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<b>let </b><font color="Maroon">c<sub>1</sub></font> be   <a href="altcat_1.html#NM4">category</a>;<br/><b>let </b><font color="Maroon">c<sub>2</sub></font>, <font color="Maroon">c<sub>3</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>4</sub></font> be   <a href="altcat_1.html#NM2">Morphism</a> of <font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>3</sub></font>;<br/>







<b>assume </b><a NAME="E1:4"/><i><font color="Green">E4</font></i>: 
( <span class="p1"><a href="altcat_1.html#K1">&lt;^</a><span class="default"><font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>3</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>3</sub></font>,<font color="Maroon">c<sub>2</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="E2:4"/>
<font color="Maroon">c<sub>4</sub></font> is <a href="altcat_3.html#V3">iso</a>
 ;<br/>

<a NAME="E3:4"/><b>then </b><i><font color="Green">E5</font></i>: 
( <font color="Maroon">c<sub>4</sub></font> is <a href="altcat_3.html#V1">retraction</a> &amp; <font color="Maroon">c<sub>4</sub></font> is <a href="altcat_3.html#V2">coretraction</a> )
 
<b>by </b><i><a class="ref" href="altcat_3.html#T5">ALTCAT_3:5</a></i>;<br/>
<b>hence </b><span class="p1">(<span class="default"><font color="Maroon">c<sub>4</sub></font> <a href="altcat_3.html#K1">"</a> </span>)</span> <a href="altcat_1.html#K5">*</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>4</sub></font> <a href="altcat_3.html#K1">"</a> </span>)</span> <a href="altcat_3.html#K1">"</a> </span>)</span> = 
<span class="p1">(<span class="default"><font color="Maroon">c<sub>4</sub></font> <a href="altcat_3.html#K1">"</a> </span>)</span> <a href="altcat_1.html#K5">*</a> <font color="Maroon">c<sub>4</sub></font>
<b>by </b><i><a class="txt" href="altcat_4.html#E1:4"><i><font color="Green">E4</font></i></a>, <a class="ref" href="altcat_3.html#T3">ALTCAT_3:3</a></i>
<br/>.= 
 <a href="altcat_1.html#K8">idm</a> <font color="Maroon">c<sub>2</sub></font>
<b>by </b><i><a class="txt" href="altcat_4.html#E1:4"><i><font color="Green">E4</font></i></a>, <a class="txt" href="altcat_4.html#E3:4"><i><font color="Green">E5</font></i></a>, <a class="ref" href="altcat_3.html#T2">ALTCAT_3:2</a></i>
;<br/> <i><font color="Red">:: according to </font></i><a class="ref" href="altcat_3.html#D5">ALTCAT_3:def 5</a><br/>

<b>thus </b><span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>4</sub></font> <a href="altcat_3.html#K1">"</a> </span>)</span> <a href="altcat_3.html#K1">"</a> </span>)</span> <a href="altcat_1.html#K5">*</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>4</sub></font> <a href="altcat_3.html#K1">"</a> </span>)</span> = 
<font color="Maroon">c<sub>4</sub></font> <a href="altcat_1.html#K5">*</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>4</sub></font> <a href="altcat_3.html#K1">"</a> </span>)</span>
<b>by </b><i><a class="txt" href="altcat_4.html#E1:4"><i><font color="Green">E4</font></i></a>, <a class="txt" href="altcat_4.html#E3:4"><i><font color="Green">E5</font></i></a>, <a class="ref" href="altcat_3.html#T3">ALTCAT_3:3</a></i>
<br/>.= 
 <a href="altcat_1.html#K8">idm</a> <font color="Maroon">c<sub>3</sub></font>
<b>by </b><i><a class="txt" href="altcat_4.html#E1:4"><i><font color="Green">E4</font></i></a>, <a class="txt" href="altcat_4.html#E3:4"><i><font color="Green">E5</font></i></a>, <a class="ref" href="altcat_3.html#T2">ALTCAT_3:2</a></i>
;<br/>


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