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<b>let </b><font color="Maroon">C</font> be   <a href="cat_1.html#NM4">Category</a>;<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">c</font> be   <a href="cat_1.html#NM1">Object</a> of <font color="Maroon">C</font>;<br/><b>let </b><font color="Maroon">d</font> be   <a href="cat_1.html#NM1">Object</a> of <font color="Maroon">C</font>;<br/><b>let </b><font color="Maroon">g</font> be    <a href="cat_1.html#M1" target="_self">Morphism</a> of <font color="Maroon">b</font>,<font color="Maroon">c</font>;<br/><b>let </b><font color="Maroon">h</font> be    <a href="cat_1.html#M1" target="_self">Morphism</a> of <font color="Maroon">c</font>,<font color="Maroon">d</font>;<br/>











<b>assume </b><b>that </b><br/><a NAME="E1:50"/><i><font color="Green">E20</font></i>: 
(  <a href="cat_1.html#K6" target="_self">Hom</a> <font color="Maroon">b</font>,<font color="Maroon">c</font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a>  <a href="xboole_0.html#K1">{}</a>  &amp;  <a href="cat_1.html#K6" target="_self">Hom</a> <font color="Maroon">c</font>,<font color="Maroon">d</font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a>  <a href="xboole_0.html#K1">{}</a>  )
 <b>and </b><br/><a NAME="E2:50"/><i><font color="Green">E21</font></i>: 
<font color="Maroon">h</font> <a href="cat_1.html#K9" target="_self">*</a> <font color="Maroon">g</font> is <a href="cat_1.html#V3" target="_self">monic</a>
 ;<br/>

<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="50_1"><b>now </b></a><div class="add"><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">f1</font> be    <a href="cat_1.html#M1" target="_self">Morphism</a> of <font color="Maroon">a</font>,<font color="Maroon">b</font>;<br/><b>let </b><font color="Maroon">f2</font> be    <a href="cat_1.html#M1" target="_self">Morphism</a> of <font color="Maroon">a</font>,<font color="Maroon">b</font>;<br/><b>assume </b><a NAME="E1:50_1"/><i><font color="Green">E22</font></i>: 
 <a href="cat_1.html#K6" target="_self">Hom</a> <font color="Maroon">a</font>,<font color="Maroon">b</font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a>  <a href="xboole_0.html#K1">{}</a> 
 ;<br/><a NAME="E2:50_1"/><b>then </b>
(  <a href="cat_1.html#K6" target="_self">Hom</a> <font color="Maroon">b</font>,<font color="Maroon">d</font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a>  <a href="xboole_0.html#K1">{}</a>  &amp; <font color="Maroon">h</font> <a href="cat_1.html#K9" target="_self">*</a> <span class="p1">(<span class="default"><font color="Maroon">g</font> <a href="cat_1.html#K9" target="_self">*</a> <font color="Maroon">f1</font></span>)</span> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><font color="Maroon">h</font> <a href="cat_1.html#K9" target="_self">*</a> <font color="Maroon">g</font></span>)</span> <a href="cat_1.html#K9" target="_self">*</a> <font color="Maroon">f1</font> &amp; <font color="Maroon">h</font> <a href="cat_1.html#K9" target="_self">*</a> <span class="p1">(<span class="default"><font color="Maroon">g</font> <a href="cat_1.html#K9" target="_self">*</a> <font color="Maroon">f2</font></span>)</span> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><font color="Maroon">h</font> <a href="cat_1.html#K9" target="_self">*</a> <font color="Maroon">g</font></span>)</span> <a href="cat_1.html#K9" target="_self">*</a> <font color="Maroon">f2</font> )
 <b>by </b><i>, <a class="ref" href="cat_1.html#T8" target="_self">Th8</a>, </i>;<br/><b>hence </b><a NAME="E3:50_1"/>
( <font color="Maroon">g</font> <a href="cat_1.html#K9" target="_self">*</a> <font color="Maroon">f1</font> <a href="hidden.html#R1">=</a> <font color="Maroon">g</font> <a href="cat_1.html#K9" target="_self">*</a> <font color="Maroon">f2</font> implies <font color="Maroon">f1</font> <a href="hidden.html#R1">=</a> <font color="Maroon">f2</font> )
 <b>by </b><i><a class="ref" href="cat_1.html#T18" target="_self">Th18</a>, <a class="ref" href="cat_1.html#D7" target="_self">Def7</a>, <a class="ref" href="cat_1.html#D4" target="_self">Def4</a></i>;<br/></div><b>end;</b></div>
<b>hence </b><a NAME="E4:50"/>
<font color="Maroon">g</font> is <a href="cat_1.html#V3" target="_self">monic</a>
 <b>by </b><i>, <a class="ref" href="cat_1.html#D4" target="_self">Def4</a></i>;<br/>


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