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<b>let </b><font color="Maroon">C</font> be   <a href="cat_4.html#NM1">Cartesian_category</a>;<br/><b>let </b><font color="Maroon">a</font> be   <a href="cat_1.html#NM1">Object</a> of <font color="Maroon">C</font>;<br/><b>let </b><font color="Maroon">b</font> be   <a href="cat_1.html#NM1">Object</a> of <font color="Maroon">C</font>;<br/>





<a NAME="E1:32"/>
( <font color="Maroon">a</font> <a href="cat_4.html#K2" target="_self">[x]</a> <font color="Maroon">b</font> <a href="cat_3.html#R2">is_a_product_wrt</a>  <a href="cat_4.html#K7" target="_self">pr1</a> <font color="Maroon">a</font>,<font color="Maroon">b</font>, <a href="cat_4.html#K8" target="_self">pr2</a> <font color="Maroon">a</font>,<font color="Maroon">b</font> &amp;  <a href="cat_1.html#K3">cod</a> <span class="p1">(<span class="default"><a href="cat_4.html#K7" target="_self">pr1</a> <font color="Maroon">a</font>,<font color="Maroon">b</font></span>)</span> <a href="hidden.html#R1">=</a> <font color="Maroon">a</font> &amp;  <a href="cat_1.html#K3">cod</a> <span class="p1">(<span class="default"><a href="cat_4.html#K8" target="_self">pr2</a> <font color="Maroon">a</font>,<font color="Maroon">b</font></span>)</span> <a href="hidden.html#R1">=</a> <font color="Maroon">b</font> )
 
<b>by </b><i>, , </i>;<br/>
<b>hence </b><a NAME="E2:32"/>
(  <a href="cat_1.html#K6">Hom</a> <font color="Maroon">a</font>,<font color="Maroon">b</font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a>  <a href="xboole_0.html#K1">{}</a>  &amp;  <a href="cat_1.html#K6">Hom</a> <font color="Maroon">b</font>,<font color="Maroon">a</font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a>  <a href="xboole_0.html#K1">{}</a>  implies (  <a href="cat_4.html#K7" target="_self">pr1</a> <font color="Maroon">a</font>,<font color="Maroon">b</font> is <a href="cat_3.html#V1">retraction</a> &amp;  <a href="cat_4.html#K8" target="_self">pr2</a> <font color="Maroon">a</font>,<font color="Maroon">b</font> is <a href="cat_3.html#V1">retraction</a> ) )
 <b>by </b><i><a class="ref" href="cat_3.html#T62">CAT_3:62</a></i>;<br/>


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