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( <font color="Maroon">c<sub>3</sub></font> is   <a href="funct_2.html#NM1">Function</a> of the <a href="cat_1.html#U2" target="_self">Morphisms</a> of <font color="Maroon">c<sub>1</sub></font>,the <a href="cat_1.html#U2" target="_self">Morphisms</a> of <font color="Maroon">c<sub>2</sub></font> &amp;  <a href="cat_1.html#K6" target="_self">Hom</a> <font color="Maroon">c<sub>4</sub></font>,<font color="Maroon">c<sub>5</sub></font> <a href="tarski.html#R1">c=</a> the <a href="cat_1.html#U2" target="_self">Morphisms</a> of <font color="Maroon">c<sub>1</sub></font> &amp; <font color="Maroon">c<sub>3</sub></font> <a href="relat_1.html#K9">.:</a> <span class="p1">(<span class="default"><a href="cat_1.html#K6" target="_self">Hom</a> <font color="Maroon">c<sub>4</sub></font>,<font color="Maroon">c<sub>5</sub></font></span>)</span> <a href="tarski.html#R1">c=</a>  <a href="cat_1.html#K6" target="_self">Hom</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="cat_1.html#K13" target="_self">.</a> <font color="Maroon">c<sub>4</sub></font></span>)</span>,<span class="p1">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="cat_1.html#K13" target="_self">.</a> <font color="Maroon">c<sub>5</sub></font></span>)</span> )
 
<b>by </b><i><a class="ref" href="cat_1.html#T129" target="_self">Th129</a></i>;<br/>
<b>hence </b><a NAME="E2:108_1_1"/>
<font color="Maroon">c<sub>3</sub></font> <a href="partfun1.html#K2">|</a> <span class="p1">(<span class="default"><a href="cat_1.html#K6" target="_self">Hom</a> <font color="Maroon">c<sub>4</sub></font>,<font color="Maroon">c<sub>5</sub></font></span>)</span> is   <a href="funct_2.html#NM1">Function</a> of  <a href="cat_1.html#K6" target="_self">Hom</a> <font color="Maroon">c<sub>4</sub></font>,<font color="Maroon">c<sub>5</sub></font>, <a href="cat_1.html#K6" target="_self">Hom</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="cat_1.html#K13" target="_self">.</a> <font color="Maroon">c<sub>4</sub></font></span>)</span>,<span class="p1">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="cat_1.html#K13" target="_self">.</a> <font color="Maroon">c<sub>5</sub></font></span>)</span>
 <b>by </b><i><a class="ref" href="cat_1.html#T4" target="_self">Th4</a></i>;<br/>


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