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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">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/>





<b>set </b><font color="Maroon" title="c4">p1</font> = the <a href="cat_4.html#U3" title="CAT_4:sel.3">Proj1</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/>
<b>set </b><font color="Maroon" title="c5">p2</font> = the <a href="cat_4.html#U4" title="CAT_4:sel.4">Proj2</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="E1:29"/>
<font color="Maroon" title="c2">a</font> <a href="cat_4.html#K2" title="CAT_4:func.2">[x]</a> <font color="Maroon" title="c3">b</font> <a href="cat_3.html#R2" title="CAT_3:pred.2">is_a_product_wrt</a> the <a href="cat_4.html#U3" title="CAT_4:sel.3">Proj1</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#U4" title="CAT_4:sel.4">Proj2</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>
 
<b>by </b><i><a class="ref" href="cat_4.html#D9" target="_self" title="CAT_4:def.9">Def9</a></i>;<br/>
<b>hence </b><a NAME="E2:29"/>
(  <a href="cat_1.html#K3" title="CAT_1:func.3">dom</a> <span class="p1">(<span class="default"><a href="cat_4.html#K3" title="CAT_4:func.3">pr1</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> <a href="cat_4.html#K2" title="CAT_4:func.2">[x]</a> <font color="Maroon" title="c3">b</font> &amp;  <a href="cat_1.html#K4" title="CAT_1:func.4">cod</a> <span class="p1">(<span class="default"><a href="cat_4.html#K3" title="CAT_4:func.3">pr1</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> )
 <b>by </b><i><a class="ref" href="cat_4.html#D9" target="_self" title="CAT_4:def.9">Def9</a>, <a class="ref" href="cat_3.html#D16" title="CAT_3:def.16">CAT_3:def 16</a></i>;<br/>


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