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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  non <a href="struct_0.html#V3">empty</a> <a href="altcat_2.html#NM2">subcategory</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="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>5</sub></font>, <font color="Maroon">c<sub>6</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>7</sub></font>, <font color="Maroon">c<sub>8</sub></font> be   <a href="altcat_1.html#NM1">object</a> of <font color="Maroon">c<sub>3</sub></font>;<br/>









<b>assume </b><a NAME="E1:41"/><i><font color="Green">E25</font></i>: 
( <font color="Maroon">c<sub>7</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>5</sub></font> &amp; <font color="Maroon">c<sub>8</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>6</sub></font> &amp; <span class="p1"><a href="altcat_1.html#K1">&lt;^</a><span class="default"><font color="Maroon">c<sub>7</sub></font>,<font color="Maroon">c<sub>8</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/>

<a NAME="E2:41"/><b>then </b><i><font color="Green">E26</font></i>: 
( <span class="p1">(<span class="default"><a href="yellow20.html#K3" target="_self">incl</a> <font color="Maroon">c<sub>3</sub></font></span>)</span> <a href="functor0.html#K3">.</a> <font color="Maroon">c<sub>7</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>5</sub></font> &amp; <span class="p1">(<span class="default"><a href="yellow20.html#K3" target="_self">incl</a> <font color="Maroon">c<sub>3</sub></font></span>)</span> <a href="functor0.html#K3">.</a> <font color="Maroon">c<sub>8</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>6</sub></font> )
 
<b>by </b><i><a class="ref" href="functor0.html#T28">FUNCTOR0:28</a></i>;<br/>
<b>let </b><font color="Maroon">c<sub>9</sub></font> be   <a href="altcat_1.html#NM2">Morphism</a> of <font color="Maroon">c<sub>5</sub></font>,<font color="Maroon">c<sub>6</sub></font>;<br/><b>let </b><font color="Maroon">c<sub>10</sub></font> be   <a href="altcat_1.html#NM2">Morphism</a> of <font color="Maroon">c<sub>7</sub></font>,<font color="Maroon">c<sub>8</sub></font>;<br/>



<b>assume </b><a NAME="E3:41"/>
<font color="Maroon">c<sub>10</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>9</sub></font>
 ;<br/>

<a NAME="E4:41"/><b>then </b>
<span class="p1">(<span class="default"><a href="yellow20.html#K3" target="_self">incl</a> <font color="Maroon">c<sub>3</sub></font></span>)</span> <a href="functor0.html#K6">.</a> <font color="Maroon">c<sub>10</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>9</sub></font>
 
<b>by </b><i><a class="txt" href="yellow20.html#E1:41"><i><font color="Green">E25</font></i></a>, <a class="ref" href="yellow20.html#T28" target="_self">Th28</a></i>;<br/>
<b>hence </b><a NAME="E5:41"/>
<span class="p1">(<span class="default"><font color="Maroon">c<sub>4</sub></font> <a href="yellow20.html#K4" target="_self">|</a> <font color="Maroon">c<sub>3</sub></font></span>)</span> <a href="functor0.html#K6">.</a> <font color="Maroon">c<sub>10</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>4</sub></font> <a href="functor0.html#K6">.</a> <font color="Maroon">c<sub>9</sub></font>
 <b>by </b><i><a class="txt" href="yellow20.html#E1:41"><i><font color="Green">E25</font></i></a>, <a class="txt" href="yellow20.html#E2:41"><i><font color="Green">E26</font></i></a>, <a class="ref" href="functor3.html#T6">FUNCTOR3:6</a></i>;<br/>


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