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<b>let </b><font color="Maroon" title="c1">x</font>, <font color="Maroon" title="c2">y1</font>, <font color="Maroon" title="c3">y2</font> be    <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a> ;<br/>

<b>assume </b><b>that </b><br/><a NAME="E1:76"/><i><font color="Green" title="E42">A1</font></i>: 
 <a href="grcat_1.html#R1" title="GRCAT_1:pred.1">GO</a> <font color="Maroon" title="c1">x</font>,<font color="Maroon" title="c2">y1</font>
 <b>and </b><br/><a NAME="E2:76"/><i><font color="Green" title="E43">A2</font></i>: 
 <a href="grcat_1.html#R1" title="GRCAT_1:pred.1">GO</a> <font color="Maroon" title="c1">x</font>,<font color="Maroon" title="c3">y2</font>
 ;<br/>

<b>consider </b><font color="Maroon" title="c4">a1</font>, <font color="Maroon" title="c5">a2</font>, <font color="Maroon" title="c6">a3</font>, <font color="Maroon" title="c7">a4</font> being    <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a> <b> such that </b><br/><a NAME="E4:76"/><i><font color="Green" title="E44">A3</font></i>: 
<font color="Maroon" title="c1">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1"><a href="mcart_1.html#K4" title="MCART_1:func.4">[</a><span class="default"><font color="Maroon" title="c4">a1</font>,<font color="Maroon" title="c5">a2</font>,<font color="Maroon" title="c6">a3</font>,<font color="Maroon" title="c7">a4</font></span><a href="mcart_1.html#K4" title="MCART_1:func.4">]</a></span>
 <b>and </b><br/><a NAME="E5:76"/><i><font color="Green" title="E45">A4</font></i>: 
 ex <font color="Olive" title="b1">G</font> being <a href="rlvect_1.html#V1" title="RLVECT_1:attr.1">strict</a> <a href="mod_1.html#NM1" title="MOD_1:NM.1">AddGroup</a> st <br/>( <font color="Maroon" title="c2">y1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b1">G</font> &amp; <font color="Maroon" title="c4">a1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Olive" title="b1">G</font> &amp; <font color="Maroon" title="c5">a2</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> the <a href="rlvect_1.html#U1" title="RLVECT_1:sel.1">add</a> of <font color="Olive" title="b1">G</font> &amp; <font color="Maroon" title="c6">a3</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="vectsp_1.html#K7" title="VECTSP_1:func.7">comp</a> <font color="Olive" title="b1">G</font> &amp; <font color="Maroon" title="c7">a4</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> the <a href="struct_0.html#U2" title="STRUCT_0:sel.2">Zero</a> of <font color="Olive" title="b1">G</font> )
 <b>by </b><i><a class="txt" href="grcat_1.html#E1:76"><i><font color="Green" title="E42">A1</font></i></a>, <a class="ref" href="grcat_1.html#D28" target="_self" title="GRCAT_1:def.28">Def28</a></i>;<br/>
<b>consider </b><font color="Maroon" title="c8">b1</font>, <font color="Maroon" title="c9">b2</font>, <font color="Maroon" title="c10">b3</font>, <font color="Maroon" title="c11">b4</font> being    <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a> <b> such that </b><br/><a NAME="E7:76"/><i><font color="Green" title="E46">A5</font></i>: 
<font color="Maroon" title="c1">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1"><a href="mcart_1.html#K4" title="MCART_1:func.4">[</a><span class="default"><font color="Maroon" title="c8">b1</font>,<font color="Maroon" title="c9">b2</font>,<font color="Maroon" title="c10">b3</font>,<font color="Maroon" title="c11">b4</font></span><a href="mcart_1.html#K4" title="MCART_1:func.4">]</a></span>
 <b>and </b><br/><a NAME="E8:76"/><i><font color="Green" title="E47">A6</font></i>: 
 ex <font color="Olive" title="b1">G</font> being <a href="rlvect_1.html#V1" title="RLVECT_1:attr.1">strict</a> <a href="mod_1.html#NM1" title="MOD_1:NM.1">AddGroup</a> st <br/>( <font color="Maroon" title="c3">y2</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b1">G</font> &amp; <font color="Maroon" title="c8">b1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Olive" title="b1">G</font> &amp; <font color="Maroon" title="c9">b2</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> the <a href="rlvect_1.html#U1" title="RLVECT_1:sel.1">add</a> of <font color="Olive" title="b1">G</font> &amp; <font color="Maroon" title="c10">b3</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="vectsp_1.html#K7" title="VECTSP_1:func.7">comp</a> <font color="Olive" title="b1">G</font> &amp; <font color="Maroon" title="c11">b4</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> the <a href="struct_0.html#U2" title="STRUCT_0:sel.2">Zero</a> of <font color="Olive" title="b1">G</font> )
 <b>by </b><i><a class="txt" href="grcat_1.html#E2:76"><i><font color="Green" title="E43">A2</font></i></a>, <a class="ref" href="grcat_1.html#D28" target="_self" title="GRCAT_1:def.28">Def28</a></i>;<br/>
<b>consider </b><font color="Maroon" title="c12">G1</font> being  <a href="rlvect_1.html#V1" title="RLVECT_1:attr.1">strict</a> <a href="mod_1.html#NM1" title="MOD_1:NM.1">AddGroup</a><b> such that </b><br/><a NAME="E10:76"/><i><font color="Green" title="E48">A7</font></i>: 
( <font color="Maroon" title="c2">y1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c12">G1</font> &amp; <font color="Maroon" title="c4">a1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c12">G1</font> &amp; <font color="Maroon" title="c5">a2</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> the <a href="rlvect_1.html#U1" title="RLVECT_1:sel.1">add</a> of <font color="Maroon" title="c12">G1</font> &amp; <font color="Maroon" title="c6">a3</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="vectsp_1.html#K7" title="VECTSP_1:func.7">comp</a> <font color="Maroon" title="c12">G1</font> &amp; <font color="Maroon" title="c7">a4</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> the <a href="struct_0.html#U2" title="STRUCT_0:sel.2">Zero</a> of <font color="Maroon" title="c12">G1</font> )
 <b>by </b><i><a class="txt" href="grcat_1.html#E5:76"><i><font color="Green" title="E45">A4</font></i></a></i>;<br/>
<b>consider </b><font color="Maroon" title="c13">G2</font> being  <a href="rlvect_1.html#V1" title="RLVECT_1:attr.1">strict</a> <a href="mod_1.html#NM1" title="MOD_1:NM.1">AddGroup</a><b> such that </b><br/><a NAME="E12:76"/><i><font color="Green" title="E49">A8</font></i>: 
( <font color="Maroon" title="c3">y2</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c13">G2</font> &amp; <font color="Maroon" title="c8">b1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c13">G2</font> &amp; <font color="Maroon" title="c9">b2</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> the <a href="rlvect_1.html#U1" title="RLVECT_1:sel.1">add</a> of <font color="Maroon" title="c13">G2</font> &amp; <font color="Maroon" title="c10">b3</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="vectsp_1.html#K7" title="VECTSP_1:func.7">comp</a> <font color="Maroon" title="c13">G2</font> &amp; <font color="Maroon" title="c11">b4</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> the <a href="struct_0.html#U2" title="STRUCT_0:sel.2">Zero</a> of <font color="Maroon" title="c13">G2</font> )
 <b>by </b><i><a class="txt" href="grcat_1.html#E8:76"><i><font color="Green" title="E47">A6</font></i></a></i>;<br/>
<a NAME="E13:76"/>
( the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c12">G1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c13">G2</font> &amp; the <a href="rlvect_1.html#U1" title="RLVECT_1:sel.1">add</a> of <font color="Maroon" title="c12">G1</font> <a href="funct_2.html#R1" title="FUNCT_2:pred.1">=</a> the <a href="rlvect_1.html#U1" title="RLVECT_1:sel.1">add</a> of <font color="Maroon" title="c13">G2</font> &amp;  <a href="vectsp_1.html#K7" title="VECTSP_1:func.7">comp</a> <font color="Maroon" title="c12">G1</font> <a href="funct_2.html#R1" title="FUNCT_2:pred.1">=</a>  <a href="vectsp_1.html#K7" title="VECTSP_1:func.7">comp</a> <font color="Maroon" title="c13">G2</font> &amp; the <a href="struct_0.html#U2" title="STRUCT_0:sel.2">Zero</a> of <font color="Maroon" title="c12">G1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> the <a href="struct_0.html#U2" title="STRUCT_0:sel.2">Zero</a> of <font color="Maroon" title="c13">G2</font> )
 
<b>by </b><i><a class="txt" href="grcat_1.html#E4:76"><i><font color="Green" title="E44">A3</font></i></a>, <a class="txt" href="grcat_1.html#E7:76"><i><font color="Green" title="E46">A5</font></i></a>, <a class="txt" href="grcat_1.html#E10:76"><i><font color="Green" title="E48">A7</font></i></a>, <a class="txt" href="grcat_1.html#E12:76"><i><font color="Green" title="E49">A8</font></i></a>, <a class="ref" href="mcart_1.html#T33" title="MCART_1:th.33">MCART_1:33</a></i>;<br/>
<b>hence </b><a NAME="E14:76"/>
<font color="Maroon" title="c2">y1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c3">y2</font>
 <b>by </b><i><a class="txt" href="grcat_1.html#E10:76"><i><font color="Green" title="E48">A7</font></i></a>, <a class="txt" href="grcat_1.html#E12:76"><i><font color="Green" title="E49">A8</font></i></a></i>;<br/>


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