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<b>let </b><font color="Maroon">x</font> be    <a href="hidden.html#M1">set</a> , <font color="Maroon">y1</font> be    <a href="hidden.html#M1">set</a> , <font color="Maroon">y2</font> be    <a href="hidden.html#M1">set</a> ;<br/>

<b>assume </b><b>that </b><br/><a NAME="E1:78"/><i><font color="Green">E29</font></i>: 
 <a href="grcat_1.html#R1" target="_self">GO</a> <font color="Maroon">x</font>,<font color="Maroon">y1</font>
 <b>and </b><br/><a NAME="E2:78"/><i><font color="Green">E42</font></i>: 
 <a href="grcat_1.html#R1" target="_self">GO</a> <font color="Maroon">x</font>,<font color="Maroon">y2</font>
 ;<br/>

<b>consider </b><font color="Maroon">a1</font> being    <a href="hidden.html#M1">set</a> , <font color="Maroon">a2</font> being    <a href="hidden.html#M1">set</a> , <font color="Maroon">a3</font> being    <a href="hidden.html#M1">set</a> , <font color="Maroon">a4</font> being    <a href="hidden.html#M1">set</a> <b> such that </b><br/><a NAME="E4:78"/><i><font color="Green">E43</font></i>: 
<font color="Maroon">x</font> <a href="hidden.html#R1">=</a> <span class="p1"><a href="mcart_1.html#K4">[</a><span class="default"><font color="Maroon">a1</font>,<font color="Maroon">a2</font>,<font color="Maroon">a3</font>,<font color="Maroon">a4</font></span><a href="mcart_1.html#K4">]</a></span>
 <b>and </b><br/><a NAME="E5:78"/><i><font color="Green">E44</font></i>: 
 ex <font color="Olive">G</font> being <a href="rlvect_1.html#V1">strict</a> <a href="mod_1.html#NM1">AddGroup</a> st <br/>( <font color="Maroon">y1</font> <a href="hidden.html#R1">=</a> <font color="Olive">G</font> &amp; <font color="Maroon">a1</font> <a href="hidden.html#R1">=</a> the <a href="struct_0.html#U1">carrier</a> of <font color="Olive">G</font> &amp; <font color="Maroon">a2</font> <a href="hidden.html#R1">=</a> the <a href="rlvect_1.html#U1">add</a> of <font color="Olive">G</font> &amp; <font color="Maroon">a3</font> <a href="hidden.html#R1">=</a>  <a href="vectsp_1.html#K7">comp</a> <font color="Olive">G</font> &amp; <font color="Maroon">a4</font> <a href="hidden.html#R1">=</a> the <a href="struct_0.html#U2">Zero</a> of <font color="Olive">G</font> )
 <b>by </b><i><a class="txt" href="grcat_1.html#E2:78"><i><font color="Green">E42</font></i></a>, </i>;<br/>
<b>consider </b><font color="Maroon">b1</font> being    <a href="hidden.html#M1">set</a> , <font color="Maroon">b2</font> being    <a href="hidden.html#M1">set</a> , <font color="Maroon">b3</font> being    <a href="hidden.html#M1">set</a> , <font color="Maroon">b4</font> being    <a href="hidden.html#M1">set</a> <b> such that </b><br/><a NAME="E7:78"/><i><font color="Green">E90</font></i>: 
<font color="Maroon">x</font> <a href="hidden.html#R1">=</a> <span class="p1"><a href="mcart_1.html#K4">[</a><span class="default"><font color="Maroon">b1</font>,<font color="Maroon">b2</font>,<font color="Maroon">b3</font>,<font color="Maroon">b4</font></span><a href="mcart_1.html#K4">]</a></span>
 <b>and </b><br/><a NAME="E8:78"/><i><font color="Green">E91</font></i>: 
 ex <font color="Olive">G</font> being <a href="rlvect_1.html#V1">strict</a> <a href="mod_1.html#NM1">AddGroup</a> st <br/>( <font color="Maroon">y2</font> <a href="hidden.html#R1">=</a> <font color="Olive">G</font> &amp; <font color="Maroon">b1</font> <a href="hidden.html#R1">=</a> the <a href="struct_0.html#U1">carrier</a> of <font color="Olive">G</font> &amp; <font color="Maroon">b2</font> <a href="hidden.html#R1">=</a> the <a href="rlvect_1.html#U1">add</a> of <font color="Olive">G</font> &amp; <font color="Maroon">b3</font> <a href="hidden.html#R1">=</a>  <a href="vectsp_1.html#K7">comp</a> <font color="Olive">G</font> &amp; <font color="Maroon">b4</font> <a href="hidden.html#R1">=</a> the <a href="struct_0.html#U2">Zero</a> of <font color="Olive">G</font> )
 <b>by </b><i><a class="txt" href="grcat_1.html#E4:78"><i><font color="Green">E43</font></i></a>, </i>;<br/>
<b>consider </b><font color="Maroon">G1</font> being  <a href="rlvect_1.html#V1">strict</a> <a href="mod_1.html#NM1">AddGroup</a><b> such that </b><br/><a NAME="E10:78"/><i><font color="Green">E92</font></i>: 
( <font color="Maroon">y1</font> <a href="hidden.html#R1">=</a> <font color="Maroon">G1</font> &amp; <font color="Maroon">a1</font> <a href="hidden.html#R1">=</a> the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">G1</font> &amp; <font color="Maroon">a2</font> <a href="hidden.html#R1">=</a> the <a href="rlvect_1.html#U1">add</a> of <font color="Maroon">G1</font> &amp; <font color="Maroon">a3</font> <a href="hidden.html#R1">=</a>  <a href="vectsp_1.html#K7">comp</a> <font color="Maroon">G1</font> &amp; <font color="Maroon">a4</font> <a href="hidden.html#R1">=</a> the <a href="struct_0.html#U2">Zero</a> of <font color="Maroon">G1</font> )
 <b>by </b><i/>;<br/>
<b>consider </b><font color="Maroon">G2</font> being  <a href="rlvect_1.html#V1">strict</a> <a href="mod_1.html#NM1">AddGroup</a><b> such that </b><br/><a NAME="E12:78"/><i><font color="Green">E96</font></i>: 
( <font color="Maroon">y2</font> <a href="hidden.html#R1">=</a> <font color="Maroon">G2</font> &amp; <font color="Maroon">b1</font> <a href="hidden.html#R1">=</a> the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">G2</font> &amp; <font color="Maroon">b2</font> <a href="hidden.html#R1">=</a> the <a href="rlvect_1.html#U1">add</a> of <font color="Maroon">G2</font> &amp; <font color="Maroon">b3</font> <a href="hidden.html#R1">=</a>  <a href="vectsp_1.html#K7">comp</a> <font color="Maroon">G2</font> &amp; <font color="Maroon">b4</font> <a href="hidden.html#R1">=</a> the <a href="struct_0.html#U2">Zero</a> of <font color="Maroon">G2</font> )
 <b>by </b><i><a class="ref" href="grcat_1.html#T6" target="_self">Th6</a></i>;<br/>
<a NAME="E13:78"/>
( the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">G1</font> <a href="hidden.html#R1">=</a> the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">G2</font> &amp; the <a href="rlvect_1.html#U1">add</a> of <font color="Maroon">G1</font> <a href="funct_2.html#R1">=</a> the <a href="rlvect_1.html#U1">add</a> of <font color="Maroon">G2</font> &amp;  <a href="vectsp_1.html#K7">comp</a> <font color="Maroon">G1</font> <a href="funct_2.html#R1">=</a>  <a href="vectsp_1.html#K7">comp</a> <font color="Maroon">G2</font> &amp; the <a href="struct_0.html#U2">Zero</a> of <font color="Maroon">G1</font> <a href="hidden.html#R1">=</a> the <a href="struct_0.html#U2">Zero</a> of <font color="Maroon">G2</font> )
 
<b>by </b><i><a class="txt" href="grcat_1.html#E5:78"><i><font color="Green">E44</font></i></a>, <a class="ref" href="grcat_1.html#T5" target="_self">Th5</a>, <a class="ref" href="grcat_1.html#T7" target="_self">Th7</a>, , <a class="ref" href="mcart_1.html#T33">MCART_1:33</a></i>;<br/>
<b>hence </b><a NAME="E14:78"/>
<font color="Maroon">y1</font> <a href="hidden.html#R1">=</a> <font color="Maroon">y2</font>
 <b>by </b><i><a class="ref" href="grcat_1.html#T7" target="_self">Th7</a>, </i>;<br/>


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