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<span class="kw">let </span><font color="Maroon" title="c1">C</font> be   <a href="cat_4.html#NM2" title="CAT_4:NM.2">Cocartesian_category</a>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide">  for <font color="Olive" title="b1">a</font>, <font color="Olive" title="b2">b</font> being   <a href="cat_1.html#NM1" title="CAT_1:NM.1">Object</a> of <font color="Maroon" title="c1">C</font> holds <br/> (  <a href="cat_1.html#K3" title="CAT_1:func.3">Hom</a> (<font color="Olive" title="b1">a</font>,<span class="p1">(<span class="default"><font color="Olive" title="b1">a</font> <a href="cat_4.html#K20" title="CAT_4:func.20">+</a> <font color="Olive" title="b2">b</font></span>)</span>) <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a>  <a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a>  &amp;  <a href="cat_1.html#K3" title="CAT_1:func.3">Hom</a> (<font color="Olive" title="b2">b</font>,<span class="p1">(<span class="default"><font color="Olive" title="b1">a</font> <a href="cat_4.html#K20" title="CAT_4:func.20">+</a> <font color="Olive" title="b2">b</font></span>)</span>) <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a>  <a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a>  )</span><br/><span class="kw">let </span><font color="Maroon" title="c2">a</font>, <font color="Maroon" title="c3">b</font> be   <a href="cat_1.html#NM1" title="CAT_1:NM.1">Object</a> of <font color="Maroon" title="c1">C</font>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> (  <a href="cat_1.html#K3" title="CAT_1:func.3">Hom</a> (<font color="Maroon" title="c2">a</font>,<span class="p1">(<span class="default"><font color="Maroon" title="c2">a</font> <a href="cat_4.html#K20" title="CAT_4:func.20">+</a> <font color="Maroon" title="c3">b</font></span>)</span>) <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a>  <a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a>  &amp;  <a href="cat_1.html#K3" title="CAT_1:func.3">Hom</a> (<font color="Maroon" title="c3">b</font>,<span class="p1">(<span class="default"><font color="Maroon" title="c2">a</font> <a href="cat_4.html#K20" title="CAT_4:func.20">+</a> <font color="Maroon" title="c3">b</font></span>)</span>) <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a>  <a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a>  )</span><br/>





<span class="kw">set </span><font color="Maroon" title="c4">c</font> =  the <a href="cat_4.html#U6" title="CAT_4:sel.6">Coproduct</a> of <font color="Maroon" title="c1">C</font> <a href="binop_1.html#K4" title="BINOP_1:func.4">.</a> (<font color="Maroon" title="c2">a</font>,<font color="Maroon" title="c3">b</font>);<br/>
<span class="kw">set </span><font color="Maroon" title="c5">i1</font> =  the <a href="cat_4.html#U7" title="CAT_4:sel.7">Incl1</a> of <font color="Maroon" title="c1">C</font> <a href="binop_1.html#K2" title="BINOP_1:func.2">.</a> (<font color="Maroon" title="c2">a</font>,<font color="Maroon" title="c3">b</font>);<br/>
<span class="kw">set </span><font color="Maroon" title="c6">i2</font> =  the <a href="cat_4.html#U8" title="CAT_4:sel.8">Incl2</a> of <font color="Maroon" title="c1">C</font> <a href="binop_1.html#K2" title="BINOP_1:func.2">.</a> (<font color="Maroon" title="c2">a</font>,<font color="Maroon" title="c3">b</font>);<br/>
<a NAME="E1:89"/>
 the <a href="cat_4.html#U6" title="CAT_4:sel.6">Coproduct</a> of <font color="Maroon" title="c1">C</font> <a href="binop_1.html#K4" title="BINOP_1:func.4">.</a> (<font color="Maroon" title="c2">a</font>,<font color="Maroon" title="c3">b</font>) <a href="cat_3.html#R4" title="CAT_3:pred.4">is_a_coproduct_wrt</a>  the <a href="cat_4.html#U7" title="CAT_4:sel.7">Incl1</a> of <font color="Maroon" title="c1">C</font> <a href="binop_1.html#K2" title="BINOP_1:func.2">.</a> (<font color="Maroon" title="c2">a</font>,<font color="Maroon" title="c3">b</font>), the <a href="cat_4.html#U8" title="CAT_4:sel.8">Incl2</a> of <font color="Maroon" title="c1">C</font> <a href="binop_1.html#K2" title="BINOP_1:func.2">.</a> (<font color="Maroon" title="c2">a</font>,<font color="Maroon" title="c3">b</font>)
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="cat_4.html#D26" target="_self" title="CAT_4:def.26">Def27</a></span>;<br/>
<a NAME="E2:89"/><span class="kw">then </span><span class="lab"><font color="Green" title="E43">A1</font></span>: 
(  <a href="graph_1.html#K2" title="GRAPH_1:func.2">cod</a> <span class="p1">(<span class="default"> the <a href="cat_4.html#U7" title="CAT_4:sel.7">Incl1</a> of <font color="Maroon" title="c1">C</font> <a href="binop_1.html#K2" title="BINOP_1:func.2">.</a> (<font color="Maroon" title="c2">a</font>,<font color="Maroon" title="c3">b</font>)</span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  the <a href="cat_4.html#U6" title="CAT_4:sel.6">Coproduct</a> of <font color="Maroon" title="c1">C</font> <a href="binop_1.html#K4" title="BINOP_1:func.4">.</a> (<font color="Maroon" title="c2">a</font>,<font color="Maroon" title="c3">b</font>) &amp;  <a href="graph_1.html#K2" title="GRAPH_1:func.2">cod</a> <span class="p1">(<span class="default"> the <a href="cat_4.html#U8" title="CAT_4:sel.8">Incl2</a> of <font color="Maroon" title="c1">C</font> <a href="binop_1.html#K2" title="BINOP_1:func.2">.</a> (<font color="Maroon" title="c2">a</font>,<font color="Maroon" title="c3">b</font>)</span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  the <a href="cat_4.html#U6" title="CAT_4:sel.6">Coproduct</a> of <font color="Maroon" title="c1">C</font> <a href="binop_1.html#K4" title="BINOP_1:func.4">.</a> (<font color="Maroon" title="c2">a</font>,<font color="Maroon" title="c3">b</font>) )
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="cat_3.html#D17" title="CAT_3:def.17">CAT_3:def 17</a></span>;<br/>
<a NAME="E3:89"/>
(  <a href="graph_1.html#K1" title="GRAPH_1:func.1">dom</a> <span class="p1">(<span class="default"> the <a href="cat_4.html#U7" title="CAT_4:sel.7">Incl1</a> of <font color="Maroon" title="c1">C</font> <a href="binop_1.html#K2" title="BINOP_1:func.2">.</a> (<font color="Maroon" title="c2">a</font>,<font color="Maroon" title="c3">b</font>)</span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c2">a</font> &amp;  <a href="graph_1.html#K1" title="GRAPH_1:func.1">dom</a> <span class="p1">(<span class="default"> the <a href="cat_4.html#U8" title="CAT_4:sel.8">Incl2</a> of <font color="Maroon" title="c1">C</font> <a href="binop_1.html#K2" title="BINOP_1:func.2">.</a> (<font color="Maroon" title="c2">a</font>,<font color="Maroon" title="c3">b</font>)</span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c3">b</font> )
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="cat_4.html#D26" target="_self" title="CAT_4:def.26">Def27</a></span>;<br/>
<span class="kw">hence </span><a NAME="E4:89"/>
(  <a href="cat_1.html#K3" title="CAT_1:func.3">Hom</a> (<font color="Maroon" title="c2">a</font>,<span class="p1">(<span class="default"><font color="Maroon" title="c2">a</font> <a href="cat_4.html#K20" title="CAT_4:func.20">+</a> <font color="Maroon" title="c3">b</font></span>)</span>) <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a>  <a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a>  &amp;  <a href="cat_1.html#K3" title="CAT_1:func.3">Hom</a> (<font color="Maroon" title="c3">b</font>,<span class="p1">(<span class="default"><font color="Maroon" title="c2">a</font> <a href="cat_4.html#K20" title="CAT_4:func.20">+</a> <font color="Maroon" title="c3">b</font></span>)</span>) <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a>  <a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a>  )
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:89"><span class="lab"><font color="Green" title="E43">A1</font></span></a>, <a class="ref" href="cat_1.html#T1" title="CAT_1:th.1">CAT_1:1</a></span>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> verum</span><br/>


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