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<b>let </b><font color="Maroon">M1</font> be   <a href="altcat_1.html#NM2">Morphism</a> of <font color="Maroon">o2</font>,<font color="Maroon">o1</font>, <font color="Maroon">M2</font> be   <a href="altcat_1.html#NM2">Morphism</a> of <font color="Maroon">o2</font>,<font color="Maroon">o1</font>;<br/>

<b>assume </b><b>that </b><br/><a NAME="E1:6_1_2"/><i><font color="Green">E31</font></i>: 
( <font color="Maroon">M1</font> <a href="altcat_3.html#R1" target="_self">is_left_inverse_of</a> <font color="Maroon">A</font> &amp; <font color="Maroon">M1</font> <a href="altcat_3.html#NR2" target="_self">is_right_inverse_of</a> <font color="Maroon">A</font> )
 <b>and </b><br/><a NAME="E2:6_1_2"/><i><font color="Green">E32</font></i>: 
( <font color="Maroon">M2</font> <a href="altcat_3.html#R1" target="_self">is_left_inverse_of</a> <font color="Maroon">A</font> &amp; <font color="Maroon">M2</font> <a href="altcat_3.html#NR2" target="_self">is_right_inverse_of</a> <font color="Maroon">A</font> )
 ;<br/>

<b>thus </b><font color="Maroon">M1</font> = 
<font color="Maroon">M1</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">o2</font></span>)</span>
<b>by </b><i>, <a class="ref" href="altcat_1.html#D19">ALTCAT_1:def 19</a></i>
<br/>.= 
<font color="Maroon">M1</font> <a href="altcat_1.html#K5">*</a> <span class="p1">(<span class="default"><font color="Maroon">A</font> <a href="altcat_1.html#K5">*</a> <font color="Maroon">M2</font></span>)</span>
<b>by </b><i>, </i>
<br/>.= 
<span class="p1">(<span class="default"><font color="Maroon">M1</font> <a href="altcat_1.html#K5">*</a> <font color="Maroon">A</font></span>)</span> <a href="altcat_1.html#K5">*</a> <font color="Maroon">M2</font>
<b>by </b><i>, <a class="ref" href="altcat_1.html#T25">ALTCAT_1:25</a></i>
<br/>.= 
<span class="p1">(<span class="default"><a href="altcat_1.html#K8">idm</a> <font color="Maroon">o1</font></span>)</span> <a href="altcat_1.html#K5">*</a> <font color="Maroon">M2</font>
<b>by </b><i>, </i>
<br/>.= 
<font color="Maroon">M2</font>
<b>by </b><i>, <a class="ref" href="altcat_1.html#T24">ALTCAT_1:24</a></i>
;<br/>


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