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<b>let </b><font color="Maroon">C</font> be    <a href="cat_1.html#L1" target="_self">CatStr</a> ;<br/><b>let </b><font color="Maroon">a</font> be   <a href="cat_1.html#NM1">Object</a> of <font color="Maroon">C</font>;<br/><b>let </b><font color="Maroon">b</font> be   <a href="cat_1.html#NM1">Object</a> of <font color="Maroon">C</font>;<br/><b>let </b><font color="Maroon">f</font> be   <a href="cat_1.html#NM2">Morphism</a> of <font color="Maroon">C</font>;<br/>







<b>thus </b><a NAME="E1:12"/>
( <font color="Maroon">f</font> <a href="hidden.html#R2">in</a>  <a href="cat_1.html#K6" target="_self">Hom</a> <font color="Maroon">a</font>,<font color="Maroon">b</font> implies (  <a href="cat_1.html#K2" target="_self">dom</a> <font color="Maroon">f</font> <a href="hidden.html#R1">=</a> <font color="Maroon">a</font> &amp;  <a href="cat_1.html#K3" target="_self">cod</a> <font color="Maroon">f</font> <a href="hidden.html#R1">=</a> <font color="Maroon">b</font> ) )
 <div><a class="txt" onclick="hs2(this)" href="javascript:()" title="12_1"><b>proof </b></a><div class="add">

<b>assume </b><a NAME="E1:12_1"/>
<font color="Maroon">f</font> <a href="hidden.html#R2">in</a>  <a href="cat_1.html#K6" target="_self">Hom</a> <font color="Maroon">a</font>,<font color="Maroon">b</font>
 ;<br/>

<a NAME="E2:12_1"/><b>then </b>
 ex <font color="Olive">g</font> being  <a href="cat_1.html#NM2">Morphism</a> of <font color="Maroon">C</font> st <br/>( <font color="Maroon">f</font> <a href="hidden.html#R1">=</a> <font color="Olive">g</font> &amp;  <a href="cat_1.html#K2" target="_self">dom</a> <font color="Olive">g</font> <a href="hidden.html#R1">=</a> <font color="Maroon">a</font> &amp;  <a href="cat_1.html#K3" target="_self">cod</a> <font color="Olive">g</font> <a href="hidden.html#R1">=</a> <font color="Maroon">b</font> )
 
;<br/>
<b>hence </b><a NAME="E3:12_1"/>
(  <a href="cat_1.html#K2" target="_self">dom</a> <font color="Maroon">f</font> <a href="hidden.html#R1">=</a> <font color="Maroon">a</font> &amp;  <a href="cat_1.html#K3" target="_self">cod</a> <font color="Maroon">f</font> <a href="hidden.html#R1">=</a> <font color="Maroon">b</font> )
 ;<br/>


</div><b>end;</b></div>

<b>thus </b><a NAME="E2:12"/>
(  <a href="cat_1.html#K2" target="_self">dom</a> <font color="Maroon">f</font> <a href="hidden.html#R1">=</a> <font color="Maroon">a</font> &amp;  <a href="cat_1.html#K3" target="_self">cod</a> <font color="Maroon">f</font> <a href="hidden.html#R1">=</a> <font color="Maroon">b</font> implies <font color="Maroon">f</font> <a href="hidden.html#R2">in</a>  <a href="cat_1.html#K6" target="_self">Hom</a> <font color="Maroon">a</font>,<font color="Maroon">b</font> )
 ;<br/>


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