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<b>let </b><font color="Maroon" title="c1">C</font> be   <a href="cat_4.html#NM2" title="CAT_4:NM.2">Cocartesian_category</a>;<br/><b>let </b><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>;<br/>





<a NAME="E1:89"/>
( <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> <a href="cat_3.html#R4" title="CAT_3:pred.4">is_a_coproduct_wrt</a>  <a href="cat_4.html#K21" title="CAT_4:func.21">in1</a> <font color="Maroon" title="c2">a</font>,<font color="Maroon" title="c3">b</font>, <a href="cat_4.html#K22" title="CAT_4:func.22">in2</a> <font color="Maroon" title="c2">a</font>,<font color="Maroon" title="c3">b</font> &amp;  <a href="cat_1.html#K2" title="CAT_1:func.2">dom</a> <span class="p1">(<span class="default"><a href="cat_4.html#K21" title="CAT_4:func.21">in1</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="cat_1.html#K2" title="CAT_1:func.2">dom</a> <span class="p1">(<span class="default"><a href="cat_4.html#K22" title="CAT_4:func.22">in2</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> )
 
<b>by </b><i><a class="ref" href="cat_4.html#T64" target="_self" title="CAT_4:th.64">Th64</a>, <a class="ref" href="cat_4.html#T65" target="_self" title="CAT_4:th.65">Th65</a>, <a class="ref" href="cat_4.html#T67" target="_self" title="CAT_4:th.67">Th67</a></i>;<br/>
<b>hence </b><a NAME="E2:89"/>
(  <a href="cat_1.html#K6" title="CAT_1:func.6">Hom</a> <font color="Maroon" title="c2">a</font>,<font color="Maroon" title="c3">b</font> <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#K6" title="CAT_1:func.6">Hom</a> <font color="Maroon" title="c3">b</font>,<font color="Maroon" title="c2">a</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a>  <a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a>  implies (  <a href="cat_4.html#K21" title="CAT_4:func.21">in1</a> <font color="Maroon" title="c2">a</font>,<font color="Maroon" title="c3">b</font> is <a href="cat_3.html#V2" title="CAT_3:attr.2">coretraction</a> &amp;  <a href="cat_4.html#K22" title="CAT_4:func.22">in2</a> <font color="Maroon" title="c2">a</font>,<font color="Maroon" title="c3">b</font> is <a href="cat_3.html#V2" title="CAT_3:attr.2">coretraction</a> ) )
 <b>by </b><i><a class="ref" href="cat_3.html#T88" title="CAT_3:th.88">CAT_3:88</a></i>;<br/>


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