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<b>let </b><font color="Maroon">X1</font> be    <a href="subset_1.html#M1">Element</a> of <font color="Maroon">DX</font>, <font color="Maroon">X2</font> be    <a href="subset_1.html#M1">Element</a> of <font color="Maroon">DX</font>;<br/>

<b>assume </b><b>that </b><br/><a NAME="E1:2_1_2"/><i><font color="Green">E45</font></i>: 
 ex <font color="Olive">p1</font> being   <a href="finseq_1.html#M2">FinSequence</a> of <font color="Maroon">DX</font> st <br/>( <font color="Olive">p1</font> is <a href="funct_1.html#V2">one-to-one</a> &amp;  <a href="relat_1.html#K2">rng</a> <font color="Olive">p1</font> <a href="hidden.html#R1">=</a> <font color="Maroon">Y</font> &amp; <font color="Maroon">X1</font> <a href="hidden.html#R1">=</a> <font color="Maroon">f</font> <a href="finsop_1.html#K2">"**"</a> <font color="Olive">p1</font> )
 <b>and </b><br/><a NAME="E2:2_1_2"/><i><font color="Green">E46</font></i>: 
 ex <font color="Olive">p2</font> being   <a href="finseq_1.html#M2">FinSequence</a> of <font color="Maroon">DX</font> st <br/>( <font color="Olive">p2</font> is <a href="funct_1.html#V2">one-to-one</a> &amp;  <a href="relat_1.html#K2">rng</a> <font color="Olive">p2</font> <a href="hidden.html#R1">=</a> <font color="Maroon">Y</font> &amp; <font color="Maroon">X2</font> <a href="hidden.html#R1">=</a> <font color="Maroon">f</font> <a href="finsop_1.html#K2">"**"</a> <font color="Olive">p2</font> )
 ;<br/>

<b>consider </b><font color="Maroon">p1</font> being    <a href="finseq_1.html#M2">FinSequence</a> of <font color="Maroon">DX</font><b> such that </b><br/><a NAME="E4:2_1_2"/><i><font color="Green">E47</font></i>: 
<font color="Maroon">p1</font> is <a href="funct_1.html#V2">one-to-one</a>
 <b>and </b><br/><a NAME="E5:2_1_2"/><i><font color="Green">E48</font></i>: 
 <a href="relat_1.html#K2">rng</a> <font color="Maroon">p1</font> <a href="hidden.html#R1">=</a> <font color="Maroon">Y</font>
 <b>and </b><br/><a NAME="E6:2_1_2"/><i><font color="Green">E49</font></i>: 
<font color="Maroon">X1</font> <a href="hidden.html#R1">=</a> <font color="Maroon">f</font> <a href="finsop_1.html#K2">"**"</a> <font color="Maroon">p1</font>
 <b>by </b><i/>;<br/>
<b>consider </b><font color="Maroon">p2</font> being    <a href="finseq_1.html#M2">FinSequence</a> of <font color="Maroon">DX</font><b> such that </b><br/><a NAME="E8:2_1_2"/><i><font color="Green">E50</font></i>: 
<font color="Maroon">p2</font> is <a href="funct_1.html#V2">one-to-one</a>
 <b>and </b><br/><a NAME="E9:2_1_2"/><i><font color="Green">E52</font></i>: 
 <a href="relat_1.html#K2">rng</a> <font color="Maroon">p2</font> <a href="hidden.html#R1">=</a> <font color="Maroon">Y</font>
 <b>and </b><br/><a NAME="E10:2_1_2"/><i><font color="Green">E53</font></i>: 
<font color="Maroon">X2</font> <a href="hidden.html#R1">=</a> <font color="Maroon">f</font> <a href="finsop_1.html#K2">"**"</a> <font color="Maroon">p2</font>
 <b>by </b><i/>;<br/>
<a NAME="E11:2_1_2"/>
(  <a href="finsop_1.html#K5">dom</a> <font color="Maroon">p1</font> <a href="hidden.html#R1">=</a>  <a href="finsop_1.html#K5">dom</a> <font color="Maroon">p2</font> &amp;  ex <font color="Olive">P</font> being  <a href="funct_2.html#NM2">Permutation</a> of  <a href="finsop_1.html#K5">dom</a> <font color="Maroon">p1</font> st <br/>( <font color="Maroon">p2</font> <a href="hidden.html#R1">=</a> <font color="Maroon">p1</font> <a href="funct_1.html#NK3" target="_self">*</a> <font color="Olive">P</font> &amp;  <a href="relat_1.html#K1">dom</a> <font color="Olive">P</font> <a href="hidden.html#R1">=</a>  <a href="finsop_1.html#K5">dom</a> <font color="Maroon">p1</font> &amp;  <a href="relat_1.html#K2">rng</a> <font color="Olive">P</font> <a href="hidden.html#R1">=</a>  <a href="finsop_1.html#K5">dom</a> <font color="Maroon">p1</font> ) )
 
<b>by </b><i>, , , , </i>;<br/>
<b>then consider </b><font color="Maroon">P</font> being   <a href="funct_2.html#NM2">Permutation</a> of  <a href="finsop_1.html#K5">dom</a> <font color="Maroon">p1</font><b> such that </b><br/><a NAME="E13:2_1_2"/><i><font color="Green">E55</font></i>: 
<font color="Maroon">p2</font> <a href="hidden.html#R1">=</a> <font color="Maroon">p1</font> <a href="funct_1.html#NK3" target="_self">*</a> <font color="Maroon">P</font>
 ;<br/>
<b>thus </b><a NAME="E14:2_1_2"/>
<font color="Maroon">X1</font> <a href="hidden.html#R1">=</a> <font color="Maroon">X2</font>
 <b>by </b><i>, , , , <a class="ref" href="finsop_1.html#T8">FINSOP_1:8</a></i>;<br/>


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