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<b>let </b><font color="Maroon" title="c1">n</font> be   <a href="nat_1.html#NM1" title="NAT_1:NM.1">Nat</a>;<br/>

<b>reconsider </b><font color="Maroon" title="c2">e'</font> =  <a href="finseq_2.html#K1" title="FINSEQ_2:func.1">idseq</a> <font color="Maroon" title="c1">n</font> as    <a href="matrix_2.html#M1" title="MATRIX_2:mode.1">Element</a> of  <a href="matrix_2.html#K12" title="MATRIX_2:func.12">Permutations</a> <font color="Maroon" title="c1">n</font> <b>by </b><i><a class="ref" href="matrix_2.html#D11" target="_self" title="MATRIX_2:def.11">Def11</a></i>;<br/>
<b>reconsider </b><font color="Maroon" title="c3">e</font> =  <a href="finseq_2.html#K1" title="FINSEQ_2:func.1">idseq</a> <font color="Maroon" title="c1">n</font> as   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <span class="p1">(<span class="default"><a href="matrix_2.html#K13" title="MATRIX_2:func.13">Group_of_Perm</a> <font color="Maroon" title="c1">n</font></span>)</span> <b>by </b><i><a class="ref" href="matrix_2.html#T23" target="_self" title="MATRIX_2:th.23">Th23</a></i>;<br/>
<a NAME="E3:50"/>
for <font color="Olive" title="b1">p</font> being  <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <span class="p1">(<span class="default"><a href="matrix_2.html#K13" title="MATRIX_2:func.13">Group_of_Perm</a> <font color="Maroon" title="c1">n</font></span>)</span> holds <br/> ( <font color="Olive" title="b1">p</font> <a href="algstr_0.html#K6" title="ALGSTR_0:func.6">*</a> <font color="Maroon" title="c3">e</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b1">p</font> &amp; <font color="Maroon" title="c3">e</font> <a href="algstr_0.html#K6" title="ALGSTR_0:func.6">*</a> <font color="Olive" title="b1">p</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b1">p</font> )
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="50_1"><b>proof </b></a><div class="add">

<b>let </b><font color="Maroon" title="c4">p</font> be   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <span class="p1">(<span class="default"><a href="matrix_2.html#K13" title="MATRIX_2:func.13">Group_of_Perm</a> <font color="Maroon" title="c1">n</font></span>)</span>;<br/>

<b>reconsider </b><font color="Maroon" title="c5">p'</font> = <font color="Maroon" title="c4">p</font> as    <a href="matrix_2.html#M1" title="MATRIX_2:mode.1">Element</a> of  <a href="matrix_2.html#K12" title="MATRIX_2:func.12">Permutations</a> <font color="Maroon" title="c1">n</font> <b>by </b><i><a class="ref" href="matrix_2.html#D13" target="_self" title="MATRIX_2:def.13">Def13</a></i>;<br/>
<i><font color="Green" title="E19">A1</font></i>: <font color="Maroon" title="c4">p</font> <a href="algstr_0.html#K6" title="ALGSTR_0:func.6">*</a> <font color="Maroon" title="c3">e</font> = 
<font color="Maroon" title="c2">e'</font> <a href="partfun1.html#K1" title="PARTFUN1:func.1">*</a> <font color="Maroon" title="c5">p'</font>
<b>by </b><i><a class="ref" href="matrix_2.html#D13" target="_self" title="MATRIX_2:def.13">Def13</a></i>
<br/>.= 
<font color="Maroon" title="c4">p</font>
<b>by </b><i><a class="ref" href="matrix_2.html#T24" target="_self" title="MATRIX_2:th.24">Th24</a></i>
;<br/>
<font color="Maroon" title="c3">e</font> <a href="algstr_0.html#K6" title="ALGSTR_0:func.6">*</a> <font color="Maroon" title="c4">p</font> = 
<font color="Maroon" title="c5">p'</font> <a href="partfun1.html#K1" title="PARTFUN1:func.1">*</a> <font color="Maroon" title="c2">e'</font>
<b>by </b><i><a class="ref" href="matrix_2.html#D13" target="_self" title="MATRIX_2:def.13">Def13</a></i>
<br/>.= 
<font color="Maroon" title="c4">p</font>
<b>by </b><i><a class="ref" href="matrix_2.html#T24" target="_self" title="MATRIX_2:th.24">Th24</a></i>
;<br/>
<b>hence </b><a NAME="E4:50_1"/>
( <font color="Maroon" title="c4">p</font> <a href="algstr_0.html#K6" title="ALGSTR_0:func.6">*</a> <font color="Maroon" title="c3">e</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c4">p</font> &amp; <font color="Maroon" title="c3">e</font> <a href="algstr_0.html#K6" title="ALGSTR_0:func.6">*</a> <font color="Maroon" title="c4">p</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c4">p</font> )
 <b>by </b><i><a class="txt" href="matrix_2.html#E2:50_1"><i><font color="Green" title="E19">A1</font></i></a></i>;<br/>


</div><b>end;</b></div>
<b>hence </b><a NAME="E4:50"/>
 <a href="finseq_2.html#K1" title="FINSEQ_2:func.1">idseq</a> <font color="Maroon" title="c1">n</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="group_1.html#K1" title="GROUP_1:func.1">1_</a> <span class="p1">(<span class="default"><a href="matrix_2.html#K13" title="MATRIX_2:func.13">Group_of_Perm</a> <font color="Maroon" title="c1">n</font></span>)</span>
 <b>by </b><i><a class="ref" href="group_1.html#T10" title="GROUP_1:th.10">GROUP_1:10</a></i>;<br/>


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