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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>, <font color="Maroon">c<sub>4</sub></font>, <font color="Maroon">c<sub>5</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>assume </b><a NAME="E1:18"/><i><font color="Green">E17</font></i>: 
<font color="Maroon">c<sub>3</sub></font> <a href="functor2.html#R1" target="_self">is_transformable_to</a> <font color="Maroon">c<sub>4</sub></font>
 ; <i><font color="Red">:: according to </font></i><a class="ref" href="functor2.html#D6" target="_self">FUNCTOR2:def 6</a><br/>

<b>given </b><font color="Maroon">c<sub>6</sub></font> being    <a href="functor2.html#M1" target="_self">transformation</a> of <font color="Maroon">c<sub>3</sub></font>,<font color="Maroon">c<sub>4</sub></font><b> such that </b><a NAME="E2:18"/><i><font color="Green">E18</font></i>: 
for <font color="Olive">b<sub>1</sub></font>, <font color="Olive">b<sub>2</sub></font> being  <a href="altcat_1.html#NM1">object</a> of <font color="Maroon">c<sub>1</sub></font> st <span class="p1"><a href="altcat_1.html#K1">&lt;^</a><span class="default"><font color="Olive">b<sub>1</sub></font>,<font color="Olive">b<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>  holds <br/>for <font color="Olive">b<sub>3</sub></font> being  <a href="altcat_1.html#NM2">Morphism</a> of <font color="Olive">b<sub>1</sub></font>,<font color="Olive">b<sub>2</sub></font> holds <span class="p1">(<span class="default"><font color="Maroon">c<sub>6</sub></font> <a href="functor2.html#K2" target="_self">!</a> <font color="Olive">b<sub>2</sub></font></span>)</span> <a href="altcat_1.html#K5">*</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="functor0.html#K6">.</a> <font color="Olive">b<sub>3</sub></font></span>)</span> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>4</sub></font> <a href="functor0.html#K6">.</a> <font color="Olive">b<sub>3</sub></font></span>)</span> <a href="altcat_1.html#K5">*</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>6</sub></font> <a href="functor2.html#K2" target="_self">!</a> <font color="Olive">b<sub>1</sub></font></span>)</span>
 ;<br/>

<b>assume </b><a NAME="E3:18"/><i><font color="Green">E19</font></i>: 
<font color="Maroon">c<sub>4</sub></font> <a href="functor2.html#R1" target="_self">is_transformable_to</a> <font color="Maroon">c<sub>5</sub></font>
 ; <i><font color="Red">:: according to </font></i><a class="ref" href="functor2.html#D6" target="_self">FUNCTOR2:def 6</a><br/>

<b>given </b><font color="Maroon">c<sub>7</sub></font> being    <a href="functor2.html#M1" target="_self">transformation</a> of <font color="Maroon">c<sub>4</sub></font>,<font color="Maroon">c<sub>5</sub></font><b> such that </b><a NAME="E4:18"/><i><font color="Green">E20</font></i>: 
for <font color="Olive">b<sub>1</sub></font>, <font color="Olive">b<sub>2</sub></font> being  <a href="altcat_1.html#NM1">object</a> of <font color="Maroon">c<sub>1</sub></font> st <span class="p1"><a href="altcat_1.html#K1">&lt;^</a><span class="default"><font color="Olive">b<sub>1</sub></font>,<font color="Olive">b<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>  holds <br/>for <font color="Olive">b<sub>3</sub></font> being  <a href="altcat_1.html#NM2">Morphism</a> of <font color="Olive">b<sub>1</sub></font>,<font color="Olive">b<sub>2</sub></font> holds <span class="p1">(<span class="default"><font color="Maroon">c<sub>7</sub></font> <a href="functor2.html#K2" target="_self">!</a> <font color="Olive">b<sub>2</sub></font></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="functor0.html#K6">.</a> <font color="Olive">b<sub>3</sub></font></span>)</span> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>5</sub></font> <a href="functor0.html#K6">.</a> <font color="Olive">b<sub>3</sub></font></span>)</span> <a href="altcat_1.html#K5">*</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>7</sub></font> <a href="functor2.html#K2" target="_self">!</a> <font color="Olive">b<sub>1</sub></font></span>)</span>
 ;<br/>

<b>thus </b><a NAME="E5:18"/>
<font color="Maroon">c<sub>3</sub></font> <a href="functor2.html#R1" target="_self">is_transformable_to</a> <font color="Maroon">c<sub>5</sub></font>
 <b>by </b><i><a class="txt" href="functor2.html#E1:18"><i><font color="Green">E17</font></i></a>, <a class="txt" href="functor2.html#E3:18"><i><font color="Green">E19</font></i></a>, <a class="ref" href="functor2.html#T4" target="_self">Th4</a></i>; <i><font color="Red">:: according to </font></i><a class="ref" href="functor2.html#D6" target="_self">FUNCTOR2:def 6</a><br/>

<b>take </b>
<font color="Maroon">c<sub>7</sub></font> <a href="functor2.html#K3" target="_self">`*`</a> <font color="Maroon">c<sub>6</sub></font>
;<br/>

<b>thus </b><a NAME="E6:18"/>
for <font color="Olive">b<sub>1</sub></font>, <font color="Olive">b<sub>2</sub></font> being  <a href="altcat_1.html#NM1">object</a> of <font color="Maroon">c<sub>1</sub></font> st <span class="p1"><a href="altcat_1.html#K1">&lt;^</a><span class="default"><font color="Olive">b<sub>1</sub></font>,<font color="Olive">b<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>  holds <br/>for <font color="Olive">b<sub>3</sub></font> being  <a href="altcat_1.html#NM2">Morphism</a> of <font color="Olive">b<sub>1</sub></font>,<font color="Olive">b<sub>2</sub></font> holds <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>7</sub></font> <a href="functor2.html#K3" target="_self">`*`</a> <font color="Maroon">c<sub>6</sub></font></span>)</span> <a href="functor2.html#K2" target="_self">!</a> <font color="Olive">b<sub>2</sub></font></span>)</span> <a href="altcat_1.html#K5">*</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="functor0.html#K6">.</a> <font color="Olive">b<sub>3</sub></font></span>)</span> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>5</sub></font> <a href="functor0.html#K6">.</a> <font color="Olive">b<sub>3</sub></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">c<sub>7</sub></font> <a href="functor2.html#K3" target="_self">`*`</a> <font color="Maroon">c<sub>6</sub></font></span>)</span> <a href="functor2.html#K2" target="_self">!</a> <font color="Olive">b<sub>1</sub></font></span>)</span>
 <b>by </b><i><a class="txt" href="functor2.html#E1:18"><i><font color="Green">E17</font></i></a>, <a class="txt" href="functor2.html#E2:18"><i><font color="Green">E18</font></i></a>, <a class="txt" href="functor2.html#E3:18"><i><font color="Green">E19</font></i></a>, <a class="txt" href="functor2.html#E4:18"><i><font color="Green">E20</font></i></a>, <a class="txt" href="functor2.html#E17"><i><font color="Green">Lemma15</font></i></a></i>;<br/>


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