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<span class="kw">let </span><font color="Maroon" title="c1">C</font> be   <a href="cat_4.html#NM1" title="CAT_4:NM.1">Cartesian_category</a>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> for <font color="Olive" title="b1">a</font> being  <a href="cat_1.html#NM1" title="CAT_1:NM.1">Object</a> of <font color="Maroon" title="c1">C</font> holds <br/> (  <a href="graph_1.html#K1" title="GRAPH_1:func.1">dom</a> <span class="p1">(<span class="default"><a href="cat_4.html#K6" title="CAT_4:func.6">term</a> <font color="Olive" title="b1">a</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b1">a</font> &amp;  <a href="graph_1.html#K2" title="GRAPH_1:func.2">cod</a> <span class="p1">(<span class="default"><a href="cat_4.html#K6" title="CAT_4:func.6">term</a> <font color="Olive" title="b1">a</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="cat_4.html#K1" title="CAT_4:func.1">[1]</a> <font color="Maroon" title="c1">C</font> )</span><br/><span class="kw">let </span><font color="Maroon" title="c2">a</font> be   <a href="cat_1.html#NM1" title="CAT_1:NM.1">Object</a> of <font color="Maroon" title="c1">C</font>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> (  <a href="graph_1.html#K1" title="GRAPH_1:func.1">dom</a> <span class="p1">(<span class="default"><a href="cat_4.html#K6" title="CAT_4:func.6">term</a> <font color="Maroon" title="c2">a</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c2">a</font> &amp;  <a href="graph_1.html#K2" title="GRAPH_1:func.2">cod</a> <span class="p1">(<span class="default"><a href="cat_4.html#K6" title="CAT_4:func.6">term</a> <font color="Maroon" title="c2">a</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="cat_4.html#K1" title="CAT_4:func.1">[1]</a> <font color="Maroon" title="c1">C</font> )</span><br/>



<a NAME="E1:28"/>
(  <a href="cat_4.html#K1" title="CAT_4:func.1">[1]</a> <font color="Maroon" title="c1">C</font> is  <a href="cat_1.html#V6" title="CAT_1:attr.6">terminal</a>  &amp;  <a href="cat_4.html#K6" title="CAT_4:func.6">term</a> <font color="Maroon" title="c2">a</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="cat_3.html#K9" title="CAT_3:func.9">term</a> <font color="Maroon" title="c2">a</font>,<span class="p1">(<span class="default"><a href="cat_4.html#K1" title="CAT_4:func.1">[1]</a> <font color="Maroon" title="c1">C</font></span>)</span> )
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="cat_4.html#D9" target="_self" title="CAT_4:def.9">Def9</a>, <a class="ref" href="cat_4.html#T16" target="_self" title="CAT_4:th.16">Th16</a></span>;<br/>
<span class="kw">hence </span><a NAME="E2:28"/>
(  <a href="graph_1.html#K1" title="GRAPH_1:func.1">dom</a> <span class="p1">(<span class="default"><a href="cat_4.html#K6" title="CAT_4:func.6">term</a> <font color="Maroon" title="c2">a</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c2">a</font> &amp;  <a href="graph_1.html#K2" title="GRAPH_1:func.2">cod</a> <span class="p1">(<span class="default"><a href="cat_4.html#K6" title="CAT_4:func.6">term</a> <font color="Maroon" title="c2">a</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="cat_4.html#K1" title="CAT_4:func.1">[1]</a> <font color="Maroon" title="c1">C</font> )
 <span class="kw">by</span> <span class="lab"><a class="ref" href="cat_3.html#T39" title="CAT_3:th.39">CAT_3:39</a></span>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> verum</span><br/>


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