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<a NAME="E1:33_1_1"/>
(  <a href="cat_1.html#K6">Hom</a> <span class="p1">(<span class="default"><font color="Maroon">a</font> <a href="cat_4.html#K2" target="_self">[x]</a> <font color="Maroon">b</font></span>)</span>,<font color="Maroon">a</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> <span class="p1">(<span class="default"><font color="Maroon">a</font> <a href="cat_4.html#K2" target="_self">[x]</a> <font color="Maroon">b</font></span>)</span>,<font color="Maroon">b</font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a>  <a href="xboole_0.html#K1">{}</a>  &amp; <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> )
 
<b>by </b><i>, </i>;<br/>
<b>then consider </b><font color="Maroon">h</font> being    <a href="cat_1.html#M1">Morphism</a> of <font color="Maroon">c</font>,<font color="Maroon">a</font> <a href="cat_4.html#K2" target="_self">[x]</a> <font color="Maroon">b</font><b> such that </b><br/><a NAME="E3:33_1_1"/><i><font color="Green">E35</font></i>: 
for <font color="Olive">h1</font> being   <a href="cat_1.html#M1">Morphism</a> of <font color="Maroon">c</font>,<font color="Maroon">a</font> <a href="cat_4.html#K2" target="_self">[x]</a> <font color="Maroon">b</font> holds <br/> ( ( <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="cat_1.html#K9">*</a> <font color="Olive">h1</font> <a href="hidden.html#R1">=</a> <font color="Maroon">f</font> &amp; <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="cat_1.html#K9">*</a> <font color="Olive">h1</font> <a href="hidden.html#R1">=</a> <font color="Maroon">g</font> ) iff <font color="Maroon">h</font> <a href="hidden.html#R1">=</a> <font color="Olive">h1</font> )
 <b>by </b><i>, <a class="ref" href="cat_3.html#T60">CAT_3:60</a></i>;<br/>
<b>take </b>
<font color="Maroon">h</font>
;<br/>

<b>thus </b><a NAME="E4:33_1_1"/>
( <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="cat_1.html#K9">*</a> <font color="Maroon">h</font> <a href="hidden.html#R1">=</a> <font color="Maroon">f</font> &amp; <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="cat_1.html#K9">*</a> <font color="Maroon">h</font> <a href="hidden.html#R1">=</a> <font color="Maroon">g</font> )
 <b>by </b><i/>;<br/>


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