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<b>let </b><font color="Maroon">c<sub>1</sub></font>, <font color="Maroon">c<sub>2</sub></font> be  non <a href="struct_0.html#V3">empty</a> <a href="altcat_1.html#V2">transitive</a> <a href="altcat_1.html#V12">with_units</a>  <a href="altcat_1.html#L2">AltCatStr</a> ;<br/><b>let </b><font color="Maroon">c<sub>3</sub></font> be  <a href="functor0.html#V15">covariant</a>  <a href="functor0.html#M2">Functor</a> of <font color="Maroon">c<sub>1</sub></font>,<font color="Maroon">c<sub>2</sub></font>;<br/><b>let </b><font color="Maroon">c<sub>4</sub></font>, <font color="Maroon">c<sub>5</sub></font> be   <a href="altcat_1.html#NM1">object</a> of <font color="Maroon">c<sub>1</sub></font>;<br/><b>let </b><font color="Maroon">c<sub>6</sub></font> be   <a href="altcat_1.html#NM2">Morphism</a> of <font color="Maroon">c<sub>4</sub></font>,<font color="Maroon">c<sub>5</sub></font>;<br/>







<b>assume </b><a NAME="E1:22"/><i><font color="Green">E12</font></i>: 
( <span class="p1"><a href="altcat_1.html#K1">&lt;^</a><span class="default"><font color="Maroon">c<sub>4</sub></font>,<font color="Maroon">c<sub>5</sub></font></span><a href="altcat_1.html#K1">^&gt;</a></span> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a>  <a href="xboole_0.html#K1">{}</a>  &amp; <span class="p1"><a href="altcat_1.html#K1">&lt;^</a><span class="default"><font color="Maroon">c<sub>5</sub></font>,<font color="Maroon">c<sub>4</sub></font></span><a href="altcat_1.html#K1">^&gt;</a></span> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a>  <a href="xboole_0.html#K1">{}</a>  )
 ;<br/>

<b>assume </b><a NAME="E2:22"/>
<font color="Maroon">c<sub>6</sub></font> is <a href="altcat_3.html#V2">coretraction</a>
 ;<br/>

<b>then consider </b><font color="Maroon">c<sub>7</sub></font> being   <a href="altcat_1.html#NM2">Morphism</a> of <font color="Maroon">c<sub>5</sub></font>,<font color="Maroon">c<sub>4</sub></font><b> such that </b><br/><a NAME="E4:22"/><i><font color="Green">E13</font></i>: 
<font color="Maroon">c<sub>6</sub></font> <a href="altcat_3.html#NR2" target="_self">is_right_inverse_of</a> <font color="Maroon">c<sub>7</sub></font>
 <b>by </b><i><a class="ref" href="altcat_3.html#D3">ALTCAT_3:def 3</a></i>;<br/>
<b>take </b>
<font color="Maroon">c<sub>3</sub></font> <a href="functor0.html#K6">.</a> <font color="Maroon">c<sub>7</sub></font>
; <i><font color="Red">:: according to </font></i><a class="ref" href="altcat_3.html#D3">ALTCAT_3:def 3</a><br/>

<a NAME="E5:22"/>
<font color="Maroon">c<sub>7</sub></font> <a href="altcat_1.html#K5">*</a> <font color="Maroon">c<sub>6</sub></font> <a href="hidden.html#R1">=</a>  <a href="altcat_1.html#K8">idm</a> <font color="Maroon">c<sub>4</sub></font>
 
<b>by </b><i><a class="txt" href="altcat_4.html#E4:22"><i><font color="Green">E13</font></i></a>, <a class="ref" href="altcat_3.html#D1">ALTCAT_3:def 1</a></i>;<br/>
<b>hence </b><span class="p1">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="functor0.html#K6">.</a> <font color="Maroon">c<sub>7</sub></font></span>)</span> <a href="altcat_1.html#K5">*</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="functor0.html#K6">.</a> <font color="Maroon">c<sub>6</sub></font></span>)</span> = 
<font color="Maroon">c<sub>3</sub></font> <a href="functor0.html#K6">.</a> <span class="p1">(<span class="default"><a href="altcat_1.html#K8">idm</a> <font color="Maroon">c<sub>4</sub></font></span>)</span>
<b>by </b><i><a class="txt" href="altcat_4.html#E1:22"><i><font color="Green">E12</font></i></a>, <a class="ref" href="functor0.html#D24">FUNCTOR0:def 24</a></i>
<br/>.= 
 <a href="altcat_1.html#K8">idm</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="functor0.html#K3">.</a> <font color="Maroon">c<sub>4</sub></font></span>)</span>
<b>by </b><i><a class="ref" href="functor2.html#T2">FUNCTOR2:2</a></i>
;<br/> <i><font color="Red">:: according to </font></i><a class="ref" href="altcat_3.html#D1">ALTCAT_3:def 1</a><br/>


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