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<b>let </b><font color="Maroon" title="c4">X1</font>, <font color="Maroon" title="c5">X2</font> be    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of <font color="Maroon" title="c1">DX</font>;<br/>

<b>assume </b><b>that </b><br/><a NAME="E1:2_1_2"/><i><font color="Green" title="E3">A4</font></i>: 
 ex <font color="Olive" title="b1">p1</font> being   <a href="finseq_1.html#M2" title="FINSEQ_1:mode.2">FinSequence</a> of <font color="Maroon" title="c1">DX</font> st <br/>( <font color="Olive" title="b1">p1</font> is <a href="funct_1.html#V2" title="FUNCT_1:attr.2">one-to-one</a> &amp;  <a href="relat_1.html#K2" title="RELAT_1:func.2">rng</a> <font color="Olive" title="b1">p1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c3">Y</font> &amp; <font color="Maroon" title="c4">X1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c2">f</font> <a href="finsop_1.html#K2" title="FINSOP_1:func.2">"**"</a> <font color="Olive" title="b1">p1</font> )
 <b>and </b><br/><a NAME="E2:2_1_2"/><i><font color="Green" title="E4">A5</font></i>: 
 ex <font color="Olive" title="b1">p2</font> being   <a href="finseq_1.html#M2" title="FINSEQ_1:mode.2">FinSequence</a> of <font color="Maroon" title="c1">DX</font> st <br/>( <font color="Olive" title="b1">p2</font> is <a href="funct_1.html#V2" title="FUNCT_1:attr.2">one-to-one</a> &amp;  <a href="relat_1.html#K2" title="RELAT_1:func.2">rng</a> <font color="Olive" title="b1">p2</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c3">Y</font> &amp; <font color="Maroon" title="c5">X2</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c2">f</font> <a href="finsop_1.html#K2" title="FINSOP_1:func.2">"**"</a> <font color="Olive" title="b1">p2</font> )
 ;<br/>

<b>consider </b><font color="Maroon" title="c6">p1</font> being    <a href="finseq_1.html#M2" title="FINSEQ_1:mode.2">FinSequence</a> of <font color="Maroon" title="c1">DX</font><b> such that </b><br/><a NAME="E4:2_1_2"/><i><font color="Green" title="E5">A6</font></i>: 
<font color="Maroon" title="c6">p1</font> is <a href="funct_1.html#V2" title="FUNCT_1:attr.2">one-to-one</a>
 <b>and </b><br/><a NAME="E5:2_1_2"/><i><font color="Green" title="E6">A7</font></i>: 
 <a href="relat_1.html#K2" title="RELAT_1:func.2">rng</a> <font color="Maroon" title="c6">p1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c3">Y</font>
 <b>and </b><br/><a NAME="E6:2_1_2"/><i><font color="Green" title="E7">A8</font></i>: 
<font color="Maroon" title="c4">X1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c2">f</font> <a href="finsop_1.html#K2" title="FINSOP_1:func.2">"**"</a> <font color="Maroon" title="c6">p1</font>
 <b>by </b><i><a class="txt" href="bhsp_5.html#E1:2_1_2"><i><font color="Green" title="E3">A4</font></i></a></i>;<br/>
<b>consider </b><font color="Maroon" title="c7">p2</font> being    <a href="finseq_1.html#M2" title="FINSEQ_1:mode.2">FinSequence</a> of <font color="Maroon" title="c1">DX</font><b> such that </b><br/><a NAME="E8:2_1_2"/><i><font color="Green" title="E8">A9</font></i>: 
<font color="Maroon" title="c7">p2</font> is <a href="funct_1.html#V2" title="FUNCT_1:attr.2">one-to-one</a>
 <b>and </b><br/><a NAME="E9:2_1_2"/><i><font color="Green" title="E9">A10</font></i>: 
 <a href="relat_1.html#K2" title="RELAT_1:func.2">rng</a> <font color="Maroon" title="c7">p2</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c3">Y</font>
 <b>and </b><br/><a NAME="E10:2_1_2"/><i><font color="Green" title="E10">A11</font></i>: 
<font color="Maroon" title="c5">X2</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c2">f</font> <a href="finsop_1.html#K2" title="FINSOP_1:func.2">"**"</a> <font color="Maroon" title="c7">p2</font>
 <b>by </b><i><a class="txt" href="bhsp_5.html#E2:2_1_2"><i><font color="Green" title="E4">A5</font></i></a></i>;<br/>
<a NAME="E11:2_1_2"/>
(  <a href="finseq_1.html#K4" title="FINSEQ_1:func.4">dom</a> <font color="Maroon" title="c6">p1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="finseq_1.html#K4" title="FINSEQ_1:func.4">dom</a> <font color="Maroon" title="c7">p2</font> &amp;  ex <font color="Olive" title="b1">P</font> being  <a href="funct_2.html#NM2" title="FUNCT_2:NM.2">Permutation</a> of  <a href="finseq_1.html#K4" title="FINSEQ_1:func.4">dom</a> <font color="Maroon" title="c6">p1</font> st <br/>( <font color="Maroon" title="c7">p2</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c6">p1</font> <a href="funct_1.html#NK3" title="FUNCT_1:NK.3">*</a> <font color="Olive" title="b1">P</font> &amp;  <a href="relat_1.html#K1" title="RELAT_1:func.1">dom</a> <font color="Olive" title="b1">P</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="finseq_1.html#K4" title="FINSEQ_1:func.4">dom</a> <font color="Maroon" title="c6">p1</font> &amp;  <a href="relat_1.html#K2" title="RELAT_1:func.2">rng</a> <font color="Olive" title="b1">P</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="finseq_1.html#K4" title="FINSEQ_1:func.4">dom</a> <font color="Maroon" title="c6">p1</font> ) )
 
<b>by </b><i><a class="txt" href="bhsp_5.html#E4:2_1_2"><i><font color="Green" title="E5">A6</font></i></a>, <a class="txt" href="bhsp_5.html#E5:2_1_2"><i><font color="Green" title="E6">A7</font></i></a>, <a class="txt" href="bhsp_5.html#E8:2_1_2"><i><font color="Green" title="E8">A9</font></i></a>, <a class="txt" href="bhsp_5.html#E9:2_1_2"><i><font color="Green" title="E9">A10</font></i></a>, <a class="ref" href="bhsp_5.html#T1" target="_self" title="BHSP_5:th.1">Th1</a></i>;<br/>
<b>then consider </b><font color="Maroon" title="c8">P</font> being   <a href="funct_2.html#NM2" title="FUNCT_2:NM.2">Permutation</a> of  <a href="finseq_1.html#K4" title="FINSEQ_1:func.4">dom</a> <font color="Maroon" title="c6">p1</font><b> such that </b><br/><a NAME="E13:2_1_2"/><i><font color="Green" title="E11">A12</font></i>: 
<font color="Maroon" title="c7">p2</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c6">p1</font> <a href="funct_1.html#NK3" title="FUNCT_1:NK.3">*</a> <font color="Maroon" title="c8">P</font>
 ;<br/>
<b>thus </b><a NAME="E14:2_1_2"/>
<font color="Maroon" title="c4">X1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c5">X2</font>
 <b>by </b><i><a class="txt" href="bhsp_5.html#E1:2"><i><font color="Green" title="E2">A1</font></i></a>, <a class="txt" href="bhsp_5.html#E6:2_1_2"><i><font color="Green" title="E7">A8</font></i></a>, <a class="txt" href="bhsp_5.html#E10:2_1_2"><i><font color="Green" title="E10">A11</font></i></a>, <a class="txt" href="bhsp_5.html#E13:2_1_2"><i><font color="Green" title="E11">A12</font></i></a>, <a class="ref" href="finsop_1.html#T8" title="FINSOP_1:th.8">FINSOP_1:8</a></i>;<br/>


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