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<b>let </b><font color="Maroon">c<sub>1</sub></font> be   <a href="cat_4.html#NM2">Cocartesian_category</a>;<br/><b>let </b><font color="Maroon">c<sub>2</sub></font>, <font color="Maroon">c<sub>3</sub></font> be   <a href="cat_1.html#NM1">Object</a> of <font color="Maroon">c<sub>1</sub></font>;<br/>





<b>set </b><font color="Maroon">c<sub>4</sub></font> = the <a href="cat_4.html#U7" target="_self">Incl1</a> of <font color="Maroon">c<sub>1</sub></font> <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>2</sub></font>,<font color="Maroon">c<sub>3</sub></font></span><a href="domain_1.html#K1">]</a></span>;<br/>
<b>set </b><font color="Maroon">c<sub>5</sub></font> = the <a href="cat_4.html#U8" target="_self">Incl2</a> of <font color="Maroon">c<sub>1</sub></font> <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>2</sub></font>,<font color="Maroon">c<sub>3</sub></font></span><a href="domain_1.html#K1">]</a></span>;<br/>
<a NAME="E1:86"/>
the <a href="cat_4.html#U6" target="_self">Coproduct</a> of <font color="Maroon">c<sub>1</sub></font> <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>2</sub></font>,<font color="Maroon">c<sub>3</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 <font color="Maroon">c<sub>1</sub></font> <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>2</sub></font>,<font color="Maroon">c<sub>3</sub></font></span><a href="domain_1.html#K1">]</a></span>,the <a href="cat_4.html#U8" target="_self">Incl2</a> of <font color="Maroon">c<sub>1</sub></font> <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>2</sub></font>,<font color="Maroon">c<sub>3</sub></font></span><a href="domain_1.html#K1">]</a></span>
 
<b>by </b><i><a class="ref" href="cat_4.html#D27" target="_self">Def27</a></i>;<br/>
<a NAME="E2:86"/><b>then </b>
<font color="Maroon">c<sub>2</sub></font> <a href="cat_4.html#K20" target="_self">+</a> <font color="Maroon">c<sub>3</sub></font> <a href="cat_3.html#R4">is_a_coproduct_wrt</a> the <a href="cat_4.html#U7" target="_self">Incl1</a> of <font color="Maroon">c<sub>1</sub></font> <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>2</sub></font>,<font color="Maroon">c<sub>3</sub></font></span><a href="domain_1.html#K1">]</a></span>,the <a href="cat_4.html#U8" target="_self">Incl2</a> of <font color="Maroon">c<sub>1</sub></font> <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>2</sub></font>,<font color="Maroon">c<sub>3</sub></font></span><a href="domain_1.html#K1">]</a></span>
 
;<br/>
<a NAME="E3:86"/><b>then </b>
(  <a href="cat_1.html#K3">cod</a> <span class="p1">(<span class="default">the <a href="cat_4.html#U8" target="_self">Incl2</a> of <font color="Maroon">c<sub>1</sub></font> <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>2</sub></font>,<font color="Maroon">c<sub>3</sub></font></span><a href="domain_1.html#K1">]</a></span></span>)</span> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>2</sub></font> <a href="cat_4.html#K20" target="_self">+</a> <font color="Maroon">c<sub>3</sub></font> &amp;  <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 <font color="Maroon">c<sub>1</sub></font> <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>2</sub></font>,<font color="Maroon">c<sub>3</sub></font></span><a href="domain_1.html#K1">]</a></span></span>)</span> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>3</sub></font> )
 
<b>by </b><i><a class="ref" href="cat_4.html#D27" target="_self">Def27</a>, <a class="ref" href="cat_3.html#D19">CAT_3:def 19</a></i>;<br/>
<b>hence </b><a NAME="E4:86"/>
(  <a href="cat_1.html#K2">dom</a> <span class="p1">(<span class="default"><a href="cat_4.html#K22" target="_self">in2</a> <font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>3</sub></font></span>)</span> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>3</sub></font> &amp;  <a href="cat_1.html#K3">cod</a> <span class="p1">(<span class="default"><a href="cat_4.html#K22" target="_self">in2</a> <font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>3</sub></font></span>)</span> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>2</sub></font> <a href="cat_4.html#K20" target="_self">+</a> <font color="Maroon">c<sub>3</sub></font> )
 ;<br/>


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