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<b>let </b><font color="Maroon" title="c1">C</font> be   <a href="cat_4.html#NM1" title="CAT_4:NM.1">Cartesian_category</a>;<br/><b>let </b><font color="Maroon" title="c2">c</font>, <font color="Maroon" title="c3">a</font>, <font color="Maroon" title="c4">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="E1:34"/>
(  <a href="cat_1.html#K6" title="CAT_1:func.6">Hom</a> <span class="p1">(<span class="default"><font color="Maroon" title="c3">a</font> <a href="cat_4.html#K2" title="CAT_4:func.2">[x]</a> <font color="Maroon" title="c4">b</font></span>)</span>,<font color="Maroon" title="c3">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>  &amp;  <a href="cat_1.html#K6" title="CAT_1:func.6">Hom</a> <span class="p1">(<span class="default"><font color="Maroon" title="c3">a</font> <a href="cat_4.html#K2" title="CAT_4:func.2">[x]</a> <font color="Maroon" title="c4">b</font></span>)</span>,<font color="Maroon" title="c4">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; <font color="Maroon" title="c3">a</font> <a href="cat_4.html#K2" title="CAT_4:func.2">[x]</a> <font color="Maroon" title="c4">b</font> <a href="cat_3.html#R2" title="CAT_3:pred.2">is_a_product_wrt</a>  <a href="cat_4.html#K7" title="CAT_4:func.7">pr1</a> <font color="Maroon" title="c3">a</font>,<font color="Maroon" title="c4">b</font>, <a href="cat_4.html#K8" title="CAT_4:func.8">pr2</a> <font color="Maroon" title="c3">a</font>,<font color="Maroon" title="c4">b</font> )
 
<b>by </b><i><a class="ref" href="cat_4.html#T21" target="_self" title="CAT_4:th.21">Th21</a>, <a class="ref" href="cat_4.html#T22" target="_self" title="CAT_4:th.22">Th22</a></i>;<br/>
<b>hence </b><a NAME="E2:34"/>
(  <a href="cat_1.html#K6" title="CAT_1:func.6">Hom</a> <font color="Maroon" title="c2">c</font>,<font color="Maroon" title="c3">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>  &amp;  <a href="cat_1.html#K6" title="CAT_1:func.6">Hom</a> <font color="Maroon" title="c2">c</font>,<font color="Maroon" title="c4">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>  implies  <a href="cat_1.html#K6" title="CAT_1:func.6">Hom</a> <font color="Maroon" title="c2">c</font>,<span class="p1">(<span class="default"><font color="Maroon" title="c3">a</font> <a href="cat_4.html#K2" title="CAT_4:func.2">[x]</a> <font color="Maroon" title="c4">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>  )
 <b>by </b><i><a class="ref" href="cat_3.html#T60" title="CAT_3:th.60">CAT_3:60</a></i>;<br/>


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