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

<b>let </b><font color="Maroon">c<sub>1</sub></font> be   <a href="zf_lang.html#NM2">ZF-formula</a>;<br/>

<b>assume </b><a NAME="E1:31"/><i><font color="Green">E18</font></i>: 
<font color="Maroon">c<sub>1</sub></font> is <a href="zf_lang.html#V7" target="_self">atomic</a>
 ;<br/>

<div><i><font color="Green">E19</font></i>: <a class="txt" onclick="hs2(this)" href="javascript:()" title="31_1"><b>now </b></a><div class="add"><b>assume </b><a NAME="E1:31_1"/>
<font color="Maroon">c<sub>1</sub></font> <a href="zf_lang.html#NR1" target="_self">is_equality</a> 
 ;<br/><b>then consider </b><font color="Maroon">c<sub>2</sub></font>, <font color="Maroon">c<sub>3</sub></font> being   <a href="zf_lang.html#NM1">Variable</a><b> such that </b><br/><a NAME="E3:31_1"/><i><font color="Green">E20</font></i>: 
<font color="Maroon">c<sub>1</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>2</sub></font> <a href="zf_lang.html#K4" target="_self">'='</a> <font color="Maroon">c<sub>3</sub></font>
 <b>by </b><i><a class="ref" href="zf_lang.html#D10" target="_self">Def10</a></i>;<br/><font color="Maroon">c<sub>1</sub></font> = 
<span class="p1">(<span class="default"><span class="p2"><a href="finseq_1.html#K12">&lt;*</a><span class="default">0</span><a href="finseq_1.html#K12">*&gt;</a></span> <a href="finseq_1.html#K8">^</a> <span class="p2"><a href="zf_lang.html#K3" target="_self">&lt;*</a><span class="default"><font color="Maroon">c<sub>2</sub></font></span><a href="zf_lang.html#K3" target="_self">*&gt;</a></span></span>)</span> <a href="finseq_1.html#K8">^</a> <span class="p1"><a href="zf_lang.html#K3" target="_self">&lt;*</a><span class="default"><font color="Maroon">c<sub>3</sub></font></span><a href="zf_lang.html#K3" target="_self">*&gt;</a></span>
<b>by </b><i><a class="txt" href="zf_lang.html#E3:31_1"><i><font color="Green">E20</font></i></a></i>
<br/>.= 
<span class="p1"><a href="finseq_1.html#K11">&lt;*</a><span class="default">0,<font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>3</sub></font></span><a href="finseq_1.html#K11">*&gt;</a></span>
<b>by </b><i><a class="ref" href="finseq_1.html#D10">FINSEQ_1:def 10</a></i>
;<br/><b>hence </b><a NAME="E5:31_1"/>
 <a href="finseq_1.html#K3">len</a> <font color="Maroon">c<sub>1</sub></font> <a href="hidden.html#R1">=</a> 3
 <b>by </b><i><a class="ref" href="finseq_1.html#T62">FINSEQ_1:62</a></i>;<br/></div><b>end;</b></div>
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="31_2"><b>now </b></a><div class="add"><b>assume </b><a NAME="E1:31_2"/>
<font color="Maroon">c<sub>1</sub></font> <a href="zf_lang.html#NR2" target="_self">is_membership</a> 
 ;<br/><b>then consider </b><font color="Maroon">c<sub>2</sub></font>, <font color="Maroon">c<sub>3</sub></font> being   <a href="zf_lang.html#NM1">Variable</a><b> such that </b><br/><a NAME="E3:31_2"/><i><font color="Green">E20</font></i>: 
<font color="Maroon">c<sub>1</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>2</sub></font> <a href="zf_lang.html#K5" target="_self">'in'</a> <font color="Maroon">c<sub>3</sub></font>
 <b>by </b><i><a class="ref" href="zf_lang.html#D11" target="_self">Def11</a></i>;<br/><font color="Maroon">c<sub>1</sub></font> = 
<span class="p1">(<span class="default"><span class="p2"><a href="finseq_1.html#K12">&lt;*</a><span class="default">1</span><a href="finseq_1.html#K12">*&gt;</a></span> <a href="finseq_1.html#K8">^</a> <span class="p2"><a href="zf_lang.html#K3" target="_self">&lt;*</a><span class="default"><font color="Maroon">c<sub>2</sub></font></span><a href="zf_lang.html#K3" target="_self">*&gt;</a></span></span>)</span> <a href="finseq_1.html#K8">^</a> <span class="p1"><a href="zf_lang.html#K3" target="_self">&lt;*</a><span class="default"><font color="Maroon">c<sub>3</sub></font></span><a href="zf_lang.html#K3" target="_self">*&gt;</a></span>
<b>by </b><i><a class="txt" href="zf_lang.html#E3:31_2"><i><font color="Green">E20</font></i></a></i>
<br/>.= 
<span class="p1"><a href="finseq_1.html#K11">&lt;*</a><span class="default">1,<font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>3</sub></font></span><a href="finseq_1.html#K11">*&gt;</a></span>
<b>by </b><i><a class="ref" href="finseq_1.html#D10">FINSEQ_1:def 10</a></i>
;<br/><b>hence </b><a NAME="E5:31_2"/>
 <a href="finseq_1.html#K3">len</a> <font color="Maroon">c<sub>1</sub></font> <a href="hidden.html#R1">=</a> 3
 <b>by </b><i><a class="ref" href="finseq_1.html#T62">FINSEQ_1:62</a></i>;<br/></div><b>end;</b></div>
<b>hence </b><a NAME="E4:31"/>
 <a href="finseq_1.html#K3">len</a> <font color="Maroon">c<sub>1</sub></font> <a href="hidden.html#R1">=</a> 3
 <b>by </b><i><a class="txt" href="zf_lang.html#E1:31"><i><font color="Green">E18</font></i></a>, <a class="txt" href="zf_lang.html#E2:31"><i><font color="Green">E19</font></i></a>, <a class="ref" href="zf_lang.html#D15" target="_self">Def15</a></i>;<br/>


</div>
