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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  <a href="functor0.html#V16">contravariant</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="E1:7"/><i><font color="Green">E6</font></i>: 
<font color="Maroon">c<sub>3</sub></font> is <a href="functor0.html#V21">bijective</a>
 ;<br/>

<b>let </b><font color="Maroon">c<sub>4</sub></font> be  <a href="functor0.html#V16">contravariant</a>  <a href="functor0.html#M2">Functor</a> of <font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>1</sub></font>;<br/>

<b>assume </b><b>that </b><br/><a NAME="E2:7"/><i><font color="Green">E7</font></i>: 
for <font color="Olive">b<sub>1</sub></font> being  <a href="altcat_1.html#NM1">object</a> of <font color="Maroon">c<sub>2</sub></font> holds <font color="Maroon">c<sub>3</sub></font> <a href="functor0.html#K3">.</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>4</sub></font> <a href="functor0.html#K3">.</a> <font color="Olive">b<sub>1</sub></font></span>)</span> <a href="hidden.html#R1">=</a> <font color="Olive">b<sub>1</sub></font>
 <b>and </b><br/><a NAME="E3:7"/><i><font color="Green">E8</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>2</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 <font color="Maroon">c<sub>3</sub></font> <a href="functor0.html#K8">.</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>4</sub></font> <a href="functor0.html#K8">.</a> <font color="Olive">b<sub>3</sub></font></span>)</span> <a href="hidden.html#R1">=</a> <font color="Olive">b<sub>3</sub></font>
 ;<br/>

<div><i><font color="Green">E9</font></i>: <a class="txt" onclick="hs2(this)" href="javascript:()" title="7_1"><b>now </b></a><div class="add"><b>let </b><font color="Maroon">c<sub>5</sub></font> be   <a href="altcat_1.html#NM1">object</a> of <font color="Maroon">c<sub>2</sub></font>;<br/><b>thus </b><span class="p1">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="functor3.html#K2">*</a> <font color="Maroon">c<sub>4</sub></font></span>)</span> <a href="functor0.html#K3">.</a> <font color="Maroon">c<sub>5</sub></font> = 
<font color="Maroon">c<sub>3</sub></font> <a href="functor0.html#K3">.</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>4</sub></font> <a href="functor0.html#K3">.</a> <font color="Maroon">c<sub>5</sub></font></span>)</span>
<b>by </b><i><a class="ref" href="functor0.html#T34">FUNCTOR0:34</a></i>
<br/>.= 
<font color="Maroon">c<sub>5</sub></font>
<b>by </b><i><a class="txt" href="yellow20.html#E2:7"><i><font color="Green">E7</font></i></a></i>
<br/>.= 
<span class="p1">(<span class="default"><a href="functor0.html#K12">id</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="functor0.html#K3">.</a> <font color="Maroon">c<sub>5</sub></font>
<b>by </b><i><a class="ref" href="functor0.html#T30">FUNCTOR0:30</a></i>
;<br/></div><b>end;</b></div>
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="7_2"><b>now </b></a><div class="add"><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>2</sub></font>;<br/><b>assume </b><a NAME="E1:7_2"/><i><font color="Green">E10</font></i>: 
<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>6</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/><b>let </b><font color="Maroon">c<sub>7</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>thus </b><span class="p1">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="functor3.html#K2">*</a> <font color="Maroon">c<sub>4</sub></font></span>)</span> <a href="functor0.html#K6">.</a> <font color="Maroon">c<sub>7</sub></font> = 
<font color="Maroon">c<sub>3</sub></font> <a href="functor0.html#K8">.</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>4</sub></font> <a href="functor0.html#K8">.</a> <font color="Maroon">c<sub>7</sub></font></span>)</span>
<b>by </b><i><a class="txt" href="yellow20.html#E1:7_2"><i><font color="Green">E10</font></i></a>, <a class="ref" href="functor3.html#T7">FUNCTOR3:7</a></i>
<br/>.= 
<font color="Maroon">c<sub>7</sub></font>
<b>by </b><i><a class="txt" href="yellow20.html#E3:7"><i><font color="Green">E8</font></i></a>, <a class="txt" href="yellow20.html#E1:7_2"><i><font color="Green">E10</font></i></a></i>
<br/>.= 
<span class="p1">(<span class="default"><a href="functor0.html#K12">id</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="functor0.html#K6">.</a> <font color="Maroon">c<sub>7</sub></font>
<b>by </b><i><a class="txt" href="yellow20.html#E1:7_2"><i><font color="Green">E10</font></i></a>, <a class="ref" href="functor0.html#T32">FUNCTOR0:32</a></i>
;<br/></div><b>end;</b></div>
<a NAME="E6:7"/><b>then </b>
<font color="Maroon">c<sub>3</sub></font> <a href="functor3.html#K2">*</a> <font color="Maroon">c<sub>4</sub></font> <a href="hidden.html#R1">=</a>  <a href="functor0.html#K12">id</a> <font color="Maroon">c<sub>2</sub></font>
 
<b>by </b><i><a class="txt" href="yellow20.html#E4:7"><i><font color="Green">E9</font></i></a>, <a class="ref" href="yellow18.html#T1">YELLOW18:1</a></i>;<br/>
<b>hence </b><a NAME="E7:7"/>
 <a href="functor0.html#G2">FunctorStr</a>(# the <a href="functor0.html#U1">ObjectMap</a> of <font color="Maroon">c<sub>4</sub></font>,the <a href="functor0.html#U2">MorphMap</a> of <font color="Maroon">c<sub>4</sub></font> #) <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>3</sub></font> <a href="functor0.html#K15">"</a> 
 <b>by </b><i><a class="txt" href="yellow20.html#E1:7"><i><font color="Green">E6</font></i></a>, <a class="ref" href="yellow20.html#T4" target="_self">Th4</a></i>;<br/>


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