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<span class="kw">consider </span><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><span class="kw"> such that </span><br/><a NAME="E2:6_1_1"/><span class="lab"><font color="Green" title="E8">A4</font></span>: 
<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 class="kw">by</span> <span class="lab"><a class="txt" href="#E3:6"><span class="lab"><font color="Green" title="E7">A3</font></span></a>, <a class="ref" href="altcat_3.html#D2" target="_self" title="ALTCAT_3:def.2">Def2</a></span>;<br/>
<span class="kw">take </span>
<font color="Maroon" title="c5">B1</font>
; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></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/>

<span class="kw">consider </span><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><span class="kw"> such that </span><br/><a NAME="E4:6_1_1"/><span class="lab"><font color="Green" title="E9">A5</font></span>: 
<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>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E3:6"><span class="lab"><font color="Green" title="E7">A3</font></span></a>, <a class="ref" href="altcat_3.html#D3" target="_self" title="ALTCAT_3:def.3">Def3</a></span>;<br/>
<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>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:6"><span class="lab"><font color="Green" title="E6">A2</font></span></a>, <a class="ref" href="altcat_1.html#T24" title="ALTCAT_1:th.24">ALTCAT_1:24</a></span>
<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>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E4:6_1_1"><span class="lab"><font color="Green" title="E9">A5</font></span></a>, <a class="ref" href="altcat_3.html#D1" target="_self" title="ALTCAT_3:def.1">Def1</a></span>
<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>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:6"><span class="lab"><font color="Green" title="E5">A1</font></span></a>, <a class="txt" href="#E2:6"><span class="lab"><font color="Green" title="E6">A2</font></span></a>, <a class="ref" href="altcat_1.html#T25" title="ALTCAT_1:th.25">ALTCAT_1:25</a></span>
<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>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:6_1_1"><span class="lab"><font color="Green" title="E8">A4</font></span></a>, <a class="ref" href="altcat_3.html#D1" target="_self" title="ALTCAT_3:def.1">Def1</a></span>
<br/>.= 
<font color="Maroon" title="c6">B2</font>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:6"><span class="lab"><font color="Green" title="E6">A2</font></span></a>, <a class="ref" href="altcat_1.html#D19" title="ALTCAT_1:def.19">ALTCAT_1:def 19</a></span>
;<br/>
<span class="kw">hence </span><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> )
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:6_1_1"><span class="lab"><font color="Green" title="E8">A4</font></span></a>, <a class="txt" href="#E4:6_1_1"><span class="lab"><font color="Green" title="E9">A5</font></span></a></span>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> verum</span><br/>


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