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<b>let </b><font color="Maroon">c<sub>1</sub></font> be   <a href="cat_1.html#NM4">Category</a>;<br/><b>let </b><font color="Maroon">c<sub>2</sub></font>, <font color="Maroon">c<sub>3</sub></font> be   <a href="cat_1.html#NM1">Object</a> of <font color="Maroon">c<sub>1</sub></font>;<br/><b>let </b><font color="Maroon">c<sub>4</sub></font> be   <a href="cat_1.html#NM2">Morphism</a> of <font color="Maroon">c<sub>1</sub></font>;<br/>





<a NAME="E1:8"/>
( (  <a href="cat_1.html#K2">dom</a> <font color="Maroon">c<sub>4</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>2</sub></font> &amp;  <a href="cat_1.html#K3">cod</a> <font color="Maroon">c<sub>4</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>3</sub></font> implies <font color="Maroon">c<sub>4</sub></font> <a href="hidden.html#R2">in</a>  <a href="cat_1.html#K6">Hom</a> <font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>3</sub></font> ) &amp; ( <font color="Maroon">c<sub>4</sub></font> <a href="hidden.html#R2">in</a>  <a href="cat_1.html#K6">Hom</a> <font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>3</sub></font> implies (  <a href="cat_1.html#K2">dom</a> <font color="Maroon">c<sub>4</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>2</sub></font> &amp;  <a href="cat_1.html#K3">cod</a> <font color="Maroon">c<sub>4</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>3</sub></font> ) ) &amp; <font color="Maroon">c<sub>2</sub></font> <a href="oppcat_1.html#K3" target="_self">opp</a>  <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>2</sub></font> &amp; <font color="Maroon">c<sub>3</sub></font> <a href="oppcat_1.html#K3" target="_self">opp</a>  <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>3</sub></font> &amp;  <a href="cat_1.html#K2">dom</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>4</sub></font> <a href="oppcat_1.html#K5" target="_self">opp</a> </span>)</span> <a href="hidden.html#R1">=</a>  <a href="cat_1.html#K3">cod</a> <font color="Maroon">c<sub>4</sub></font> &amp;  <a href="cat_1.html#K3">cod</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>4</sub></font> <a href="oppcat_1.html#K5" target="_self">opp</a> </span>)</span> <a href="hidden.html#R1">=</a>  <a href="cat_1.html#K2">dom</a> <font color="Maroon">c<sub>4</sub></font> &amp; (  <a href="cat_1.html#K3">cod</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>4</sub></font> <a href="oppcat_1.html#K5" target="_self">opp</a> </span>)</span> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>2</sub></font> <a href="oppcat_1.html#K3" target="_self">opp</a>  &amp;  <a href="cat_1.html#K2">dom</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>4</sub></font> <a href="oppcat_1.html#K5" target="_self">opp</a> </span>)</span> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>3</sub></font> <a href="oppcat_1.html#K3" target="_self">opp</a>  implies <font color="Maroon">c<sub>4</sub></font> <a href="oppcat_1.html#K5" target="_self">opp</a>  <a href="hidden.html#R2">in</a>  <a href="cat_1.html#K6">Hom</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="oppcat_1.html#K3" target="_self">opp</a> </span>)</span>,<span class="p1">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="oppcat_1.html#K3" target="_self">opp</a> </span>)</span> ) &amp; ( <font color="Maroon">c<sub>4</sub></font> <a href="oppcat_1.html#K5" target="_self">opp</a>  <a href="hidden.html#R2">in</a>  <a href="cat_1.html#K6">Hom</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="oppcat_1.html#K3" target="_self">opp</a> </span>)</span>,<span class="p1">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="oppcat_1.html#K3" target="_self">opp</a> </span>)</span> implies (  <a href="cat_1.html#K3">cod</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>4</sub></font> <a href="oppcat_1.html#K5" target="_self">opp</a> </span>)</span> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>2</sub></font> <a href="oppcat_1.html#K3" target="_self">opp</a>  &amp;  <a href="cat_1.html#K2">dom</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>4</sub></font> <a href="oppcat_1.html#K5" target="_self">opp</a> </span>)</span> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>3</sub></font> <a href="oppcat_1.html#K3" target="_self">opp</a>  ) ) )
 
<b>by </b><i><a class="ref" href="cat_1.html#T18">CAT_1:18</a></i>;<br/>
<b>hence </b><a NAME="E2:8"/>
( <font color="Maroon">c<sub>4</sub></font> <a href="hidden.html#R2">in</a>  <a href="cat_1.html#K6">Hom</a> <font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>3</sub></font> iff <font color="Maroon">c<sub>4</sub></font> <a href="oppcat_1.html#K5" target="_self">opp</a>  <a href="hidden.html#R2">in</a>  <a href="cat_1.html#K6">Hom</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="oppcat_1.html#K3" target="_self">opp</a> </span>)</span>,<span class="p1">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="oppcat_1.html#K3" target="_self">opp</a> </span>)</span> )
 ;<br/>


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