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<b>let </b><font color="Maroon">o</font> be    <a href="hidden.html#M1">set</a> ;<br/><b>let </b><font color="Maroon">m</font> be    <a href="hidden.html#M1">set</a> ;<br/><b>let </b><font color="Maroon">c</font> be   <a href="cat_1.html#NM1">Object</a> of <span class="p1">(<span class="default"><a href="cat_4.html#K5" target="_self">c1Cat</a> <font color="Maroon">o</font>,<font color="Maroon">m</font></span>)</span>;<br/><b>let </b><font color="Maroon">p1</font> be   <a href="cat_1.html#NM2">Morphism</a> of <span class="p1">(<span class="default"><a href="cat_4.html#K5" target="_self">c1Cat</a> <font color="Maroon">o</font>,<font color="Maroon">m</font></span>)</span>, <font color="Maroon">p2</font> be   <a href="cat_1.html#NM2">Morphism</a> of <span class="p1">(<span class="default"><a href="cat_4.html#K5" target="_self">c1Cat</a> <font color="Maroon">o</font>,<font color="Maroon">m</font></span>)</span>;<br/>







<b>thus </b><a NAME="E1:16"/>
(  <a href="cat_1.html#K2">dom</a> <font color="Maroon">p1</font> <a href="hidden.html#R1">=</a> <font color="Maroon">c</font> &amp;  <a href="cat_1.html#K2">dom</a> <font color="Maroon">p2</font> <a href="hidden.html#R1">=</a> <font color="Maroon">c</font> )
 <b>by </b><i/>; <i><font color="Red">:: according to </font></i><a class="ref" href="cat_3.html#D16">CAT_3:def 16</a><br/>

<b>let </b><font color="Maroon">d</font> be   <a href="cat_1.html#NM1">Object</a> of <span class="p1">(<span class="default"><a href="cat_4.html#K5" target="_self">c1Cat</a> <font color="Maroon">o</font>,<font color="Maroon">m</font></span>)</span>;<br/><b>let </b><font color="Maroon">f</font> be   <a href="cat_1.html#NM2">Morphism</a> of <span class="p1">(<span class="default"><a href="cat_4.html#K5" target="_self">c1Cat</a> <font color="Maroon">o</font>,<font color="Maroon">m</font></span>)</span>, <font color="Maroon">g</font> be   <a href="cat_1.html#NM2">Morphism</a> of <span class="p1">(<span class="default"><a href="cat_4.html#K5" target="_self">c1Cat</a> <font color="Maroon">o</font>,<font color="Maroon">m</font></span>)</span>;<br/>



<b>assume </b><a NAME="E2:16"/>
( <font color="Maroon">f</font> <a href="hidden.html#R2">in</a>  <a href="cat_1.html#K6">Hom</a> <font color="Maroon">d</font>,<span class="p1">(<span class="default"><a href="cat_1.html#K3">cod</a> <font color="Maroon">p1</font></span>)</span> &amp; <font color="Maroon">g</font> <a href="hidden.html#R2">in</a>  <a href="cat_1.html#K6">Hom</a> <font color="Maroon">d</font>,<span class="p1">(<span class="default"><a href="cat_1.html#K3">cod</a> <font color="Maroon">p2</font></span>)</span> )
 ;<br/>

<b>take </b><font color="Maroon">h</font> = <font color="Maroon">p1</font>;<br/>

<b>thus </b><a NAME="E3:16"/>
<font color="Maroon">h</font> <a href="hidden.html#R2">in</a>  <a href="cat_1.html#K6">Hom</a> <font color="Maroon">d</font>,<font color="Maroon">c</font>
 <b>by </b><i/>;<br/>

<b>thus </b><a NAME="E4:16"/>
for <font color="Olive">b<sub>1</sub></font> being   <a href="subset_1.html#M1">Element</a> of the <a href="cat_1.html#U2">Morphisms</a> of <span class="p1">(<span class="default"><a href="cat_4.html#K5" target="_self">c1Cat</a> <font color="Maroon">o</font>,<font color="Maroon">m</font></span>)</span>  holds <br/>(  not <font color="Olive">b<sub>1</sub></font> <a href="hidden.html#R2">in</a>  <a href="cat_1.html#K6">Hom</a> <font color="Maroon">d</font>,<font color="Maroon">c</font> or ( (  not <font color="Maroon">p1</font> <a href="cat_1.html#K4">*</a> <font color="Olive">b<sub>1</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">f</font> or  not <font color="Maroon">p2</font> <a href="cat_1.html#K4">*</a> <font color="Olive">b<sub>1</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">g</font> or <font color="Maroon">h</font> <a href="hidden.html#R1">=</a> <font color="Olive">b<sub>1</sub></font> ) &amp; (  not <font color="Maroon">h</font> <a href="hidden.html#R1">=</a> <font color="Olive">b<sub>1</sub></font> or ( <font color="Maroon">p1</font> <a href="cat_1.html#K4">*</a> <font color="Olive">b<sub>1</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">f</font> &amp; <font color="Maroon">p2</font> <a href="cat_1.html#K4">*</a> <font color="Olive">b<sub>1</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">g</font> ) ) ) )
 <b>by </b><i/>;<br/>


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