<?xml version="1.0"?>
<div class="add">

<b>let </b><font color="Maroon" title="c3">X1</font>, <font color="Maroon" title="c4">X2</font> be   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Maroon" title="c1">X</font>;<br/>

<b>assume </b><b>that </b><br/><a NAME="E1:1_1_2"/><i><font color="Green" title="E2">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 the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c1">X</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="relset_1.html#K5" title="RELSET_1:func.5">rng</a> <font color="Olive" title="b1">p1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c2">Y</font> &amp; <font color="Maroon" title="c3">X1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> the <a href="algstr_0.html#U1" title="ALGSTR_0:sel.1">addF</a> of <font color="Maroon" title="c1">X</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="E2:1_1_2"/><i><font color="Green" title="E3">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 the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c1">X</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="relset_1.html#K5" title="RELSET_1:func.5">rng</a> <font color="Olive" title="b1">p2</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c2">Y</font> &amp; <font color="Maroon" title="c4">X2</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> the <a href="algstr_0.html#U1" title="ALGSTR_0:sel.1">addF</a> of <font color="Maroon" title="c1">X</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="c5">p1</font> being    <a href="finseq_1.html#M2" title="FINSEQ_1:mode.2">FinSequence</a> of the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c1">X</font><b> such that </b><br/><a NAME="E4:1_1_2"/><i><font color="Green" title="E4">A6</font></i>: 
<font color="Maroon" title="c5">p1</font> is <a href="funct_1.html#V2" title="FUNCT_1:attr.2">one-to-one</a>
 <b>and </b><br/><a NAME="E5:1_1_2"/><i><font color="Green" title="E5">A7</font></i>: 
 <a href="relset_1.html#K5" title="RELSET_1:func.5">rng</a> <font color="Maroon" title="c5">p1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c2">Y</font>
 <b>and </b><br/><a NAME="E6:1_1_2"/><i><font color="Green" title="E6">A8</font></i>: 
<font color="Maroon" title="c3">X1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> the <a href="algstr_0.html#U1" title="ALGSTR_0:sel.1">addF</a> of <font color="Maroon" title="c1">X</font> <a href="finsop_1.html#K2" title="FINSOP_1:func.2">"**"</a> <font color="Maroon" title="c5">p1</font>
 <b>by </b><i><a class="txt" href="bhsp_6.html#E1:1_1_2"><i><font color="Green" title="E2">A4</font></i></a></i>;<br/>
<b>consider </b><font color="Maroon" title="c6">p2</font> being    <a href="finseq_1.html#M2" title="FINSEQ_1:mode.2">FinSequence</a> of the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c1">X</font><b> such that </b><br/><a NAME="E8:1_1_2"/><i><font color="Green" title="E7">A9</font></i>: 
<font color="Maroon" title="c6">p2</font> is <a href="funct_1.html#V2" title="FUNCT_1:attr.2">one-to-one</a>
 <b>and </b><br/><a NAME="E9:1_1_2"/><i><font color="Green" title="E8">A10</font></i>: 
 <a href="relset_1.html#K5" title="RELSET_1:func.5">rng</a> <font color="Maroon" title="c6">p2</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c2">Y</font>
 <b>and </b><br/><a NAME="E10:1_1_2"/><i><font color="Green" title="E9">A11</font></i>: 
<font color="Maroon" title="c4">X2</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> the <a href="algstr_0.html#U1" title="ALGSTR_0:sel.1">addF</a> of <font color="Maroon" title="c1">X</font> <a href="finsop_1.html#K2" title="FINSOP_1:func.2">"**"</a> <font color="Maroon" title="c6">p2</font>
 <b>by </b><i><a class="txt" href="bhsp_6.html#E2:1_1_2"><i><font color="Green" title="E3">A5</font></i></a></i>;<br/>
<a NAME="E11:1_1_2"/>
(  <a href="finseq_1.html#K4" title="FINSEQ_1:func.4">dom</a> <font color="Maroon" title="c5">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="c6">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="c5">p1</font> st <br/>( <font color="Maroon" title="c6">p2</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c5">p1</font> <a href="partfun1.html#K1" title="PARTFUN1:func.1">*</a> <font color="Olive" title="b1">P</font> &amp;  <a href="relset_1.html#K4" title="RELSET_1:func.4">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="c5">p1</font> &amp;  <a href="relset_1.html#K5" title="RELSET_1:func.5">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="c5">p1</font> ) )
 
<b>by </b><i><a class="txt" href="bhsp_6.html#E4:1_1_2"><i><font color="Green" title="E4">A6</font></i></a>, <a class="txt" href="bhsp_6.html#E5:1_1_2"><i><font color="Green" title="E5">A7</font></i></a>, <a class="txt" href="bhsp_6.html#E8:1_1_2"><i><font color="Green" title="E7">A9</font></i></a>, <a class="txt" href="bhsp_6.html#E9:1_1_2"><i><font color="Green" title="E8">A10</font></i></a>, <a class="ref" href="bhsp_5.html#T1" title="BHSP_5:th.1">BHSP_5:1</a></i>;<br/>
<b>then consider </b><font color="Maroon" title="c7">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="c5">p1</font><b> such that </b><br/><a NAME="E13:1_1_2"/><i><font color="Green" title="E10">A12</font></i>: 
<font color="Maroon" title="c6">p2</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c5">p1</font> <a href="partfun1.html#K1" title="PARTFUN1:func.1">*</a> <font color="Maroon" title="c7">P</font>
 ;<br/>
<b>thus </b><a NAME="E14:1_1_2"/>
<font color="Maroon" title="c3">X1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c4">X2</font>
 <b>by </b><i><a class="txt" href="bhsp_6.html#E1:1"><i><font color="Green" title="E1">A1</font></i></a>, <a class="txt" href="bhsp_6.html#E6:1_1_2"><i><font color="Green" title="E6">A8</font></i></a>, <a class="txt" href="bhsp_6.html#E10:1_1_2"><i><font color="Green" title="E9">A11</font></i></a>, <a class="txt" href="bhsp_6.html#E13:1_1_2"><i><font color="Green" title="E10">A12</font></i></a>, <a class="ref" href="finsop_1.html#T8" title="FINSOP_1:th.8">FINSOP_1:8</a></i>;<br/>


</div>
