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<b>let </b><font color="Maroon">c<sub>1</sub></font> be   <a href="classes2.html#NM1">Universe</a>;<br/><b>let </b><font color="Maroon">c<sub>2</sub></font> be   <a href="funcsdom.html#NM1">Ring</a>;<br/>



<b>set </b><font color="Maroon">c<sub>3</sub></font> =  <a href="modcat_1.html#K4" target="_self">Morphs</a> <span class="p1">(<span class="default"><a href="modcat_1.html#K3" target="_self">LModObjects</a> <font color="Maroon">c<sub>1</sub></font>,<font color="Maroon">c<sub>2</sub></font></span>)</span>;<br/>
<b>let </b><font color="Maroon">c<sub>4</sub></font>, <font color="Maroon">c<sub>5</sub></font>, <font color="Maroon">c<sub>6</sub></font> be   <a href="cat_1.html#NM2">Morphism</a> of <span class="p1">(<span class="default"><a href="modcat_1.html#K12" target="_self">LModCat</a> <font color="Maroon">c<sub>1</sub></font>,<font color="Maroon">c<sub>2</sub></font></span>)</span>;<br/>

<b>assume </b><a NAME="E1:37"/><i><font color="Green">E29</font></i>: 
(  <a href="cat_1.html#K2">dom</a> <font color="Maroon">c<sub>6</sub></font> <a href="hidden.html#R1">=</a>  <a href="cat_1.html#K3">cod</a> <font color="Maroon">c<sub>5</sub></font> &amp;  <a href="cat_1.html#K2">dom</a> <font color="Maroon">c<sub>5</sub></font> <a href="hidden.html#R1">=</a>  <a href="cat_1.html#K3">cod</a> <font color="Maroon">c<sub>4</sub></font> )
 ;<br/>

<b>reconsider </b><font color="Maroon">c<sub>7</sub></font> = <font color="Maroon">c<sub>4</sub></font>, <font color="Maroon">c<sub>8</sub></font> = <font color="Maroon">c<sub>5</sub></font>, <font color="Maroon">c<sub>9</sub></font> = <font color="Maroon">c<sub>6</sub></font> as  <a href="mod_2.html#V2">strict</a>  <a href="modcat_1.html#M4" target="_self">Element</a> of  <a href="modcat_1.html#K4" target="_self">Morphs</a> <span class="p1">(<span class="default"><a href="modcat_1.html#K3" target="_self">LModObjects</a> <font color="Maroon">c<sub>1</sub></font>,<font color="Maroon">c<sub>2</sub></font></span>)</span> <b>by </b><i><a class="ref" href="modcat_1.html#T15" target="_self">Th15</a></i>;<br/>
<a NAME="E3:37"/><i><font color="Green">E30</font></i>: 
(  <a href="mod_2.html#K2">dom</a> <font color="Maroon">c<sub>9</sub></font> <a href="hidden.html#R1">=</a>  <a href="mod_2.html#K3">cod</a> <font color="Maroon">c<sub>8</sub></font> &amp;  <a href="mod_2.html#K2">dom</a> <font color="Maroon">c<sub>8</sub></font> <a href="hidden.html#R1">=</a>  <a href="mod_2.html#K3">cod</a> <font color="Maroon">c<sub>7</sub></font> )
 
<b>by </b><i><a class="txt" href="modcat_1.html#E1:37"><i><font color="Green">E29</font></i></a>, <a class="ref" href="modcat_1.html#T18" target="_self">Th18</a></i>;<br/>
<a NAME="E4:37"/><i><font color="Green">E31</font></i>: 
( <font color="Maroon">c<sub>8</sub></font> <a href="mod_2.html#K8">*</a> <font color="Maroon">c<sub>7</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>5</sub></font> <a href="cat_1.html#K4">*</a> <font color="Maroon">c<sub>4</sub></font> &amp; <font color="Maroon">c<sub>9</sub></font> <a href="mod_2.html#K8">*</a> <font color="Maroon">c<sub>8</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>6</sub></font> <a href="cat_1.html#K4">*</a> <font color="Maroon">c<sub>5</sub></font> )
 
<b>by </b><i><a class="txt" href="modcat_1.html#E1:37"><i><font color="Green">E29</font></i></a>, <a class="ref" href="modcat_1.html#T18" target="_self">Th18</a></i>;<br/>
<b>reconsider </b><font color="Maroon">c<sub>10</sub></font> = <font color="Maroon">c<sub>8</sub></font> <a href="mod_2.html#K8">*</a> <font color="Maroon">c<sub>7</sub></font>, <font color="Maroon">c<sub>11</sub></font> = <font color="Maroon">c<sub>9</sub></font> <a href="mod_2.html#K8">*</a> <font color="Maroon">c<sub>8</sub></font> as  <a href="mod_2.html#V2">strict</a>  <a href="modcat_1.html#M4" target="_self">Element</a> of  <a href="modcat_1.html#K4" target="_self">Morphs</a> <span class="p1">(<span class="default"><a href="modcat_1.html#K3" target="_self">LModObjects</a> <font color="Maroon">c<sub>1</sub></font>,<font color="Maroon">c<sub>2</sub></font></span>)</span> <b>by </b><i><a class="txt" href="modcat_1.html#E3:37"><i><font color="Green">E30</font></i></a>, <a class="ref" href="modcat_1.html#T12" target="_self">Th12</a></i>;<br/>
<a NAME="E6:37"/><i><font color="Green">E32</font></i>: 
 <a href="cat_1.html#K2">dom</a> <font color="Maroon">c<sub>6</sub></font> <a href="hidden.html#R1">=</a>  <a href="cat_1.html#K3">cod</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>5</sub></font> <a href="cat_1.html#K4">*</a> <font color="Maroon">c<sub>4</sub></font></span>)</span>
 
<b>by </b><i><a class="txt" href="modcat_1.html#E1:37"><i><font color="Green">E29</font></i></a>, <a class="txt" href="modcat_1.html#E34"><i><font color="Green">Lemma27</font></i></a></i>;<br/>
<a NAME="E7:37"/><i><font color="Green">E33</font></i>: 
 <a href="cat_1.html#K2">dom</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>6</sub></font> <a href="cat_1.html#K4">*</a> <font color="Maroon">c<sub>5</sub></font></span>)</span> <a href="hidden.html#R1">=</a>  <a href="cat_1.html#K3">cod</a> <font color="Maroon">c<sub>4</sub></font>
 
<b>by </b><i><a class="txt" href="modcat_1.html#E1:37"><i><font color="Green">E29</font></i></a>, <a class="txt" href="modcat_1.html#E34"><i><font color="Green">Lemma27</font></i></a></i>;<br/>
<font color="Maroon">c<sub>6</sub></font> <a href="cat_1.html#K4">*</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>5</sub></font> <a href="cat_1.html#K4">*</a> <font color="Maroon">c<sub>4</sub></font></span>)</span> = 
<font color="Maroon">c<sub>9</sub></font> <a href="mod_2.html#K8">*</a> <font color="Maroon">c<sub>10</sub></font>
<b>by </b><i><a class="txt" href="modcat_1.html#E4:37"><i><font color="Green">E31</font></i></a>, <a class="txt" href="modcat_1.html#E6:37"><i><font color="Green">E32</font></i></a>, <a class="ref" href="modcat_1.html#T18" target="_self">Th18</a></i>
<br/>.= 
<font color="Maroon">c<sub>11</sub></font> <a href="mod_2.html#K8">*</a> <font color="Maroon">c<sub>7</sub></font>
<b>by </b><i><a class="txt" href="modcat_1.html#E3:37"><i><font color="Green">E30</font></i></a>, <a class="ref" href="mod_2.html#T25">MOD_2:25</a></i>
<br/>.= 
<span class="p1">(<span class="default"><font color="Maroon">c<sub>6</sub></font> <a href="cat_1.html#K4">*</a> <font color="Maroon">c<sub>5</sub></font></span>)</span> <a href="cat_1.html#K4">*</a> <font color="Maroon">c<sub>4</sub></font>
<b>by </b><i><a class="txt" href="modcat_1.html#E4:37"><i><font color="Green">E31</font></i></a>, <a class="txt" href="modcat_1.html#E7:37"><i><font color="Green">E33</font></i></a>, <a class="ref" href="modcat_1.html#T18" target="_self">Th18</a></i>
;<br/>
<b>hence </b><a NAME="E9:37"/>
<font color="Maroon">c<sub>6</sub></font> <a href="cat_1.html#K4">*</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>5</sub></font> <a href="cat_1.html#K4">*</a> <font color="Maroon">c<sub>4</sub></font></span>)</span> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>6</sub></font> <a href="cat_1.html#K4">*</a> <font color="Maroon">c<sub>5</sub></font></span>)</span> <a href="cat_1.html#K4">*</a> <font color="Maroon">c<sub>4</sub></font>
 ;<br/>


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