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<b>consider </b><font color="Maroon">c<sub>5</sub></font> being   <a href="altcat_1.html#NM2">Morphism</a> of <font color="Maroon">c<sub>3</sub></font>,<font color="Maroon">c<sub>2</sub></font><b> such that </b><br/><a NAME="E2:6_1_1"/><i><font color="Green">E7</font></i>: 
<font color="Maroon">c<sub>5</sub></font> <a href="altcat_3.html#NR2" target="_self">is_right_inverse_of</a> <font color="Maroon">c<sub>4</sub></font>
 <b>by </b><i><a class="txt" href="altcat_3.html#E2:6"><i><font color="Green">E6</font></i></a>, <a class="ref" href="altcat_3.html#D2" target="_self">Def2</a></i>;<br/>
<b>consider </b><font color="Maroon">c<sub>6</sub></font> being   <a href="altcat_1.html#NM2">Morphism</a> of <font color="Maroon">c<sub>3</sub></font>,<font color="Maroon">c<sub>2</sub></font><b> such that </b><br/><a NAME="E4:6_1_1"/><i><font color="Green">E8</font></i>: 
<font color="Maroon">c<sub>6</sub></font> <a href="altcat_3.html#R1" target="_self">is_left_inverse_of</a> <font color="Maroon">c<sub>4</sub></font>
 <b>by </b><i><a class="txt" href="altcat_3.html#E2:6"><i><font color="Green">E6</font></i></a>, <a class="ref" href="altcat_3.html#D3" target="_self">Def3</a></i>;<br/>
<i><font color="Green">E9</font></i>: <font color="Maroon">c<sub>5</sub></font> = 
<span class="p1">(<span class="default"><a href="altcat_1.html#K8">idm</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="altcat_1.html#K5">*</a> <font color="Maroon">c<sub>5</sub></font>
<b>by </b><i><a class="txt" href="altcat_3.html#E1:6"><i><font color="Green">E5</font></i></a>, <a class="ref" href="altcat_1.html#T24">ALTCAT_1:24</a></i>
<br/>.= 
<span class="p1">(<span class="default"><font color="Maroon">c<sub>6</sub></font> <a href="altcat_1.html#K5">*</a> <font color="Maroon">c<sub>4</sub></font></span>)</span> <a href="altcat_1.html#K5">*</a> <font color="Maroon">c<sub>5</sub></font>
<b>by </b><i><a class="txt" href="altcat_3.html#E4:6_1_1"><i><font color="Green">E8</font></i></a>, <a class="ref" href="altcat_3.html#D1" target="_self">Def1</a></i>
<br/>.= 
<font color="Maroon">c<sub>6</sub></font> <a href="altcat_1.html#K5">*</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>4</sub></font> <a href="altcat_1.html#K5">*</a> <font color="Maroon">c<sub>5</sub></font></span>)</span>
<b>by </b><i><a class="txt" href="altcat_3.html#E1:6"><i><font color="Green">E5</font></i></a>, <a class="ref" href="altcat_1.html#T25">ALTCAT_1:25</a></i>
<br/>.= 
<font color="Maroon">c<sub>6</sub></font> <a href="altcat_1.html#K5">*</a> <span class="p1">(<span class="default"><a href="altcat_1.html#K8">idm</a> <font color="Maroon">c<sub>3</sub></font></span>)</span>
<b>by </b><i><a class="txt" href="altcat_3.html#E2:6_1_1"><i><font color="Green">E7</font></i></a>, <a class="ref" href="altcat_3.html#D1" target="_self">Def1</a></i>
<br/>.= 
<font color="Maroon">c<sub>6</sub></font>
<b>by </b><i><a class="txt" href="altcat_3.html#E1:6"><i><font color="Green">E5</font></i></a>, <a class="ref" href="altcat_1.html#D19">ALTCAT_1:def 19</a></i>
;<br/>
<b>take </b>
<font color="Maroon">c<sub>5</sub></font>
;<br/>

<b>thus </b><a NAME="E6:6_1_1"/>
( <font color="Maroon">c<sub>5</sub></font> <a href="altcat_3.html#R1" target="_self">is_left_inverse_of</a> <font color="Maroon">c<sub>4</sub></font> &amp; <font color="Maroon">c<sub>5</sub></font> <a href="altcat_3.html#NR2" target="_self">is_right_inverse_of</a> <font color="Maroon">c<sub>4</sub></font> )
 <b>by </b><i><a class="txt" href="altcat_3.html#E2:6_1_1"><i><font color="Green">E7</font></i></a>, <a class="txt" href="altcat_3.html#E4:6_1_1"><i><font color="Green">E8</font></i></a>, <a class="txt" href="altcat_3.html#E5:6_1_1"><i><font color="Green">E9</font></i></a></i>;<br/>


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