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<b>let </b><font color="Maroon" title="c2">h1</font>, <font color="Maroon" title="c3">h2</font> be   <a href="funct_2.html#NM1" title="FUNCT_2:NM.1">Function</a> of the <a href="cat_1.html#U2" title="CAT_1:sel.2">Morphisms</a> of <span class="p1"><a href="cat_2.html#K11" title="CAT_2:func.11">[:</a><span class="default"><font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c1">C</font></span><a href="cat_2.html#K11" title="CAT_2:func.11">:]</a></span>, <a href="ens_1.html#K2" title="ENS_1:func.2">Maps</a> <span class="p1">(<span class="default"><a href="ens_1.html#K17" title="ENS_1:func.17">Hom</a> <font color="Maroon" title="c1">C</font></span>)</span>;<br/>

<b>assume </b><b>that </b><br/><a NAME="E1:82_1_2"/><i><font color="Green" title="E58">A5</font></i>: 
for <font color="Olive" title="b1">f</font>, <font color="Olive" title="b2">g</font> being  <a href="cat_1.html#NM2" title="CAT_1:NM.2">Morphism</a> of <font color="Maroon" title="c1">C</font> holds  <font color="Maroon" title="c2">h1</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <span class="p1"><a href="cat_2.html#K13" title="CAT_2:func.13">[</a><span class="default"><font color="Olive" title="b1">f</font>,<font color="Olive" title="b2">g</font></span><a href="cat_2.html#K13" title="CAT_2:func.13">]</a></span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1"><a href="domain_1.html#K1" title="DOMAIN_1:func.1">[</a><span class="default"><span class="p2"><a href="domain_1.html#K1" title="DOMAIN_1:func.1">[</a><span class="default"><span class="p3">(<span class="default"><a href="cat_1.html#K6" title="CAT_1:func.6">Hom</a> <span class="p4">(<span class="default"><a href="cat_1.html#K3" title="CAT_1:func.3">cod</a> <font color="Olive" title="b1">f</font></span>)</span>,<span class="p4">(<span class="default"><a href="cat_1.html#K2" title="CAT_1:func.2">dom</a> <font color="Olive" title="b2">g</font></span>)</span></span>)</span>,<span class="p3">(<span class="default"><a href="cat_1.html#K6" title="CAT_1:func.6">Hom</a> <span class="p4">(<span class="default"><a href="cat_1.html#K2" title="CAT_1:func.2">dom</a> <font color="Olive" title="b1">f</font></span>)</span>,<span class="p4">(<span class="default"><a href="cat_1.html#K3" title="CAT_1:func.3">cod</a> <font color="Olive" title="b2">g</font></span>)</span></span>)</span></span><a href="domain_1.html#K1" title="DOMAIN_1:func.1">]</a></span>,<span class="p2">(<span class="default"><a href="ens_1.html#K22" title="ENS_1:func.22">hom</a> <font color="Olive" title="b1">f</font>,<font color="Olive" title="b2">g</font></span>)</span></span><a href="domain_1.html#K1" title="DOMAIN_1:func.1">]</a></span>
 <b>and </b><br/><a NAME="E2:82_1_2"/><i><font color="Green" title="E59">A6</font></i>: 
for <font color="Olive" title="b1">f</font>, <font color="Olive" title="b2">g</font> being  <a href="cat_1.html#NM2" title="CAT_1:NM.2">Morphism</a> of <font color="Maroon" title="c1">C</font> holds  <font color="Maroon" title="c3">h2</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <span class="p1"><a href="cat_2.html#K13" title="CAT_2:func.13">[</a><span class="default"><font color="Olive" title="b1">f</font>,<font color="Olive" title="b2">g</font></span><a href="cat_2.html#K13" title="CAT_2:func.13">]</a></span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1"><a href="domain_1.html#K1" title="DOMAIN_1:func.1">[</a><span class="default"><span class="p2"><a href="domain_1.html#K1" title="DOMAIN_1:func.1">[</a><span class="default"><span class="p3">(<span class="default"><a href="cat_1.html#K6" title="CAT_1:func.6">Hom</a> <span class="p4">(<span class="default"><a href="cat_1.html#K3" title="CAT_1:func.3">cod</a> <font color="Olive" title="b1">f</font></span>)</span>,<span class="p4">(<span class="default"><a href="cat_1.html#K2" title="CAT_1:func.2">dom</a> <font color="Olive" title="b2">g</font></span>)</span></span>)</span>,<span class="p3">(<span class="default"><a href="cat_1.html#K6" title="CAT_1:func.6">Hom</a> <span class="p4">(<span class="default"><a href="cat_1.html#K2" title="CAT_1:func.2">dom</a> <font color="Olive" title="b1">f</font></span>)</span>,<span class="p4">(<span class="default"><a href="cat_1.html#K3" title="CAT_1:func.3">cod</a> <font color="Olive" title="b2">g</font></span>)</span></span>)</span></span><a href="domain_1.html#K1" title="DOMAIN_1:func.1">]</a></span>,<span class="p2">(<span class="default"><a href="ens_1.html#K22" title="ENS_1:func.22">hom</a> <font color="Olive" title="b1">f</font>,<font color="Olive" title="b2">g</font></span>)</span></span><a href="domain_1.html#K1" title="DOMAIN_1:func.1">]</a></span>
 ;<br/>

<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="82_1_2_1"><b>now </b></a><div class="add"><b>thus </b><a NAME="E1:82_1_2_1"/>
the <a href="cat_1.html#U2" title="CAT_1:sel.2">Morphisms</a> of <span class="p1"><a href="cat_2.html#K11" title="CAT_2:func.11">[:</a><span class="default"><font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c1">C</font></span><a href="cat_2.html#K11" title="CAT_2:func.11">:]</a></span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1"><a href="zfmisc_1.html#K2" title="ZFMISC_1:func.2">[:</a><span class="default">the <a href="cat_1.html#U2" title="CAT_1:sel.2">Morphisms</a> of <font color="Maroon" title="c1">C</font>,the <a href="cat_1.html#U2" title="CAT_1:sel.2">Morphisms</a> of <font color="Maroon" title="c1">C</font></span><a href="zfmisc_1.html#K2" title="ZFMISC_1:func.2">:]</a></span>
 ;<br/><b>let </b><font color="Maroon" title="c4">f</font>, <font color="Maroon" title="c5">g</font> be   <a href="cat_1.html#NM2" title="CAT_1:NM.2">Morphism</a> of <font color="Maroon" title="c1">C</font>;<br/><b>thus </b><font color="Maroon" title="c2">h1</font> <a href="binop_1.html#K1" title="BINOP_1:func.1">.</a> <font color="Maroon" title="c4">f</font>,<font color="Maroon" title="c5">g</font> = 
<span class="p1"><a href="domain_1.html#K1" title="DOMAIN_1:func.1">[</a><span class="default"><span class="p2"><a href="domain_1.html#K1" title="DOMAIN_1:func.1">[</a><span class="default"><span class="p3">(<span class="default"><a href="cat_1.html#K6" title="CAT_1:func.6">Hom</a> <span class="p4">(<span class="default"><a href="cat_1.html#K3" title="CAT_1:func.3">cod</a> <font color="Maroon" title="c4">f</font></span>)</span>,<span class="p4">(<span class="default"><a href="cat_1.html#K2" title="CAT_1:func.2">dom</a> <font color="Maroon" title="c5">g</font></span>)</span></span>)</span>,<span class="p3">(<span class="default"><a href="cat_1.html#K6" title="CAT_1:func.6">Hom</a> <span class="p4">(<span class="default"><a href="cat_1.html#K2" title="CAT_1:func.2">dom</a> <font color="Maroon" title="c4">f</font></span>)</span>,<span class="p4">(<span class="default"><a href="cat_1.html#K3" title="CAT_1:func.3">cod</a> <font color="Maroon" title="c5">g</font></span>)</span></span>)</span></span><a href="domain_1.html#K1" title="DOMAIN_1:func.1">]</a></span>,<span class="p2">(<span class="default"><a href="ens_1.html#K22" title="ENS_1:func.22">hom</a> <font color="Maroon" title="c4">f</font>,<font color="Maroon" title="c5">g</font></span>)</span></span><a href="domain_1.html#K1" title="DOMAIN_1:func.1">]</a></span>
<b>by </b><i><a class="txt" href="ens_1.html#E1:82_1_2"><i><font color="Green" title="E58">A5</font></i></a></i>
<br/>.= 
<font color="Maroon" title="c3">h2</font> <a href="binop_1.html#K1" title="BINOP_1:func.1">.</a> <font color="Maroon" title="c4">f</font>,<font color="Maroon" title="c5">g</font>
<b>by </b><i><a class="txt" href="ens_1.html#E2:82_1_2"><i><font color="Green" title="E59">A6</font></i></a></i>
;<br/></div><b>end;</b></div>
<b>hence </b><a NAME="E4:82_1_2"/>
<font color="Maroon" title="c2">h1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c3">h2</font>
 <b>by </b><i><a class="ref" href="binop_1.html#T2" title="BINOP_1:th.2">BINOP_1:2</a></i>;<br/>


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