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<b>let </b><font color="Maroon" title="c1">C</font> be   <a href="cat_4.html#NM2" title="CAT_4:NM.2">Cocartesian_category</a>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></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="cat_1.html#K3" title="CAT_1:func.3">dom</a> <span class="p1">(<span class="default"><a href="cat_4.html#K24" title="CAT_4:func.24">init</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#K19" title="CAT_4:func.19">[0]</a> <font color="Maroon" title="c1">C</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#K24" title="CAT_4:func.24">init</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> )</span><br/><b>let </b><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:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> (  <a href="cat_1.html#K3" title="CAT_1:func.3">dom</a> <span class="p1">(<span class="default"><a href="cat_4.html#K24" title="CAT_4:func.24">init</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#K19" title="CAT_4:func.19">[0]</a> <font color="Maroon" title="c1">C</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#K24" title="CAT_4:func.24">init</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> )</span><br/>



<a NAME="E1:87"/>
(  <a href="cat_4.html#K19" title="CAT_4:func.19">[0]</a> <font color="Maroon" title="c1">C</font> is <a href="cat_1.html#V8" title="CAT_1:attr.8">initial</a> &amp;  <a href="cat_4.html#K24" title="CAT_4:func.24">init</a> <font color="Maroon" title="c2">a</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="cat_3.html#K10" title="CAT_3:func.10">init</a> <span class="p1">(<span class="default"><a href="cat_4.html#K19" title="CAT_4:func.19">[0]</a> <font color="Maroon" title="c1">C</font></span>)</span>,<font color="Maroon" title="c2">a</font> )
 
<b>by </b><i><a class="ref" href="cat_4.html#D27" target="_self" title="CAT_4:def.27">Def27</a>, <a class="ref" href="cat_4.html#T61" target="_self" title="CAT_4:th.61">Th61</a></i>;<br/>
<b>hence </b><a NAME="E2:87"/>
(  <a href="cat_1.html#K3" title="CAT_1:func.3">dom</a> <span class="p1">(<span class="default"><a href="cat_4.html#K24" title="CAT_4:func.24">init</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#K19" title="CAT_4:func.19">[0]</a> <font color="Maroon" title="c1">C</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#K24" title="CAT_4:func.24">init</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> )
 <b>by </b><i><a class="ref" href="cat_3.html#T42" title="CAT_3:th.42">CAT_3:42</a></i>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> verum</span><br/>


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