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<b>let </b><font color="Maroon">p</font> be   <a href="afinsq_1.html#NM1">XFinSequence</a>;<br/><b>let </b><font color="Maroon">i</font> be    <a href="subset_1.html#M1">Element</a> of  <a href="numbers.html#K5">NAT</a> ;<br/><b>let </b><font color="Maroon">x</font> be    <a href="hidden.html#M1">set</a> ;<br/>





<a NAME="E1:78"/><i><font color="Green">E31</font></i>: 
(  <a href="afinsq_1.html#K1" target="_self">len</a> <font color="Maroon">p</font> <a href="hidden.html#R1">=</a>  <a href="afinsq_1.html#K2" target="_self">dom</a> <font color="Maroon">p</font> &amp;  <a href="afinsq_1.html#K1" target="_self">len</a> <span class="p1">(<span class="default"><font color="Maroon">p</font> <a href="funct_7.html#K2">+*</a> <font color="Maroon">i</font>,<font color="Maroon">x</font></span>)</span> <a href="hidden.html#R1">=</a>  <a href="afinsq_1.html#K2" target="_self">dom</a> <span class="p1">(<span class="default"><font color="Maroon">p</font> <a href="funct_7.html#K2">+*</a> <font color="Maroon">i</font>,<font color="Maroon">x</font></span>)</span> )
 
<b>by </b><i/>;<br/>
<b>set </b><font color="Maroon">f</font> =  <a href="afinsq_1.html#NK13" target="_self">Replace</a> <font color="Maroon">p</font>,<font color="Maroon">i</font>,<font color="Maroon">x</font>;<br/>
<b>thus </b><a NAME="E2:78"/>
 <a href="afinsq_1.html#K1" target="_self">len</a> <span class="p1">(<span class="default"><a href="afinsq_1.html#NK13" target="_self">Replace</a> <font color="Maroon">p</font>,<font color="Maroon">i</font>,<font color="Maroon">x</font></span>)</span> <a href="hidden.html#R1">=</a>  <a href="afinsq_1.html#K1" target="_self">len</a> <font color="Maroon">p</font>
 <b>by </b><i>, <a class="ref" href="funct_7.html#T32">FUNCT_7:32</a></i>;<br/>

<a NAME="E3:78"/>
( <font color="Maroon">i</font> <a href="xxreal_0.html#NR3" target="_self">&lt;</a>  <a href="afinsq_1.html#K1" target="_self">len</a> <font color="Maroon">p</font> implies  not  <a href="afinsq_1.html#K2" target="_self">dom</a> <font color="Maroon">p</font> <a href="ordinal1.html#R1">c=</a> <font color="Maroon">i</font> )
 
<b>by </b><i>, <a class="ref" href="card_1.html#T56">CARD_1:56</a></i>;<br/>
<a NAME="E4:78"/><b>then </b>
( <font color="Maroon">i</font> <a href="xxreal_0.html#NR3" target="_self">&lt;</a>  <a href="afinsq_1.html#K1" target="_self">len</a> <font color="Maroon">p</font> implies <font color="Maroon">i</font> <a href="hidden.html#R2">in</a>  <a href="afinsq_1.html#K2" target="_self">dom</a> <font color="Maroon">p</font> )
 
<b>by </b><i><a class="ref" href="ordinal1.html#T26">ORDINAL1:26</a></i>;<br/>
<b>hence </b><a NAME="E5:78"/>
( <font color="Maroon">i</font> <a href="xxreal_0.html#NR3" target="_self">&lt;</a>  <a href="afinsq_1.html#K1" target="_self">len</a> <font color="Maroon">p</font> implies <span class="p1">(<span class="default"><a href="afinsq_1.html#NK13" target="_self">Replace</a> <font color="Maroon">p</font>,<font color="Maroon">i</font>,<font color="Maroon">x</font></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">i</font> <a href="hidden.html#R1">=</a> <font color="Maroon">x</font> )
 <b>by </b><i><a class="ref" href="funct_7.html#T33">FUNCT_7:33</a></i>;<br/>

<b>thus </b><a NAME="E6:78"/>
for <font color="Olive">j</font> being   <a href="subset_1.html#M1">Element</a> of  <a href="numbers.html#K5">NAT</a>   st <font color="Olive">j</font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> <font color="Maroon">i</font> holds <br/><span class="p1">(<span class="default"><a href="afinsq_1.html#NK13" target="_self">Replace</a> <font color="Maroon">p</font>,<font color="Maroon">i</font>,<font color="Maroon">x</font></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Olive">j</font> <a href="hidden.html#R1">=</a> <font color="Maroon">p</font> <a href="funct_1.html#K1">.</a> <font color="Olive">j</font>
 <b>by </b><i><a class="ref" href="funct_7.html#T34">FUNCT_7:34</a></i>;<br/>


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