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<b>let </b><font color="Maroon" title="c1">A</font>, <font color="Maroon" title="c2">B</font> be  non <a href="struct_0.html#V2" title="STRUCT_0:attr.2">empty</a> <a href="altcat_1.html#V2" title="ALTCAT_1:attr.2">transitive</a> <a href="altcat_1.html#V12" title="ALTCAT_1:attr.12">with_units</a>  <a href="altcat_1.html#L2" title="ALTCAT_1:struct.2">AltCatStr</a> ;<br/><b>let </b><font color="Maroon" title="c3">F</font> be  <a href="functor0.html#V15" title="FUNCTOR0:attr.15">covariant</a>  <a href="functor0.html#M2" title="FUNCTOR0:mode.2">Functor</a> of <font color="Maroon" title="c1">A</font>,<font color="Maroon" title="c2">B</font>;<br/><b>let </b><font color="Maroon" title="c4">o1</font>, <font color="Maroon" title="c5">o2</font> be   <a href="altcat_1.html#NM1" title="ALTCAT_1:NM.1">object</a> of <font color="Maroon" title="c1">A</font>;<br/><b>let </b><font color="Maroon" title="c6">a</font> be   <a href="altcat_1.html#NM2" title="ALTCAT_1:NM.2">Morphism</a> of <font color="Maroon" title="c4">o1</font>,<font color="Maroon" title="c5">o2</font>;<br/>







<b>assume </b><a NAME="E1:21"/><i><font color="Green" title="E11">A1</font></i>: 
( <span class="p1"><a href="altcat_1.html#K1" title="ALTCAT_1:func.1">&lt;^</a><span class="default"><font color="Maroon" title="c4">o1</font>,<font color="Maroon" title="c5">o2</font></span><a href="altcat_1.html#K1" title="ALTCAT_1:func.1">^&gt;</a></span> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a>  <a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a>  &amp; <span class="p1"><a href="altcat_1.html#K1" title="ALTCAT_1:func.1">&lt;^</a><span class="default"><font color="Maroon" title="c5">o2</font>,<font color="Maroon" title="c4">o1</font></span><a href="altcat_1.html#K1" title="ALTCAT_1:func.1">^&gt;</a></span> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a>  <a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a>  )
 ;<br/>

<b>assume </b><a NAME="E2:21"/>
<font color="Maroon" title="c6">a</font> is <a href="altcat_3.html#V1" title="ALTCAT_3:attr.1">retraction</a>
 ;<br/>

<b>then consider </b><font color="Maroon" title="c7">b</font> being   <a href="altcat_1.html#NM2" title="ALTCAT_1:NM.2">Morphism</a> of <font color="Maroon" title="c5">o2</font>,<font color="Maroon" title="c4">o1</font><b> such that </b><br/><a NAME="E4:21"/><i><font color="Green" title="E12">A2</font></i>: 
<font color="Maroon" title="c7">b</font> <a href="altcat_3.html#NR2" title="ALTCAT_3:NR.2">is_right_inverse_of</a> <font color="Maroon" title="c6">a</font>
 <b>by </b><i><a class="ref" href="altcat_3.html#D2" title="ALTCAT_3:def.2">ALTCAT_3:def 2</a></i>;<br/>
<b>take </b>
<font color="Maroon" title="c3">F</font> <a href="functor0.html#K6" title="FUNCTOR0:func.6">.</a> <font color="Maroon" title="c7">b</font>
; <i><font color="Red">:: according to </font></i><a class="ref" href="altcat_3.html#D2" title="ALTCAT_3:def.2">ALTCAT_3:def 2</a><br/>

<a NAME="E5:21"/>
<font color="Maroon" title="c6">a</font> <a href="altcat_1.html#K5" title="ALTCAT_1:func.5">*</a> <font color="Maroon" title="c7">b</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="altcat_1.html#K8" title="ALTCAT_1:func.8">idm</a> <font color="Maroon" title="c5">o2</font>
 
<b>by </b><i><a class="txt" href="altcat_4.html#E4:21"><i><font color="Green" title="E12">A2</font></i></a>, <a class="ref" href="altcat_3.html#D1" title="ALTCAT_3:def.1">ALTCAT_3:def 1</a></i>;<br/>
<b>hence </b><span class="p1">(<span class="default"><font color="Maroon" title="c3">F</font> <a href="functor0.html#K6" title="FUNCTOR0:func.6">.</a> <font color="Maroon" title="c6">a</font></span>)</span> <a href="altcat_1.html#K5" title="ALTCAT_1:func.5">*</a> <span class="p1">(<span class="default"><font color="Maroon" title="c3">F</font> <a href="functor0.html#K6" title="FUNCTOR0:func.6">.</a> <font color="Maroon" title="c7">b</font></span>)</span> = 
<font color="Maroon" title="c3">F</font> <a href="functor0.html#K6" title="FUNCTOR0:func.6">.</a> <span class="p1">(<span class="default"><a href="altcat_1.html#K8" title="ALTCAT_1:func.8">idm</a> <font color="Maroon" title="c5">o2</font></span>)</span>
<b>by </b><i><a class="txt" href="altcat_4.html#E1:21"><i><font color="Green" title="E11">A1</font></i></a>, <a class="ref" href="functor0.html#D24" title="FUNCTOR0:def.24">FUNCTOR0:def 24</a></i>
<br/>.= 
 <a href="altcat_1.html#K8" title="ALTCAT_1:func.8">idm</a> <span class="p1">(<span class="default"><font color="Maroon" title="c3">F</font> <a href="functor0.html#K3" title="FUNCTOR0:func.3">.</a> <font color="Maroon" title="c5">o2</font></span>)</span>
<b>by </b><i><a class="ref" href="functor2.html#T2" title="FUNCTOR2:th.2">FUNCTOR2:2</a></i>
;<br/> <i><font color="Red">:: according to </font></i><a class="ref" href="altcat_3.html#D1" title="ALTCAT_3:def.1">ALTCAT_3:def 1</a><br/>


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