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<a NAME="E1:50_2_1"/><i><font color="Green">E40</font></i>: 
( <font color="Maroon">H</font> <a href="zf_lang.html#NR1" target="_self">is_equality</a>  or <font color="Maroon">H</font> <a href="zf_lang.html#NR2" target="_self">is_membership</a>  )
 
<b>by </b><i>, </i>;<br/>
<a NAME="E2:50_2_1"/><i><font color="Green">E41</font></i>: 
(  ex <font color="Olive">x</font>, <font color="Olive">y</font> being  <a href="zf_lang.html#NM1">Variable</a> st <font color="Maroon">H</font> <a href="hidden.html#R1">=</a> <font color="Olive">x</font> <a href="zf_lang.html#K4" target="_self">'='</a> <font color="Olive">y</font> implies  ex <font color="Olive">k</font> being   <a href="subset_1.html#M1">Element</a> of  <a href="numbers.html#K5">NAT</a>  ex <font color="Olive">x</font>, <font color="Olive">y</font> being  <a href="zf_lang.html#NM1">Variable</a> st <font color="Maroon">H</font> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><span class="p2"><a href="finseq_1.html#K12">&lt;*</a><span class="default"><font color="Olive">k</font></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="Olive">x</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="Olive">y</font></span><a href="zf_lang.html#K3" target="_self">*&gt;</a></span> )
 
;<br/>
<a NAME="E3:50_2_1"/>
(  ex <font color="Olive">x</font>, <font color="Olive">y</font> being  <a href="zf_lang.html#NM1">Variable</a> st <font color="Maroon">H</font> <a href="hidden.html#R1">=</a> <font color="Olive">x</font> <a href="zf_lang.html#K5" target="_self">'in'</a> <font color="Olive">y</font> implies  ex <font color="Olive">k</font> being   <a href="subset_1.html#M1">Element</a> of  <a href="numbers.html#K5">NAT</a>  ex <font color="Olive">x</font>, <font color="Olive">y</font> being  <a href="zf_lang.html#NM1">Variable</a> st <font color="Maroon">H</font> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><span class="p2"><a href="finseq_1.html#K12">&lt;*</a><span class="default"><font color="Olive">k</font></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="Olive">x</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="Olive">y</font></span><a href="zf_lang.html#K3" target="_self">*&gt;</a></span> )
 
;<br/>
<b>then consider </b><font color="Maroon">k</font> being    <a href="subset_1.html#M1">Element</a> of  <a href="numbers.html#K5">NAT</a> , <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="E5:50_2_1"/><i><font color="Green">E42</font></i>: 
<font color="Maroon">H</font> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><span class="p2"><a href="finseq_1.html#K12">&lt;*</a><span class="default"><font color="Maroon">k</font></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">x</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">y</font></span><a href="zf_lang.html#K3" target="_self">*&gt;</a></span>
 <b>by </b><i><a class="ref" href="zf_lang.html#D8" target="_self">Def8</a>, , , </i>;<br/>
<a NAME="E6:50_2_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"><font color="Maroon">k</font>,<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="E7:50_2_1"/>
<font color="Maroon">H</font> <a href="funct_1.html#K1">.</a> 3 is   <a href="zf_lang.html#NM1">Variable</a>
 <b>by </b><i><a class="ref" href="finseq_1.html#T62">FINSEQ_1:62</a></i>;<br/>


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