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<b>consider </b><font color="Maroon" title="c5">B1</font> being   <a href="altcat_1.html#NM2" title="ALTCAT_1:NM.2">Morphism</a> of <font color="Maroon" title="c3">o2</font>,<font color="Maroon" title="c2">o1</font><b> such that </b><br/><a NAME="E2:6_1_1"/><i><font color="Green" title="E7">A3</font></i>: 
<font color="Maroon" title="c5">B1</font> <a href="altcat_3.html#NR2" title="ALTCAT_3:NR.2">is_right_inverse_of</a> <font color="Maroon" title="c4">A</font>
 <b>by </b><i><a class="txt" href="altcat_3.html#E2:6"><i><font color="Green" title="E6">A2</font></i></a>, <a class="ref" href="altcat_3.html#D2" target="_self" title="ALTCAT_3:def.2">Def2</a></i>;<br/>
<b>consider </b><font color="Maroon" title="c6">B2</font> being   <a href="altcat_1.html#NM2" title="ALTCAT_1:NM.2">Morphism</a> of <font color="Maroon" title="c3">o2</font>,<font color="Maroon" title="c2">o1</font><b> such that </b><br/><a NAME="E4:6_1_1"/><i><font color="Green" title="E8">A4</font></i>: 
<font color="Maroon" title="c6">B2</font> <a href="altcat_3.html#R1" title="ALTCAT_3:pred.1">is_left_inverse_of</a> <font color="Maroon" title="c4">A</font>
 <b>by </b><i><a class="txt" href="altcat_3.html#E2:6"><i><font color="Green" title="E6">A2</font></i></a>, <a class="ref" href="altcat_3.html#D3" target="_self" title="ALTCAT_3:def.3">Def3</a></i>;<br/>
<i><font color="Green" title="E9">A5</font></i>: <font color="Maroon" title="c5">B1</font> = 
<span class="p1">(<span class="default"><a href="altcat_1.html#K8" title="ALTCAT_1:func.8">idm</a> <font color="Maroon" title="c2">o1</font></span>)</span> <a href="altcat_1.html#K5" title="ALTCAT_1:func.5">*</a> <font color="Maroon" title="c5">B1</font>
<b>by </b><i><a class="txt" href="altcat_3.html#E1:6"><i><font color="Green" title="E5">A1</font></i></a>, <a class="ref" href="altcat_1.html#T24" title="ALTCAT_1:th.24">ALTCAT_1:24</a></i>
<br/>.= 
<span class="p1">(<span class="default"><font color="Maroon" title="c6">B2</font> <a href="altcat_1.html#K5" title="ALTCAT_1:func.5">*</a> <font color="Maroon" title="c4">A</font></span>)</span> <a href="altcat_1.html#K5" title="ALTCAT_1:func.5">*</a> <font color="Maroon" title="c5">B1</font>
<b>by </b><i><a class="txt" href="altcat_3.html#E4:6_1_1"><i><font color="Green" title="E8">A4</font></i></a>, <a class="ref" href="altcat_3.html#D1" target="_self" title="ALTCAT_3:def.1">Def1</a></i>
<br/>.= 
<font color="Maroon" title="c6">B2</font> <a href="altcat_1.html#K5" title="ALTCAT_1:func.5">*</a> <span class="p1">(<span class="default"><font color="Maroon" title="c4">A</font> <a href="altcat_1.html#K5" title="ALTCAT_1:func.5">*</a> <font color="Maroon" title="c5">B1</font></span>)</span>
<b>by </b><i><a class="txt" href="altcat_3.html#E1:6"><i><font color="Green" title="E5">A1</font></i></a>, <a class="ref" href="altcat_1.html#T25" title="ALTCAT_1:th.25">ALTCAT_1:25</a></i>
<br/>.= 
<font color="Maroon" title="c6">B2</font> <a href="altcat_1.html#K5" title="ALTCAT_1:func.5">*</a> <span class="p1">(<span class="default"><a href="altcat_1.html#K8" title="ALTCAT_1:func.8">idm</a> <font color="Maroon" title="c3">o2</font></span>)</span>
<b>by </b><i><a class="txt" href="altcat_3.html#E2:6_1_1"><i><font color="Green" title="E7">A3</font></i></a>, <a class="ref" href="altcat_3.html#D1" target="_self" title="ALTCAT_3:def.1">Def1</a></i>
<br/>.= 
<font color="Maroon" title="c6">B2</font>
<b>by </b><i><a class="txt" href="altcat_3.html#E1:6"><i><font color="Green" title="E5">A1</font></i></a>, <a class="ref" href="altcat_1.html#D19" title="ALTCAT_1:def.19">ALTCAT_1:def 19</a></i>
;<br/>
<b>take </b>
<font color="Maroon" title="c5">B1</font>
; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> ( <font color="Maroon" title="c5">B1</font> <a href="altcat_3.html#R1" title="ALTCAT_3:pred.1">is_left_inverse_of</a> <font color="Maroon" title="c4">A</font> &amp; <font color="Maroon" title="c5">B1</font> <a href="altcat_3.html#NR2" title="ALTCAT_3:NR.2">is_right_inverse_of</a> <font color="Maroon" title="c4">A</font> )</span><br/>

<b>thus </b><a NAME="E6:6_1_1"/>
( <font color="Maroon" title="c5">B1</font> <a href="altcat_3.html#R1" title="ALTCAT_3:pred.1">is_left_inverse_of</a> <font color="Maroon" title="c4">A</font> &amp; <font color="Maroon" title="c5">B1</font> <a href="altcat_3.html#NR2" title="ALTCAT_3:NR.2">is_right_inverse_of</a> <font color="Maroon" title="c4">A</font> )
 <b>by </b><i><a class="txt" href="altcat_3.html#E2:6_1_1"><i><font color="Green" title="E7">A3</font></i></a>, <a class="txt" href="altcat_3.html#E4:6_1_1"><i><font color="Green" title="E8">A4</font></i></a>, <a class="txt" href="altcat_3.html#E5:6_1_1"><i><font color="Green" title="E9">A5</font></i></a></i>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> verum</span><br/>


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