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<b>let </b><font color="Maroon">c<sub>1</sub></font>, <font color="Maroon">c<sub>2</sub></font> be   <a href="altcat_1.html#NM4">category</a>;<br/><b>let </b><font color="Maroon">c<sub>3</sub></font> be  <a href="functor0.html#V16">contravariant</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><b>that </b><br/><a NAME="E1:27"/><i><font color="Green">E16</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>  )
 <b>and </b><br/><a NAME="E2:27"/><i><font color="Green">E17</font></i>: 
<font color="Maroon">c<sub>6</sub></font> is <a href="altcat_3.html#V3">iso</a>
 ;<br/>

<a NAME="E3:27"/><i><font color="Green">E18</font></i>: 
( <span class="p1"><a href="altcat_1.html#K1">&lt;^</a><span class="default"><span class="p2">(<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>,<span class="p2">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="functor0.html#K3">.</a> <font color="Maroon">c<sub>5</sub></font></span>)</span></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"><span class="p2">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="functor0.html#K3">.</a> <font color="Maroon">c<sub>5</sub></font></span>)</span>,<span class="p2">(<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></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>  )
 
<b>by </b><i><a class="txt" href="altcat_4.html#E1:27"><i><font color="Green">E16</font></i></a>, <a class="ref" href="functor0.html#D20">FUNCTOR0:def 20</a></i>;<br/>
<a NAME="E4:27"/>
( <font color="Maroon">c<sub>6</sub></font> is <a href="altcat_3.html#V1">retraction</a> &amp; <font color="Maroon">c<sub>6</sub></font> is <a href="altcat_3.html#V2">coretraction</a> )
 
<b>by </b><i><a class="txt" href="altcat_4.html#E1:27"><i><font color="Green">E16</font></i></a>, <a class="txt" href="altcat_4.html#E2:27"><i><font color="Green">E17</font></i></a>, <a class="ref" href="altcat_3.html#T6">ALTCAT_3:6</a></i>;<br/>
<a NAME="E5:27"/><b>then </b>
( <font color="Maroon">c<sub>3</sub></font> <a href="functor0.html#K8">.</a> <font color="Maroon">c<sub>6</sub></font> is <a href="altcat_3.html#V1">retraction</a> &amp; <font color="Maroon">c<sub>3</sub></font> <a href="functor0.html#K8">.</a> <font color="Maroon">c<sub>6</sub></font> is <a href="altcat_3.html#V2">coretraction</a> )
 
<b>by </b><i><a class="txt" href="altcat_4.html#E1:27"><i><font color="Green">E16</font></i></a>, <a class="ref" href="altcat_4.html#T22" target="_self">Th22</a>, <a class="ref" href="altcat_4.html#T23" target="_self">Th23</a></i>;<br/>
<b>hence </b><a NAME="E6:27"/>
<font color="Maroon">c<sub>3</sub></font> <a href="functor0.html#K8">.</a> <font color="Maroon">c<sub>6</sub></font> is <a href="altcat_3.html#V3">iso</a>
 <b>by </b><i><a class="txt" href="altcat_4.html#E3:27"><i><font color="Green">E18</font></i></a>, <a class="ref" href="altcat_3.html#T6">ALTCAT_3:6</a></i>;<br/>


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