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<b>defpred </b><font color="Maroon">S<sub>1</sub></font>[   <a href="matrix_2.html#M3" target="_self">Element</a> of  <a href="matrix_2.html#K11" target="_self">Permutations</a> <font color="Maroon">c<sub>1</sub></font>,   <a href="matrix_2.html#M3" target="_self">Element</a> of  <a href="matrix_2.html#K11" target="_self">Permutations</a> <font color="Maroon">c<sub>1</sub></font>,   <a href="hidden.html#M1">set</a> ] means <font color="Maroon">a<sub>3</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">a<sub>2</sub></font> <a href="partfun1.html#K1">*</a> <font color="Maroon">a<sub>1</sub></font>;<br/>
<a NAME="E1:39_1_1"/><i><font color="Green">E16</font></i>: 
for <font color="Olive">b<sub>1</sub></font>, <font color="Olive">b<sub>2</sub></font> being   <a href="matrix_2.html#M3" target="_self">Element</a> of  <a href="matrix_2.html#K11" target="_self">Permutations</a> <font color="Maroon">c<sub>1</sub></font>ex <font color="Olive">b<sub>3</sub></font> being   <a href="matrix_2.html#M3" target="_self">Element</a> of  <a href="matrix_2.html#K11" target="_self">Permutations</a> <font color="Maroon">c<sub>1</sub></font> st <font color="Maroon">S<sub>1</sub></font>[<font color="Olive">b<sub>1</sub></font>,<font color="Olive">b<sub>2</sub></font>,<font color="Olive">b<sub>3</sub></font>]
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="39_1_1_1"><b>proof </b></a><div class="add">

<b>let </b><font color="Maroon">c<sub>2</sub></font>, <font color="Maroon">c<sub>3</sub></font> be    <a href="matrix_2.html#M3" target="_self">Element</a> of  <a href="matrix_2.html#K11" target="_self">Permutations</a> <font color="Maroon">c<sub>1</sub></font>;<br/>

<b>reconsider </b><font color="Maroon">c<sub>4</sub></font> = <font color="Maroon">c<sub>3</sub></font>, <font color="Maroon">c<sub>5</sub></font> = <font color="Maroon">c<sub>2</sub></font> as   <a href="funct_2.html#NM2">Permutation</a> of  <a href="finseq_1.html#K2">Seg</a> <font color="Maroon">c<sub>1</sub></font> <b>by </b><i><a class="ref" href="matrix_2.html#D11" target="_self">Def11</a></i>;<br/>
<b>reconsider </b><font color="Maroon">c<sub>6</sub></font> = <font color="Maroon">c<sub>4</sub></font> <a href="partfun1.html#K1">*</a> <font color="Maroon">c<sub>5</sub></font> as    <a href="matrix_2.html#M3" target="_self">Element</a> of  <a href="matrix_2.html#K11" target="_self">Permutations</a> <font color="Maroon">c<sub>1</sub></font> <b>by </b><i><a class="ref" href="matrix_2.html#D11" target="_self">Def11</a></i>;<br/>
<b>take </b>
<font color="Maroon">c<sub>6</sub></font>
;<br/>

<b>thus </b><a NAME="E3:39_1_1_1"/>
<font color="Maroon">S<sub>1</sub></font>[<font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>3</sub></font>,<font color="Maroon">c<sub>6</sub></font>]
 ;<br/>


</div><b>end;</b></div>
<b>consider </b><font color="Maroon">c<sub>2</sub></font> being   <a href="binop_1.html#NM2">BinOp</a> of  <a href="matrix_2.html#K11" target="_self">Permutations</a> <font color="Maroon">c<sub>1</sub></font><b> such that </b><br/><a NAME="E3:39_1_1"/><i><font color="Green">E17</font></i>: 
for <font color="Olive">b<sub>1</sub></font>, <font color="Olive">b<sub>2</sub></font> being   <a href="matrix_2.html#M3" target="_self">Element</a> of  <a href="matrix_2.html#K11" target="_self">Permutations</a> <font color="Maroon">c<sub>1</sub></font> holds <font color="Maroon">S<sub>1</sub></font>[<font color="Olive">b<sub>1</sub></font>,<font color="Olive">b<sub>2</sub></font>,<font color="Maroon">c<sub>2</sub></font> <a href="binop_1.html#K2">.</a> <font color="Olive">b<sub>1</sub></font>,<font color="Olive">b<sub>2</sub></font>]
 <b>from </b><i><a class="ref" href="binop_1.html#S3">BINOP_1:sch 3</a>(<a class="txt" href="matrix_2.html#E1:39_1_1"><i><font color="Green">E16</font></i></a>);<br/></i>
<b>take </b>
 <a href="group_1.html#G1">HGrStr</a>(# <span class="p1">(<span class="default"><a href="matrix_2.html#K11" target="_self">Permutations</a> <font color="Maroon">c<sub>1</sub></font></span>)</span>,<font color="Maroon">c<sub>2</sub></font> #)
;<br/>

<b>thus </b><a NAME="E4:39_1_1"/>
( the <a href="struct_0.html#U1">carrier</a> of <a href="group_1.html#G1">HGrStr</a>(# <span class="p1">(<span class="default"><a href="matrix_2.html#K11" target="_self">Permutations</a> <font color="Maroon">c<sub>1</sub></font></span>)</span>,<font color="Maroon">c<sub>2</sub></font> #) <a href="hidden.html#R1">=</a>  <a href="matrix_2.html#K11" target="_self">Permutations</a> <font color="Maroon">c<sub>1</sub></font> &amp; ( for <font color="Olive">b<sub>1</sub></font>, <font color="Olive">b<sub>2</sub></font> being   <a href="matrix_2.html#M3" target="_self">Element</a> of  <a href="matrix_2.html#K11" target="_self">Permutations</a> <font color="Maroon">c<sub>1</sub></font> holds the <a href="group_1.html#U1">mult</a> of <a href="group_1.html#G1">HGrStr</a>(# <span class="p1">(<span class="default"><a href="matrix_2.html#K11" target="_self">Permutations</a> <font color="Maroon">c<sub>1</sub></font></span>)</span>,<font color="Maroon">c<sub>2</sub></font> #) <a href="binop_1.html#K1">.</a> <font color="Olive">b<sub>1</sub></font>,<font color="Olive">b<sub>2</sub></font> <a href="hidden.html#R1">=</a> <font color="Olive">b<sub>2</sub></font> <a href="partfun1.html#K1">*</a> <font color="Olive">b<sub>1</sub></font> ) )
 <b>by </b><i><a class="txt" href="matrix_2.html#E3:39_1_1"><i><font color="Green">E17</font></i></a></i>;<br/>


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