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<b>let </b><font color="Maroon" title="c1">C</font> be   <a href="cat_1.html#NM4" title="CAT_1:NM.4">Category</a>;<br/><b>let </b><font color="Maroon" title="c2">g</font>, <font color="Maroon" title="c3">f</font>, <font color="Maroon" title="c4">g'</font>, <font color="Maroon" title="c5">f'</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>assume </b><a NAME="E1:80"/><i><font color="Green" title="E56">A1</font></i>: 
(  <a href="cat_1.html#K4" title="CAT_1:func.4">cod</a> <font color="Maroon" title="c2">g</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="cat_1.html#K3" title="CAT_1:func.3">dom</a> <font color="Maroon" title="c3">f</font> &amp;  <a href="cat_1.html#K3" title="CAT_1:func.3">dom</a> <font color="Maroon" title="c4">g'</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="cat_1.html#K4" title="CAT_1:func.4">cod</a> <font color="Maroon" title="c5">f'</font> )
 ;<br/>

<a NAME="E2:80"/><b>then </b><i><font color="Green" title="E57">A2</font></i>: 
(  <a href="cat_1.html#K3" title="CAT_1:func.3">dom</a> <span class="p1">(<span class="default"><font color="Maroon" title="c4">g'</font> <a href="cat_1.html#K5" title="CAT_1:func.5">*</a> <font color="Maroon" title="c5">f'</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="cat_1.html#K3" title="CAT_1:func.3">dom</a> <font color="Maroon" title="c5">f'</font> &amp;  <a href="cat_1.html#K4" title="CAT_1:func.4">cod</a> <span class="p1">(<span class="default"><font color="Maroon" title="c4">g'</font> <a href="cat_1.html#K5" title="CAT_1:func.5">*</a> <font color="Maroon" title="c5">f'</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="cat_1.html#K4" title="CAT_1:func.4">cod</a> <font color="Maroon" title="c4">g'</font> &amp;  <a href="cat_1.html#K3" title="CAT_1:func.3">dom</a> <span class="p1">(<span class="default"><font color="Maroon" title="c3">f</font> <a href="cat_1.html#K5" title="CAT_1:func.5">*</a> <font color="Maroon" title="c2">g</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="cat_1.html#K3" title="CAT_1:func.3">dom</a> <font color="Maroon" title="c2">g</font> &amp;  <a href="cat_1.html#K4" title="CAT_1:func.4">cod</a> <span class="p1">(<span class="default"><font color="Maroon" title="c3">f</font> <a href="cat_1.html#K5" title="CAT_1:func.5">*</a> <font color="Maroon" title="c2">g</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="cat_1.html#K4" title="CAT_1:func.4">cod</a> <font color="Maroon" title="c3">f</font> )
 
<b>by </b><i><a class="ref" href="cat_1.html#T42" title="CAT_1:th.42">CAT_1:42</a></i>;<br/>
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="80_1"><b>now </b></a><div class="add"><b>set </b><font color="Maroon" title="c6">h</font> =  <a href="ens_1.html#K22" title="ENS_1:func.22">hom</a> <span class="p1">(<span class="default"><font color="Maroon" title="c3">f</font> <a href="cat_1.html#K5" title="CAT_1:func.5">*</a> <font color="Maroon" title="c2">g</font></span>)</span>,<span class="p1">(<span class="default"><font color="Maroon" title="c4">g'</font> <a href="cat_1.html#K5" title="CAT_1:func.5">*</a> <font color="Maroon" title="c5">f'</font></span>)</span>;<br/><b>set </b><font color="Maroon" title="c7">h2</font> =  <a href="ens_1.html#K22" title="ENS_1:func.22">hom</a> <font color="Maroon" title="c2">g</font>,<font color="Maroon" title="c4">g'</font>;<br/><b>set </b><font color="Maroon" title="c8">h1</font> =  <a href="ens_1.html#K22" title="ENS_1:func.22">hom</a> <font color="Maroon" title="c3">f</font>,<font color="Maroon" title="c5">f'</font>;<br/><a NAME="E1:80_1"/><i><font color="Green" title="E58">A3</font></i>: 
(  <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="c2">g</font></span>)</span>,<span class="p1">(<span class="default"><a href="cat_1.html#K4" title="CAT_1:func.4">cod</a> <font color="Maroon" title="c4">g'</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a>  implies  <a href="cat_1.html#K7" title="CAT_1:func.7">Hom</a> <span class="p1">(<span class="default"><a href="cat_1.html#K4" title="CAT_1:func.4">cod</a> <font color="Maroon" title="c2">g</font></span>)</span>,<span class="p1">(<span class="default"><a href="cat_1.html#K3" title="CAT_1:func.3">dom</a> <font color="Maroon" title="c4">g'</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a>  )
 <b>by </b><i><a class="ref" href="ens_1.html#T51" target="_self" title="ENS_1:th.51">Th51</a></i>;<br/><a NAME="E2:80_1"/><i><font color="Green" title="E59">A4</font></i>: 
(  <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="c3">f</font></span>)</span>,<span class="p1">(<span class="default"><a href="cat_1.html#K4" title="CAT_1:func.4">cod</a> <font color="Maroon" title="c5">f'</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a>  implies  <a href="cat_1.html#K7" title="CAT_1:func.7">Hom</a> <span class="p1">(<span class="default"><a href="cat_1.html#K4" title="CAT_1:func.4">cod</a> <font color="Maroon" title="c3">f</font></span>)</span>,<span class="p1">(<span class="default"><a href="cat_1.html#K3" title="CAT_1:func.3">dom</a> <font color="Maroon" title="c5">f'</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a>  )
 <b>by </b><i><a class="ref" href="ens_1.html#T51" target="_self" title="ENS_1:th.51">Th51</a></i>;<br/><b>hence </b><a NAME="E3:80_1"/>
 <a href="relat_1.html#NK2" title="RELAT_1:NK.2">dom</a> <span class="p1">(<span class="default"><a href="ens_1.html#K22" title="ENS_1:func.22">hom</a> <span class="p2">(<span class="default"><font color="Maroon" title="c3">f</font> <a href="cat_1.html#K5" title="CAT_1:func.5">*</a> <font color="Maroon" title="c2">g</font></span>)</span>,<span class="p2">(<span class="default"><font color="Maroon" title="c4">g'</font> <a href="cat_1.html#K5" title="CAT_1:func.5">*</a> <font color="Maroon" title="c5">f'</font></span>)</span></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</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#K4" title="CAT_1:func.4">cod</a> <font color="Maroon" title="c3">f</font></span>)</span>,<span class="p1">(<span class="default"><a href="cat_1.html#K3" title="CAT_1:func.3">dom</a> <font color="Maroon" title="c5">f'</font></span>)</span>
 <b>by </b><i><a class="txt" href="ens_1.html#E1:80"><i><font color="Green" title="E56">A1</font></i></a>, <a class="txt" href="ens_1.html#E2:80"><i><font color="Green" title="E57">A2</font></i></a>, <a class="txt" href="ens_1.html#E1:80_1"><i><font color="Green" title="E58">A3</font></i></a>, <a class="ref" href="funct_2.html#D1" title="FUNCT_2:def.1">FUNCT_2:def 1</a></i>;<br/><a NAME="E4:80_1"/>
<span class="p1">(<span class="default"><a href="ens_1.html#K22" title="ENS_1:func.22">hom</a> <font color="Maroon" title="c2">g</font>,<font color="Maroon" title="c4">g'</font></span>)</span> <a href="partfun1.html#K1" title="PARTFUN1:func.1">*</a> <span class="p1">(<span class="default"><a href="ens_1.html#K22" title="ENS_1:func.22">hom</a> <font color="Maroon" title="c3">f</font>,<font color="Maroon" title="c5">f'</font></span>)</span> is   <a href="funct_2.html#NM1" title="FUNCT_2:NM.1">Function</a> of  <a href="cat_1.html#K7" title="CAT_1:func.7">Hom</a> <span class="p1">(<span class="default"><a href="cat_1.html#K4" title="CAT_1:func.4">cod</a> <font color="Maroon" title="c3">f</font></span>)</span>,<span class="p1">(<span class="default"><a href="cat_1.html#K3" title="CAT_1:func.3">dom</a> <font color="Maroon" title="c5">f'</font></span>)</span>, <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="c2">g</font></span>)</span>,<span class="p1">(<span class="default"><a href="cat_1.html#K4" title="CAT_1:func.4">cod</a> <font color="Maroon" title="c4">g'</font></span>)</span>
 <b>by </b><i><a class="txt" href="ens_1.html#E1:80"><i><font color="Green" title="E56">A1</font></i></a>, <a class="txt" href="ens_1.html#E2:80_1"><i><font color="Green" title="E59">A4</font></i></a>, <a class="ref" href="funct_2.html#T19" title="FUNCT_2:th.19">FUNCT_2:19</a></i>;<br/><b>hence </b><a NAME="E5:80_1"/><i><font color="Green" title="E60">A5</font></i>: 
 <a href="relat_1.html#NK2" title="RELAT_1:NK.2">dom</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ens_1.html#K22" title="ENS_1:func.22">hom</a> <font color="Maroon" title="c2">g</font>,<font color="Maroon" title="c4">g'</font></span>)</span> <a href="partfun1.html#K1" title="PARTFUN1:func.1">*</a> <span class="p2">(<span class="default"><a href="ens_1.html#K22" title="ENS_1:func.22">hom</a> <font color="Maroon" title="c3">f</font>,<font color="Maroon" title="c5">f'</font></span>)</span></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</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#K4" title="CAT_1:func.4">cod</a> <font color="Maroon" title="c3">f</font></span>)</span>,<span class="p1">(<span class="default"><a href="cat_1.html#K3" title="CAT_1:func.3">dom</a> <font color="Maroon" title="c5">f'</font></span>)</span>
 <b>by </b><i><a class="txt" href="ens_1.html#E1:80"><i><font color="Green" title="E56">A1</font></i></a>, <a class="txt" href="ens_1.html#E1:80_1"><i><font color="Green" title="E58">A3</font></i></a>, <a class="txt" href="ens_1.html#E2:80_1"><i><font color="Green" title="E59">A4</font></i></a>, <a class="ref" href="funct_2.html#D1" title="FUNCT_2:def.1">FUNCT_2:def 1</a></i>;<br/><b>let </b><font color="Maroon" title="c9">x</font> be    <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a> ;<br/><b>assume </b><a NAME="E6:80_1"/><i><font color="Green" title="E61">A6</font></i>: 
<font color="Maroon" title="c9">x</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#K4" title="CAT_1:func.4">cod</a> <font color="Maroon" title="c3">f</font></span>)</span>,<span class="p1">(<span class="default"><a href="cat_1.html#K3" title="CAT_1:func.3">dom</a> <font color="Maroon" title="c5">f'</font></span>)</span>
 ;<br/><b>then reconsider </b><font color="Maroon" title="c10">k</font> = <font color="Maroon" title="c9">x</font> as   <a href="cat_1.html#NM2" title="CAT_1:NM.2">Morphism</a> of <font color="Maroon" title="c1">C</font> ;<br/><a NAME="E8:80_1"/><i><font color="Green" title="E62">A7</font></i>: 
<span class="p1">(<span class="default"><a href="ens_1.html#K22" title="ENS_1:func.22">hom</a> <font color="Maroon" title="c3">f</font>,<font color="Maroon" title="c5">f'</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c9">x</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#K4" title="CAT_1:func.4">cod</a> <font color="Maroon" title="c2">g</font></span>)</span>,<span class="p1">(<span class="default"><a href="cat_1.html#K3" title="CAT_1:func.3">dom</a> <font color="Maroon" title="c4">g'</font></span>)</span>
 <b>by </b><i><a class="txt" href="ens_1.html#E1:80"><i><font color="Green" title="E56">A1</font></i></a>, <a class="txt" href="ens_1.html#E6:80_1"><i><font color="Green" title="E61">A6</font></i></a>, <a class="ref" href="ens_1.html#T51" target="_self" title="ENS_1:th.51">Th51</a>, <a class="ref" href="funct_2.html#T7" title="FUNCT_2:th.7">FUNCT_2:7</a></i>;<br/><b>then reconsider </b><font color="Maroon" title="c11">l</font> = <span class="p1">(<span class="default"><a href="ens_1.html#K22" title="ENS_1:func.22">hom</a> <font color="Maroon" title="c3">f</font>,<font color="Maroon" title="c5">f'</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c9">x</font> as   <a href="cat_1.html#NM2" title="CAT_1:NM.2">Morphism</a> of <font color="Maroon" title="c1">C</font> ;<br/><a NAME="E10:80_1"/><i><font color="Green" title="E63">A8</font></i>: 
 <a href="cat_1.html#K4" title="CAT_1:func.4">cod</a> <font color="Maroon" title="c10">k</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="cat_1.html#K3" title="CAT_1:func.3">dom</a> <font color="Maroon" title="c5">f'</font>
 <b>by </b><i><a class="txt" href="ens_1.html#E6:80_1"><i><font color="Green" title="E61">A6</font></i></a>, <a class="ref" href="cat_1.html#T18" title="CAT_1:th.18">CAT_1:18</a></i>;<br/><a NAME="E11:80_1"/><i><font color="Green" title="E64">A9</font></i>: 
 <a href="cat_1.html#K3" title="CAT_1:func.3">dom</a> <font color="Maroon" title="c10">k</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="cat_1.html#K4" title="CAT_1:func.4">cod</a> <font color="Maroon" title="c3">f</font>
 <b>by </b><i><a class="txt" href="ens_1.html#E6:80_1"><i><font color="Green" title="E61">A6</font></i></a>, <a class="ref" href="cat_1.html#T18" title="CAT_1:th.18">CAT_1:18</a></i>;<br/><a NAME="E12:80_1"/><b>then </b><i><font color="Green" title="E65">A10</font></i>: 
 <a href="cat_1.html#K4" title="CAT_1:func.4">cod</a> <span class="p1">(<span class="default"><font color="Maroon" title="c10">k</font> <a href="cat_1.html#K5" title="CAT_1:func.5">*</a> <span class="p2">(<span class="default"><font color="Maroon" title="c3">f</font> <a href="cat_1.html#K5" title="CAT_1:func.5">*</a> <font color="Maroon" title="c2">g</font></span>)</span></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="cat_1.html#K4" title="CAT_1:func.4">cod</a> <font color="Maroon" title="c10">k</font>
 <b>by </b><i><a class="txt" href="ens_1.html#E2:80"><i><font color="Green" title="E57">A2</font></i></a>, <a class="ref" href="cat_1.html#T42" title="CAT_1:th.42">CAT_1:42</a></i>;<br/><a NAME="E13:80_1"/><i><font color="Green" title="E66">A11</font></i>: 
(  <a href="cat_1.html#K3" title="CAT_1:func.3">dom</a> <span class="p1">(<span class="default"><font color="Maroon" title="c5">f'</font> <a href="cat_1.html#K5" title="CAT_1:func.5">*</a> <font color="Maroon" title="c10">k</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="cat_1.html#K3" title="CAT_1:func.3">dom</a> <font color="Maroon" title="c10">k</font> &amp;  <a href="cat_1.html#K4" title="CAT_1:func.4">cod</a> <span class="p1">(<span class="default"><font color="Maroon" title="c5">f'</font> <a href="cat_1.html#K5" title="CAT_1:func.5">*</a> <font color="Maroon" title="c10">k</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="cat_1.html#K4" title="CAT_1:func.4">cod</a> <font color="Maroon" title="c5">f'</font> )
 <b>by </b><i><a class="txt" href="ens_1.html#E10:80_1"><i><font color="Green" title="E63">A8</font></i></a>, <a class="ref" href="cat_1.html#T42" title="CAT_1:th.42">CAT_1:42</a></i>;<br/><a NAME="E14:80_1"/><b>then </b><i><font color="Green" title="E67">A12</font></i>: 
(  <a href="cat_1.html#K3" title="CAT_1:func.3">dom</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c5">f'</font> <a href="cat_1.html#K5" title="CAT_1:func.5">*</a> <font color="Maroon" title="c10">k</font></span>)</span> <a href="cat_1.html#K5" title="CAT_1:func.5">*</a> <font color="Maroon" title="c3">f</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="cat_1.html#K3" title="CAT_1:func.3">dom</a> <font color="Maroon" title="c3">f</font> &amp;  <a href="cat_1.html#K4" title="CAT_1:func.4">cod</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c5">f'</font> <a href="cat_1.html#K5" title="CAT_1:func.5">*</a> <font color="Maroon" title="c10">k</font></span>)</span> <a href="cat_1.html#K5" title="CAT_1:func.5">*</a> <font color="Maroon" title="c3">f</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="cat_1.html#K4" title="CAT_1:func.4">cod</a> <font color="Maroon" title="c5">f'</font> )
 <b>by </b><i><a class="txt" href="ens_1.html#E11:80_1"><i><font color="Green" title="E64">A9</font></i></a>, <a class="ref" href="cat_1.html#T42" title="CAT_1:th.42">CAT_1:42</a></i>;<br/><b>thus </b><span class="p1">(<span class="default"><a href="ens_1.html#K22" title="ENS_1:func.22">hom</a> <span class="p2">(<span class="default"><font color="Maroon" title="c3">f</font> <a href="cat_1.html#K5" title="CAT_1:func.5">*</a> <font color="Maroon" title="c2">g</font></span>)</span>,<span class="p2">(<span class="default"><font color="Maroon" title="c4">g'</font> <a href="cat_1.html#K5" title="CAT_1:func.5">*</a> <font color="Maroon" title="c5">f'</font></span>)</span></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c9">x</font> = 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c4">g'</font> <a href="cat_1.html#K5" title="CAT_1:func.5">*</a> <font color="Maroon" title="c5">f'</font></span>)</span> <a href="cat_1.html#K5" title="CAT_1:func.5">*</a> <font color="Maroon" title="c10">k</font></span>)</span> <a href="cat_1.html#K5" title="CAT_1:func.5">*</a> <span class="p1">(<span class="default"><font color="Maroon" title="c3">f</font> <a href="cat_1.html#K5" title="CAT_1:func.5">*</a> <font color="Maroon" title="c2">g</font></span>)</span>
<b>by </b><i><a class="txt" href="ens_1.html#E2:80"><i><font color="Green" title="E57">A2</font></i></a>, <a class="txt" href="ens_1.html#E6:80_1"><i><font color="Green" title="E61">A6</font></i></a>, <a class="ref" href="ens_1.html#D24" target="_self" title="ENS_1:def.24">Def24</a></i>
<br/>.= 
<span class="p1">(<span class="default"><font color="Maroon" title="c4">g'</font> <a href="cat_1.html#K5" title="CAT_1:func.5">*</a> <font color="Maroon" title="c5">f'</font></span>)</span> <a href="cat_1.html#K5" title="CAT_1:func.5">*</a> <span class="p1">(<span class="default"><font color="Maroon" title="c10">k</font> <a href="cat_1.html#K5" title="CAT_1:func.5">*</a> <span class="p2">(<span class="default"><font color="Maroon" title="c3">f</font> <a href="cat_1.html#K5" title="CAT_1:func.5">*</a> <font color="Maroon" title="c2">g</font></span>)</span></span>)</span>
<b>by </b><i><a class="txt" href="ens_1.html#E2:80"><i><font color="Green" title="E57">A2</font></i></a>, <a class="txt" href="ens_1.html#E10:80_1"><i><font color="Green" title="E63">A8</font></i></a>, <a class="txt" href="ens_1.html#E11:80_1"><i><font color="Green" title="E64">A9</font></i></a>, <a class="ref" href="cat_1.html#T43" title="CAT_1:th.43">CAT_1:43</a></i>
<br/>.= 
<font color="Maroon" title="c4">g'</font> <a href="cat_1.html#K5" title="CAT_1:func.5">*</a> <span class="p1">(<span class="default"><font color="Maroon" title="c5">f'</font> <a href="cat_1.html#K5" title="CAT_1:func.5">*</a> <span class="p2">(<span class="default"><font color="Maroon" title="c10">k</font> <a href="cat_1.html#K5" title="CAT_1:func.5">*</a> <span class="p3">(<span class="default"><font color="Maroon" title="c3">f</font> <a href="cat_1.html#K5" title="CAT_1:func.5">*</a> <font color="Maroon" title="c2">g</font></span>)</span></span>)</span></span>)</span>
<b>by </b><i><a class="txt" href="ens_1.html#E1:80"><i><font color="Green" title="E56">A1</font></i></a>, <a class="txt" href="ens_1.html#E10:80_1"><i><font color="Green" title="E63">A8</font></i></a>, <a class="txt" href="ens_1.html#E12:80_1"><i><font color="Green" title="E65">A10</font></i></a>, <a class="ref" href="cat_1.html#T43" title="CAT_1:th.43">CAT_1:43</a></i>
<br/>.= 
<font color="Maroon" title="c4">g'</font> <a href="cat_1.html#K5" title="CAT_1:func.5">*</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c5">f'</font> <a href="cat_1.html#K5" title="CAT_1:func.5">*</a> <font color="Maroon" title="c10">k</font></span>)</span> <a href="cat_1.html#K5" title="CAT_1:func.5">*</a> <span class="p2">(<span class="default"><font color="Maroon" title="c3">f</font> <a href="cat_1.html#K5" title="CAT_1:func.5">*</a> <font color="Maroon" title="c2">g</font></span>)</span></span>)</span>
<b>by </b><i><a class="txt" href="ens_1.html#E2:80"><i><font color="Green" title="E57">A2</font></i></a>, <a class="txt" href="ens_1.html#E10:80_1"><i><font color="Green" title="E63">A8</font></i></a>, <a class="txt" href="ens_1.html#E11:80_1"><i><font color="Green" title="E64">A9</font></i></a>, <a class="ref" href="cat_1.html#T43" title="CAT_1:th.43">CAT_1:43</a></i>
<br/>.= 
<font color="Maroon" title="c4">g'</font> <a href="cat_1.html#K5" title="CAT_1:func.5">*</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon" title="c5">f'</font> <a href="cat_1.html#K5" title="CAT_1:func.5">*</a> <font color="Maroon" title="c10">k</font></span>)</span> <a href="cat_1.html#K5" title="CAT_1:func.5">*</a> <font color="Maroon" title="c3">f</font></span>)</span> <a href="cat_1.html#K5" title="CAT_1:func.5">*</a> <font color="Maroon" title="c2">g</font></span>)</span>
<b>by </b><i><a class="txt" href="ens_1.html#E1:80"><i><font color="Green" title="E56">A1</font></i></a>, <a class="txt" href="ens_1.html#E11:80_1"><i><font color="Green" title="E64">A9</font></i></a>, <a class="txt" href="ens_1.html#E13:80_1"><i><font color="Green" title="E66">A11</font></i></a>, <a class="ref" href="cat_1.html#T43" title="CAT_1:th.43">CAT_1:43</a></i>
<br/>.= 
<span class="p1">(<span class="default"><font color="Maroon" title="c4">g'</font> <a href="cat_1.html#K5" title="CAT_1:func.5">*</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon" title="c5">f'</font> <a href="cat_1.html#K5" title="CAT_1:func.5">*</a> <font color="Maroon" title="c10">k</font></span>)</span> <a href="cat_1.html#K5" title="CAT_1:func.5">*</a> <font color="Maroon" title="c3">f</font></span>)</span></span>)</span> <a href="cat_1.html#K5" title="CAT_1:func.5">*</a> <font color="Maroon" title="c2">g</font>
<b>by </b><i><a class="txt" href="ens_1.html#E1:80"><i><font color="Green" title="E56">A1</font></i></a>, <a class="txt" href="ens_1.html#E14:80_1"><i><font color="Green" title="E67">A12</font></i></a>, <a class="ref" href="cat_1.html#T43" title="CAT_1:th.43">CAT_1:43</a></i>
<br/>.= 
<span class="p1">(<span class="default"><font color="Maroon" title="c4">g'</font> <a href="cat_1.html#K5" title="CAT_1:func.5">*</a> <font color="Maroon" title="c11">l</font></span>)</span> <a href="cat_1.html#K5" title="CAT_1:func.5">*</a> <font color="Maroon" title="c2">g</font>
<b>by </b><i><a class="txt" href="ens_1.html#E6:80_1"><i><font color="Green" title="E61">A6</font></i></a>, <a class="ref" href="ens_1.html#D24" target="_self" title="ENS_1:def.24">Def24</a></i>
<br/>.= 
<span class="p1">(<span class="default"><a href="ens_1.html#K22" title="ENS_1:func.22">hom</a> <font color="Maroon" title="c2">g</font>,<font color="Maroon" title="c4">g'</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c11">l</font>
<b>by </b><i><a class="txt" href="ens_1.html#E8:80_1"><i><font color="Green" title="E62">A7</font></i></a>, <a class="ref" href="ens_1.html#D24" target="_self" title="ENS_1:def.24">Def24</a></i>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ens_1.html#K22" title="ENS_1:func.22">hom</a> <font color="Maroon" title="c2">g</font>,<font color="Maroon" title="c4">g'</font></span>)</span> <a href="partfun1.html#K1" title="PARTFUN1:func.1">*</a> <span class="p2">(<span class="default"><a href="ens_1.html#K22" title="ENS_1:func.22">hom</a> <font color="Maroon" title="c3">f</font>,<font color="Maroon" title="c5">f'</font></span>)</span></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c9">x</font>
<b>by </b><i><a class="txt" href="ens_1.html#E5:80_1"><i><font color="Green" title="E60">A5</font></i></a>, <a class="txt" href="ens_1.html#E6:80_1"><i><font color="Green" title="E61">A6</font></i></a>, <a class="ref" href="funct_1.html#T22" title="FUNCT_1:th.22">FUNCT_1:22</a></i>
;<br/></div><b>end;</b></div>
<b>hence </b><a NAME="E4:80"/>
 <a href="ens_1.html#K22" title="ENS_1:func.22">hom</a> <span class="p1">(<span class="default"><font color="Maroon" title="c3">f</font> <a href="cat_1.html#K5" title="CAT_1:func.5">*</a> <font color="Maroon" title="c2">g</font></span>)</span>,<span class="p1">(<span class="default"><font color="Maroon" title="c4">g'</font> <a href="cat_1.html#K5" title="CAT_1:func.5">*</a> <font color="Maroon" title="c5">f'</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="ens_1.html#K22" title="ENS_1:func.22">hom</a> <font color="Maroon" title="c2">g</font>,<font color="Maroon" title="c4">g'</font></span>)</span> <a href="partfun1.html#K1" title="PARTFUN1:func.1">*</a> <span class="p1">(<span class="default"><a href="ens_1.html#K22" title="ENS_1:func.22">hom</a> <font color="Maroon" title="c3">f</font>,<font color="Maroon" title="c5">f'</font></span>)</span>
 <b>by </b><i><a class="ref" href="funct_1.html#T9" title="FUNCT_1:th.9">FUNCT_1:9</a></i>;<br/>


</div>
