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<b>let </b><font color="Maroon">c<sub>4</sub></font>, <font color="Maroon">c<sub>5</sub></font> be  <a href="cat_1.html#V1">strict</a>  <a href="cat_2.html#M3">Subcategory</a> of <font color="Maroon">c<sub>2</sub></font>;<br/>

<b>assume </b><b>that </b><br/><a NAME="E1:16_1_2"/><i><font color="Green">E9</font></i>: 
( the <a href="cat_1.html#U1">Objects</a> of <font color="Maroon">c<sub>4</sub></font> <a href="hidden.html#R1">=</a>  <a href="relset_1.html#K5">rng</a> <span class="p1">(<span class="default"><a href="cat_1.html#K12">Obj</a> <font color="Maroon">c<sub>3</sub></font></span>)</span> &amp;  <a href="relset_1.html#K5">rng</a> <font color="Maroon">c<sub>3</sub></font> <a href="tarski.html#R1">c=</a> the <a href="cat_1.html#U2">Morphisms</a> of <font color="Maroon">c<sub>4</sub></font> )
 <b>and </b><br/><a NAME="E2:16_1_2"/><i><font color="Green">E10</font></i>: 
for <font color="Olive">b<sub>1</sub></font> being   <a href="cat_2.html#M3">Subcategory</a> of <font color="Maroon">c<sub>2</sub></font> st the <a href="cat_1.html#U1">Objects</a> of <font color="Olive">b<sub>1</sub></font> <a href="hidden.html#R1">=</a>  <a href="relset_1.html#K5">rng</a> <span class="p1">(<span class="default"><a href="cat_1.html#K12">Obj</a> <font color="Maroon">c<sub>3</sub></font></span>)</span> &amp;  <a href="relset_1.html#K5">rng</a> <font color="Maroon">c<sub>3</sub></font> <a href="tarski.html#R1">c=</a> the <a href="cat_1.html#U2">Morphisms</a> of <font color="Olive">b<sub>1</sub></font> holds <br/><font color="Maroon">c<sub>4</sub></font> is    <a href="cat_2.html#M3">Subcategory</a> of <font color="Olive">b<sub>1</sub></font>
 <b>and </b><br/><a NAME="E3:16_1_2"/><i><font color="Green">E11</font></i>: 
( the <a href="cat_1.html#U1">Objects</a> of <font color="Maroon">c<sub>5</sub></font> <a href="hidden.html#R1">=</a>  <a href="relset_1.html#K5">rng</a> <span class="p1">(<span class="default"><a href="cat_1.html#K12">Obj</a> <font color="Maroon">c<sub>3</sub></font></span>)</span> &amp;  <a href="relset_1.html#K5">rng</a> <font color="Maroon">c<sub>3</sub></font> <a href="tarski.html#R1">c=</a> the <a href="cat_1.html#U2">Morphisms</a> of <font color="Maroon">c<sub>5</sub></font> )
 <b>and </b><br/><a NAME="E4:16_1_2"/><i><font color="Green">E12</font></i>: 
for <font color="Olive">b<sub>1</sub></font> being   <a href="cat_2.html#M3">Subcategory</a> of <font color="Maroon">c<sub>2</sub></font> st the <a href="cat_1.html#U1">Objects</a> of <font color="Olive">b<sub>1</sub></font> <a href="hidden.html#R1">=</a>  <a href="relset_1.html#K5">rng</a> <span class="p1">(<span class="default"><a href="cat_1.html#K12">Obj</a> <font color="Maroon">c<sub>3</sub></font></span>)</span> &amp;  <a href="relset_1.html#K5">rng</a> <font color="Maroon">c<sub>3</sub></font> <a href="tarski.html#R1">c=</a> the <a href="cat_1.html#U2">Morphisms</a> of <font color="Olive">b<sub>1</sub></font> holds <br/><font color="Maroon">c<sub>5</sub></font> is    <a href="cat_2.html#M3">Subcategory</a> of <font color="Olive">b<sub>1</sub></font>
 ;<br/>

<a NAME="E5:16_1_2"/>
( <font color="Maroon">c<sub>4</sub></font> is    <a href="cat_2.html#M3">Subcategory</a> of <font color="Maroon">c<sub>5</sub></font> &amp; <font color="Maroon">c<sub>5</sub></font> is    <a href="cat_2.html#M3">Subcategory</a> of <font color="Maroon">c<sub>4</sub></font> )
 
<b>by </b><i><a class="txt" href="cat_5.html#E1:16_1_2"><i><font color="Green">E9</font></i></a>, <a class="txt" href="cat_5.html#E2:16_1_2"><i><font color="Green">E10</font></i></a>, <a class="txt" href="cat_5.html#E3:16_1_2"><i><font color="Green">E11</font></i></a>, <a class="txt" href="cat_5.html#E4:16_1_2"><i><font color="Green">E12</font></i></a></i>;<br/>
<b>hence </b><a NAME="E6:16_1_2"/>
<font color="Maroon">c<sub>4</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>5</sub></font>
 <b>by </b><i><a class="ref" href="cat_5.html#T3" target="_self">Th3</a></i>;<br/>


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