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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="hidden.html#M1">set</a> ;<br/>

<b>set </b><font color="Maroon">c<sub>3</sub></font> =  <a href="cat_4.html#K23" target="_self">c1Cat*</a> <font color="Maroon">c<sub>1</sub></font>,<font color="Maroon">c<sub>2</sub></font>;<br/>
<b>thus </b><a NAME="E1:76"/>
the <a href="cat_4.html#U5" target="_self">Initial</a> of <span class="p1">(<span class="default"><a href="cat_4.html#K23" target="_self">c1Cat*</a> <font color="Maroon">c<sub>1</sub></font>,<font color="Maroon">c<sub>2</sub></font></span>)</span> is <a href="cat_1.html#V7">initial</a>
 <b>by </b><i><a class="ref" href="cat_4.html#T55" target="_self">Th55</a></i>; <i><font color="Red">:: according to </font></i><a class="ref" href="cat_4.html#D27" target="_self">CAT_4:def 27</a><br/>

<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#NM1">Object</a> of <span class="p1">(<span class="default"><a href="cat_4.html#K23" target="_self">c1Cat*</a> <font color="Maroon">c<sub>1</sub></font>,<font color="Maroon">c<sub>2</sub></font></span>)</span>;<br/>

<b>thus </b><a NAME="E2:76"/>
 <a href="cat_1.html#K2">dom</a> <span class="p1">(<span class="default">the <a href="cat_4.html#U7" target="_self">Incl1</a> of <span class="p2">(<span class="default"><a href="cat_4.html#K23" target="_self">c1Cat*</a> <font color="Maroon">c<sub>1</sub></font>,<font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="funct_2.html#K3">.</a> <span class="p2"><a href="domain_1.html#K1">[</a><span class="default"><font color="Maroon">c<sub>4</sub></font>,<font color="Maroon">c<sub>5</sub></font></span><a href="domain_1.html#K1">]</a></span></span>)</span> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>4</sub></font>
 <b>by </b><i><a class="ref" href="cat_4.html#T49" target="_self">Th49</a></i>;<br/>

<b>thus </b><a NAME="E3:76"/>
 <a href="cat_1.html#K2">dom</a> <span class="p1">(<span class="default">the <a href="cat_4.html#U8" target="_self">Incl2</a> of <span class="p2">(<span class="default"><a href="cat_4.html#K23" target="_self">c1Cat*</a> <font color="Maroon">c<sub>1</sub></font>,<font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="funct_2.html#K3">.</a> <span class="p2"><a href="domain_1.html#K1">[</a><span class="default"><font color="Maroon">c<sub>4</sub></font>,<font color="Maroon">c<sub>5</sub></font></span><a href="domain_1.html#K1">]</a></span></span>)</span> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>5</sub></font>
 <b>by </b><i><a class="ref" href="cat_4.html#T49" target="_self">Th49</a></i>;<br/>

<b>thus </b><a NAME="E4:76"/>
the <a href="cat_4.html#U6" target="_self">Coproduct</a> of <span class="p1">(<span class="default"><a href="cat_4.html#K23" target="_self">c1Cat*</a> <font color="Maroon">c<sub>1</sub></font>,<font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="funct_2.html#K3">.</a> <span class="p1"><a href="domain_1.html#K1">[</a><span class="default"><font color="Maroon">c<sub>4</sub></font>,<font color="Maroon">c<sub>5</sub></font></span><a href="domain_1.html#K1">]</a></span> <a href="cat_3.html#R4">is_a_coproduct_wrt</a> the <a href="cat_4.html#U7" target="_self">Incl1</a> of <span class="p1">(<span class="default"><a href="cat_4.html#K23" target="_self">c1Cat*</a> <font color="Maroon">c<sub>1</sub></font>,<font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="funct_2.html#K3">.</a> <span class="p1"><a href="domain_1.html#K1">[</a><span class="default"><font color="Maroon">c<sub>4</sub></font>,<font color="Maroon">c<sub>5</sub></font></span><a href="domain_1.html#K1">]</a></span>,the <a href="cat_4.html#U8" target="_self">Incl2</a> of <span class="p1">(<span class="default"><a href="cat_4.html#K23" target="_self">c1Cat*</a> <font color="Maroon">c<sub>1</sub></font>,<font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="funct_2.html#K3">.</a> <span class="p1"><a href="domain_1.html#K1">[</a><span class="default"><font color="Maroon">c<sub>4</sub></font>,<font color="Maroon">c<sub>5</sub></font></span><a href="domain_1.html#K1">]</a></span>
 <b>by </b><i><a class="ref" href="cat_4.html#T56" target="_self">Th56</a></i>;<br/>


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