<?xml version="1.0"?>
<div class="add">

<b>let </b><font color="Maroon">C</font> be   <a href="cat_1.html#NM4">Category</a>;<br/><b>let </b><font color="Maroon">B</font> be   <a href="cat_1.html#NM4">Category</a>;<br/><b>let </b><font color="Maroon">D</font> be   <a href="cat_1.html#NM4">Category</a>;<br/><b>let </b><font color="Maroon">L</font> be   <a href="funct_2.html#NM1">Function</a> of the <a href="cat_1.html#U1">Objects</a> of <font color="Maroon">C</font>, <a href="cat_2.html#K7" target="_self">Funct</a> <font color="Maroon">B</font>,<font color="Maroon">D</font>;<br/><b>let </b><font color="Maroon">M</font> be   <a href="funct_2.html#NM1">Function</a> of the <a href="cat_1.html#U1">Objects</a> of <font color="Maroon">B</font>, <a href="cat_2.html#K7" target="_self">Funct</a> <font color="Maroon">C</font>,<font color="Maroon">D</font>;<br/>









<b>assume </b><b>that </b><br/><a NAME="E1:54"/><i><font color="Green">E18</font></i>: 
for <font color="Olive">c</font> being  <a href="cat_1.html#NM1">Object</a> of <font color="Maroon">C</font><br/> for <font color="Olive">b</font> being  <a href="cat_1.html#NM1">Object</a> of <font color="Maroon">B</font> holds  <span class="p1">(<span class="default"><font color="Maroon">M</font> <a href="cat_2.html#K6" target="_self">.</a> <font color="Olive">b</font></span>)</span> <a href="funct_2.html#K3">.</a> <span class="p1">(<span class="default"><a href="cat_1.html#K10">id</a> <font color="Olive">c</font></span>)</span> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><font color="Maroon">L</font> <a href="cat_2.html#K6" target="_self">.</a> <font color="Olive">c</font></span>)</span> <a href="funct_2.html#K3">.</a> <span class="p1">(<span class="default"><a href="cat_1.html#K10">id</a> <font color="Olive">b</font></span>)</span>
 <b>and </b><br/><a NAME="E2:54"/><i><font color="Green">E19</font></i>: 
for <font color="Olive">f</font> being  <a href="cat_1.html#NM2">Morphism</a> of <font color="Maroon">B</font><br/> for <font color="Olive">g</font> being  <a href="cat_1.html#NM2">Morphism</a> of <font color="Maroon">C</font> holds  <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">M</font> <a href="cat_2.html#K6" target="_self">.</a> <span class="p3">(<span class="default"><a href="cat_1.html#K3">cod</a> <font color="Olive">f</font></span>)</span></span>)</span> <a href="funct_2.html#K3">.</a> <font color="Olive">g</font></span>)</span> <a href="cat_1.html#K4">*</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">L</font> <a href="cat_2.html#K6" target="_self">.</a> <span class="p3">(<span class="default"><a href="cat_1.html#K2">dom</a> <font color="Olive">g</font></span>)</span></span>)</span> <a href="funct_2.html#K3">.</a> <font color="Olive">f</font></span>)</span> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">L</font> <a href="cat_2.html#K6" target="_self">.</a> <span class="p3">(<span class="default"><a href="cat_1.html#K3">cod</a> <font color="Olive">g</font></span>)</span></span>)</span> <a href="funct_2.html#K3">.</a> <font color="Olive">f</font></span>)</span> <a href="cat_1.html#K4">*</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">M</font> <a href="cat_2.html#K6" target="_self">.</a> <span class="p3">(<span class="default"><a href="cat_1.html#K2">dom</a> <font color="Olive">f</font></span>)</span></span>)</span> <a href="funct_2.html#K3">.</a> <font color="Olive">g</font></span>)</span>
 ;<br/>

<b>deffunc </b><font color="Maroon">H<sub>1</sub></font>(  <a href="cat_1.html#NM4">Category</a>) <b>-&gt; </b>   <a href="hidden.html#M1">set</a>  = the <a href="cat_1.html#U2">Morphisms</a> of <font color="Maroon">a<sub>1</sub></font>;<br/>
<b>deffunc </b><font color="Maroon">H<sub>2</sub></font>(   <a href="subset_1.html#M1">Element</a> of <font color="Maroon">H<sub>1</sub></font>(<font color="Maroon">B</font>),   <a href="subset_1.html#M1">Element</a> of <font color="Maroon">H<sub>1</sub></font>(<font color="Maroon">C</font>)) <b>-&gt; </b>   <a href="subset_1.html#M1">Element</a> of the <a href="cat_1.html#U2">Morphisms</a> of <font color="Maroon">D</font> = <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">L</font> <a href="cat_2.html#K6" target="_self">.</a> <span class="p3">(<span class="default"><a href="cat_1.html#K3">cod</a> <font color="Maroon">a<sub>2</sub></font></span>)</span></span>)</span> <a href="funct_2.html#K3">.</a> <font color="Maroon">a<sub>1</sub></font></span>)</span> <a href="cat_1.html#K4">*</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">M</font> <a href="cat_2.html#K6" target="_self">.</a> <span class="p3">(<span class="default"><a href="cat_1.html#K2">dom</a> <font color="Maroon">a<sub>1</sub></font></span>)</span></span>)</span> <a href="funct_2.html#K3">.</a> <font color="Maroon">a<sub>2</sub></font></span>)</span>;<br/>
<b>consider </b><font color="Maroon">S</font> being   <a href="funct_2.html#NM1">Function</a> of <span class="p1"><a href="zfmisc_1.html#K2">[:</a><span class="default"><font color="Maroon">H<sub>1</sub></font>(<font color="Maroon">B</font>),<font color="Maroon">H<sub>1</sub></font>(<font color="Maroon">C</font>)</span><a href="zfmisc_1.html#K2">:]</a></span>,<font color="Maroon">H<sub>1</sub></font>(<font color="Maroon">D</font>)<b> such that </b><br/><a NAME="E4:54"/><i><font color="Green">E21</font></i>: 
for <font color="Olive">f</font> being  <a href="cat_1.html#NM2">Morphism</a> of <font color="Maroon">B</font><br/> for <font color="Olive">g</font> being  <a href="cat_1.html#NM2">Morphism</a> of <font color="Maroon">C</font> holds  <font color="Maroon">S</font> <a href="binop_1.html#K2">.</a> <font color="Olive">f</font>,<font color="Olive">g</font> <a href="hidden.html#R1">=</a> <font color="Maroon">H<sub>2</sub></font>(<font color="Olive">f</font>,<font color="Olive">g</font>)
 <b>from </b><i><a class="ref" href="binop_1.html#S4">BINOP_1:sch 4</a>();<br/></i>
<b>reconsider </b><font color="Maroon">T</font> = <font color="Maroon">S</font> as   <a href="funct_2.html#NM1">Function</a> of <font color="Maroon">H<sub>1</sub></font>(<span class="p1"><a href="cat_2.html#K11" target="_self">[:</a><span class="default"><font color="Maroon">B</font>,<font color="Maroon">C</font></span><a href="cat_2.html#K11" target="_self">:]</a></span>),<font color="Maroon">H<sub>1</sub></font>(<font color="Maroon">D</font>) ;<br/>
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="54_1"><b>now </b></a><div class="add"><b>thus </b><a NAME="E1:54_1"/>
for <font color="Olive">bc</font> being  <a href="cat_1.html#NM1">Object</a> of <span class="p1"><a href="cat_2.html#K11" target="_self">[:</a><span class="default"><font color="Maroon">B</font>,<font color="Maroon">C</font></span><a href="cat_2.html#K11" target="_self">:]</a></span>  ex <font color="Olive">d</font> being  <a href="cat_1.html#NM1">Object</a> of <font color="Maroon">D</font> st <font color="Maroon">T</font> <a href="funct_2.html#K3">.</a> <span class="p1">(<span class="default"><a href="cat_1.html#K10">id</a> <font color="Olive">bc</font></span>)</span> <a href="hidden.html#R1">=</a>  <a href="cat_1.html#K10">id</a> <font color="Olive">d</font>
 <div><a class="txt" onclick="hs2(this)" href="javascript:()" title="54_1_1"><b>proof </b></a><div class="add">

<b>let </b><font color="Maroon">bc</font> be   <a href="cat_1.html#NM1">Object</a> of <span class="p1"><a href="cat_2.html#K11" target="_self">[:</a><span class="default"><font color="Maroon">B</font>,<font color="Maroon">C</font></span><a href="cat_2.html#K11" target="_self">:]</a></span>;<br/>

<b>consider </b><font color="Maroon">b</font> being   <a href="cat_1.html#NM1">Object</a> of <font color="Maroon">B</font>, <font color="Maroon">c</font> being   <a href="cat_1.html#NM1">Object</a> of <font color="Maroon">C</font><b> such that </b><br/><a NAME="E2:54_1_1"/><i><font color="Green">E23</font></i>: 
<font color="Maroon">bc</font> <a href="hidden.html#R1">=</a> <span class="p1"><a href="cat_2.html#K12" target="_self">[</a><span class="default"><font color="Maroon">b</font>,<font color="Maroon">c</font></span><a href="cat_2.html#K12" target="_self">]</a></span>
 <b>by </b><i><a class="ref" href="domain_1.html#T9">DOMAIN_1:9</a></i>;<br/>
<b>consider </b><font color="Maroon">d</font> being   <a href="cat_1.html#NM1">Object</a> of <font color="Maroon">D</font><b> such that </b><br/><a NAME="E4:54_1_1"/><i><font color="Green">E24</font></i>: 
<span class="p1">(<span class="default"><font color="Maroon">L</font> <a href="cat_2.html#K6" target="_self">.</a> <font color="Maroon">c</font></span>)</span> <a href="funct_2.html#K3">.</a> <span class="p1">(<span class="default"><a href="cat_1.html#K10">id</a> <font color="Maroon">b</font></span>)</span> <a href="hidden.html#R1">=</a>  <a href="cat_1.html#K10">id</a> <font color="Maroon">d</font>
 <b>by </b><i><a class="ref" href="cat_1.html#T97">CAT_1:97</a></i>;<br/>
<b>take </b>
<font color="Maroon">d</font>
;<br/>

<a NAME="E5:54_1_1"/>
 <a href="cat_1.html#K6">Hom</a> <font color="Maroon">d</font>,<font color="Maroon">d</font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a>  <a href="xboole_0.html#K1">{}</a> 
 
<b>by </b><i><a class="ref" href="cat_1.html#T56">CAT_1:56</a></i>;<br/>
<a NAME="E6:54_1_1"/><b>then </b>
( <span class="p1">(<span class="default"><a href="cat_1.html#K10">id</a> <font color="Maroon">d</font></span>)</span> <a href="cat_1.html#K9">*</a> <span class="p1">(<span class="default"><a href="cat_1.html#K10">id</a> <font color="Maroon">d</font></span>)</span> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><a href="cat_1.html#K10">id</a> <font color="Maroon">d</font></span>)</span> <a href="cat_1.html#K4">*</a> <span class="p1">(<span class="default"><a href="cat_1.html#K10">id</a> <font color="Maroon">d</font></span>)</span> &amp;  <a href="cat_1.html#K3">cod</a> <span class="p1">(<span class="default"><a href="cat_1.html#K10">id</a> <font color="Maroon">c</font></span>)</span> <a href="hidden.html#R1">=</a> <font color="Maroon">c</font> &amp;  <a href="cat_1.html#K2">dom</a> <span class="p1">(<span class="default"><a href="cat_1.html#K10">id</a> <font color="Maroon">b</font></span>)</span> <a href="hidden.html#R1">=</a> <font color="Maroon">b</font> &amp; <span class="p1">(<span class="default"><font color="Maroon">L</font> <a href="cat_2.html#K6" target="_self">.</a> <font color="Maroon">c</font></span>)</span> <a href="funct_2.html#K3">.</a> <span class="p1">(<span class="default"><a href="cat_1.html#K10">id</a> <font color="Maroon">b</font></span>)</span> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><font color="Maroon">M</font> <a href="cat_2.html#K6" target="_self">.</a> <font color="Maroon">b</font></span>)</span> <a href="funct_2.html#K3">.</a> <span class="p1">(<span class="default"><a href="cat_1.html#K10">id</a> <font color="Maroon">c</font></span>)</span> )
 
<b>by </b><i><a class="ref" href="cat_2.html#T3" target="_self">Th3</a>, <a class="ref" href="cat_1.html#T44">CAT_1:44</a>, <a class="ref" href="cat_1.html#D13">CAT_1:def 13</a></i>;<br/>
<a NAME="E7:54_1_1"/><b>then </b>
( <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">L</font> <a href="cat_2.html#K6" target="_self">.</a> <span class="p3">(<span class="default"><a href="cat_1.html#K3">cod</a> <span class="p4">(<span class="default"><a href="cat_1.html#K10">id</a> <font color="Maroon">c</font></span>)</span></span>)</span></span>)</span> <a href="funct_2.html#K3">.</a> <span class="p2">(<span class="default"><a href="cat_1.html#K10">id</a> <font color="Maroon">b</font></span>)</span></span>)</span> <a href="cat_1.html#K4">*</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">M</font> <a href="cat_2.html#K6" target="_self">.</a> <span class="p3">(<span class="default"><a href="cat_1.html#K2">dom</a> <span class="p4">(<span class="default"><a href="cat_1.html#K10">id</a> <font color="Maroon">b</font></span>)</span></span>)</span></span>)</span> <a href="funct_2.html#K3">.</a> <span class="p2">(<span class="default"><a href="cat_1.html#K10">id</a> <font color="Maroon">c</font></span>)</span></span>)</span> <a href="hidden.html#R1">=</a>  <a href="cat_1.html#K10">id</a> <font color="Maroon">d</font> &amp;  <a href="cat_1.html#K10">id</a> <font color="Maroon">bc</font> <a href="hidden.html#R1">=</a> <span class="p1"><a href="cat_2.html#K13" target="_self">[</a><span class="default"><span class="p2">(<span class="default"><a href="cat_1.html#K10">id</a> <font color="Maroon">b</font></span>)</span>,<span class="p2">(<span class="default"><a href="cat_1.html#K10">id</a> <font color="Maroon">c</font></span>)</span></span><a href="cat_2.html#K13" target="_self">]</a></span> )
 
<b>by </b><i>, , <a class="txt" href="cat_2.html#E4:54_1_1"><i><font color="Green">E24</font></i></a>, <a class="ref" href="cat_1.html#T59">CAT_1:59</a></i>;<br/>
<a NAME="E8:54_1_1"/><b>then </b>
<font color="Maroon">T</font> <a href="binop_1.html#K1">.</a> <span class="p1">(<span class="default"><a href="cat_1.html#K10">id</a> <font color="Maroon">b</font></span>)</span>,<span class="p1">(<span class="default"><a href="cat_1.html#K10">id</a> <font color="Maroon">c</font></span>)</span> <a href="hidden.html#R1">=</a>  <a href="cat_1.html#K10">id</a> <font color="Maroon">d</font>
 
<b>by </b><i/>;<br/>
<b>hence </b><a NAME="E9:54_1_1"/>
<font color="Maroon">T</font> <a href="funct_2.html#K3">.</a> <span class="p1">(<span class="default"><a href="cat_1.html#K10">id</a> <font color="Maroon">bc</font></span>)</span> <a href="hidden.html#R1">=</a>  <a href="cat_1.html#K10">id</a> <font color="Maroon">d</font>
 <b>by </b><i>, <a class="txt" href="cat_2.html#E4:54_1_1"><i><font color="Green">E24</font></i></a></i>;<br/>


</div><b>end;</b></div><b>thus </b><a NAME="E2:54_1"/>
for <font color="Olive">fg</font> being  <a href="cat_1.html#NM2">Morphism</a> of <span class="p1"><a href="cat_2.html#K11" target="_self">[:</a><span class="default"><font color="Maroon">B</font>,<font color="Maroon">C</font></span><a href="cat_2.html#K11" target="_self">:]</a></span> holds <br/> ( <font color="Maroon">T</font> <a href="funct_2.html#K3">.</a> <span class="p1">(<span class="default"><a href="cat_1.html#K10">id</a> <span class="p2">(<span class="default"><a href="cat_1.html#K2">dom</a> <font color="Olive">fg</font></span>)</span></span>)</span> <a href="hidden.html#R1">=</a>  <a href="cat_1.html#K10">id</a> <span class="p1">(<span class="default"><a href="cat_1.html#K2">dom</a> <span class="p2">(<span class="default"><font color="Maroon">T</font> <a href="funct_2.html#K3">.</a> <font color="Olive">fg</font></span>)</span></span>)</span> &amp; <font color="Maroon">T</font> <a href="funct_2.html#K3">.</a> <span class="p1">(<span class="default"><a href="cat_1.html#K10">id</a> <span class="p2">(<span class="default"><a href="cat_1.html#K3">cod</a> <font color="Olive">fg</font></span>)</span></span>)</span> <a href="hidden.html#R1">=</a>  <a href="cat_1.html#K10">id</a> <span class="p1">(<span class="default"><a href="cat_1.html#K3">cod</a> <span class="p2">(<span class="default"><font color="Maroon">T</font> <a href="funct_2.html#K3">.</a> <font color="Olive">fg</font></span>)</span></span>)</span> )
 <div><a class="txt" onclick="hs2(this)" href="javascript:()" title="54_1_2"><b>proof </b></a><div class="add">

<b>let </b><font color="Maroon">fg</font> be   <a href="cat_1.html#NM2">Morphism</a> of <span class="p1"><a href="cat_2.html#K11" target="_self">[:</a><span class="default"><font color="Maroon">B</font>,<font color="Maroon">C</font></span><a href="cat_2.html#K11" target="_self">:]</a></span>;<br/>

<b>consider </b><font color="Maroon">f</font> being   <a href="cat_1.html#NM2">Morphism</a> of <font color="Maroon">B</font>, <font color="Maroon">g</font> being   <a href="cat_1.html#NM2">Morphism</a> of <font color="Maroon">C</font><b> such that </b><br/><a NAME="E2:54_1_2"/><i><font color="Green">E25</font></i>: 
<font color="Maroon">fg</font> <a href="hidden.html#R1">=</a> <span class="p1"><a href="cat_2.html#K13" target="_self">[</a><span class="default"><font color="Maroon">f</font>,<font color="Maroon">g</font></span><a href="cat_2.html#K13" target="_self">]</a></span>
 <b>by </b><i><a class="ref" href="domain_1.html#T9">DOMAIN_1:9</a></i>;<br/>
<b>set </b><font color="Maroon">b</font> =  <a href="cat_1.html#K2">dom</a> <font color="Maroon">f</font>;<br/>
<b>set </b><font color="Maroon">c</font> =  <a href="cat_1.html#K2">dom</a> <font color="Maroon">g</font>;<br/>
<b>set </b><font color="Maroon">g'</font> =  <a href="cat_1.html#K10">id</a> <span class="p1">(<span class="default"><a href="cat_1.html#K2">dom</a> <font color="Maroon">g</font></span>)</span>;<br/>
<b>set </b><font color="Maroon">f'</font> =  <a href="cat_1.html#K10">id</a> <span class="p1">(<span class="default"><a href="cat_1.html#K2">dom</a> <font color="Maroon">f</font></span>)</span>;<br/>
<a NAME="E3:54_1_2"/><i><font color="Green">E58</font></i>: 
 <a href="cat_1.html#K6">Hom</a> <span class="p1">(<span class="default"><a href="cat_1.html#K2">dom</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">M</font> <a href="cat_2.html#K6" target="_self">.</a> <span class="p4">(<span class="default"><a href="cat_1.html#K2">dom</a> <font color="Maroon">f</font></span>)</span></span>)</span> <a href="funct_2.html#K3">.</a> <font color="Maroon">g</font></span>)</span></span>)</span>,<span class="p1">(<span class="default"><a href="cat_1.html#K2">dom</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">M</font> <a href="cat_2.html#K6" target="_self">.</a> <span class="p4">(<span class="default"><a href="cat_1.html#K2">dom</a> <font color="Maroon">f</font></span>)</span></span>)</span> <a href="funct_2.html#K3">.</a> <font color="Maroon">g</font></span>)</span></span>)</span> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a>  <a href="xboole_0.html#K1">{}</a> 
 
<b>by </b><i><a class="ref" href="cat_1.html#T56">CAT_1:56</a></i>;<br/>
 <a href="cat_1.html#K10">id</a> <span class="p1">(<span class="default"><a href="cat_1.html#K2">dom</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">L</font> <a href="cat_2.html#K6" target="_self">.</a> <span class="p4">(<span class="default"><a href="cat_1.html#K3">cod</a> <font color="Maroon">g</font></span>)</span></span>)</span> <a href="funct_2.html#K3">.</a> <font color="Maroon">f</font></span>)</span></span>)</span> = 
<span class="p1">(<span class="default"><font color="Maroon">L</font> <a href="cat_2.html#K6" target="_self">.</a> <span class="p2">(<span class="default"><a href="cat_1.html#K3">cod</a> <font color="Maroon">g</font></span>)</span></span>)</span> <a href="funct_2.html#K3">.</a> <span class="p1">(<span class="default"><a href="cat_1.html#K10">id</a> <span class="p2">(<span class="default"><a href="cat_1.html#K2">dom</a> <font color="Maroon">f</font></span>)</span></span>)</span>
<b>by </b><i><a class="ref" href="cat_1.html#T98">CAT_1:98</a></i>
<br/>.= 
<span class="p1">(<span class="default"><font color="Maroon">M</font> <a href="cat_2.html#K6" target="_self">.</a> <span class="p2">(<span class="default"><a href="cat_1.html#K2">dom</a> <font color="Maroon">f</font></span>)</span></span>)</span> <a href="funct_2.html#K3">.</a> <span class="p1">(<span class="default"><a href="cat_1.html#K10">id</a> <span class="p2">(<span class="default"><a href="cat_1.html#K3">cod</a> <font color="Maroon">g</font></span>)</span></span>)</span>
<b>by </b><i><a class="ref" href="cat_2.html#T3" target="_self">Th3</a></i>
<br/>.= 
 <a href="cat_1.html#K10">id</a> <span class="p1">(<span class="default"><a href="cat_1.html#K3">cod</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">M</font> <a href="cat_2.html#K6" target="_self">.</a> <span class="p4">(<span class="default"><a href="cat_1.html#K2">dom</a> <font color="Maroon">f</font></span>)</span></span>)</span> <a href="funct_2.html#K3">.</a> <font color="Maroon">g</font></span>)</span></span>)</span>
<b>by </b><i><a class="ref" href="cat_1.html#T98">CAT_1:98</a></i>
;<br/>
<a NAME="E5:54_1_2"/><b>then </b><i><font color="Green">E59</font></i>: 
 <a href="cat_1.html#K2">dom</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">L</font> <a href="cat_2.html#K6" target="_self">.</a> <span class="p3">(<span class="default"><a href="cat_1.html#K3">cod</a> <font color="Maroon">g</font></span>)</span></span>)</span> <a href="funct_2.html#K3">.</a> <font color="Maroon">f</font></span>)</span> <a href="hidden.html#R1">=</a>  <a href="cat_1.html#K3">cod</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">M</font> <a href="cat_2.html#K6" target="_self">.</a> <span class="p3">(<span class="default"><a href="cat_1.html#K2">dom</a> <font color="Maroon">f</font></span>)</span></span>)</span> <a href="funct_2.html#K3">.</a> <font color="Maroon">g</font></span>)</span>
 
<b>by </b><i><a class="ref" href="cat_1.html#T45">CAT_1:45</a></i>;<br/>
<b>thus </b><font color="Maroon">T</font> <a href="funct_2.html#K3">.</a> <span class="p1">(<span class="default"><a href="cat_1.html#K10">id</a> <span class="p2">(<span class="default"><a href="cat_1.html#K2">dom</a> <font color="Maroon">fg</font></span>)</span></span>)</span> = 
<font color="Maroon">S</font> <a href="funct_1.html#K1">.</a> <span class="p1">(<span class="default"><a href="cat_1.html#K10">id</a> <span class="p2"><a href="cat_2.html#K12" target="_self">[</a><span class="default"><span class="p3">(<span class="default"><a href="cat_1.html#K2">dom</a> <font color="Maroon">f</font></span>)</span>,<span class="p3">(<span class="default"><a href="cat_1.html#K2">dom</a> <font color="Maroon">g</font></span>)</span></span><a href="cat_2.html#K12" target="_self">]</a></span></span>)</span>
<b>by </b><i>, <a class="txt" href="cat_2.html#E4:54"><i><font color="Green">E21</font></i></a></i>
<br/>.= 
<font color="Maroon">S</font> <a href="binop_1.html#K2">.</a> <span class="p1">(<span class="default"><a href="cat_1.html#K10">id</a> <span class="p2">(<span class="default"><a href="cat_1.html#K2">dom</a> <font color="Maroon">f</font></span>)</span></span>)</span>,<span class="p1">(<span class="default"><a href="cat_1.html#K10">id</a> <span class="p2">(<span class="default"><a href="cat_1.html#K2">dom</a> <font color="Maroon">g</font></span>)</span></span>)</span>
<b>by </b><i/>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">L</font> <a href="cat_2.html#K6" target="_self">.</a> <span class="p3">(<span class="default"><a href="cat_1.html#K3">cod</a> <span class="p4">(<span class="default"><a href="cat_1.html#K10">id</a> <span class="p5">(<span class="default"><a href="cat_1.html#K2">dom</a> <font color="Maroon">g</font></span>)</span></span>)</span></span>)</span></span>)</span> <a href="funct_2.html#K3">.</a> <span class="p2">(<span class="default"><a href="cat_1.html#K10">id</a> <span class="p3">(<span class="default"><a href="cat_1.html#K2">dom</a> <font color="Maroon">f</font></span>)</span></span>)</span></span>)</span> <a href="cat_1.html#K4">*</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">M</font> <a href="cat_2.html#K6" target="_self">.</a> <span class="p3">(<span class="default"><a href="cat_1.html#K2">dom</a> <span class="p4">(<span class="default"><a href="cat_1.html#K10">id</a> <span class="p5">(<span class="default"><a href="cat_1.html#K2">dom</a> <font color="Maroon">f</font></span>)</span></span>)</span></span>)</span></span>)</span> <a href="funct_2.html#K3">.</a> <span class="p2">(<span class="default"><a href="cat_1.html#K10">id</a> <span class="p3">(<span class="default"><a href="cat_1.html#K2">dom</a> <font color="Maroon">g</font></span>)</span></span>)</span></span>)</span>
<b>by </b><i/>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">L</font> <a href="cat_2.html#K6" target="_self">.</a> <span class="p3">(<span class="default"><a href="cat_1.html#K2">dom</a> <font color="Maroon">g</font></span>)</span></span>)</span> <a href="funct_2.html#K3">.</a> <span class="p2">(<span class="default"><a href="cat_1.html#K10">id</a> <span class="p3">(<span class="default"><a href="cat_1.html#K2">dom</a> <font color="Maroon">f</font></span>)</span></span>)</span></span>)</span> <a href="cat_1.html#K4">*</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">M</font> <a href="cat_2.html#K6" target="_self">.</a> <span class="p3">(<span class="default"><a href="cat_1.html#K2">dom</a> <span class="p4">(<span class="default"><a href="cat_1.html#K10">id</a> <span class="p5">(<span class="default"><a href="cat_1.html#K2">dom</a> <font color="Maroon">f</font></span>)</span></span>)</span></span>)</span></span>)</span> <a href="funct_2.html#K3">.</a> <span class="p2">(<span class="default"><a href="cat_1.html#K10">id</a> <span class="p3">(<span class="default"><a href="cat_1.html#K2">dom</a> <font color="Maroon">g</font></span>)</span></span>)</span></span>)</span>
<b>by </b><i><a class="ref" href="cat_1.html#T44">CAT_1:44</a></i>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">L</font> <a href="cat_2.html#K6" target="_self">.</a> <span class="p3">(<span class="default"><a href="cat_1.html#K2">dom</a> <font color="Maroon">g</font></span>)</span></span>)</span> <a href="funct_2.html#K3">.</a> <span class="p2">(<span class="default"><a href="cat_1.html#K10">id</a> <span class="p3">(<span class="default"><a href="cat_1.html#K2">dom</a> <font color="Maroon">f</font></span>)</span></span>)</span></span>)</span> <a href="cat_1.html#K4">*</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">M</font> <a href="cat_2.html#K6" target="_self">.</a> <span class="p3">(<span class="default"><a href="cat_1.html#K2">dom</a> <font color="Maroon">f</font></span>)</span></span>)</span> <a href="funct_2.html#K3">.</a> <span class="p2">(<span class="default"><a href="cat_1.html#K10">id</a> <span class="p3">(<span class="default"><a href="cat_1.html#K2">dom</a> <font color="Maroon">g</font></span>)</span></span>)</span></span>)</span>
<b>by </b><i><a class="ref" href="cat_1.html#T44">CAT_1:44</a></i>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">M</font> <a href="cat_2.html#K6" target="_self">.</a> <span class="p3">(<span class="default"><a href="cat_1.html#K2">dom</a> <font color="Maroon">f</font></span>)</span></span>)</span> <a href="funct_2.html#K3">.</a> <span class="p2">(<span class="default"><a href="cat_1.html#K10">id</a> <span class="p3">(<span class="default"><a href="cat_1.html#K2">dom</a> <font color="Maroon">g</font></span>)</span></span>)</span></span>)</span> <a href="cat_1.html#K4">*</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">M</font> <a href="cat_2.html#K6" target="_self">.</a> <span class="p3">(<span class="default"><a href="cat_1.html#K2">dom</a> <font color="Maroon">f</font></span>)</span></span>)</span> <a href="funct_2.html#K3">.</a> <span class="p2">(<span class="default"><a href="cat_1.html#K10">id</a> <span class="p3">(<span class="default"><a href="cat_1.html#K2">dom</a> <font color="Maroon">g</font></span>)</span></span>)</span></span>)</span>
<b>by </b><i><a class="ref" href="cat_2.html#T3" target="_self">Th3</a></i>
<br/>.= 
<span class="p1">(<span class="default"><a href="cat_1.html#K10">id</a> <span class="p2">(<span class="default"><a href="cat_1.html#K2">dom</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">M</font> <a href="cat_2.html#K6" target="_self">.</a> <span class="p5">(<span class="default"><a href="cat_1.html#K2">dom</a> <font color="Maroon">f</font></span>)</span></span>)</span> <a href="funct_2.html#K3">.</a> <font color="Maroon">g</font></span>)</span></span>)</span></span>)</span> <a href="cat_1.html#K4">*</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">M</font> <a href="cat_2.html#K6" target="_self">.</a> <span class="p3">(<span class="default"><a href="cat_1.html#K2">dom</a> <font color="Maroon">f</font></span>)</span></span>)</span> <a href="funct_2.html#K3">.</a> <span class="p2">(<span class="default"><a href="cat_1.html#K10">id</a> <span class="p3">(<span class="default"><a href="cat_1.html#K2">dom</a> <font color="Maroon">g</font></span>)</span></span>)</span></span>)</span>
<b>by </b><i><a class="ref" href="cat_1.html#T98">CAT_1:98</a></i>
<br/>.= 
<span class="p1">(<span class="default"><a href="cat_1.html#K10">id</a> <span class="p2">(<span class="default"><a href="cat_1.html#K2">dom</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">M</font> <a href="cat_2.html#K6" target="_self">.</a> <span class="p5">(<span class="default"><a href="cat_1.html#K2">dom</a> <font color="Maroon">f</font></span>)</span></span>)</span> <a href="funct_2.html#K3">.</a> <font color="Maroon">g</font></span>)</span></span>)</span></span>)</span> <a href="cat_1.html#K4">*</a> <span class="p1">(<span class="default"><a href="cat_1.html#K10">id</a> <span class="p2">(<span class="default"><a href="cat_1.html#K2">dom</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">M</font> <a href="cat_2.html#K6" target="_self">.</a> <span class="p5">(<span class="default"><a href="cat_1.html#K2">dom</a> <font color="Maroon">f</font></span>)</span></span>)</span> <a href="funct_2.html#K3">.</a> <font color="Maroon">g</font></span>)</span></span>)</span></span>)</span>
<b>by </b><i><a class="ref" href="cat_1.html#T98">CAT_1:98</a></i>
<br/>.= 
<span class="p1">(<span class="default"><a href="cat_1.html#K10">id</a> <span class="p2">(<span class="default"><a href="cat_1.html#K2">dom</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">M</font> <a href="cat_2.html#K6" target="_self">.</a> <span class="p5">(<span class="default"><a href="cat_1.html#K2">dom</a> <font color="Maroon">f</font></span>)</span></span>)</span> <a href="funct_2.html#K3">.</a> <font color="Maroon">g</font></span>)</span></span>)</span></span>)</span> <a href="cat_1.html#K9">*</a> <span class="p1">(<span class="default"><a href="cat_1.html#K10">id</a> <span class="p2">(<span class="default"><a href="cat_1.html#K2">dom</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">M</font> <a href="cat_2.html#K6" target="_self">.</a> <span class="p5">(<span class="default"><a href="cat_1.html#K2">dom</a> <font color="Maroon">f</font></span>)</span></span>)</span> <a href="funct_2.html#K3">.</a> <font color="Maroon">g</font></span>)</span></span>)</span></span>)</span>
<b>by </b><i>, <a class="ref" href="cat_1.html#D13">CAT_1:def 13</a></i>
<br/>.= 
 <a href="cat_1.html#K10">id</a> <span class="p1">(<span class="default"><a href="cat_1.html#K2">dom</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">M</font> <a href="cat_2.html#K6" target="_self">.</a> <span class="p4">(<span class="default"><a href="cat_1.html#K2">dom</a> <font color="Maroon">f</font></span>)</span></span>)</span> <a href="funct_2.html#K3">.</a> <font color="Maroon">g</font></span>)</span></span>)</span>
<b>by </b><i><a class="ref" href="cat_1.html#T59">CAT_1:59</a></i>
<br/>.= 
 <a href="cat_1.html#K10">id</a> <span class="p1">(<span class="default"><a href="cat_1.html#K2">dom</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">L</font> <a href="cat_2.html#K6" target="_self">.</a> <span class="p5">(<span class="default"><a href="cat_1.html#K3">cod</a> <font color="Maroon">g</font></span>)</span></span>)</span> <a href="funct_2.html#K3">.</a> <font color="Maroon">f</font></span>)</span> <a href="cat_1.html#K4">*</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">M</font> <a href="cat_2.html#K6" target="_self">.</a> <span class="p5">(<span class="default"><a href="cat_1.html#K2">dom</a> <font color="Maroon">f</font></span>)</span></span>)</span> <a href="funct_2.html#K3">.</a> <font color="Maroon">g</font></span>)</span></span>)</span></span>)</span>
<b>by </b><i>, <a class="ref" href="cat_1.html#T42">CAT_1:42</a></i>
<br/>.= 
 <a href="cat_1.html#K10">id</a> <span class="p1">(<span class="default"><a href="cat_1.html#K2">dom</a> <span class="p2">(<span class="default"><font color="Maroon">S</font> <a href="binop_1.html#K2">.</a> <font color="Maroon">f</font>,<font color="Maroon">g</font></span>)</span></span>)</span>
<b>by </b><i/>
<br/>.= 
 <a href="cat_1.html#K10">id</a> <span class="p1">(<span class="default"><a href="cat_1.html#K2">dom</a> <span class="p2">(<span class="default"><font color="Maroon">T</font> <a href="funct_2.html#K3">.</a> <font color="Maroon">fg</font></span>)</span></span>)</span>
<b>by </b><i/>
;<br/>

<b>set </b><font color="Maroon">b</font> =  <a href="cat_1.html#K3">cod</a> <font color="Maroon">f</font>;<br/>
<b>set </b><font color="Maroon">c</font> =  <a href="cat_1.html#K3">cod</a> <font color="Maroon">g</font>;<br/>
<b>set </b><font color="Maroon">g'</font> =  <a href="cat_1.html#K10">id</a> <span class="p1">(<span class="default"><a href="cat_1.html#K3">cod</a> <font color="Maroon">g</font></span>)</span>;<br/>
<b>set </b><font color="Maroon">f'</font> =  <a href="cat_1.html#K10">id</a> <span class="p1">(<span class="default"><a href="cat_1.html#K3">cod</a> <font color="Maroon">f</font></span>)</span>;<br/>
<a NAME="E7:54_1_2"/><i><font color="Green">E60</font></i>: 
 <a href="cat_1.html#K6">Hom</a> <span class="p1">(<span class="default"><a href="cat_1.html#K3">cod</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">L</font> <a href="cat_2.html#K6" target="_self">.</a> <span class="p4">(<span class="default"><a href="cat_1.html#K3">cod</a> <font color="Maroon">g</font></span>)</span></span>)</span> <a href="funct_2.html#K3">.</a> <font color="Maroon">f</font></span>)</span></span>)</span>,<span class="p1">(<span class="default"><a href="cat_1.html#K3">cod</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">L</font> <a href="cat_2.html#K6" target="_self">.</a> <span class="p4">(<span class="default"><a href="cat_1.html#K3">cod</a> <font color="Maroon">g</font></span>)</span></span>)</span> <a href="funct_2.html#K3">.</a> <font color="Maroon">f</font></span>)</span></span>)</span> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a>  <a href="xboole_0.html#K1">{}</a> 
 
<b>by </b><i><a class="ref" href="cat_1.html#T56">CAT_1:56</a></i>;<br/>
<b>thus </b><font color="Maroon">T</font> <a href="funct_2.html#K3">.</a> <span class="p1">(<span class="default"><a href="cat_1.html#K10">id</a> <span class="p2">(<span class="default"><a href="cat_1.html#K3">cod</a> <font color="Maroon">fg</font></span>)</span></span>)</span> = 
<font color="Maroon">S</font> <a href="funct_1.html#K1">.</a> <span class="p1">(<span class="default"><a href="cat_1.html#K10">id</a> <span class="p2"><a href="cat_2.html#K12" target="_self">[</a><span class="default"><span class="p3">(<span class="default"><a href="cat_1.html#K3">cod</a> <font color="Maroon">f</font></span>)</span>,<span class="p3">(<span class="default"><a href="cat_1.html#K3">cod</a> <font color="Maroon">g</font></span>)</span></span><a href="cat_2.html#K12" target="_self">]</a></span></span>)</span>
<b>by </b><i>, <a class="txt" href="cat_2.html#E4:54"><i><font color="Green">E21</font></i></a></i>
<br/>.= 
<font color="Maroon">S</font> <a href="binop_1.html#K2">.</a> <span class="p1">(<span class="default"><a href="cat_1.html#K10">id</a> <span class="p2">(<span class="default"><a href="cat_1.html#K3">cod</a> <font color="Maroon">f</font></span>)</span></span>)</span>,<span class="p1">(<span class="default"><a href="cat_1.html#K10">id</a> <span class="p2">(<span class="default"><a href="cat_1.html#K3">cod</a> <font color="Maroon">g</font></span>)</span></span>)</span>
<b>by </b><i/>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">L</font> <a href="cat_2.html#K6" target="_self">.</a> <span class="p3">(<span class="default"><a href="cat_1.html#K3">cod</a> <span class="p4">(<span class="default"><a href="cat_1.html#K10">id</a> <span class="p5">(<span class="default"><a href="cat_1.html#K3">cod</a> <font color="Maroon">g</font></span>)</span></span>)</span></span>)</span></span>)</span> <a href="funct_2.html#K3">.</a> <span class="p2">(<span class="default"><a href="cat_1.html#K10">id</a> <span class="p3">(<span class="default"><a href="cat_1.html#K3">cod</a> <font color="Maroon">f</font></span>)</span></span>)</span></span>)</span> <a href="cat_1.html#K4">*</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">M</font> <a href="cat_2.html#K6" target="_self">.</a> <span class="p3">(<span class="default"><a href="cat_1.html#K2">dom</a> <span class="p4">(<span class="default"><a href="cat_1.html#K10">id</a> <span class="p5">(<span class="default"><a href="cat_1.html#K3">cod</a> <font color="Maroon">f</font></span>)</span></span>)</span></span>)</span></span>)</span> <a href="funct_2.html#K3">.</a> <span class="p2">(<span class="default"><a href="cat_1.html#K10">id</a> <span class="p3">(<span class="default"><a href="cat_1.html#K3">cod</a> <font color="Maroon">g</font></span>)</span></span>)</span></span>)</span>
<b>by </b><i/>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">L</font> <a href="cat_2.html#K6" target="_self">.</a> <span class="p3">(<span class="default"><a href="cat_1.html#K3">cod</a> <font color="Maroon">g</font></span>)</span></span>)</span> <a href="funct_2.html#K3">.</a> <span class="p2">(<span class="default"><a href="cat_1.html#K10">id</a> <span class="p3">(<span class="default"><a href="cat_1.html#K3">cod</a> <font color="Maroon">f</font></span>)</span></span>)</span></span>)</span> <a href="cat_1.html#K4">*</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">M</font> <a href="cat_2.html#K6" target="_self">.</a> <span class="p3">(<span class="default"><a href="cat_1.html#K2">dom</a> <span class="p4">(<span class="default"><a href="cat_1.html#K10">id</a> <span class="p5">(<span class="default"><a href="cat_1.html#K3">cod</a> <font color="Maroon">f</font></span>)</span></span>)</span></span>)</span></span>)</span> <a href="funct_2.html#K3">.</a> <span class="p2">(<span class="default"><a href="cat_1.html#K10">id</a> <span class="p3">(<span class="default"><a href="cat_1.html#K3">cod</a> <font color="Maroon">g</font></span>)</span></span>)</span></span>)</span>
<b>by </b><i><a class="ref" href="cat_1.html#T44">CAT_1:44</a></i>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">L</font> <a href="cat_2.html#K6" target="_self">.</a> <span class="p3">(<span class="default"><a href="cat_1.html#K3">cod</a> <font color="Maroon">g</font></span>)</span></span>)</span> <a href="funct_2.html#K3">.</a> <span class="p2">(<span class="default"><a href="cat_1.html#K10">id</a> <span class="p3">(<span class="default"><a href="cat_1.html#K3">cod</a> <font color="Maroon">f</font></span>)</span></span>)</span></span>)</span> <a href="cat_1.html#K4">*</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">M</font> <a href="cat_2.html#K6" target="_self">.</a> <span class="p3">(<span class="default"><a href="cat_1.html#K3">cod</a> <font color="Maroon">f</font></span>)</span></span>)</span> <a href="funct_2.html#K3">.</a> <span class="p2">(<span class="default"><a href="cat_1.html#K10">id</a> <span class="p3">(<span class="default"><a href="cat_1.html#K3">cod</a> <font color="Maroon">g</font></span>)</span></span>)</span></span>)</span>
<b>by </b><i><a class="ref" href="cat_1.html#T44">CAT_1:44</a></i>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">L</font> <a href="cat_2.html#K6" target="_self">.</a> <span class="p3">(<span class="default"><a href="cat_1.html#K3">cod</a> <font color="Maroon">g</font></span>)</span></span>)</span> <a href="funct_2.html#K3">.</a> <span class="p2">(<span class="default"><a href="cat_1.html#K10">id</a> <span class="p3">(<span class="default"><a href="cat_1.html#K3">cod</a> <font color="Maroon">f</font></span>)</span></span>)</span></span>)</span> <a href="cat_1.html#K4">*</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">L</font> <a href="cat_2.html#K6" target="_self">.</a> <span class="p3">(<span class="default"><a href="cat_1.html#K3">cod</a> <font color="Maroon">g</font></span>)</span></span>)</span> <a href="funct_2.html#K3">.</a> <span class="p2">(<span class="default"><a href="cat_1.html#K10">id</a> <span class="p3">(<span class="default"><a href="cat_1.html#K3">cod</a> <font color="Maroon">f</font></span>)</span></span>)</span></span>)</span>
<b>by </b><i><a class="ref" href="cat_2.html#T3" target="_self">Th3</a></i>
<br/>.= 
<span class="p1">(<span class="default"><a href="cat_1.html#K10">id</a> <span class="p2">(<span class="default"><a href="cat_1.html#K3">cod</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">L</font> <a href="cat_2.html#K6" target="_self">.</a> <span class="p5">(<span class="default"><a href="cat_1.html#K3">cod</a> <font color="Maroon">g</font></span>)</span></span>)</span> <a href="funct_2.html#K3">.</a> <font color="Maroon">f</font></span>)</span></span>)</span></span>)</span> <a href="cat_1.html#K4">*</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">L</font> <a href="cat_2.html#K6" target="_self">.</a> <span class="p3">(<span class="default"><a href="cat_1.html#K3">cod</a> <font color="Maroon">g</font></span>)</span></span>)</span> <a href="funct_2.html#K3">.</a> <span class="p2">(<span class="default"><a href="cat_1.html#K10">id</a> <span class="p3">(<span class="default"><a href="cat_1.html#K3">cod</a> <font color="Maroon">f</font></span>)</span></span>)</span></span>)</span>
<b>by </b><i><a class="ref" href="cat_1.html#T98">CAT_1:98</a></i>
<br/>.= 
<span class="p1">(<span class="default"><a href="cat_1.html#K10">id</a> <span class="p2">(<span class="default"><a href="cat_1.html#K3">cod</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">L</font> <a href="cat_2.html#K6" target="_self">.</a> <span class="p5">(<span class="default"><a href="cat_1.html#K3">cod</a> <font color="Maroon">g</font></span>)</span></span>)</span> <a href="funct_2.html#K3">.</a> <font color="Maroon">f</font></span>)</span></span>)</span></span>)</span> <a href="cat_1.html#K4">*</a> <span class="p1">(<span class="default"><a href="cat_1.html#K10">id</a> <span class="p2">(<span class="default"><a href="cat_1.html#K3">cod</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">L</font> <a href="cat_2.html#K6" target="_self">.</a> <span class="p5">(<span class="default"><a href="cat_1.html#K3">cod</a> <font color="Maroon">g</font></span>)</span></span>)</span> <a href="funct_2.html#K3">.</a> <font color="Maroon">f</font></span>)</span></span>)</span></span>)</span>
<b>by </b><i><a class="ref" href="cat_1.html#T98">CAT_1:98</a></i>
<br/>.= 
<span class="p1">(<span class="default"><a href="cat_1.html#K10">id</a> <span class="p2">(<span class="default"><a href="cat_1.html#K3">cod</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">L</font> <a href="cat_2.html#K6" target="_self">.</a> <span class="p5">(<span class="default"><a href="cat_1.html#K3">cod</a> <font color="Maroon">g</font></span>)</span></span>)</span> <a href="funct_2.html#K3">.</a> <font color="Maroon">f</font></span>)</span></span>)</span></span>)</span> <a href="cat_1.html#K9">*</a> <span class="p1">(<span class="default"><a href="cat_1.html#K10">id</a> <span class="p2">(<span class="default"><a href="cat_1.html#K3">cod</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">L</font> <a href="cat_2.html#K6" target="_self">.</a> <span class="p5">(<span class="default"><a href="cat_1.html#K3">cod</a> <font color="Maroon">g</font></span>)</span></span>)</span> <a href="funct_2.html#K3">.</a> <font color="Maroon">f</font></span>)</span></span>)</span></span>)</span>
<b>by </b><i>, <a class="ref" href="cat_1.html#D13">CAT_1:def 13</a></i>
<br/>.= 
 <a href="cat_1.html#K10">id</a> <span class="p1">(<span class="default"><a href="cat_1.html#K3">cod</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">L</font> <a href="cat_2.html#K6" target="_self">.</a> <span class="p4">(<span class="default"><a href="cat_1.html#K3">cod</a> <font color="Maroon">g</font></span>)</span></span>)</span> <a href="funct_2.html#K3">.</a> <font color="Maroon">f</font></span>)</span></span>)</span>
<b>by </b><i><a class="ref" href="cat_1.html#T59">CAT_1:59</a></i>
<br/>.= 
 <a href="cat_1.html#K10">id</a> <span class="p1">(<span class="default"><a href="cat_1.html#K3">cod</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">L</font> <a href="cat_2.html#K6" target="_self">.</a> <span class="p5">(<span class="default"><a href="cat_1.html#K3">cod</a> <font color="Maroon">g</font></span>)</span></span>)</span> <a href="funct_2.html#K3">.</a> <font color="Maroon">f</font></span>)</span> <a href="cat_1.html#K4">*</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">M</font> <a href="cat_2.html#K6" target="_self">.</a> <span class="p5">(<span class="default"><a href="cat_1.html#K2">dom</a> <font color="Maroon">f</font></span>)</span></span>)</span> <a href="funct_2.html#K3">.</a> <font color="Maroon">g</font></span>)</span></span>)</span></span>)</span>
<b>by </b><i>, <a class="ref" href="cat_1.html#T42">CAT_1:42</a></i>
<br/>.= 
 <a href="cat_1.html#K10">id</a> <span class="p1">(<span class="default"><a href="cat_1.html#K3">cod</a> <span class="p2">(<span class="default"><font color="Maroon">S</font> <a href="binop_1.html#K2">.</a> <font color="Maroon">f</font>,<font color="Maroon">g</font></span>)</span></span>)</span>
<b>by </b><i/>
<br/>.= 
 <a href="cat_1.html#K10">id</a> <span class="p1">(<span class="default"><a href="cat_1.html#K3">cod</a> <span class="p2">(<span class="default"><font color="Maroon">T</font> <a href="funct_2.html#K3">.</a> <font color="Maroon">fg</font></span>)</span></span>)</span>
<b>by </b><i/>
;<br/>


</div><b>end;</b></div><b>let </b><font color="Maroon">fg1</font> be   <a href="cat_1.html#NM2">Morphism</a> of <span class="p1"><a href="cat_2.html#K11" target="_self">[:</a><span class="default"><font color="Maroon">B</font>,<font color="Maroon">C</font></span><a href="cat_2.html#K11" target="_self">:]</a></span>, <font color="Maroon">fg2</font> be   <a href="cat_1.html#NM2">Morphism</a> of <span class="p1"><a href="cat_2.html#K11" target="_self">[:</a><span class="default"><font color="Maroon">B</font>,<font color="Maroon">C</font></span><a href="cat_2.html#K11" target="_self">:]</a></span>;<br/><b>assume </b><a NAME="E3:54_1"/><i><font color="Green">E69</font></i>: 
 <a href="cat_1.html#K2">dom</a> <font color="Maroon">fg2</font> <a href="hidden.html#R1">=</a>  <a href="cat_1.html#K3">cod</a> <font color="Maroon">fg1</font>
 ;<br/><b>consider </b><font color="Maroon">f1</font> being   <a href="cat_1.html#NM2">Morphism</a> of <font color="Maroon">B</font>, <font color="Maroon">g1</font> being   <a href="cat_1.html#NM2">Morphism</a> of <font color="Maroon">C</font><b> such that </b><br/><a NAME="E5:54_1"/><i><font color="Green">E70</font></i>: 
<font color="Maroon">fg1</font> <a href="hidden.html#R1">=</a> <span class="p1"><a href="cat_2.html#K13" target="_self">[</a><span class="default"><font color="Maroon">f1</font>,<font color="Maroon">g1</font></span><a href="cat_2.html#K13" target="_self">]</a></span>
 <b>by </b><i><a class="ref" href="domain_1.html#T9">DOMAIN_1:9</a></i>;<br/><b>consider </b><font color="Maroon">f2</font> being   <a href="cat_1.html#NM2">Morphism</a> of <font color="Maroon">B</font>, <font color="Maroon">g2</font> being   <a href="cat_1.html#NM2">Morphism</a> of <font color="Maroon">C</font><b> such that </b><br/><a NAME="E7:54_1"/><i><font color="Green">E71</font></i>: 
<font color="Maroon">fg2</font> <a href="hidden.html#R1">=</a> <span class="p1"><a href="cat_2.html#K13" target="_self">[</a><span class="default"><font color="Maroon">f2</font>,<font color="Maroon">g2</font></span><a href="cat_2.html#K13" target="_self">]</a></span>
 <b>by </b><i><a class="ref" href="domain_1.html#T9">DOMAIN_1:9</a></i>;<br/><a NAME="E8:54_1"/>
( <span class="p1"><a href="cat_2.html#K12" target="_self">[</a><span class="default"><span class="p2">(<span class="default"><a href="cat_1.html#K2">dom</a> <font color="Maroon">f2</font></span>)</span>,<span class="p2">(<span class="default"><a href="cat_1.html#K2">dom</a> <font color="Maroon">g2</font></span>)</span></span><a href="cat_2.html#K12" target="_self">]</a></span> <a href="hidden.html#R1">=</a>  <a href="cat_1.html#K2">dom</a> <font color="Maroon">fg2</font> &amp; <span class="p1"><a href="cat_2.html#K12" target="_self">[</a><span class="default"><span class="p2">(<span class="default"><a href="cat_1.html#K3">cod</a> <font color="Maroon">f1</font></span>)</span>,<span class="p2">(<span class="default"><a href="cat_1.html#K3">cod</a> <font color="Maroon">g1</font></span>)</span></span><a href="cat_2.html#K12" target="_self">]</a></span> <a href="hidden.html#R1">=</a>  <a href="cat_1.html#K3">cod</a> <font color="Maroon">fg1</font> )
 <b>by </b><i>, , <a class="txt" href="cat_2.html#E4:54"><i><font color="Green">E21</font></i></a></i>;<br/><a NAME="E9:54_1"/><b>then </b><i><font color="Green">E72</font></i>: 
(  <a href="cat_1.html#K2">dom</a> <font color="Maroon">f2</font> <a href="hidden.html#R1">=</a>  <a href="cat_1.html#K3">cod</a> <font color="Maroon">f1</font> &amp;  <a href="cat_1.html#K2">dom</a> <font color="Maroon">g2</font> <a href="hidden.html#R1">=</a>  <a href="cat_1.html#K3">cod</a> <font color="Maroon">g1</font> )
 <b>by </b><i>, <a class="ref" href="zfmisc_1.html#T33">ZFMISC_1:33</a></i>;<br/><b>set </b><font color="Maroon">f</font> = <font color="Maroon">f2</font> <a href="cat_1.html#K4">*</a> <font color="Maroon">f1</font>;<br/><b>set </b><font color="Maroon">g</font> = <font color="Maroon">g2</font> <a href="cat_1.html#K4">*</a> <font color="Maroon">g1</font>;<br/><b>set </b><font color="Maroon">L1</font> = <font color="Maroon">L</font> <a href="cat_2.html#K6" target="_self">.</a> <span class="p1">(<span class="default"><a href="cat_1.html#K3">cod</a> <font color="Maroon">g1</font></span>)</span>;<br/><b>set </b><font color="Maroon">L2</font> = <font color="Maroon">L</font> <a href="cat_2.html#K6" target="_self">.</a> <span class="p1">(<span class="default"><a href="cat_1.html#K3">cod</a> <font color="Maroon">g2</font></span>)</span>;<br/><b>set </b><font color="Maroon">M1</font> = <font color="Maroon">M</font> <a href="cat_2.html#K6" target="_self">.</a> <span class="p1">(<span class="default"><a href="cat_1.html#K2">dom</a> <font color="Maroon">f1</font></span>)</span>;<br/><b>set </b><font color="Maroon">M2</font> = <font color="Maroon">M</font> <a href="cat_2.html#K6" target="_self">.</a> <span class="p1">(<span class="default"><a href="cat_1.html#K2">dom</a> <font color="Maroon">f2</font></span>)</span>;<br/><a NAME="E10:54_1"/><i><font color="Green">E73</font></i>: 
(  <a href="cat_1.html#K2">dom</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">L</font> <a href="cat_2.html#K6" target="_self">.</a> <span class="p3">(<span class="default"><a href="cat_1.html#K3">cod</a> <font color="Maroon">g2</font></span>)</span></span>)</span> <a href="funct_2.html#K3">.</a> <font color="Maroon">f2</font></span>)</span> <a href="hidden.html#R1">=</a>  <a href="cat_1.html#K3">cod</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">L</font> <a href="cat_2.html#K6" target="_self">.</a> <span class="p3">(<span class="default"><a href="cat_1.html#K3">cod</a> <font color="Maroon">g2</font></span>)</span></span>)</span> <a href="funct_2.html#K3">.</a> <font color="Maroon">f1</font></span>)</span> &amp;  <a href="cat_1.html#K2">dom</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">M</font> <a href="cat_2.html#K6" target="_self">.</a> <span class="p3">(<span class="default"><a href="cat_1.html#K2">dom</a> <font color="Maroon">f1</font></span>)</span></span>)</span> <a href="funct_2.html#K3">.</a> <font color="Maroon">g2</font></span>)</span> <a href="hidden.html#R1">=</a>  <a href="cat_1.html#K3">cod</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">M</font> <a href="cat_2.html#K6" target="_self">.</a> <span class="p3">(<span class="default"><a href="cat_1.html#K2">dom</a> <font color="Maroon">f1</font></span>)</span></span>)</span> <a href="funct_2.html#K3">.</a> <font color="Maroon">g1</font></span>)</span> )
 <b>by </b><i>, <a class="ref" href="cat_1.html#T99">CAT_1:99</a></i>;<br/><a NAME="E11:54_1"/><b>then </b><i><font color="Green">E74</font></i>: 
 <a href="cat_1.html#K3">cod</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">M</font> <a href="cat_2.html#K6" target="_self">.</a> <span class="p4">(<span class="default"><a href="cat_1.html#K2">dom</a> <font color="Maroon">f1</font></span>)</span></span>)</span> <a href="funct_2.html#K3">.</a> <font color="Maroon">g2</font></span>)</span> <a href="cat_1.html#K4">*</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">M</font> <a href="cat_2.html#K6" target="_self">.</a> <span class="p4">(<span class="default"><a href="cat_1.html#K2">dom</a> <font color="Maroon">f1</font></span>)</span></span>)</span> <a href="funct_2.html#K3">.</a> <font color="Maroon">g1</font></span>)</span></span>)</span> <a href="hidden.html#R1">=</a>  <a href="cat_1.html#K3">cod</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">M</font> <a href="cat_2.html#K6" target="_self">.</a> <span class="p3">(<span class="default"><a href="cat_1.html#K2">dom</a> <font color="Maroon">f1</font></span>)</span></span>)</span> <a href="funct_2.html#K3">.</a> <font color="Maroon">g2</font></span>)</span>
 <b>by </b><i><a class="ref" href="cat_1.html#T42">CAT_1:42</a></i>;<br/> <a href="cat_1.html#K10">id</a> <span class="p1">(<span class="default"><a href="cat_1.html#K2">dom</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">L</font> <a href="cat_2.html#K6" target="_self">.</a> <span class="p4">(<span class="default"><a href="cat_1.html#K3">cod</a> <font color="Maroon">g2</font></span>)</span></span>)</span> <a href="funct_2.html#K3">.</a> <font color="Maroon">f1</font></span>)</span></span>)</span> = 
<span class="p1">(<span class="default"><font color="Maroon">L</font> <a href="cat_2.html#K6" target="_self">.</a> <span class="p2">(<span class="default"><a href="cat_1.html#K3">cod</a> <font color="Maroon">g2</font></span>)</span></span>)</span> <a href="funct_2.html#K3">.</a> <span class="p1">(<span class="default"><a href="cat_1.html#K10">id</a> <span class="p2">(<span class="default"><a href="cat_1.html#K2">dom</a> <font color="Maroon">f1</font></span>)</span></span>)</span>
<b>by </b><i><a class="ref" href="cat_1.html#T98">CAT_1:98</a></i>
<br/>.= 
<span class="p1">(<span class="default"><font color="Maroon">M</font> <a href="cat_2.html#K6" target="_self">.</a> <span class="p2">(<span class="default"><a href="cat_1.html#K2">dom</a> <font color="Maroon">f1</font></span>)</span></span>)</span> <a href="funct_2.html#K3">.</a> <span class="p1">(<span class="default"><a href="cat_1.html#K10">id</a> <span class="p2">(<span class="default"><a href="cat_1.html#K3">cod</a> <font color="Maroon">g2</font></span>)</span></span>)</span>
<b>by </b><i><a class="ref" href="cat_2.html#T3" target="_self">Th3</a></i>
<br/>.= 
 <a href="cat_1.html#K10">id</a> <span class="p1">(<span class="default"><a href="cat_1.html#K3">cod</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">M</font> <a href="cat_2.html#K6" target="_self">.</a> <span class="p4">(<span class="default"><a href="cat_1.html#K2">dom</a> <font color="Maroon">f1</font></span>)</span></span>)</span> <a href="funct_2.html#K3">.</a> <font color="Maroon">g2</font></span>)</span></span>)</span>
<b>by </b><i><a class="ref" href="cat_1.html#T98">CAT_1:98</a></i>
;<br/><a NAME="E13:54_1"/><b>then </b><i><font color="Green">E75</font></i>: 
 <a href="cat_1.html#K2">dom</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">L</font> <a href="cat_2.html#K6" target="_self">.</a> <span class="p3">(<span class="default"><a href="cat_1.html#K3">cod</a> <font color="Maroon">g2</font></span>)</span></span>)</span> <a href="funct_2.html#K3">.</a> <font color="Maroon">f1</font></span>)</span> <a href="hidden.html#R1">=</a>  <a href="cat_1.html#K3">cod</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">M</font> <a href="cat_2.html#K6" target="_self">.</a> <span class="p3">(<span class="default"><a href="cat_1.html#K2">dom</a> <font color="Maroon">f1</font></span>)</span></span>)</span> <a href="funct_2.html#K3">.</a> <font color="Maroon">g2</font></span>)</span>
 <b>by </b><i><a class="ref" href="cat_1.html#T45">CAT_1:45</a></i>;<br/> <a href="cat_1.html#K10">id</a> <span class="p1">(<span class="default"><a href="cat_1.html#K2">dom</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">L</font> <a href="cat_2.html#K6" target="_self">.</a> <span class="p4">(<span class="default"><a href="cat_1.html#K3">cod</a> <font color="Maroon">g1</font></span>)</span></span>)</span> <a href="funct_2.html#K3">.</a> <font color="Maroon">f1</font></span>)</span></span>)</span> = 
<span class="p1">(<span class="default"><font color="Maroon">L</font> <a href="cat_2.html#K6" target="_self">.</a> <span class="p2">(<span class="default"><a href="cat_1.html#K3">cod</a> <font color="Maroon">g1</font></span>)</span></span>)</span> <a href="funct_2.html#K3">.</a> <span class="p1">(<span class="default"><a href="cat_1.html#K10">id</a> <span class="p2">(<span class="default"><a href="cat_1.html#K2">dom</a> <font color="Maroon">f1</font></span>)</span></span>)</span>
<b>by </b><i><a class="ref" href="cat_1.html#T98">CAT_1:98</a></i>
<br/>.= 
<span class="p1">(<span class="default"><font color="Maroon">M</font> <a href="cat_2.html#K6" target="_self">.</a> <span class="p2">(<span class="default"><a href="cat_1.html#K2">dom</a> <font color="Maroon">f1</font></span>)</span></span>)</span> <a href="funct_2.html#K3">.</a> <span class="p1">(<span class="default"><a href="cat_1.html#K10">id</a> <span class="p2">(<span class="default"><a href="cat_1.html#K3">cod</a> <font color="Maroon">g1</font></span>)</span></span>)</span>
<b>by </b><i><a class="ref" href="cat_2.html#T3" target="_self">Th3</a></i>
<br/>.= 
 <a href="cat_1.html#K10">id</a> <span class="p1">(<span class="default"><a href="cat_1.html#K3">cod</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">M</font> <a href="cat_2.html#K6" target="_self">.</a> <span class="p4">(<span class="default"><a href="cat_1.html#K2">dom</a> <font color="Maroon">f1</font></span>)</span></span>)</span> <a href="funct_2.html#K3">.</a> <font color="Maroon">g1</font></span>)</span></span>)</span>
<b>by </b><i><a class="ref" href="cat_1.html#T98">CAT_1:98</a></i>
;<br/><a NAME="E15:54_1"/><b>then </b><i><font color="Green">E76</font></i>: 
 <a href="cat_1.html#K2">dom</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">L</font> <a href="cat_2.html#K6" target="_self">.</a> <span class="p3">(<span class="default"><a href="cat_1.html#K3">cod</a> <font color="Maroon">g1</font></span>)</span></span>)</span> <a href="funct_2.html#K3">.</a> <font color="Maroon">f1</font></span>)</span> <a href="hidden.html#R1">=</a>  <a href="cat_1.html#K3">cod</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">M</font> <a href="cat_2.html#K6" target="_self">.</a> <span class="p3">(<span class="default"><a href="cat_1.html#K2">dom</a> <font color="Maroon">f1</font></span>)</span></span>)</span> <a href="funct_2.html#K3">.</a> <font color="Maroon">g1</font></span>)</span>
 <b>by </b><i><a class="ref" href="cat_1.html#T45">CAT_1:45</a></i>;<br/> <a href="cat_1.html#K10">id</a> <span class="p1">(<span class="default"><a href="cat_1.html#K2">dom</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">M</font> <a href="cat_2.html#K6" target="_self">.</a> <span class="p4">(<span class="default"><a href="cat_1.html#K2">dom</a> <font color="Maroon">f2</font></span>)</span></span>)</span> <a href="funct_2.html#K3">.</a> <font color="Maroon">g2</font></span>)</span></span>)</span> = 
<span class="p1">(<span class="default"><font color="Maroon">M</font> <a href="cat_2.html#K6" target="_self">.</a> <span class="p2">(<span class="default"><a href="cat_1.html#K2">dom</a> <font color="Maroon">f2</font></span>)</span></span>)</span> <a href="funct_2.html#K3">.</a> <span class="p1">(<span class="default"><a href="cat_1.html#K10">id</a> <span class="p2">(<span class="default"><a href="cat_1.html#K2">dom</a> <font color="Maroon">g2</font></span>)</span></span>)</span>
<b>by </b><i><a class="ref" href="cat_1.html#T98">CAT_1:98</a></i>
<br/>.= 
<span class="p1">(<span class="default"><font color="Maroon">L</font> <a href="cat_2.html#K6" target="_self">.</a> <span class="p2">(<span class="default"><a href="cat_1.html#K3">cod</a> <font color="Maroon">g1</font></span>)</span></span>)</span> <a href="funct_2.html#K3">.</a> <span class="p1">(<span class="default"><a href="cat_1.html#K10">id</a> <span class="p2">(<span class="default"><a href="cat_1.html#K3">cod</a> <font color="Maroon">f1</font></span>)</span></span>)</span>
<b>by </b><i><a class="ref" href="cat_2.html#T3" target="_self">Th3</a>, </i>
<br/>.= 
 <a href="cat_1.html#K10">id</a> <span class="p1">(<span class="default"><a href="cat_1.html#K3">cod</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">L</font> <a href="cat_2.html#K6" target="_self">.</a> <span class="p4">(<span class="default"><a href="cat_1.html#K3">cod</a> <font color="Maroon">g1</font></span>)</span></span>)</span> <a href="funct_2.html#K3">.</a> <font color="Maroon">f1</font></span>)</span></span>)</span>
<b>by </b><i><a class="ref" href="cat_1.html#T98">CAT_1:98</a></i>
;<br/><a NAME="E17:54_1"/><b>then </b><i><font color="Green">E77</font></i>: 
 <a href="cat_1.html#K2">dom</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">M</font> <a href="cat_2.html#K6" target="_self">.</a> <span class="p3">(<span class="default"><a href="cat_1.html#K2">dom</a> <font color="Maroon">f2</font></span>)</span></span>)</span> <a href="funct_2.html#K3">.</a> <font color="Maroon">g2</font></span>)</span> <a href="hidden.html#R1">=</a>  <a href="cat_1.html#K3">cod</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">L</font> <a href="cat_2.html#K6" target="_self">.</a> <span class="p3">(<span class="default"><a href="cat_1.html#K3">cod</a> <font color="Maroon">g1</font></span>)</span></span>)</span> <a href="funct_2.html#K3">.</a> <font color="Maroon">f1</font></span>)</span>
 <b>by </b><i><a class="ref" href="cat_1.html#T45">CAT_1:45</a></i>;<br/> <a href="cat_1.html#K10">id</a> <span class="p1">(<span class="default"><a href="cat_1.html#K2">dom</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">L</font> <a href="cat_2.html#K6" target="_self">.</a> <span class="p4">(<span class="default"><a href="cat_1.html#K3">cod</a> <font color="Maroon">g2</font></span>)</span></span>)</span> <a href="funct_2.html#K3">.</a> <font color="Maroon">f2</font></span>)</span></span>)</span> = 
<span class="p1">(<span class="default"><font color="Maroon">L</font> <a href="cat_2.html#K6" target="_self">.</a> <span class="p2">(<span class="default"><a href="cat_1.html#K3">cod</a> <font color="Maroon">g2</font></span>)</span></span>)</span> <a href="funct_2.html#K3">.</a> <span class="p1">(<span class="default"><a href="cat_1.html#K10">id</a> <span class="p2">(<span class="default"><a href="cat_1.html#K2">dom</a> <font color="Maroon">f2</font></span>)</span></span>)</span>
<b>by </b><i><a class="ref" href="cat_1.html#T98">CAT_1:98</a></i>
<br/>.= 
<span class="p1">(<span class="default"><font color="Maroon">M</font> <a href="cat_2.html#K6" target="_self">.</a> <span class="p2">(<span class="default"><a href="cat_1.html#K2">dom</a> <font color="Maroon">f2</font></span>)</span></span>)</span> <a href="funct_2.html#K3">.</a> <span class="p1">(<span class="default"><a href="cat_1.html#K10">id</a> <span class="p2">(<span class="default"><a href="cat_1.html#K3">cod</a> <font color="Maroon">g2</font></span>)</span></span>)</span>
<b>by </b><i><a class="ref" href="cat_2.html#T3" target="_self">Th3</a></i>
<br/>.= 
 <a href="cat_1.html#K10">id</a> <span class="p1">(<span class="default"><a href="cat_1.html#K3">cod</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">M</font> <a href="cat_2.html#K6" target="_self">.</a> <span class="p4">(<span class="default"><a href="cat_1.html#K2">dom</a> <font color="Maroon">f2</font></span>)</span></span>)</span> <a href="funct_2.html#K3">.</a> <font color="Maroon">g2</font></span>)</span></span>)</span>
<b>by </b><i><a class="ref" href="cat_1.html#T98">CAT_1:98</a></i>
;<br/><a NAME="E19:54_1"/><b>then </b><i><font color="Green">E78</font></i>: 
 <a href="cat_1.html#K2">dom</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">L</font> <a href="cat_2.html#K6" target="_self">.</a> <span class="p3">(<span class="default"><a href="cat_1.html#K3">cod</a> <font color="Maroon">g2</font></span>)</span></span>)</span> <a href="funct_2.html#K3">.</a> <font color="Maroon">f2</font></span>)</span> <a href="hidden.html#R1">=</a>  <a href="cat_1.html#K3">cod</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">M</font> <a href="cat_2.html#K6" target="_self">.</a> <span class="p3">(<span class="default"><a href="cat_1.html#K2">dom</a> <font color="Maroon">f2</font></span>)</span></span>)</span> <a href="funct_2.html#K3">.</a> <font color="Maroon">g2</font></span>)</span>
 <b>by </b><i><a class="ref" href="cat_1.html#T45">CAT_1:45</a></i>;<br/><a NAME="E20:54_1"/><i><font color="Green">E79</font></i>: 
 <a href="cat_1.html#K3">cod</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">L</font> <a href="cat_2.html#K6" target="_self">.</a> <span class="p4">(<span class="default"><a href="cat_1.html#K3">cod</a> <font color="Maroon">g1</font></span>)</span></span>)</span> <a href="funct_2.html#K3">.</a> <font color="Maroon">f1</font></span>)</span> <a href="cat_1.html#K4">*</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">M</font> <a href="cat_2.html#K6" target="_self">.</a> <span class="p4">(<span class="default"><a href="cat_1.html#K2">dom</a> <font color="Maroon">f1</font></span>)</span></span>)</span> <a href="funct_2.html#K3">.</a> <font color="Maroon">g1</font></span>)</span></span>)</span> <a href="hidden.html#R1">=</a>  <a href="cat_1.html#K3">cod</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">L</font> <a href="cat_2.html#K6" target="_self">.</a> <span class="p3">(<span class="default"><a href="cat_1.html#K3">cod</a> <font color="Maroon">g1</font></span>)</span></span>)</span> <a href="funct_2.html#K3">.</a> <font color="Maroon">f1</font></span>)</span>
 <b>by </b><i>, <a class="ref" href="cat_1.html#T42">CAT_1:42</a></i>;<br/><b>thus </b><font color="Maroon">T</font> <a href="funct_2.html#K3">.</a> <span class="p1">(<span class="default"><font color="Maroon">fg2</font> <a href="cat_1.html#K4">*</a> <font color="Maroon">fg1</font></span>)</span> = 
<font color="Maroon">S</font> <a href="binop_1.html#K2">.</a> <span class="p1">(<span class="default"><font color="Maroon">f2</font> <a href="cat_1.html#K4">*</a> <font color="Maroon">f1</font></span>)</span>,<span class="p1">(<span class="default"><font color="Maroon">g2</font> <a href="cat_1.html#K4">*</a> <font color="Maroon">g1</font></span>)</span>
<b>by </b><i>, , , </i>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">L</font> <a href="cat_2.html#K6" target="_self">.</a> <span class="p3">(<span class="default"><a href="cat_1.html#K3">cod</a> <span class="p4">(<span class="default"><font color="Maroon">g2</font> <a href="cat_1.html#K4">*</a> <font color="Maroon">g1</font></span>)</span></span>)</span></span>)</span> <a href="funct_2.html#K3">.</a> <span class="p2">(<span class="default"><font color="Maroon">f2</font> <a href="cat_1.html#K4">*</a> <font color="Maroon">f1</font></span>)</span></span>)</span> <a href="cat_1.html#K4">*</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">M</font> <a href="cat_2.html#K6" target="_self">.</a> <span class="p3">(<span class="default"><a href="cat_1.html#K2">dom</a> <span class="p4">(<span class="default"><font color="Maroon">f2</font> <a href="cat_1.html#K4">*</a> <font color="Maroon">f1</font></span>)</span></span>)</span></span>)</span> <a href="funct_2.html#K3">.</a> <span class="p2">(<span class="default"><font color="Maroon">g2</font> <a href="cat_1.html#K4">*</a> <font color="Maroon">g1</font></span>)</span></span>)</span>
<b>by </b><i/>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">L</font> <a href="cat_2.html#K6" target="_self">.</a> <span class="p3">(<span class="default"><a href="cat_1.html#K3">cod</a> <font color="Maroon">g2</font></span>)</span></span>)</span> <a href="funct_2.html#K3">.</a> <span class="p2">(<span class="default"><font color="Maroon">f2</font> <a href="cat_1.html#K4">*</a> <font color="Maroon">f1</font></span>)</span></span>)</span> <a href="cat_1.html#K4">*</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">M</font> <a href="cat_2.html#K6" target="_self">.</a> <span class="p3">(<span class="default"><a href="cat_1.html#K2">dom</a> <span class="p4">(<span class="default"><font color="Maroon">f2</font> <a href="cat_1.html#K4">*</a> <font color="Maroon">f1</font></span>)</span></span>)</span></span>)</span> <a href="funct_2.html#K3">.</a> <span class="p2">(<span class="default"><font color="Maroon">g2</font> <a href="cat_1.html#K4">*</a> <font color="Maroon">g1</font></span>)</span></span>)</span>
<b>by </b><i>, <a class="ref" href="cat_1.html#T42">CAT_1:42</a></i>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">L</font> <a href="cat_2.html#K6" target="_self">.</a> <span class="p3">(<span class="default"><a href="cat_1.html#K3">cod</a> <font color="Maroon">g2</font></span>)</span></span>)</span> <a href="funct_2.html#K3">.</a> <span class="p2">(<span class="default"><font color="Maroon">f2</font> <a href="cat_1.html#K4">*</a> <font color="Maroon">f1</font></span>)</span></span>)</span> <a href="cat_1.html#K4">*</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">M</font> <a href="cat_2.html#K6" target="_self">.</a> <span class="p3">(<span class="default"><a href="cat_1.html#K2">dom</a> <font color="Maroon">f1</font></span>)</span></span>)</span> <a href="funct_2.html#K3">.</a> <span class="p2">(<span class="default"><font color="Maroon">g2</font> <a href="cat_1.html#K4">*</a> <font color="Maroon">g1</font></span>)</span></span>)</span>
<b>by </b><i>, <a class="ref" href="cat_1.html#T42">CAT_1:42</a></i>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">L</font> <a href="cat_2.html#K6" target="_self">.</a> <span class="p4">(<span class="default"><a href="cat_1.html#K3">cod</a> <font color="Maroon">g2</font></span>)</span></span>)</span> <a href="funct_2.html#K3">.</a> <font color="Maroon">f2</font></span>)</span> <a href="cat_1.html#K4">*</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">L</font> <a href="cat_2.html#K6" target="_self">.</a> <span class="p4">(<span class="default"><a href="cat_1.html#K3">cod</a> <font color="Maroon">g2</font></span>)</span></span>)</span> <a href="funct_2.html#K3">.</a> <font color="Maroon">f1</font></span>)</span></span>)</span> <a href="cat_1.html#K4">*</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">M</font> <a href="cat_2.html#K6" target="_self">.</a> <span class="p3">(<span class="default"><a href="cat_1.html#K2">dom</a> <font color="Maroon">f1</font></span>)</span></span>)</span> <a href="funct_2.html#K3">.</a> <span class="p2">(<span class="default"><font color="Maroon">g2</font> <a href="cat_1.html#K4">*</a> <font color="Maroon">g1</font></span>)</span></span>)</span>
<b>by </b><i>, <a class="ref" href="cat_1.html#T99">CAT_1:99</a></i>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">L</font> <a href="cat_2.html#K6" target="_self">.</a> <span class="p4">(<span class="default"><a href="cat_1.html#K3">cod</a> <font color="Maroon">g2</font></span>)</span></span>)</span> <a href="funct_2.html#K3">.</a> <font color="Maroon">f2</font></span>)</span> <a href="cat_1.html#K4">*</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">L</font> <a href="cat_2.html#K6" target="_self">.</a> <span class="p4">(<span class="default"><a href="cat_1.html#K3">cod</a> <font color="Maroon">g2</font></span>)</span></span>)</span> <a href="funct_2.html#K3">.</a> <font color="Maroon">f1</font></span>)</span></span>)</span> <a href="cat_1.html#K4">*</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">M</font> <a href="cat_2.html#K6" target="_self">.</a> <span class="p4">(<span class="default"><a href="cat_1.html#K2">dom</a> <font color="Maroon">f1</font></span>)</span></span>)</span> <a href="funct_2.html#K3">.</a> <font color="Maroon">g2</font></span>)</span> <a href="cat_1.html#K4">*</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">M</font> <a href="cat_2.html#K6" target="_self">.</a> <span class="p4">(<span class="default"><a href="cat_1.html#K2">dom</a> <font color="Maroon">f1</font></span>)</span></span>)</span> <a href="funct_2.html#K3">.</a> <font color="Maroon">g1</font></span>)</span></span>)</span>
<b>by </b><i>, <a class="ref" href="cat_1.html#T99">CAT_1:99</a></i>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">L</font> <a href="cat_2.html#K6" target="_self">.</a> <span class="p3">(<span class="default"><a href="cat_1.html#K3">cod</a> <font color="Maroon">g2</font></span>)</span></span>)</span> <a href="funct_2.html#K3">.</a> <font color="Maroon">f2</font></span>)</span> <a href="cat_1.html#K4">*</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">L</font> <a href="cat_2.html#K6" target="_self">.</a> <span class="p4">(<span class="default"><a href="cat_1.html#K3">cod</a> <font color="Maroon">g2</font></span>)</span></span>)</span> <a href="funct_2.html#K3">.</a> <font color="Maroon">f1</font></span>)</span> <a href="cat_1.html#K4">*</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">M</font> <a href="cat_2.html#K6" target="_self">.</a> <span class="p5">(<span class="default"><a href="cat_1.html#K2">dom</a> <font color="Maroon">f1</font></span>)</span></span>)</span> <a href="funct_2.html#K3">.</a> <font color="Maroon">g2</font></span>)</span> <a href="cat_1.html#K4">*</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">M</font> <a href="cat_2.html#K6" target="_self">.</a> <span class="p5">(<span class="default"><a href="cat_1.html#K2">dom</a> <font color="Maroon">f1</font></span>)</span></span>)</span> <a href="funct_2.html#K3">.</a> <font color="Maroon">g1</font></span>)</span></span>)</span></span>)</span>
<b>by </b><i><a class="ref" href="cat_2.html#D2" target="_self">Def2</a>, , , <a class="ref" href="cat_1.html#T43">CAT_1:43</a></i>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">L</font> <a href="cat_2.html#K6" target="_self">.</a> <span class="p3">(<span class="default"><a href="cat_1.html#K3">cod</a> <font color="Maroon">g2</font></span>)</span></span>)</span> <a href="funct_2.html#K3">.</a> <font color="Maroon">f2</font></span>)</span> <a href="cat_1.html#K4">*</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">L</font> <a href="cat_2.html#K6" target="_self">.</a> <span class="p5">(<span class="default"><a href="cat_1.html#K3">cod</a> <font color="Maroon">g2</font></span>)</span></span>)</span> <a href="funct_2.html#K3">.</a> <font color="Maroon">f1</font></span>)</span> <a href="cat_1.html#K4">*</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">M</font> <a href="cat_2.html#K6" target="_self">.</a> <span class="p5">(<span class="default"><a href="cat_1.html#K2">dom</a> <font color="Maroon">f1</font></span>)</span></span>)</span> <a href="funct_2.html#K3">.</a> <font color="Maroon">g2</font></span>)</span></span>)</span> <a href="cat_1.html#K4">*</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">M</font> <a href="cat_2.html#K6" target="_self">.</a> <span class="p4">(<span class="default"><a href="cat_1.html#K2">dom</a> <font color="Maroon">f1</font></span>)</span></span>)</span> <a href="funct_2.html#K3">.</a> <font color="Maroon">g1</font></span>)</span></span>)</span>
<b>by </b><i><a class="ref" href="cat_2.html#D2" target="_self">Def2</a>, , <a class="ref" href="cat_1.html#T43">CAT_1:43</a></i>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">L</font> <a href="cat_2.html#K6" target="_self">.</a> <span class="p3">(<span class="default"><a href="cat_1.html#K3">cod</a> <font color="Maroon">g2</font></span>)</span></span>)</span> <a href="funct_2.html#K3">.</a> <font color="Maroon">f2</font></span>)</span> <a href="cat_1.html#K4">*</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">M</font> <a href="cat_2.html#K6" target="_self">.</a> <span class="p5">(<span class="default"><a href="cat_1.html#K2">dom</a> <font color="Maroon">f2</font></span>)</span></span>)</span> <a href="funct_2.html#K3">.</a> <font color="Maroon">g2</font></span>)</span> <a href="cat_1.html#K4">*</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">L</font> <a href="cat_2.html#K6" target="_self">.</a> <span class="p5">(<span class="default"><a href="cat_1.html#K3">cod</a> <font color="Maroon">g1</font></span>)</span></span>)</span> <a href="funct_2.html#K3">.</a> <font color="Maroon">f1</font></span>)</span></span>)</span> <a href="cat_1.html#K4">*</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">M</font> <a href="cat_2.html#K6" target="_self">.</a> <span class="p4">(<span class="default"><a href="cat_1.html#K2">dom</a> <font color="Maroon">f1</font></span>)</span></span>)</span> <a href="funct_2.html#K3">.</a> <font color="Maroon">g1</font></span>)</span></span>)</span>
<b>by </b><i><a class="ref" href="cat_2.html#T4" target="_self">Th4</a>, </i>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">L</font> <a href="cat_2.html#K6" target="_self">.</a> <span class="p3">(<span class="default"><a href="cat_1.html#K3">cod</a> <font color="Maroon">g2</font></span>)</span></span>)</span> <a href="funct_2.html#K3">.</a> <font color="Maroon">f2</font></span>)</span> <a href="cat_1.html#K4">*</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">M</font> <a href="cat_2.html#K6" target="_self">.</a> <span class="p4">(<span class="default"><a href="cat_1.html#K2">dom</a> <font color="Maroon">f2</font></span>)</span></span>)</span> <a href="funct_2.html#K3">.</a> <font color="Maroon">g2</font></span>)</span> <a href="cat_1.html#K4">*</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">L</font> <a href="cat_2.html#K6" target="_self">.</a> <span class="p5">(<span class="default"><a href="cat_1.html#K3">cod</a> <font color="Maroon">g1</font></span>)</span></span>)</span> <a href="funct_2.html#K3">.</a> <font color="Maroon">f1</font></span>)</span> <a href="cat_1.html#K4">*</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">M</font> <a href="cat_2.html#K6" target="_self">.</a> <span class="p5">(<span class="default"><a href="cat_1.html#K2">dom</a> <font color="Maroon">f1</font></span>)</span></span>)</span> <a href="funct_2.html#K3">.</a> <font color="Maroon">g1</font></span>)</span></span>)</span></span>)</span>
<b>by </b><i>, <a class="ref" href="cat_2.html#D3" target="_self">Def3</a>, <a class="ref" href="cat_1.html#T43">CAT_1:43</a></i>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">L</font> <a href="cat_2.html#K6" target="_self">.</a> <span class="p4">(<span class="default"><a href="cat_1.html#K3">cod</a> <font color="Maroon">g2</font></span>)</span></span>)</span> <a href="funct_2.html#K3">.</a> <font color="Maroon">f2</font></span>)</span> <a href="cat_1.html#K4">*</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">M</font> <a href="cat_2.html#K6" target="_self">.</a> <span class="p4">(<span class="default"><a href="cat_1.html#K2">dom</a> <font color="Maroon">f2</font></span>)</span></span>)</span> <a href="funct_2.html#K3">.</a> <font color="Maroon">g2</font></span>)</span></span>)</span> <a href="cat_1.html#K4">*</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">L</font> <a href="cat_2.html#K6" target="_self">.</a> <span class="p4">(<span class="default"><a href="cat_1.html#K3">cod</a> <font color="Maroon">g1</font></span>)</span></span>)</span> <a href="funct_2.html#K3">.</a> <font color="Maroon">f1</font></span>)</span> <a href="cat_1.html#K4">*</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">M</font> <a href="cat_2.html#K6" target="_self">.</a> <span class="p4">(<span class="default"><a href="cat_1.html#K2">dom</a> <font color="Maroon">f1</font></span>)</span></span>)</span> <a href="funct_2.html#K3">.</a> <font color="Maroon">g1</font></span>)</span></span>)</span>
<b>by </b><i><a class="ref" href="cat_2.html#D3" target="_self">Def3</a>, , <a class="ref" href="cat_2.html#D4" target="_self">Def4</a>, <a class="ref" href="cat_1.html#T43">CAT_1:43</a></i>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">L</font> <a href="cat_2.html#K6" target="_self">.</a> <span class="p4">(<span class="default"><a href="cat_1.html#K3">cod</a> <font color="Maroon">g2</font></span>)</span></span>)</span> <a href="funct_2.html#K3">.</a> <font color="Maroon">f2</font></span>)</span> <a href="cat_1.html#K4">*</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">M</font> <a href="cat_2.html#K6" target="_self">.</a> <span class="p4">(<span class="default"><a href="cat_1.html#K2">dom</a> <font color="Maroon">f2</font></span>)</span></span>)</span> <a href="funct_2.html#K3">.</a> <font color="Maroon">g2</font></span>)</span></span>)</span> <a href="cat_1.html#K4">*</a> <span class="p1">(<span class="default"><font color="Maroon">S</font> <a href="binop_1.html#K2">.</a> <font color="Maroon">f1</font>,<font color="Maroon">g1</font></span>)</span>
<b>by </b><i/>
<br/>.= 
<span class="p1">(<span class="default"><font color="Maroon">S</font> <a href="binop_1.html#K2">.</a> <font color="Maroon">f2</font>,<font color="Maroon">g2</font></span>)</span> <a href="cat_1.html#K4">*</a> <span class="p1">(<span class="default"><font color="Maroon">T</font> <a href="funct_2.html#K3">.</a> <font color="Maroon">fg1</font></span>)</span>
<b>by </b><i>, </i>
<br/>.= 
<span class="p1">(<span class="default"><font color="Maroon">T</font> <a href="funct_2.html#K3">.</a> <font color="Maroon">fg2</font></span>)</span> <a href="cat_1.html#K4">*</a> <span class="p1">(<span class="default"><font color="Maroon">T</font> <a href="funct_2.html#K3">.</a> <font color="Maroon">fg1</font></span>)</span>
<b>by </b><i/>
;<br/></div><b>end;</b></div>
<b>then reconsider </b><font color="Maroon">T</font> = <font color="Maroon">T</font> as    <a href="cat_1.html#M2">Functor</a> of <span class="p1"><a href="cat_2.html#K11" target="_self">[:</a><span class="default"><font color="Maroon">B</font>,<font color="Maroon">C</font></span><a href="cat_2.html#K11" target="_self">:]</a></span>,<font color="Maroon">D</font> <b>by </b><i><a class="ref" href="cat_1.html#T96">CAT_1:96</a></i>;<br/>
<b>take </b>
<font color="Maroon">T</font>
;<br/>

<b>thus </b><a NAME="E8:54"/>
for <font color="Olive">f</font> being  <a href="cat_1.html#NM2">Morphism</a> of <font color="Maroon">B</font><br/> for <font color="Olive">g</font> being  <a href="cat_1.html#NM2">Morphism</a> of <font color="Maroon">C</font> holds  <font color="Maroon">T</font> <a href="cat_2.html#K14" target="_self">.</a> <font color="Olive">f</font>,<font color="Olive">g</font> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">L</font> <a href="cat_2.html#K6" target="_self">.</a> <span class="p3">(<span class="default"><a href="cat_1.html#K3">cod</a> <font color="Olive">g</font></span>)</span></span>)</span> <a href="funct_2.html#K3">.</a> <font color="Olive">f</font></span>)</span> <a href="cat_1.html#K4">*</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">M</font> <a href="cat_2.html#K6" target="_self">.</a> <span class="p3">(<span class="default"><a href="cat_1.html#K2">dom</a> <font color="Olive">f</font></span>)</span></span>)</span> <a href="funct_2.html#K3">.</a> <font color="Olive">g</font></span>)</span>
 <b>by </b><i/>;<br/>


</div>
