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

<b>assume </b><a NAME="E1:31"/><i><font color="Green">E31</font></i>: 
<font color="Maroon">H</font> is <a href="zf_lang.html#V7" target="_self">atomic</a>
 ;<br/>

<div><i><font color="Green">E32</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">H</font> <a href="zf_lang.html#NR1" target="_self">is_equality</a> 
 ;<br/><b>then consider </b><font color="Maroon">x</font> being   <a href="zf_lang.html#NM1">Variable</a>, <font color="Maroon">y</font> being   <a href="zf_lang.html#NM1">Variable</a><b> such that </b><br/><a NAME="E3:31_1"/><i><font color="Green">E35</font></i>: 
<font color="Maroon">H</font> <a href="hidden.html#R1">=</a> <font color="Maroon">x</font> <a href="zf_lang.html#K4" target="_self">'='</a> <font color="Maroon">y</font>
 <b>by </b><i/>;<br/><a NAME="E4:31_1"/>
<font color="Maroon">H</font> <a href="hidden.html#R1">=</a> <span class="p1"><a href="finseq_1.html#K11">&lt;*</a><span class="default">0,<font color="Maroon">x</font>,<font color="Maroon">y</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">H</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">H</font> <a href="zf_lang.html#NR2" target="_self">is_membership</a> 
 ;<br/><b>then consider </b><font color="Maroon">x</font> being   <a href="zf_lang.html#NM1">Variable</a>, <font color="Maroon">y</font> being   <a href="zf_lang.html#NM1">Variable</a><b> such that </b><br/><a NAME="E3:31_2"/><i><font color="Green">E36</font></i>: 
<font color="Maroon">H</font> <a href="hidden.html#R1">=</a> <font color="Maroon">x</font> <a href="zf_lang.html#K5" target="_self">'in'</a> <font color="Maroon">y</font>
 <b>by </b><i/>;<br/><a NAME="E4:31_2"/>
<font color="Maroon">H</font> <a href="hidden.html#R1">=</a> <span class="p1"><a href="finseq_1.html#K11">&lt;*</a><span class="default">1,<font color="Maroon">x</font>,<font color="Maroon">y</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">H</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">H</font> <a href="hidden.html#R1">=</a> 3
 <b>by </b><i>, , </i>;<br/>


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