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<b>let </b><font color="Maroon">c<sub>1</sub></font> be   <a href="grcat_1.html#NM3">Group_DOMAIN</a>;<br/>

<b>set </b><font color="Maroon">c<sub>2</sub></font> =  <a href="grcat_1.html#K20" target="_self">Morphs</a> <font color="Maroon">c<sub>1</sub></font>;<br/>
<b>defpred </b><font color="Maroon">S<sub>1</sub></font>[   <a href="grcat_1.html#M3" target="_self">Element</a> of  <a href="grcat_1.html#K20" target="_self">Morphs</a> <font color="Maroon">c<sub>1</sub></font>,   <a href="grcat_1.html#M3" target="_self">Element</a> of  <a href="grcat_1.html#K20" target="_self">Morphs</a> <font color="Maroon">c<sub>1</sub></font>] means  <a href="grcat_1.html#K21" target="_self">dom</a> <font color="Maroon">a<sub>1</sub></font> <a href="hidden.html#R1">=</a>  <a href="grcat_1.html#K22" target="_self">cod</a> <font color="Maroon">a<sub>2</sub></font>;<br/>
<b>let </b><font color="Maroon">c<sub>3</sub></font>, <font color="Maroon">c<sub>4</sub></font> be    <a href="grcat_1.html#M3" target="_self">Element</a> of  <a href="grcat_1.html#K20" target="_self">Morphs</a> <font color="Maroon">c<sub>1</sub></font>;<br/>

<b>assume </b><a NAME="E1:89"/><i><font color="Green">E51</font></i>: 
<font color="Maroon">S<sub>1</sub></font>[<font color="Maroon">c<sub>3</sub></font>,<font color="Maroon">c<sub>4</sub></font>]
 ;<br/>

<b>consider </b><font color="Maroon">c<sub>5</sub></font>, <font color="Maroon">c<sub>6</sub></font> being  <a href="rlvect_1.html#V1">strict</a>  <a href="grcat_1.html#M2" target="_self">Element</a> of <font color="Maroon">c<sub>1</sub></font><b> such that </b><br/><a NAME="E3:89"/><i><font color="Green">E52</font></i>: 
<font color="Maroon">c<sub>3</sub></font> is  <a href="grcat_1.html#V2" target="_self">strict</a>  <a href="grcat_1.html#M1" target="_self">Morphism</a> of <font color="Maroon">c<sub>5</sub></font>,<font color="Maroon">c<sub>6</sub></font>
 <b>by </b><i><a class="ref" href="grcat_1.html#D30" target="_self">Def30</a></i>;<br/>
<a NAME="E4:89"/><i><font color="Green">E53</font></i>: 
<font color="Maroon">c<sub>5</sub></font> <a href="hidden.html#R1">=</a>  <a href="grcat_1.html#K21" target="_self">dom</a> <font color="Maroon">c<sub>3</sub></font>
 
<b>by </b><i><a class="txt" href="grcat_1.html#E3:89"><i><font color="Green">E52</font></i></a>, <a class="ref" href="grcat_1.html#D19" target="_self">Def19</a></i>;<br/>
<b>consider </b><font color="Maroon">c<sub>7</sub></font>, <font color="Maroon">c<sub>8</sub></font> being  <a href="rlvect_1.html#V1">strict</a>  <a href="grcat_1.html#M2" target="_self">Element</a> of <font color="Maroon">c<sub>1</sub></font><b> such that </b><br/><a NAME="E6:89"/><i><font color="Green">E54</font></i>: 
<font color="Maroon">c<sub>4</sub></font> is  <a href="grcat_1.html#V2" target="_self">strict</a>  <a href="grcat_1.html#M1" target="_self">Morphism</a> of <font color="Maroon">c<sub>7</sub></font>,<font color="Maroon">c<sub>8</sub></font>
 <b>by </b><i><a class="ref" href="grcat_1.html#D30" target="_self">Def30</a></i>;<br/>
<a NAME="E7:89"/>
<font color="Maroon">c<sub>8</sub></font> <a href="hidden.html#R1">=</a>  <a href="grcat_1.html#K22" target="_self">cod</a> <font color="Maroon">c<sub>4</sub></font>
 
<b>by </b><i><a class="txt" href="grcat_1.html#E6:89"><i><font color="Green">E54</font></i></a>, <a class="ref" href="grcat_1.html#D19" target="_self">Def19</a></i>;<br/>
<b>hence </b><a NAME="E8:89"/>
ex <font color="Olive">b<sub>1</sub></font>, <font color="Olive">b<sub>2</sub></font>, <font color="Olive">b<sub>3</sub></font> being <a href="rlvect_1.html#V1">strict</a>  <a href="grcat_1.html#M2" target="_self">Element</a> of <font color="Maroon">c<sub>1</sub></font> st <br/>( <font color="Maroon">c<sub>3</sub></font> is    <a href="grcat_1.html#M1" target="_self">Morphism</a> of <font color="Olive">b<sub>2</sub></font>,<font color="Olive">b<sub>3</sub></font> &amp; <font color="Maroon">c<sub>4</sub></font> is    <a href="grcat_1.html#M1" target="_self">Morphism</a> of <font color="Olive">b<sub>1</sub></font>,<font color="Olive">b<sub>2</sub></font> )
 <b>by </b><i><a class="txt" href="grcat_1.html#E1:89"><i><font color="Green">E51</font></i></a>, <a class="txt" href="grcat_1.html#E3:89"><i><font color="Green">E52</font></i></a>, <a class="txt" href="grcat_1.html#E4:89"><i><font color="Green">E53</font></i></a>, <a class="txt" href="grcat_1.html#E6:89"><i><font color="Green">E54</font></i></a></i>;<br/>


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