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<b>let </b><font color="Maroon" title="c1">o</font>, <font color="Maroon" title="c2">m</font> be    <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a> ;<br/><b>let </b><font color="Maroon" title="c3">c</font> be   <a href="cat_1.html#NM1" title="CAT_1:NM.1">Object</a> of <span class="p1">(<span class="default"><a href="cat_4.html#K23" title="CAT_4:func.23">c1Cat*</a> <font color="Maroon" title="c1">o</font>,<font color="Maroon" title="c2">m</font></span>)</span>;<br/><b>let </b><font color="Maroon" title="c4">i1</font>, <font color="Maroon" title="c5">i2</font> be   <a href="cat_1.html#NM2" title="CAT_1:NM.2">Morphism</a> of <span class="p1">(<span class="default"><a href="cat_4.html#K23" title="CAT_4:func.23">c1Cat*</a> <font color="Maroon" title="c1">o</font>,<font color="Maroon" title="c2">m</font></span>)</span>;<br/>







<b>thus </b><a NAME="E1:78"/>
(  <a href="cat_1.html#K4" title="CAT_1:func.4">cod</a> <font color="Maroon" title="c4">i1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c3">c</font> &amp;  <a href="cat_1.html#K4" title="CAT_1:func.4">cod</a> <font color="Maroon" title="c5">i2</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c3">c</font> )
 <b>by </b><i><a class="ref" href="cat_4.html#T49" target="_self" title="CAT_4:th.49">Th49</a></i>; <i><font color="Red">:: according to </font></i><a class="ref" href="cat_3.html#D19" title="CAT_3:def.19">CAT_3:def 19</a><br/>

<b>let </b><font color="Maroon" title="c6">d</font> be   <a href="cat_1.html#NM1" title="CAT_1:NM.1">Object</a> of <span class="p1">(<span class="default"><a href="cat_4.html#K23" title="CAT_4:func.23">c1Cat*</a> <font color="Maroon" title="c1">o</font>,<font color="Maroon" title="c2">m</font></span>)</span>;<br/><b>let </b><font color="Maroon" title="c7">f</font>, <font color="Maroon" title="c8">g</font> be   <a href="cat_1.html#NM2" title="CAT_1:NM.2">Morphism</a> of <span class="p1">(<span class="default"><a href="cat_4.html#K23" title="CAT_4:func.23">c1Cat*</a> <font color="Maroon" title="c1">o</font>,<font color="Maroon" title="c2">m</font></span>)</span>;<br/>



<b>assume </b><a NAME="E2:78"/>
( <font color="Maroon" title="c7">f</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="cat_1.html#K7" title="CAT_1:func.7">Hom</a> <span class="p1">(<span class="default"><a href="cat_1.html#K3" title="CAT_1:func.3">dom</a> <font color="Maroon" title="c4">i1</font></span>)</span>,<font color="Maroon" title="c6">d</font> &amp; <font color="Maroon" title="c8">g</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="cat_1.html#K7" title="CAT_1:func.7">Hom</a> <span class="p1">(<span class="default"><a href="cat_1.html#K3" title="CAT_1:func.3">dom</a> <font color="Maroon" title="c5">i2</font></span>)</span>,<font color="Maroon" title="c6">d</font> )
 ;<br/>

<b>take </b><font color="Maroon" title="c9">h</font> = <font color="Maroon" title="c4">i1</font>;<br/>

<b>thus </b><a NAME="E3:78"/>
<font color="Maroon" title="c9">h</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="cat_1.html#K7" title="CAT_1:func.7">Hom</a> <font color="Maroon" title="c3">c</font>,<font color="Maroon" title="c6">d</font>
 <b>by </b><i><a class="ref" href="cat_4.html#T52" target="_self" title="CAT_4:th.52">Th52</a></i>;<br/>

<b>thus </b><a NAME="E4:78"/>
for <font color="Olive">b<sub>1</sub></font> being   <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of the <a href="graph_1.html#U2" title="GRAPH_1:sel.2">Edges</a> of <span class="p1">(<span class="default"><a href="cat_4.html#K23" title="CAT_4:func.23">c1Cat*</a> <font color="Maroon" title="c1">o</font>,<font color="Maroon" title="c2">m</font></span>)</span>  holds <br/>(  not <font color="Olive">b<sub>1</sub></font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="cat_1.html#K7" title="CAT_1:func.7">Hom</a> <font color="Maroon" title="c3">c</font>,<font color="Maroon" title="c6">d</font> or ( (  not <font color="Olive">b<sub>1</sub></font> <a href="cat_1.html#K5" title="CAT_1:func.5">*</a> <font color="Maroon" title="c4">i1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c7">f</font> or  not <font color="Olive">b<sub>1</sub></font> <a href="cat_1.html#K5" title="CAT_1:func.5">*</a> <font color="Maroon" title="c5">i2</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c8">g</font> or <font color="Maroon" title="c9">h</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive">b<sub>1</sub></font> ) &amp; (  not <font color="Maroon" title="c9">h</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive">b<sub>1</sub></font> or ( <font color="Olive">b<sub>1</sub></font> <a href="cat_1.html#K5" title="CAT_1:func.5">*</a> <font color="Maroon" title="c4">i1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c7">f</font> &amp; <font color="Olive">b<sub>1</sub></font> <a href="cat_1.html#K5" title="CAT_1:func.5">*</a> <font color="Maroon" title="c5">i2</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c8">g</font> ) ) ) )
 <b>by </b><i><a class="ref" href="cat_4.html#T51" target="_self" title="CAT_4:th.51">Th51</a></i>;<br/>


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