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<b>let </b><font color="Maroon">A</font> be   <a href="altcat_1.html#NM4">category</a>, <font color="Maroon">B</font> be   <a href="altcat_1.html#NM4">category</a>;<br/><b>let </b><font color="Maroon">F</font> be  <a href="functor0.html#V15">covariant</a>  <a href="functor0.html#M2">Functor</a> of <font color="Maroon">A</font>,<font color="Maroon">B</font>, <font color="Maroon">F1</font> be  <a href="functor0.html#V15">covariant</a>  <a href="functor0.html#M2">Functor</a> of <font color="Maroon">A</font>,<font color="Maroon">B</font>, <font color="Maroon">F2</font> be  <a href="functor0.html#V15">covariant</a>  <a href="functor0.html#M2">Functor</a> of <font color="Maroon">A</font>,<font color="Maroon">B</font>;<br/>



<b>assume </b><b>that </b><br/><a NAME="E1:17"/><i><font color="Green">E20</font></i>: 
<font color="Maroon">F</font> <a href="functor2.html#R1" target="_self">is_transformable_to</a> <font color="Maroon">F1</font>
 <b>and </b><br/><a NAME="E2:17"/><i><font color="Green">E28</font></i>: 
<font color="Maroon">F1</font> <a href="functor2.html#R1" target="_self">is_transformable_to</a> <font color="Maroon">F2</font>
 ;<br/>

<b>let </b><font color="Maroon">t1</font> be    <a href="functor2.html#M1" target="_self">transformation</a> of <font color="Maroon">F</font>,<font color="Maroon">F1</font>;<br/>

<b>assume </b><a NAME="E3:17"/><i><font color="Green">E30</font></i>: 
for <font color="Olive">a</font>, <font color="Olive">b</font> being  <a href="altcat_1.html#NM1">object</a> of <font color="Maroon">A</font>  st <span class="p1"><a href="altcat_1.html#K1">&lt;^</a><span class="default"><font color="Olive">a</font>,<font color="Olive">b</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>  holds <br/>for <font color="Olive">f</font> being  <a href="altcat_1.html#NM2">Morphism</a> of <font color="Olive">a</font>,<font color="Olive">b</font> holds  <span class="p1">(<span class="default"><font color="Maroon">t1</font> <a href="functor2.html#K2" target="_self">!</a> <font color="Olive">b</font></span>)</span> <a href="altcat_1.html#K5">*</a> <span class="p1">(<span class="default"><font color="Maroon">F</font> <a href="functor0.html#K6">.</a> <font color="Olive">f</font></span>)</span> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><font color="Maroon">F1</font> <a href="functor0.html#K6">.</a> <font color="Olive">f</font></span>)</span> <a href="altcat_1.html#K5">*</a> <span class="p1">(<span class="default"><font color="Maroon">t1</font> <a href="functor2.html#K2" target="_self">!</a> <font color="Olive">a</font></span>)</span>
 ;<br/>

<b>let </b><font color="Maroon">t2</font> be    <a href="functor2.html#M1" target="_self">transformation</a> of <font color="Maroon">F1</font>,<font color="Maroon">F2</font>;<br/>

<b>assume </b><a NAME="E4:17"/><i><font color="Green">E32</font></i>: 
for <font color="Olive">a</font>, <font color="Olive">b</font> being  <a href="altcat_1.html#NM1">object</a> of <font color="Maroon">A</font>  st <span class="p1"><a href="altcat_1.html#K1">&lt;^</a><span class="default"><font color="Olive">a</font>,<font color="Olive">b</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>  holds <br/>for <font color="Olive">f</font> being  <a href="altcat_1.html#NM2">Morphism</a> of <font color="Olive">a</font>,<font color="Olive">b</font> holds  <span class="p1">(<span class="default"><font color="Maroon">t2</font> <a href="functor2.html#K2" target="_self">!</a> <font color="Olive">b</font></span>)</span> <a href="altcat_1.html#K5">*</a> <span class="p1">(<span class="default"><font color="Maroon">F1</font> <a href="functor0.html#K6">.</a> <font color="Olive">f</font></span>)</span> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><font color="Maroon">F2</font> <a href="functor0.html#K6">.</a> <font color="Olive">f</font></span>)</span> <a href="altcat_1.html#K5">*</a> <span class="p1">(<span class="default"><font color="Maroon">t2</font> <a href="functor2.html#K2" target="_self">!</a> <font color="Olive">a</font></span>)</span>
 ;<br/>

<b>let </b><font color="Maroon">a</font> be   <a href="altcat_1.html#NM1">object</a> of <font color="Maroon">A</font>, <font color="Maroon">b</font> be   <a href="altcat_1.html#NM1">object</a> of <font color="Maroon">A</font>;<br/>

<b>assume </b><a NAME="E5:17"/><i><font color="Green">E34</font></i>: 
<span class="p1"><a href="altcat_1.html#K1">&lt;^</a><span class="default"><font color="Maroon">a</font>,<font color="Maroon">b</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="E6:17"/><b>then </b><i><font color="Green">E37</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">F</font> <a href="functor0.html#K3">.</a> <font color="Maroon">a</font></span>)</span>,<span class="p2">(<span class="default"><font color="Maroon">F</font> <a href="functor0.html#K3">.</a> <font color="Maroon">b</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">F</font> <a href="functor0.html#K3">.</a> <font color="Maroon">b</font></span>)</span>,<span class="p2">(<span class="default"><font color="Maroon">F1</font> <a href="functor0.html#K3">.</a> <font color="Maroon">b</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="ref" href="functor0.html#D19">FUNCTOR0:def 19</a></i>;<br/>
<a NAME="E7:17"/><i><font color="Green">E38</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">F</font> <a href="functor0.html#K3">.</a> <font color="Maroon">a</font></span>)</span>,<span class="p2">(<span class="default"><font color="Maroon">F1</font> <a href="functor0.html#K3">.</a> <font color="Maroon">a</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">F1</font> <a href="functor0.html#K3">.</a> <font color="Maroon">a</font></span>)</span>,<span class="p2">(<span class="default"><font color="Maroon">F2</font> <a href="functor0.html#K3">.</a> <font color="Maroon">a</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="ref" href="functor2.html#T2" target="_self">Th2</a>, </i>;<br/>
<a NAME="E8:17"/><i><font color="Green">E44</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">F1</font> <a href="functor0.html#K3">.</a> <font color="Maroon">b</font></span>)</span>,<span class="p2">(<span class="default"><font color="Maroon">F2</font> <a href="functor0.html#K3">.</a> <font color="Maroon">b</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="ref" href="functor2.html#T2" target="_self">Th2</a>, </i>;<br/>
<a NAME="E9:17"/><i><font color="Green">E45</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">F2</font> <a href="functor0.html#K3">.</a> <font color="Maroon">a</font></span>)</span>,<span class="p2">(<span class="default"><font color="Maroon">F2</font> <a href="functor0.html#K3">.</a> <font color="Maroon">b</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="functor2.html#E1:17"><i><font color="Green">E20</font></i></a>, <a class="ref" href="functor0.html#D19">FUNCTOR0:def 19</a></i>;<br/>
<a NAME="E10:17"/><i><font color="Green">E46</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">F1</font> <a href="functor0.html#K3">.</a> <font color="Maroon">a</font></span>)</span>,<span class="p2">(<span class="default"><font color="Maroon">F1</font> <a href="functor0.html#K3">.</a> <font color="Maroon">b</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="functor2.html#E1:17"><i><font color="Green">E20</font></i></a>, <a class="ref" href="functor0.html#D19">FUNCTOR0:def 19</a></i>;<br/>
<b>let </b><font color="Maroon">f</font> be   <a href="altcat_1.html#NM2">Morphism</a> of <font color="Maroon">a</font>,<font color="Maroon">b</font>;<br/>

<b>thus </b><span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">t2</font> <a href="functor2.html#K3" target="_self">`*`</a> <font color="Maroon">t1</font></span>)</span> <a href="functor2.html#K2" target="_self">!</a> <font color="Maroon">b</font></span>)</span> <a href="altcat_1.html#K5">*</a> <span class="p1">(<span class="default"><font color="Maroon">F</font> <a href="functor0.html#K6">.</a> <font color="Maroon">f</font></span>)</span> = 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">t2</font> <a href="functor2.html#K2" target="_self">!</a> <font color="Maroon">b</font></span>)</span> <a href="altcat_1.html#K5">*</a> <span class="p2">(<span class="default"><font color="Maroon">t1</font> <a href="functor2.html#K2" target="_self">!</a> <font color="Maroon">b</font></span>)</span></span>)</span> <a href="altcat_1.html#K5">*</a> <span class="p1">(<span class="default"><font color="Maroon">F</font> <a href="functor0.html#K6">.</a> <font color="Maroon">f</font></span>)</span>
<b>by </b><i>, <a class="ref" href="functor2.html#T2" target="_self">Th2</a>, </i>
<br/>.= 
<span class="p1">(<span class="default"><font color="Maroon">t2</font> <a href="functor2.html#K2" target="_self">!</a> <font color="Maroon">b</font></span>)</span> <a href="altcat_1.html#K5">*</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">t1</font> <a href="functor2.html#K2" target="_self">!</a> <font color="Maroon">b</font></span>)</span> <a href="altcat_1.html#K5">*</a> <span class="p2">(<span class="default"><font color="Maroon">F</font> <a href="functor0.html#K6">.</a> <font color="Maroon">f</font></span>)</span></span>)</span>
<b>by </b><i>, <a class="ref" href="functor2.html#D1" target="_self">Def1</a>, <a class="ref" href="altcat_1.html#T25">ALTCAT_1:25</a></i>
<br/>.= 
<span class="p1">(<span class="default"><font color="Maroon">t2</font> <a href="functor2.html#K2" target="_self">!</a> <font color="Maroon">b</font></span>)</span> <a href="altcat_1.html#K5">*</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">F1</font> <a href="functor0.html#K6">.</a> <font color="Maroon">f</font></span>)</span> <a href="altcat_1.html#K5">*</a> <span class="p2">(<span class="default"><font color="Maroon">t1</font> <a href="functor2.html#K2" target="_self">!</a> <font color="Maroon">a</font></span>)</span></span>)</span>
<b>by </b><i>, <a class="txt" href="functor2.html#E1:17"><i><font color="Green">E20</font></i></a></i>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">t2</font> <a href="functor2.html#K2" target="_self">!</a> <font color="Maroon">b</font></span>)</span> <a href="altcat_1.html#K5">*</a> <span class="p2">(<span class="default"><font color="Maroon">F1</font> <a href="functor0.html#K6">.</a> <font color="Maroon">f</font></span>)</span></span>)</span> <a href="altcat_1.html#K5">*</a> <span class="p1">(<span class="default"><font color="Maroon">t1</font> <a href="functor2.html#K2" target="_self">!</a> <font color="Maroon">a</font></span>)</span>
<b>by </b><i>, <a class="ref" href="functor2.html#D1" target="_self">Def1</a>, <a class="ref" href="functor2.html#D2" target="_self">Def2</a>, <a class="ref" href="altcat_1.html#T25">ALTCAT_1:25</a></i>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">F2</font> <a href="functor0.html#K6">.</a> <font color="Maroon">f</font></span>)</span> <a href="altcat_1.html#K5">*</a> <span class="p2">(<span class="default"><font color="Maroon">t2</font> <a href="functor2.html#K2" target="_self">!</a> <font color="Maroon">a</font></span>)</span></span>)</span> <a href="altcat_1.html#K5">*</a> <span class="p1">(<span class="default"><font color="Maroon">t1</font> <a href="functor2.html#K2" target="_self">!</a> <font color="Maroon">a</font></span>)</span>
<b>by </b><i>, <a class="txt" href="functor2.html#E1:17"><i><font color="Green">E20</font></i></a></i>
<br/>.= 
<span class="p1">(<span class="default"><font color="Maroon">F2</font> <a href="functor0.html#K6">.</a> <font color="Maroon">f</font></span>)</span> <a href="altcat_1.html#K5">*</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">t2</font> <a href="functor2.html#K2" target="_self">!</a> <font color="Maroon">a</font></span>)</span> <a href="altcat_1.html#K5">*</a> <span class="p2">(<span class="default"><font color="Maroon">t1</font> <a href="functor2.html#K2" target="_self">!</a> <font color="Maroon">a</font></span>)</span></span>)</span>
<b>by </b><i>, <a class="ref" href="functor2.html#T4" target="_self">Th4</a>, <a class="ref" href="altcat_1.html#T25">ALTCAT_1:25</a></i>
<br/>.= 
<span class="p1">(<span class="default"><font color="Maroon">F2</font> <a href="functor0.html#K6">.</a> <font color="Maroon">f</font></span>)</span> <a href="altcat_1.html#K5">*</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">t2</font> <a href="functor2.html#K3" target="_self">`*`</a> <font color="Maroon">t1</font></span>)</span> <a href="functor2.html#K2" target="_self">!</a> <font color="Maroon">a</font></span>)</span>
<b>by </b><i>, <a class="ref" href="functor2.html#T2" target="_self">Th2</a>, </i>
;<br/>


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