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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>, <font color="Maroon">c<sub>4</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="E1:15"/><i><font color="Green">E14</font></i>: 
<font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>3</sub></font> <a href="altcat_3.html#R2" target="_self">are_iso</a> 
 <b>and </b><br/><a NAME="E2:15"/><i><font color="Green">E15</font></i>: 
<font color="Maroon">c<sub>3</sub></font>,<font color="Maroon">c<sub>4</sub></font> <a href="altcat_3.html#R2" target="_self">are_iso</a> 
 ;<br/>

<a NAME="E3:15"/><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>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>  &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>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>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>  )
 
<b>by </b><i><a class="txt" href="altcat_3.html#E1:15"><i><font color="Green">E14</font></i></a>, <a class="txt" href="altcat_3.html#E2:15"><i><font color="Green">E15</font></i></a>, <a class="ref" href="altcat_3.html#D6" target="_self">Def6</a></i>;<br/>
<b>hence </b><a NAME="E4:15"/><i><font color="Green">E17</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>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>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>  )
 <b>by </b><i><a class="ref" href="altcat_1.html#D4">ALTCAT_1:def 4</a></i>; <i><font color="Red">:: according to </font></i><a class="ref" href="altcat_3.html#D6" target="_self">ALTCAT_3:def 6</a><br/>

<b>consider </b><font color="Maroon">c<sub>5</sub></font> being   <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><b> such that </b><br/><a NAME="E6:15"/><i><font color="Green">E18</font></i>: 
<font color="Maroon">c<sub>5</sub></font> is <a href="altcat_3.html#V3" target="_self">iso</a>
 <b>by </b><i><a class="txt" href="altcat_3.html#E1:15"><i><font color="Green">E14</font></i></a>, <a class="ref" href="altcat_3.html#D6" target="_self">Def6</a></i>;<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>3</sub></font>,<font color="Maroon">c<sub>4</sub></font><b> such that </b><br/><a NAME="E8:15"/><i><font color="Green">E19</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#E2:15"><i><font color="Green">E15</font></i></a>, <a class="ref" href="altcat_3.html#D6" target="_self">Def6</a></i>;<br/>
<b>take </b>
<font color="Maroon">c<sub>6</sub></font> <a href="altcat_1.html#K5">*</a> <font color="Maroon">c<sub>5</sub></font>
;<br/>

<b>thus </b><a NAME="E9:15"/>
<font color="Maroon">c<sub>6</sub></font> <a href="altcat_1.html#K5">*</a> <font color="Maroon">c<sub>5</sub></font> is <a href="altcat_3.html#V3" target="_self">iso</a>
 <b>by </b><i><a class="txt" href="altcat_3.html#E3:15"><i><font color="Green">E16</font></i></a>, <a class="txt" href="altcat_3.html#E4:15"><i><font color="Green">E17</font></i></a>, <a class="txt" href="altcat_3.html#E6:15"><i><font color="Green">E18</font></i></a>, <a class="txt" href="altcat_3.html#E8:15"><i><font color="Green">E19</font></i></a>, <a class="ref" href="altcat_3.html#T7" target="_self">Th7</a></i>;<br/>


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