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<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>assume </b><b>that </b><br/><a NAME="E1:14_1_2"/><i><font color="Green">E13</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="E2:14_1_2"/><i><font color="Green">E14</font></i>: 
ex <font color="Olive">b<sub>1</sub></font> being  <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> st <font color="Olive">b<sub>1</sub></font> is <a href="altcat_3.html#V3" target="_self">iso</a>
 ;<br/>

<b>consider </b><font color="Maroon">c<sub>6</sub></font> being   <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><b> such that </b><br/><a NAME="E4:14_1_2"/><i><font color="Green">E15</font></i>: 
<font color="Maroon">c<sub>6</sub></font> is <a href="altcat_3.html#V3" target="_self">iso</a>
 <b>by </b><i><a class="txt" href="altcat_3.html#E2:14_1_2"><i><font color="Green">E14</font></i></a></i>;<br/>
<a NAME="E5:14_1_2"/><i><font color="Green">E16</font></i>: 
( <font color="Maroon">c<sub>6</sub></font> is <a href="altcat_3.html#V1" target="_self">retraction</a> &amp; <font color="Maroon">c<sub>6</sub></font> is <a href="altcat_3.html#V2" target="_self">coretraction</a> )
 
<b>by </b><i><a class="txt" href="altcat_3.html#E4:14_1_2"><i><font color="Green">E15</font></i></a>, <a class="ref" href="altcat_3.html#T5" target="_self">Th5</a></i>;<br/>
<b>thus </b><a NAME="E6:14_1_2"/>
( <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>  &amp; <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>  )
 <b>by </b><i><a class="txt" href="altcat_3.html#E1:14_1_2"><i><font color="Green">E13</font></i></a></i>;<br/>

<b>take </b><font color="Maroon">c<sub>7</sub></font> = <font color="Maroon">c<sub>6</sub></font> <a href="altcat_3.html#K1" target="_self">"</a> ;<br/>

<i><font color="Green">E17</font></i>: <font color="Maroon">c<sub>7</sub></font> <a href="altcat_1.html#K5">*</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>7</sub></font> <a href="altcat_3.html#K1" target="_self">"</a> </span>)</span> = 
<span class="p1">(<span class="default"><font color="Maroon">c<sub>6</sub></font> <a href="altcat_3.html#K1" target="_self">"</a> </span>)</span> <a href="altcat_1.html#K5">*</a> <font color="Maroon">c<sub>6</sub></font>
<b>by </b><i><a class="txt" href="altcat_3.html#E1:14_1_2"><i><font color="Green">E13</font></i></a>, <a class="txt" href="altcat_3.html#E5:14_1_2"><i><font color="Green">E16</font></i></a>, <a class="ref" href="altcat_3.html#T3" target="_self">Th3</a></i>
<br/>.= 
 <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_3.html#E1:14_1_2"><i><font color="Green">E13</font></i></a>, <a class="txt" href="altcat_3.html#E5:14_1_2"><i><font color="Green">E16</font></i></a>, <a class="ref" href="altcat_3.html#T2" target="_self">Th2</a></i>
;<br/>
<span class="p1">(<span class="default"><font color="Maroon">c<sub>7</sub></font> <a href="altcat_3.html#K1" target="_self">"</a> </span>)</span> <a href="altcat_1.html#K5">*</a> <font color="Maroon">c<sub>7</sub></font> = 
<font color="Maroon">c<sub>6</sub></font> <a href="altcat_1.html#K5">*</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>6</sub></font> <a href="altcat_3.html#K1" target="_self">"</a> </span>)</span>
<b>by </b><i><a class="txt" href="altcat_3.html#E1:14_1_2"><i><font color="Green">E13</font></i></a>, <a class="txt" href="altcat_3.html#E5:14_1_2"><i><font color="Green">E16</font></i></a>, <a class="ref" href="altcat_3.html#T3" target="_self">Th3</a></i>
<br/>.= 
 <a href="altcat_1.html#K8">idm</a> <font color="Maroon">c<sub>5</sub></font>
<b>by </b><i><a class="txt" href="altcat_3.html#E1:14_1_2"><i><font color="Green">E13</font></i></a>, <a class="txt" href="altcat_3.html#E5:14_1_2"><i><font color="Green">E16</font></i></a>, <a class="ref" href="altcat_3.html#T2" target="_self">Th2</a></i>
;<br/>
<b>hence </b><a NAME="E9:14_1_2"/>
<font color="Maroon">c<sub>7</sub></font> is <a href="altcat_3.html#V3" target="_self">iso</a>
 <b>by </b><i><a class="txt" href="altcat_3.html#E7:14_1_2"><i><font color="Green">E17</font></i></a>, <a class="ref" href="altcat_3.html#D5" target="_self">Def5</a></i>;<br/>


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