zf_lang.html#K19">Var2</a> <span class="p1">(<span class="default"><font color="Maroon">x1</font> <a href="zf_lang.html#K4">'='</a> <font color="Maroon">x2</font></span>)</span> <a href="hidden.html#R1">=</a> <font color="Maroon">x2</font> &amp;  <a href="zf_lang.html#K18">Var1</a> <span class="p1">(<span class="default"><font color="Maroon">z1</font> <a href="zf_lang.html#K4">'='</a> <font color="Maroon">z2</font></span>)</span> <a href="hidden.html#R1">=</a> <font color="Maroon">z1</font> &amp;  <a href="zf_lang.html#K19">Var2</a> <span class="p1">(<span class="default"><font color="Maroon">z1</font> <a href="zf_lang.html#K4">'='</a> <font color="Maroon">z2</font></span>)</span> <a href="hidden.html#R1">=</a> <font color="Maroon">z2</font> )
 
<b>by </b><i/>;<br/>
<a NAME="E6:149"/><b>then </b><i><font color="Green">E65</font></i>: 
( <span class="p1">(<span class="default"><font color="Maroon">x1</font> <a href="zf_lang.html#K4">'='</a> <font color="Maroon">x2</font></span>)</span> <a href="funct_1.html#K1">.</a> 1 <a href="hidden.html#R1">=</a> 0 &amp; <span class="p1">(<span class="default"><font color="Maroon">x1</font> <a href="zf_lang.html#K4">'='</a> <font color="Maroon">x2</font></span>)</span> <a href="funct_1.html#K1">.</a> 2 <a href="hidden.html#R1">=</a> <font color="Maroon">x1</font> &amp; <span class="p1">(<span class="default"><font color="Maroon">x1</font> <a href="zf_lang.html#K4">'='</a> <font color="Maroon">x2</font></span>)</span> <a href="funct_1.html#K1">.</a> 3 <a href="hidden.html#R1">=</a> <font color="Maroon">x2</font> &amp; <span class="p1">(<span class="default"><font color="Maroon">z1</font> <a href="zf_lang.html#K4">'='</a> <font color="Maroon">z2</font></span>)</span> <a href="funct_1.html#K1">.</a> 1 <a href="hidden.html#R1">=</a> 0 &amp; <span class="p1">(<span class="default"><font color="Maroon">z1</font> <a href="zf_lang.html#K4">'='</a> <font color="Maroon">z2</font></span>)</span> <a href="funct_1.html#K1">.</a> 2 <a href="hidden.html#R1">=</a> <font color="Maroon">z1</font> &amp; <span class="p1">(<span class="default"><font color="Maroon">z1</font> <a href="zf_lang.html#K4">'='</a> <font color="Maroon">z2</font></span>)</span> <a href="funct_1.html#K1">.</a> 3 <a href="hidden.html#R1">=</a> <font color="Maroon">z2</font> )
 
<b>by </b><i><a class="ref" href="zf_lang1.html#T63" target="_self">Th63</a>, <a class="ref" href="zf_lang.html#T31">ZF_LANG:31</a>, <a class="ref" href="zf_lang.html#T52">ZF_LANG:52</a></i>;<br/>
<b>thus </b><a NAME="E7:149"/>
(  not <span class="p1">(<span class="default"><font color="Maroon">x1</font> <a href="zf_lang.html#K4">'='</a> <font color="Maroon">x2</font></span>)</span> <a href="zf_lang1.html#K5" target="_self">/</a> <font color="Maroon">y1</font>,<font color="Maroon">y2</font> <a href="hidden.html#R1">=</a> <font color="Maroon">z1</font> <a href="zf_lang.html#K4">'='</a> <font color="Maroon">z2</font> or ( <font color="Maroon">x1</font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> <font color="Maroon">y1</font> &amp; <font color="Maroon">x2</font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> <font color="Maroon">y1</font> &amp; <font color="Maroon">z1</font> <a href="hidden.html#R1">=</a> <font color="Maroon">x1</font> &amp; <font color="Maroon">z2</font> <a href="hidden.html#R1">=</a> <font color="Maroon">x2</font> ) or ( <font color="Maroon">x1</font> <a href="hidden.html#R1">=</a> <font color="Maroon">y1</font> &amp; <font color="Maroon">x2</font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> <font color="Maroon">y1</font> &amp; <font color="Maroon">z1</font> <a href="hidden.html#R1">=</a> <font color="Maroon">y2</font> &amp; <font color="Maroon">z2</font> <a href="hidden.html#R1">=</a> <font color="Maroon">x2</font> ) or ( <font color="Maroon">x1</font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> <font color="Maroon">y1</font> &amp; <font color="Maroon">x2</font> <a href="hidden.html#R1">=</a> <font color="Maroon">y1</font> &amp; <font color="Maroon">z1</font> <a href="hidden.html#R1">=</a> <font color="Maroon">x1</font> &amp; <font color="Maroon">z2</font> <a href="hidden.html#R1">=</a> <font color="Maroon">y2</font> ) or ( <font color="Maroon">x1</font> <a href="hidden.html#R1">=</a> <font color="Maroon">y1</font> &amp; <font color="Maroon">x2</font> <a href="hidden.html#R1">=</a> <font color="Maroon">y1</font> &amp; <font color="Maroon">z1</font> <a href="hidden.html#R1">=</a> <font color="Maroon">y2</font> &amp; <font color="Maroon">z2</font> <a href="hidden.html#R1">=</a> <font color="Maroon">y2</font> ) )
 <div><a class="txt" onclick="hs2(this)" href="javascript:()" title="149_1"><b>proof </b></a><div class="add">

<b>assume </b><a NAME="E1:149_1"/><i><font color="Green">E66</font></i>: 
<span class="p1">(<span class="default"><font color="Maroon">x1</font> <a href="zf_lang.html#K4">'='</a> <font color="Maroon">x2</font></span>)</span> <a href="zf_lang1.html#K5" target="_self">/</a> <font color="Maroon">y1</font>,<font color="Maroon">y2</font> <a href="hidden.html#R1">=</a> <font color="Maroon">z1</font> <a href="zf_lang.html#K4">'='</a> <font color="Maroon">z2</font>
 ;<br/>

<div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="149_1_1"><b>per </b></a><a class="txt" onclick="hs(this)" href="javascript:()"><b>cases </b></a><span class="hide"><a NAME="E1:149_1_1"/>
( ( <font color="Maroon">x1</font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> <font color="Maroon">y1</font> &amp; <font color="Maroon">x2</font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> <font color="Maroon">y1</font> ) or ( <font color="Maroon">x1</font> <a href="hidden.html#R1">=</a> <font color="Maroon">y1</font> &amp; <font color="Maroon">x2</font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> <font color="Maroon">y1</font> ) or ( <font color="Maroon">x1</font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> <font color="Maroon">y1</font> &amp; <font color="Maroon">x2</font> <a href="hidden.html#R1">=</a> <font color="Maroon">y1</font> ) or ( <font color="Maroon">x1</font> <a href="hidden.html#R1">=</a> <font color="Maroon">y1</font> &amp; <font color="Maroon">x2</font> <a href="hidden.html#R1">=</a> <font color="Maroon">y1</font> ) )
 </span>;<br/><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="149_1_1_1"><b>case </b></a><a NAME="E1:149_1_1_1"/>
( <font color="Maroon">x1</font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> <font color="Maroon">y1</font> &amp; <font color="Maroon">x2</font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> <font color="Maroon">y1</font> )
 ;<br/><div class="add"><a NAME="E2:149_1_1_1"/><b>then </b>
( <span class="p1">(<span class="default"><font color="Maroon">x1</font> <a href="zf_lang.html#K4">'='</a> <font color="Maroon">x2</font></span>)</span> <a href="funct_1.html#K1">.</a> 2 <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> <font color="Maroon">y1</font> &amp; <span class="p1">(<span class="default"><font color="Maroon">x1</font> <a href="zf_lang.html#K4">'='</a> <font color="Maroon">x2</font></span>)</span> <a href="funct_1.html#K1">.</a> 3 <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> <font color="Maroon">y1</font> &amp; 2 <a href="hidden.html#R2">in</a>  <a href="finseq_1.html#K4">dom</a> <span class="p1">(<span class="default"><font color="Maroon">x1</font> <a href="zf_lang.html#K4">'='</a> <font color="Maroon">x2</font></span>)</span> &amp; 3 <a href="hidden.html#R2">in</a>  <a href="finseq_1.html#K4">dom</a> <span class="p1">(<span class="default"><font color="Maroon">x1</font> <a href="zf_lang.html#K4">'='</a> <font color="Maroon">x2</font></span>)</span> )
 <b>by </b><i><a class="ref" href="zf_lang1.html#T63" target="_self">Th63</a>, <a class="ref" href="zf_lang1.html#T65" target="_self">Th65</a>, <a class="ref" href="zf_lang1.html#T66" target="_self">Th66</a>, <a class="ref" href="enumset1.html#D1">ENUMSET1:def 1</a>, <a class="ref" href="zf_lang.html#T52">ZF_LANG:52</a></i>;<br/><b>hence </b><a NAME="E3:149_1_1_1"/>
( <font color="Maroon">z1</font> <a href="hidden.html#R1">=</a> <font color="Maroon">x1</font> &amp; <font color="Maroon">z2</font> <a href="hidden.html#R1">=</a> <font color="Maroon">x2</font> )
 <b>by </b><i><a class="ref" href="zf_lang1.html#T67" target="_self">Th67</a>, <a class="ref" href="zf_lang1.html#T69" target="_self">Th69</a>, <a class="txt" href="zf_lang1.html#E5:149"><i><font color="Green">E52</font></i></a></i>;<br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="149_1_1_2"><b>case </b></a><a NAME="E1:149_1_1_2"/>
( <font color="Maroon">x1</font> <a href="hidden.html#R1">=</a> <font color="Maroon">y1</font> &amp; <font color="Maroon">x2</font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> <font color="Maroon">y1</font> )
 ;<br/><div class="add"><a NAME="E2:149_1_1_2"/><b>then </b>
( <span class="p1">(<span class="default"><font color="Maroon">x1</font> <a href="zf_lang.html#K4">'='</a> <font color="Maroon">x2</font></span>)</span> <a href="funct_1.html#K1">.</a> 2 <a href="hidden.html#R1">=</a> <font color="Maroon">y1</font> &amp; <span class="p1">(<span class="default"><font color="Maroon">x1</font> <a href="zf_lang.html#K4">'='</a> <font color="Maroon">x2</font></span>)</span> <a href="funct_1.html#K1">.</a> 3 <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> <font color="Maroon">y1</font> &amp; 2 <a href="hidden.html#R2">in</a>  <a href="finseq_1.html#K4">dom</a> <span class="p1">(<span class="default"><font color="Maroon">x1</font> <a href="zf_lang.html#K4">'='</a> <font color="Maroon">x2</font></span>)</span> &amp; 3 <a href="hidden.html#R2">in</a>  <a href="finseq_1.html#K4">dom</a> <span class="p1">(<span class="default"><font color="Maroon">x1</font> <a href="zf_lang.html#K4">'='</a> <font color="Maroon">x2</font></span>)</span> )
 <b>by </b><i><a class="ref" href="zf_lang1.html#T63" target="_self">Th63</a>, <a class="ref" href="zf_lang1.html#T65" target="_self">Th65</a>, <a class="ref" href="zf_lang1.html#T66" target="_self">Th66</a>, <a class="ref" href="enumset1.html#D1">ENUMSET1:def 1</a>, <a class="ref" href="zf_lang.html#T52">ZF_LANG:52</a></i>;<br/><b>hence </b><a NAME="E3:149_1_1_2"/>
( <font color="Maroon">z1</font> <a href="hidden.html#R1">=</a> <font color="Maroon">y2</font> &amp; <font color="Maroon">z2</font> <a href="hidden.html#R1">=</a> <font color="Maroon">x2</font> )
 <b>by </b><i><a class="ref" href="zf_lang1.html#T67" target="_self">Th67</a>, <a class="ref" href="zf_lang1.html#T69" target="_self">Th69</a>, <a class="txt" href="zf_lang1.html#E5:149"><i><font color="Green">E52</font></i></a></i>;<br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="149_1_1_3"><b>case </b></a><a NAME="E1:149_1_1_3"/>
( <font color="Maroon">x1</font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> <font color="Maroon">y1</font> &amp; <font color="Maroon">x2</font> <a href="hidden.html#R1">=</a> <font color="Maroon">y1</font> )
 ;<br/><div class="add"><a NAME="E2:149_1_1_3"/><b>then </b>
( <span class="p1">(<span class="default"><font color="Maroon">x1</font> <a href="zf_lang.html#K4">'='</a> <font color="Maroon">x2</font></span>)</span> <a href="funct_1.html#K1">.</a> 2 <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> <font color="Maroon">y1</font> &amp; <span class="p1">(<span class="default"><font color="Maroon">x1</font> <a href="zf_lang.html#K4">'='</a> <font color="Maroon">x2</font></span>)</span> <a href="funct_1.html#K1">.</a> 3 <a href="hidden.html#R1">=</a> <font color="Maroon">y1</font> &amp; 2 <a href="hidden.html#R2">in</a>  <a href="finseq_1.html#K4">dom</a> <span class="p1">(<span class="default"><font color="Maroon">x1</font> <a href="zf_lang.html#K4">'='</a> <font color="Maroon">x2</font></span>)</span> &amp; 3 <a href="hidden.html#R2">in</a>  <a href="finseq_1.html#K4">dom</a> <span class="p1">(<span class="default"><font color="Maroon">x1</font> <a href="zf_lang.html#K4">'='</a> <font color="Maroon">x2</font></span>)</span> )
 <b>by </b><i><a class="ref" href="zf_lang1.html#T63" target="_self">Th63</a>, <a class="ref" href="zf_lang1.html#T65" target="_self">Th65</a>, <a class="ref" href="zf_lang1.html#T66" target="_self">Th66</a>, <a class="ref" href="enumset1.html#D1">ENUMSET1:def 1</a>, <a class="ref" href="zf_lang.html#T52">ZF_LANG:52</a></i>;<br/><b>hence </b><a NAME="E3:149_1_1_3"/>
( <font color="Maroon">z1</font> <a href="hidden.html#R1">=</a> <font color="Maroon">x1</font> &amp; <font color="Maroon">z2</font> <a href="hidden.html#R1">=</a> <font color="Maroon">y2</font> )
 <b>by </b><i><a class="ref" href="zf_lang1.html#T67" target="_self">Th67</a>, <a class="ref" href="zf_lang1.html#T69" target="_self">Th69</a>, <a class="txt" href="zf_lang1.html#E5:149"><i><font color="Green">E52</font></i></a></i>;<br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="149_1_1_4"><b>case </b></a><a NAME="E1:149_1_1_4"/>
( <font color="Maroon">x1</font> <a href="hidden.html#R1">=</a> <font color="Maroon">y1</font> &amp; <font color="Maroon">x2</font> <a href="hidden.html#R1">=</a> <font color="Maroon">y1</font> )
 ;<br/><div class="add"><a NAME="E2:149_1_1_4"/><b>then </b>
( <span class="p1">(<span class="default"><font color="Maroon">x1</font> <a href="zf_lang.html#K4">'='</a> <font color="Maroon">x2</font></span>)</span> <a href="funct_1.html#K1">.</a> 2 <a href="hidden.html#R1">=</a> <font color="Maroon">y1</font> &amp; <span class="p1">(<span class="default"><font color="Maroon">x1</font> <a href="zf_lang.html#K4">'='</a> <font color="Maroon">x2</font></span>)</span> <a href="funct_1.html#K1">.</a> 3 <a href="hidden.html#R1">=</a> <font color="Maroon">y1</font> &amp; 2 <a href="hidden.html#R2">in</a>  <a href="finseq_1.html#K4">dom</a> <span class="p1">(<span class="default"><font color="Maroon">x1</font> <a href="zf_lang.html#K4">'='</a> <font color="Maroon">x2</font></span>)</span> &amp; 3 <a href="hidden.html#R2">in</a>  <a href="finseq_1.html#K4">dom</a> <span class="p1">(<span class="default"><font color="Maroon">x1</font> <a href="zf_lang.html#K4">'='</a> <font color="Maroon">x2</font></span>)</span> )
 <b>by </b><i><a class="ref" href="zf_lang1.html#T63" target="_self">Th63</a>, <a class="ref" href="zf_lang1.html#T65" target="_self">Th65</a>, <a class="ref" href="zf_lang1.html#T66" target="_self">Th66</a>, <a class="ref" href="enumset1.html#D1">ENUMSET1:def 1</a>, <a class="ref" href="zf_lang.html#T52">ZF_LANG:52</a></i>;<br/><b>hence </b><a NAME="E3:149_1_1_4"/>
( <font color="Maroon">z1</font> <a href="hidden.html#R1">=</a> <font color="Maroon">y2</font> &amp; <font color="Maroon">z2</font> <a href="hidden.html#R1">=</a> <font color="Maroon">y2</font> )
 <b>by </b><i><a class="ref" href="zf_lang1.html#T67" target="_self">Th67</a>, <a class="ref" href="zf_lang1.html#T69" target="_self">Th69</a>, <a class="txt" href="zf_lang1.html#E5:149"><i><font color="Green">E52</font></i></a></i>;<br/></div><b>end;</b></div></div><b>end;</b></div>

</div><b>end;</b></div>

<a NAME="E8:149"/><i><font color="Green">E67</font></i>: 
(  <a href="relat_1.html#K1">dom</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">x1</font> <a href="zf_lang.html#K4">'='</a> <font color="Maroon">x2</font></span>)</span> <a href="zf_lang1.html#K5" target="_self">/</a> <font color="Maroon">y1</font>,<font color="Maroon">y2</font></span>)</span> <a href="hidden.html#R1">=</a>  <a href="finseq_1.html#K4">dom</a> <span class="p1">(<span class="default"><font color="Maroon">x1</font> <a href="zf_lang.html#K4">'='</a> <font color="Maroon">x2</font></span>)</span> &amp;  <a href="finseq_1.html#K4">dom</a> <span class="p1">(<span class="default"><font color="Maroon">x1</font> <a href="zf_lang.html#K4">'='</a> <font color="Maroon">x2</font></span>)</span> <a href="hidden.html#R1">=</a>  <a href="finseq_1.html#K2">Seg</a> 3 &amp;  <a href="finseq_1.html#K4">dom</a> <span class="p1">(<span class="default"><font color="Maroon">z1</font> <a href="zf_lang.html#K4">'='</a> <font color="Maroon">z2</font></span>)</span> <a href="hidden.html#R1">=</a>  <a href="finseq_1.html#K2">Seg</a> 3 )
 
<b>by </b><i><a class="ref" href="zf_lang1.html#T64" target="_self">Th64</a>, <a class="txt" href="zf_lang1.html#E5:149"><i><font color="Green">E52</font></i></a>, <a class="ref" href="finseq_1.html#D3">FINSEQ_1:def 3</a></i>;<br/>
<a NAME="E9:149"/><i><font color="Green">E68</font></i>: 
<font color="Maroon">y1</font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> 0
 
<b>by </b><i><a class="ref" href="zf_lang1.html#T3" target="_self">Th3</a></i>;<br/>
<div><i><font color="Green">E69</font></i>: <a class="txt" onclick="hs2(this)" href="javascript:()" title="149_2"><b>now </b></a><div class="add"><b>assume </b><a NAME="E1:149_2"/><i><font color="Green">E70</font></i>: 
( <font color="Maroon">x1</font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> <font color="Maroon">y1</font> &amp; <font color="Maroon">x2</font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> <font color="Maroon">y1</font> &amp; <font color="Maroon">z1</font> <a href="hidden.html#R1">=</a> <font color="Maroon">x1</font> &amp; <font color="Maroon">z2</font> <a href="hidden.html#R1">=</a> <font color="Maroon">x2</font> )
 ;<br/><div><a class="txt" onclick="hs2(this)" href="javascript:()" title="149_2_1"><b>now </b></a><div class="add"><b>let </b><font color="Maroon">a</font> be    <a href="hidden.html#M1">set</a> ;<br/><b>assume </b><a NAME="E1:149_2_1"/><i><font color="Green">E71</font></i>: 
<font color="Maroon">a</font> <a href="hidden.html#R2">in</a>  <a href="finseq_1.html#K4">dom</a> <span class="p1">(<span class="default"><font color="Maroon">x1</font> <a href="zf_lang.html#K4">'='</a> <font color="Maroon">x2</font></span>)</span>
 ;<br/><a NAME="E2:149_2_1"/><b>then </b>
( <font color="Maroon">a</font> <a href="hidden.html#R1">=</a> 1 or <font color="Maroon">a</font> <a href="hidden.html#R1">=</a> 2 or <font color="Maroon">a</font> <a href="hidden.html#R1">=</a> 3 )
 <b>by </b><i><a class="ref" href="zf_lang1.html#T65" target="_self">Th65</a>, <a class="ref" href="enumset1.html#D1">ENUMSET1:def 1</a></i>;<br/><b>hence </b><a NAME="E3:149_2_1"/>
<span class="p1">(<span class="default"><font color="Maroon">z1</font> <a href="zf_lang.html#K4">'='</a> <font color="Maroon">z2</font></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">a</font> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">x1</font> <a href="zf_lang.html#K4">'='</a> <font color="Maroon">x2</font></span>)</span> <a href="zf_lang1.html#K5" target="_self">/</a> <font color="Maroon">y1</font>,<font color="Maroon">y2</font></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">a</font>
 <b>by </b><i><a class="ref" href="zf_lang1.html#T67" target="_self">Th67</a>, <a class="ref" href="zf_lang1.html#T71" target="_self">Th71</a>, <a class="ref" href="zf_lang1.html#T74" target="_self">Th74</a>, , <a class="txt" href="zf_lang1.html#E5:149"><i><font color="Green">E52</font></i></a></i>;<br/></div><b>end;</b></div><b>hence </b><a NAME="E3:149_2"/>
<span class="p1">(<span class="default"><font color="Maroon">x1</font> <a href="zf_lang.html#K4">'='</a> <font color="Maroon">x2</font></span>)</span> <a href="zf_lang1.html#K5" target="_self">/</a> <font color="Maroon">y1</font>,<font color="Maroon">y2</font> <a href="hidden.html#R1">=</a> <font color="Maroon">z1</font> <a href="zf_lang.html#K4">'='</a> <font color="Maroon">z2</font>
 <b>by </b><i><a class="ref" href="zf_lang1.html#T69" target="_self">Th69</a>, <a class="ref" href="funct_1.html#T9">FUNCT_1:9</a></i>;<br/></div><b>end;</b></div>
<div><i><font color="Green">E72</font></i>: <a class="txt" onclick="hs2(this)" href="javascript:()" title="149_3"><b>now </b></a><div class="add"><b>assume </b><a NAME="E1:149_3"/><i><font color="Green">E93</font></i>: 
( <font color="Maroon">x1</font> <a href="hidden.html#R1">=</a> <font color="Maroon">y1</font> &amp; <font color="Maroon">x2</font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> <font color="Maroon">y1</font> &amp; <font color="Maroon">z1</font> <a href="hidden.html#R1">=</a> <font color="Maroon">y2</font> &amp; <font color="Maroon">z2</font> <a href="hidden.html#R1">=</a> <font color="Maroon">x2</font> )
 ;<br/><div><a class="txt" onclick="hs2(this)" href="javascript:()" title="149_3_1"><b>now </b></a><div class="add"><b>let </b><font color="Maroon">a</font> be    <a href="hidden.html#M1">set</a> ;<br/><b>assume </b><a NAME="E1:149_3_1"/><i><font color="Green">E94</font></i>: 
<font color="Maroon">a</font> <a href="hidden.html#R2">in</a>  <a href="finseq_1.html#K4">dom</a> <span class="p1">(<span class="default"><font color="Maroon">x1</font> <a href="zf_lang.html#K4">'='</a> <font color="Maroon">x2</font></span>)</span>
 ;<br/><a NAME="E2:149_3_1"/><b>then </b>
( <font color="Maroon">a</font> <a href="hidden.html#R1">=</a> 1 or <font color="Maroon">a</font> <a href="hidden.html#R1">=</a> 2 or <font color="Maroon">a</font> <a href="hidden.html#R1">=</a> 3 )
 <b>by </b><i><a class="ref" href="zf_lang1.html#T65" target="_self">Th65</a>, <a class="ref" href="enumset1.html#D1">ENUMSET1:def 1</a></i>;<br/><b>hence </b><a NAME="E3:149_3_1"/>
<span class="p1">(<span class="default"><font color="Maroon">z1</font> <a href="zf_lang.html#K4">'='</a> <font color="Maroon">z2</font></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">a</font> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">x1</font> <a href="zf_lang.html#K4">'='</a> <font color="Maroon">x2</font></span>)</span> <a href="zf_lang1.html#K5" target="_self">/</a> <font color="Maroon">y1</font>,<font color="Maroon">y2</font></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">a</font>
 <b>by </b><i><a class="ref" href="zf_lang1.html#T67" target="_self">Th67</a>, <a class="ref" href="zf_lang1.html#T71" target="_self">Th71</a>, , , <a class="txt" href="zf_lang1.html#E5:149"><i><font color="Green">E52</font></i></a></i>;<br/></div><b>end;</b></div><b>hence </b><a NAME="E3:149_3"/>
<span class="p1">(<span class="default"><font color="Maroon">x1</font> <a href="zf_lang.html#K4">'='</a> <font color="Maroon">x2</font></span>)</span> <a href="zf_lang1.html#K5" target="_self">/</a> <font color="Maroon">y1</font>,<font color="Maroon">y2</font> <a href="hidden.html#R1">=</a> <font color="Maroon">z1</font> <a href="zf_lang.html#K4">'='</a> <font color="Maroon">z2</font>
 <b>by </b><i><a class="ref" href="zf_lang1.html#T69" target="_self">Th69</a>, <a class="ref" href="funct_1.html#T9">FUNCT_1:9</a></i>;<br/></div><b>end;</b></div>
<div><i><font color="Green">E95</font></i>: <a class="txt" onclick="hs2(this)" href="javascript:()" title="149_4"><b>now </b></a><div class="add"><b>assume </b><a NAME="E1:149_4"/><i><font color="Green">E96</font></i>: 
( <font color="Maroon">x1</font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> <font color="Maroon">y1</font> &amp; <font color="Maroon">x2</font> <a href="hidden.html#R1">=</a> <font color="Maroon">y1</font> &amp; <font color="Maroon">z1</font> <a href="hidden.html#R1">=</a> <font color="Maroon">x1</font> &amp; <font color="Maroon">z2</font> <a href="hidden.html#R1">=</a> <font color="Maroon">y2</font> )
 ;<br/><div><a class="txt" onclick="hs2(this)" href="javascript:()" title="149_4_1"><b>now </b></a><div class="add"><b>let </b><font color="Maroon">a</font> be    <a href="hidden.html#M1">set</a> ;<br/><b>assume </b><a NAME="E1:149_4_1"/><i><font color="Green">E97</font></i>: 
<font color="Maroon">a</font> <a href="hidden.html#R2">in</a>  <a href="finseq_1.html#K4">dom</a> <span class="p1">(<span class="default"><font color="Maroon">x1</font> <a href="zf_lang.html#K4">'='</a> <font color="Maroon">x2</font></span>)</span>
 ;<br/><a NAME="E2:149_4_1"/><b>then </b>
( <font color="Maroon">a</font> <a href="hidden.html#R1">=</a> 1 or <font color="Maroon">a</font> <a href="hidden.html#R1">=</a> 2 or <font color="Maroon">a</font> <a href="hidden.html#R1">=</a> 3 )
 <b>by </b><i><a class="ref" href="zf_lang1.html#T65" target="_self">Th65</a>, <a class="ref" href="enumset1.html#D1">ENUMSET1:def 1</a></i>;<br/><b>hence </b><a NAME="E3:149_4_1"/>
<span class="p1">(<span class="default"><font color="Maroon">z1</font> <a href="zf_lang.html#K4">'='</a> <font color="Maroon">z2</font></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">a</font> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">x1</font> <a href="zf_lang.html#K4">'='</a> <font color="Maroon">x2</font></span>)</span> <a href="zf_lang1.html#K5" target="_self">/</a> <font color="Maroon">y1</font>,<font color="Maroon">y2</font></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">a</font>
 <b>by </b><i><a class="ref" href="zf_lang1.html#T67" target="_self">Th67</a>, <a class="ref" href="zf_lang1.html#T71" target="_self">Th71</a>, , <a class="txt" href="zf_lang1.html#E6:149"><i><font color="Green">E65</font></i></a>, <a class="txt" href="zf_lang1.html#E5:149"><i><font color="Green">E52</font></i></a></i>;<br/></div><b>end;</b></div><b>hence </b><a NAME="E3:149_4"/>
<span class="p1">(<span class="default"><font color="Maroon">x1</font> <a href="zf_lang.html#K4">'='</a> <font color="Maroon">x2</font></span>)</span> <a href="zf_lang1.html#K5" target="_self">/</a> <font color="Maroon">y1</font>,<font color="Maroon">y2</font> <a href="hidden.html#R1">=</a> <font color="Maroon">z1</font> <a href="zf_lang.html#K4">'='</a> <font color="Maroon">z2</font>
 <b>by </b><i><a class="ref" href="zf_lang1.html#T69" target="_self">Th69</a>, <a class="ref" href="funct_1.html#T9">FUNCT_1:9</a></i>;<br/></div><b>end;</b></div>
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="149_5"><b>now </b></a><div class="add"><b>assume </b><a NAME="E1:149_5"/><i><font color="Green">E98</font></i>: 
( <font color="Maroon">x1</font> <a href="hidden.html#R1">=</a> <font color="Maroon">y1</font> &amp; <font color="Maroon">x2</font> <a href="hidden.html#R1">=</a> <font color="Maroon">y1</font> &amp; <font color="Maroon">z1</font> <a href="hidden.html#R1">=</a> <font color="Maroon">y2</font> &amp; <font color="Maroon">z2</font> <a href="hidden.html#R1">=</a> <font color="Maroon">y2</font> )
 ;<br/><div><a class="txt" onclick="hs2(this)" href="javascript:()" title="149_5_1"><b>now </b></a><div class="add"><b>let </b><font color="Maroon">a</font> be    <a href="hidden.html#M1">set</a> ;<br/><b>assume </b><a NAME="E1:149_5_1"/><i><font color="Green">E99</font></i>: 
<font color="Maroon">a</font> <a href="hidden.html#R2">in</a>  <a href="finseq_1.html#K4">dom</a> <span class="p1">(<span class="default"><font color="Maroon">x1</font> <a href="zf_lang.html#K4">'='</a> <font color="Maroon">x2</font></span>)</span>
 ;<br/><a NAME="E2:149_5_1"/><b>then </b>
( <font color="Maroon">a</font> <a href="hidden.html#R1">=</a> 1 or <font color="Maroon">a</font> <a href="hidden.html#R1">=</a> 2 or <font color="Maroon">a</font> <a href="hidden.html#R1">=</a> 3 )
 <b>by </b><i><a class="ref" href="zf_lang1.html#T65" target="_self">Th65</a>, <a class="ref" href="enumset1.html#D1">ENUMSET1:def 1</a></i>;<br/><b>hence </b><a NAME="E3:149_5_1"/>
<span class="p1">(<span class="default"><font color="Maroon">z1</font> <a href="zf_lang.html#K4">'='</a> <font color="Maroon">z2</font></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">a</font> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">x1</font> <a href="zf_lang.html#K4">'='</a> <font color="Maroon">x2</font></span>)</span> <a href="zf_lang1.html#K5" target="_self">/</a> <font color="Maroon">y1</font>,<font color="Maroon">y2</font></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">a</font>
 <b>by </b><i><a class="ref" href="zf_lang1.html#T67" target="_self">Th67</a>, <a class="ref" href="zf_lang1.html#T71" target="_self">Th71</a>, , <a class="txt" href="zf_lang1.html#E6:149"><i><font color="Green">E65</font></i></a>, <a class="txt" href="zf_lang1.html#E5:149"><i><font color="Green">E52</font></i></a></i>;<br/></div><b>end;</b></div><b>hence </b><a NAME="E3:149_5"/>
<span class="p1">(<span class="default"><font color="Maroon">x1</font> <a href="zf_lang.html#K4">'='</a> <font color="Maroon">x2</font></span>)</span> <a href="zf_lang1.html#K5" target="_self">/</a> <font color="Maroon">y1</font>,<font color="Maroon">y2</font> <a href="hidden.html#R1">=</a> <font color="Maroon">z1</font> <a href="zf_lang.html#K4">'='</a> <font color="Maroon">z2</font>
 <b>by </b><i><a class="ref" href="zf_lang1.html#T69" target="_self">Th69</a>, <a class="ref" href="funct_1.html#T9">FUNCT_1:9</a></i>;<br/></div><b>end;</b></div>
<b>hence </b><a NAME="E14:149"/>
( ( ( <font color="Maroon">x1</font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> <font color="Maroon">y1</font> &amp; <font color="Maroon">x2</font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> <font color="Maroon">y1</font> &amp; <font color="Maroon">z1</font> <a href="hidden.html#R1">=</a> <font color="Maroon">x1</font> &amp; <font color="Maroon">z2</font> <a href="hidden.html#R1">=</a> <font color="Maroon">x2</font> ) or ( <font color="Maroon">x1</font> <a href="hidden.html#R1">=</a> <font color="Maroon">y1</font> &amp; <font color="Maroon">x2</font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> <font color="Maroon">y1</font> &amp; <font color="Maroon">z1</font> <a href="hidden.html#R1">=</a> <font color="Maroon">y2</font> &amp; <font color="Maroon">z2</font> <a href="hidden.html#R1">=</a> <font color="Maroon">x2</font> ) or ( <font color="Maroon">x1</font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> <font color="Maroon">y1</font> &amp; <font color="Maroon">x2</font> <a href="hidden.html#R1">=</a> <font color="Maroon">y1</font> &amp; <font color="Maroon">z1</font> <a href="hidden.html#R1">=</a> <font color="Maroon">x1</font> &amp; <font color="Maroon">z2</font> <a href="hidden.html#R1">=</a> <font color="Maroon">y2</font> ) or ( <font color="Maroon">x1</font> <a href="hidden.html#R1">=</a> <font color="Maroon">y1</font> &amp; <font color="Maroon">x2</font> <a href="hidden.html#R1">=</a> <font color="Maroon">y1</font> &amp; <font color="Maroon">z1</font> <a href="hidden.html#R1">=</a> <font color="Maroon">y2</font> &amp; <font color="Maroon">z2</font> <a href="hidden.html#R1">=</a> <font color="Maroon">y2</font> ) ) implies <span class="p1">(<span class="default"><font color="Maroon">x1</font> <a href="zf_lang.html#K4">'='</a> <font color="Maroon">x2</font></span>)</span> <a href="zf_lang1.html#K5" target="_self">/</a> <font color="Maroon">y1</font>,<font color="Maroon">y2</font> <a href="hidden.html#R1">=</a> <font color="Maroon">z1</font> <a href="zf_lang.html#K4">'='</a> <font color="Maroon">z2</font> )
 <b>by </b><i><a class="ref" href="zf_lang1.html#T72" target="_self">Th72</a>, <a class="ref" href="zf_lang1.html#T74" target="_self">Th74</a>, </i>;<br/>


</div>
