<?xml version="1.0"?>
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<b>let </b><font color="Maroon">C1</font> be   <a href="cat_1.html#NM4">Category</a>, <font color="Maroon">C2</font> be   <a href="cat_1.html#NM4">Category</a>;<br/><b>let </b><font color="Maroon">F</font> be    <a href="cat_1.html#M2">Functor</a> of <font color="Maroon">C1</font>,<font color="Maroon">C2</font>;<br/>



<b>set </b><font color="Maroon">CS1</font> =  <a href="catalg_1.html#K3" target="_self">CatSign</a> the <a href="cat_1.html#U1">Objects</a> of <font color="Maroon">C1</font>;<br/>
<b>set </b><font color="Maroon">CS2</font> =  <a href="catalg_1.html#K3" target="_self">CatSign</a> the <a href="cat_1.html#U1">Objects</a> of <font color="Maroon">C2</font>;<br/>
<b>set </b><font color="Maroon">A1</font> =  <a href="catalg_1.html#K13" target="_self">MSAlg</a> <font color="Maroon">C1</font>;<br/>
<b>set </b><font color="Maroon">A2</font> =  <a href="catalg_1.html#K13" target="_self">MSAlg</a> <font color="Maroon">C2</font>;<br/>
<b>set </b><font color="Maroon">u</font> =  <a href="catalg_1.html#K11" target="_self">Upsilon</a> <font color="Maroon">F</font>;<br/>
<b>set </b><font color="Maroon">p</font> =  <a href="catalg_1.html#K12" target="_self">Psi</a> <font color="Maroon">F</font>;<br/>
<b>set </b><font color="Maroon">B</font> = <span class="p1">(<span class="default"><a href="catalg_1.html#K13" target="_self">MSAlg</a> <font color="Maroon">C2</font></span>)</span> <a href="instalg1.html#K1">|</a> <span class="p1">(<span class="default"><a href="catalg_1.html#K3" target="_self">CatSign</a> the <a href="cat_1.html#U1">Objects</a> of <font color="Maroon">C1</font></span>)</span>,<span class="p1">(<span class="default"><a href="catalg_1.html#K11" target="_self">Upsilon</a> <font color="Maroon">F</font></span>)</span>,<span class="p1">(<span class="default"><a href="catalg_1.html#K12" target="_self">Psi</a> <font color="Maroon">F</font></span>)</span>;<br/>
<b>let </b><font color="Maroon">a</font> be   <a href="cat_1.html#NM1">Object</a> of <font color="Maroon">C1</font>, <font color="Maroon">b</font> be   <a href="cat_1.html#NM1">Object</a> of <font color="Maroon">C1</font>, <font color="Maroon">c</font> be   <a href="cat_1.html#NM1">Object</a> of <font color="Maroon">C1</font>;<br/>

<b>set </b><font color="Maroon">o</font> =  <a href="catalg_1.html#K10" target="_self">compsym</a> <font color="Maroon">a</font>,<font color="Maroon">b</font>,<font color="Maroon">c</font>;<br/>
<b>let </b><font color="Maroon">f</font> be   <a href="cat_1.html#NM2">Morphism</a> of <font color="Maroon">C1</font>, <font color="Maroon">g</font> be   <a href="cat_1.html#NM2">Morphism</a> of <font color="Maroon">C1</font>;<br/>

<b>assume </b><a NAME="E1:76"/><i><font color="Green">E37</font></i>: 
( <font color="Maroon">f</font> <a href="hidden.html#R2">in</a>  <a href="cat_1.html#K6">Hom</a> <font color="Maroon">a</font>,<font color="Maroon">b</font> &amp; <font color="Maroon">g</font> <a href="hidden.html#R2">in</a>  <a href="cat_1.html#K6">Hom</a> <font color="Maroon">b</font>,<font color="Maroon">c</font> )
 ;<br/>

<b>let </b><font color="Maroon">x</font> be    <a href="subset_1.html#M1">Element</a> of  <a href="msualg_1.html#K3">Args</a> <span class="p1">(<span class="default"><a href="catalg_1.html#K10" target="_self">compsym</a> <font color="Maroon">a</font>,<font color="Maroon">b</font>,<font color="Maroon">c</font></span>)</span>,<span class="p1">(<span class="default"><a href="catalg_1.html#K13" target="_self">MSAlg</a> <font color="Maroon">C1</font></span>)</span>;<br/>

<b>assume </b><a NAME="E2:76"/><i><font color="Green">E41</font></i>: 
<font color="Maroon">x</font> <a href="hidden.html#R1">=</a> <span class="p1"><a href="finseq_4.html#K2">&lt;*</a><span class="default"><font color="Maroon">g</font>,<font color="Maroon">f</font></span><a href="finseq_4.html#K2">*&gt;</a></span>
 ;<br/>

<a NAME="E3:76"/>
(  <a href="cat_1.html#K2">dom</a> <font color="Maroon">f</font> <a href="hidden.html#R1">=</a> <font color="Maroon">a</font> &amp;  <a href="cat_1.html#K3">cod</a> <font color="Maroon">f</font> <a href="hidden.html#R1">=</a> <font color="Maroon">b</font> &amp;  <a href="cat_1.html#K2">dom</a> <font color="Maroon">g</font> <a href="hidden.html#R1">=</a> <font color="Maroon">b</font> &amp;  <a href="cat_1.html#K3">cod</a> <font color="Maroon">g</font> <a href="hidden.html#R1">=</a> <font color="Maroon">c</font> )
 
<b>by </b><i>, <a class="ref" href="cat_1.html#T18">CAT_1:18</a></i>;<br/>
<a NAME="E4:76"/><b>then </b><i><font color="Green">E42</font></i>: 
<font color="Maroon">x</font> <a href="hidden.html#R2">in</a>  <a href="msualg_1.html#K3">Args</a> <span class="p1">(<span class="default"><a href="catalg_1.html#K10" target="_self">compsym</a> <font color="Maroon">a</font>,<font color="Maroon">b</font>,<font color="Maroon">c</font></span>)</span>,<span class="p1">(<span class="default"><a href="catalg_1.html#K13" target="_self">MSAlg</a> <font color="Maroon">C1</font></span>)</span>
 
<b>by </b><i>, <a class="txt" href="catalg_1.html#E2:76"><i><font color="Green">E41</font></i></a></i>;<br/>
<a NAME="E5:76"/><i><font color="Green">E45</font></i>: 
( <span class="p1"><a href="finseq_4.html#K2">&lt;*</a><span class="default"><font color="Maroon">g</font>,<font color="Maroon">f</font></span><a href="finseq_4.html#K2">*&gt;</a></span> <a href="funct_1.html#K1">.</a> 1 <a href="hidden.html#R1">=</a> <font color="Maroon">g</font> &amp; <span class="p1"><a href="finseq_4.html#K2">&lt;*</a><span class="default"><font color="Maroon">g</font>,<font color="Maroon">f</font></span><a href="finseq_4.html#K2">*&gt;</a></span> <a href="funct_1.html#K1">.</a> 2 <a href="hidden.html#R1">=</a> <font color="Maroon">f</font> )
 
<b>by </b><i><a class="ref" href="finseq_1.html#T61">FINSEQ_1:61</a></i>;<br/>
<b>let </b><font color="Maroon">H</font> be   <a href="msualg_3.html#NM1">ManySortedFunction</a> of <span class="p1">(<span class="default"><a href="catalg_1.html#K13" target="_self">MSAlg</a> <font color="Maroon">C1</font></span>)</span>,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="catalg_1.html#K13" target="_self">MSAlg</a> <font color="Maroon">C2</font></span>)</span> <a href="instalg1.html#K1">|</a> <span class="p2">(<span class="default"><a href="catalg_1.html#K3" target="_self">CatSign</a> the <a href="cat_1.html#U1">Objects</a> of <font color="Maroon">C1</font></span>)</span>,<span class="p2">(<span class="default"><a href="catalg_1.html#K11" target="_self">Upsilon</a> <font color="Maroon">F</font></span>)</span>,<span class="p2">(<span class="default"><a href="catalg_1.html#K12" target="_self">Psi</a> <font color="Maroon">F</font></span>)</span></span>)</span>;<br/>

<b>assume </b><a NAME="E6:76"/><i><font color="Green">E46</font></i>: 
<font color="Maroon">H</font> <a href="pboole.html#R6">=</a> <font color="Maroon">F</font> <a href="catalg_1.html#K1" target="_self">-MSF</a> the <a href="struct_0.html#U1">carrier</a> of <span class="p1">(<span class="default"><a href="catalg_1.html#K3" target="_self">CatSign</a> the <a href="cat_1.html#U1">Objects</a> of <font color="Maroon">C1</font></span>)</span>,the <a href="msualg_1.html#U4">Sorts</a> of <span class="p1">(<span class="default"><a href="catalg_1.html#K13" target="_self">MSAlg</a> <font color="Maroon">C1</font></span>)</span>
 ;<br/>

<a NAME="E7:76"/>
( <font color="Maroon">F</font> <a href="funct_2.html#K3">.</a> <font color="Maroon">f</font> <a href="hidden.html#R2">in</a>  <a href="cat_1.html#K6">Hom</a> <span class="p1">(<span class="default"><font color="Maroon">F</font> <a href="cat_1.html#K13">.</a> <font color="Maroon">a</font></span>)</span>,<span class="p1">(<span class="default"><font color="Maroon">F</font> <a href="cat_1.html#K13">.</a> <font color="Maroon">b</font></span>)</span> &amp; <font color="Maroon">F</font> <a href="funct_2.html#K3">.</a> <font color="Maroon">g</font> <a href="hidden.html#R2">in</a>  <a href="cat_1.html#K6">Hom</a> <span class="p1">(<span class="default"><font color="Maroon">F</font> <a href="cat_1.html#K13">.</a> <font color="Maroon">b</font></span>)</span>,<span class="p1">(<span class="default"><font color="Maroon">F</font> <a href="cat_1.html#K13">.</a> <font color="Maroon">c</font></span>)</span> )
 
<b>by </b><i>, <a class="ref" href="cat_1.html#T123">CAT_1:123</a></i>;<br/>
<a NAME="E8:76"/><b>then </b>
(  <a href="cat_1.html#K2">dom</a> <span class="p1">(<span class="default"><font color="Maroon">F</font> <a href="funct_2.html#K3">.</a> <font color="Maroon">f</font></span>)</span> <a href="hidden.html#R1">=</a> <font color="Maroon">F</font> <a href="cat_1.html#K13">.</a> <font color="Maroon">a</font> &amp;  <a href="cat_1.html#K3">cod</a> <span class="p1">(<span class="default"><font color="Maroon">F</font> <a href="funct_2.html#K3">.</a> <font color="Maroon">f</font></span>)</span> <a href="hidden.html#R1">=</a> <font color="Maroon">F</font> <a href="cat_1.html#K13">.</a> <font color="Maroon">b</font> &amp;  <a href="cat_1.html#K2">dom</a> <span class="p1">(<span class="default"><font color="Maroon">F</font> <a href="funct_2.html#K3">.</a> <font color="Maroon">g</font></span>)</span> <a href="hidden.html#R1">=</a> <font color="Maroon">F</font> <a href="cat_1.html#K13">.</a> <font color="Maroon">b</font> &amp;  <a href="cat_1.html#K3">cod</a> <span class="p1">(<span class="default"><font color="Maroon">F</font> <a href="funct_2.html#K3">.</a> <font color="Maroon">g</font></span>)</span> <a href="hidden.html#R1">=</a> <font color="Maroon">F</font> <a href="cat_1.html#K13">.</a> <font color="Maroon">c</font> )
 
<b>by </b><i><a class="ref" href="cat_1.html#T18">CAT_1:18</a></i>;<br/>
<a NAME="E9:76"/><b>then </b><i><font color="Green">E74</font></i>: 
<span class="p1"><a href="finseq_4.html#K2">&lt;*</a><span class="default"><span class="p2">(<span class="default"><font color="Maroon">F</font> <a href="funct_2.html#K3">.</a> <font color="Maroon">g</font></span>)</span>,<span class="p2">(<span class="default"><font color="Maroon">F</font> <a href="funct_2.html#K3">.</a> <font color="Maroon">f</font></span>)</span></span><a href="finseq_4.html#K2">*&gt;</a></span> <a href="hidden.html#R2">in</a>  <a href="msualg_1.html#K3">Args</a> <span class="p1">(<span class="default"><a href="catalg_1.html#K10" target="_self">compsym</a> <span class="p2">(<span class="default"><font color="Maroon">F</font> <a href="cat_1.html#K13">.</a> <font color="Maroon">a</font></span>)</span>,<span class="p2">(<span class="default"><font color="Maroon">F</font> <a href="cat_1.html#K13">.</a> <font color="Maroon">b</font></span>)</span>,<span class="p2">(<span class="default"><font color="Maroon">F</font> <a href="cat_1.html#K13">.</a> <font color="Maroon">c</font></span>)</span></span>)</span>,<span class="p1">(<span class="default"><a href="catalg_1.html#K13" target="_self">MSAlg</a> <font color="Maroon">C2</font></span>)</span>
 
<b>by </b><i><a class="txt" href="catalg_1.html#E2:76"><i><font color="Green">E41</font></i></a></i>;<br/>
<a NAME="E10:76"/>
 <a href="catalg_1.html#K11" target="_self">Upsilon</a> <font color="Maroon">F</font>, <a href="catalg_1.html#K12" target="_self">Psi</a> <font color="Maroon">F</font> <a href="pua2mss1.html#R3">form_morphism_between</a>  <a href="catalg_1.html#K3" target="_self">CatSign</a> the <a href="cat_1.html#U1">Objects</a> of <font color="Maroon">C1</font>, <a href="catalg_1.html#K3" target="_self">CatSign</a> the <a href="cat_1.html#U1">Objects</a> of <font color="Maroon">C2</font>
 
<b>by </b><i><a class="ref" href="catalg_1.html#D1" target="_self">Def1</a></i>;<br/>
<b>then </b><i><font color="Green">E75</font></i>:  <a href="msualg_1.html#K3">Args</a> <span class="p1">(<span class="default"><a href="catalg_1.html#K10" target="_self">compsym</a> <font color="Maroon">a</font>,<font color="Maroon">b</font>,<font color="Maroon">c</font></span>)</span>,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="catalg_1.html#K13" target="_self">MSAlg</a> <font color="Maroon">C2</font></span>)</span> <a href="instalg1.html#K1">|</a> <span class="p2">(<span class="default"><a href="catalg_1.html#K3" target="_self">CatSign</a> the <a href="cat_1.html#U1">Objects</a> of <font color="Maroon">C1</font></span>)</span>,<span class="p2">(<span class="default"><a href="catalg_1.html#K11" target="_self">Upsilon</a> <font color="Maroon">F</font></span>)</span>,<span class="p2">(<span class="default"><a href="catalg_1.html#K12" target="_self">Psi</a> <font color="Maroon">F</font></span>)</span></span>)</span> = 
 <a href="msualg_1.html#K3">Args</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="catalg_1.html#K12" target="_self">Psi</a> <font color="Maroon">F</font></span>)</span> <a href="funct_2.html#K3">.</a> <span class="p2">(<span class="default"><a href="catalg_1.html#K10" target="_self">compsym</a> <font color="Maroon">a</font>,<font color="Maroon">b</font>,<font color="Maroon">c</font></span>)</span></span>)</span>,<span class="p1">(<span class="default"><a href="catalg_1.html#K13" target="_self">MSAlg</a> <font color="Maroon">C2</font></span>)</span>
<b>by </b><i><a class="ref" href="instalg1.html#T25">INSTALG1:25</a></i>
<br/>.= 
 <a href="msualg_1.html#K3">Args</a> <span class="p1">(<span class="default"><a href="catalg_1.html#K10" target="_self">compsym</a> <span class="p2">(<span class="default"><font color="Maroon">F</font> <a href="cat_1.html#K13">.</a> <font color="Maroon">a</font></span>)</span>,<span class="p2">(<span class="default"><font color="Maroon">F</font> <a href="cat_1.html#K13">.</a> <font color="Maroon">b</font></span>)</span>,<span class="p2">(<span class="default"><font color="Maroon">F</font> <a href="cat_1.html#K13">.</a> <font color="Maroon">c</font></span>)</span></span>)</span>,<span class="p1">(<span class="default"><a href="catalg_1.html#K13" target="_self">MSAlg</a> <font color="Maroon">C2</font></span>)</span>
<b>by </b><i/>
;<br/>
<b>then consider </b><font color="Maroon">g'</font> being   <a href="cat_1.html#NM2">Morphism</a> of <font color="Maroon">C2</font>, <font color="Maroon">f'</font> being   <a href="cat_1.html#NM2">Morphism</a> of <font color="Maroon">C2</font><b> such that </b><br/><a NAME="E13:76"/><i><font color="Green">E76</font></i>: 
( <font color="Maroon">H</font> <a href="msualg_3.html#K5">#</a> <font color="Maroon">x</font> <a href="hidden.html#R1">=</a> <span class="p1"><a href="finseq_4.html#K2">&lt;*</a><span class="default"><font color="Maroon">g'</font>,<font color="Maroon">f'</font></span><a href="finseq_4.html#K2">*&gt;</a></span> &amp;  <a href="cat_1.html#K2">dom</a> <font color="Maroon">f'</font> <a href="hidden.html#R1">=</a> <font color="Maroon">F</font> <a href="cat_1.html#K13">.</a> <font color="Maroon">a</font> &amp;  <a href="cat_1.html#K3">cod</a> <font color="Maroon">f'</font> <a href="hidden.html#R1">=</a> <font color="Maroon">F</font> <a href="cat_1.html#K13">.</a> <font color="Maroon">b</font> &amp;  <a href="cat_1.html#K2">dom</a> <font color="Maroon">g'</font> <a href="hidden.html#R1">=</a> <font color="Maroon">F</font> <a href="cat_1.html#K13">.</a> <font color="Maroon">b</font> &amp;  <a href="cat_1.html#K3">cod</a> <font color="Maroon">g'</font> <a href="hidden.html#R1">=</a> <font color="Maroon">F</font> <a href="cat_1.html#K13">.</a> <font color="Maroon">c</font> )
 <b>by </b><i>, <a class="txt" href="catalg_1.html#E2:76"><i><font color="Green">E41</font></i></a></i>;<br/>
<a NAME="E14:76"/>
 <a href="finseq_1.html#K4">dom</a> <span class="p1"><a href="finseq_4.html#K2">&lt;*</a><span class="default"><span class="p2">(<span class="default"><a href="catalg_1.html#K9" target="_self">homsym</a> <font color="Maroon">b</font>,<font color="Maroon">c</font></span>)</span>,<span class="p2">(<span class="default"><a href="catalg_1.html#K9" target="_self">homsym</a> <font color="Maroon">a</font>,<font color="Maroon">b</font></span>)</span></span><a href="finseq_4.html#K2">*&gt;</a></span> <a href="hidden.html#R1">=</a>  <a href="finseq_1.html#K2">Seg</a> 2
 
<b>by </b><i><a class="ref" href="finseq_3.html#T29">FINSEQ_3:29</a></i>;<br/>
<a NAME="E15:76"/><b>then </b>
( 1 <a href="hidden.html#R2">in</a>  <a href="finseq_1.html#K4">dom</a> <span class="p1"><a href="finseq_4.html#K2">&lt;*</a><span class="default"><span class="p2">(<span class="default"><a href="catalg_1.html#K9" target="_self">homsym</a> <font color="Maroon">b</font>,<font color="Maroon">c</font></span>)</span>,<span class="p2">(<span class="default"><a href="catalg_1.html#K9" target="_self">homsym</a> <font color="Maroon">a</font>,<font color="Maroon">b</font></span>)</span></span><a href="finseq_4.html#K2">*&gt;</a></span> &amp; 2 <a href="hidden.html#R2">in</a>  <a href="finseq_1.html#K4">dom</a> <span class="p1"><a href="finseq_4.html#K2">&lt;*</a><span class="default"><span class="p2">(<span class="default"><a href="catalg_1.html#K9" target="_self">homsym</a> <font color="Maroon">b</font>,<font color="Maroon">c</font></span>)</span>,<span class="p2">(<span class="default"><a href="catalg_1.html#K9" target="_self">homsym</a> <font color="Maroon">a</font>,<font color="Maroon">b</font></span>)</span></span><a href="finseq_4.html#K2">*&gt;</a></span> &amp;  <a href="msualg_1.html#K1">the_arity_of</a> <span class="p1">(<span class="default"><a href="catalg_1.html#K10" target="_self">compsym</a> <font color="Maroon">a</font>,<font color="Maroon">b</font>,<font color="Maroon">c</font></span>)</span> <a href="hidden.html#R1">=</a> <span class="p1"><a href="finseq_4.html#K2">&lt;*</a><span class="default"><span class="p2">(<span class="default"><a href="catalg_1.html#K9" target="_self">homsym</a> <font color="Maroon">b</font>,<font color="Maroon">c</font></span>)</span>,<span class="p2">(<span class="default"><a href="catalg_1.html#K9" target="_self">homsym</a> <font color="Maroon">a</font>,<font color="Maroon">b</font></span>)</span></span><a href="finseq_4.html#K2">*&gt;</a></span> )
 
<b>by </b><i>, <a class="ref" href="finseq_1.html#T4">FINSEQ_1:4</a>, <a class="ref" href="tarski.html#D2">TARSKI:def 2</a></i>;<br/>
<a NAME="E16:76"/><b>then </b><i><font color="Green">E77</font></i>: 
( <span class="p1">(<span class="default"><a href="msualg_1.html#K1">the_arity_of</a> <span class="p2">(<span class="default"><a href="catalg_1.html#K10" target="_self">compsym</a> <font color="Maroon">a</font>,<font color="Maroon">b</font>,<font color="Maroon">c</font></span>)</span></span>)</span> <a href="finseq_4.html#K4">/.</a> 1 <a href="hidden.html#R1">=</a>  <a href="catalg_1.html#K9" target="_self">homsym</a> <font color="Maroon">b</font>,<font color="Maroon">c</font> &amp; <span class="p1">(<span class="default"><a href="msualg_1.html#K1">the_arity_of</a> <span class="p2">(<span class="default"><a href="catalg_1.html#K10" target="_self">compsym</a> <font color="Maroon">a</font>,<font color="Maroon">b</font>,<font color="Maroon">c</font></span>)</span></span>)</span> <a href="finseq_4.html#K4">/.</a> 2 <a href="hidden.html#R1">=</a>  <a href="catalg_1.html#K9" target="_self">homsym</a> <font color="Maroon">a</font>,<font color="Maroon">b</font> )
 
<b>by </b><i><a class="ref" href="finseq_4.html#T26">FINSEQ_4:26</a></i>;<br/>
<a NAME="E17:76"/>
( the <a href="msualg_1.html#U4">Sorts</a> of <span class="p1">(<span class="default"><a href="catalg_1.html#K13" target="_self">MSAlg</a> <font color="Maroon">C1</font></span>)</span> <a href="funct_1.html#K1">.</a> <span class="p1">(<span class="default"><a href="catalg_1.html#K9" target="_self">homsym</a> <font color="Maroon">a</font>,<font color="Maroon">b</font></span>)</span> <a href="hidden.html#R1">=</a>  <a href="cat_1.html#K6">Hom</a> <font color="Maroon">a</font>,<font color="Maroon">b</font> &amp; the <a href="msualg_1.html#U4">Sorts</a> of <span class="p1">(<span class="default"><a href="catalg_1.html#K13" target="_self">MSAlg</a> <font color="Maroon">C1</font></span>)</span> <a href="funct_1.html#K1">.</a> <span class="p1">(<span class="default"><a href="catalg_1.html#K9" target="_self">homsym</a> <font color="Maroon">b</font>,<font color="Maroon">c</font></span>)</span> <a href="hidden.html#R1">=</a>  <a href="cat_1.html#K6">Hom</a> <font color="Maroon">b</font>,<font color="Maroon">c</font> )
 
<b>by </b><i><a class="txt" href="catalg_1.html#E1:76"><i><font color="Green">E37</font></i></a></i>;<br/>
<a NAME="E18:76"/><b>then </b>
( <font color="Maroon">H</font> <a href="msualg_3.html#K1">.</a> <span class="p1">(<span class="default"><a href="catalg_1.html#K9" target="_self">homsym</a> <font color="Maroon">a</font>,<font color="Maroon">b</font></span>)</span> <a href="hidden.html#R1">=</a> <font color="Maroon">F</font> <a href="partfun1.html#K2">|</a> <span class="p1">(<span class="default"><a href="cat_1.html#K6">Hom</a> <font color="Maroon">a</font>,<font color="Maroon">b</font></span>)</span> &amp; <font color="Maroon">H</font> <a href="msualg_3.html#K1">.</a> <span class="p1">(<span class="default"><a href="catalg_1.html#K9" target="_self">homsym</a> <font color="Maroon">b</font>,<font color="Maroon">c</font></span>)</span> <a href="hidden.html#R1">=</a> <font color="Maroon">F</font> <a href="partfun1.html#K2">|</a> <span class="p1">(<span class="default"><a href="cat_1.html#K6">Hom</a> <font color="Maroon">b</font>,<font color="Maroon">c</font></span>)</span> )
 
<b>by </b><i><a class="ref" href="catalg_1.html#T4" target="_self">Th4</a>, </i>;<br/>
<a NAME="E19:76"/><b>then </b><i><font color="Green">E78</font></i>: 
( <span class="p1">(<span class="default"><font color="Maroon">H</font> <a href="msualg_3.html#K1">.</a> <span class="p2">(<span class="default"><a href="catalg_1.html#K9" target="_self">homsym</a> <font color="Maroon">a</font>,<font color="Maroon">b</font></span>)</span></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">f</font> <a href="hidden.html#R1">=</a> <font color="Maroon">F</font> <a href="funct_2.html#K3">.</a> <font color="Maroon">f</font> &amp; <span class="p1">(<span class="default"><font color="Maroon">H</font> <a href="msualg_3.html#K1">.</a> <span class="p2">(<span class="default"><a href="catalg_1.html#K9" target="_self">homsym</a> <font color="Maroon">b</font>,<font color="Maroon">c</font></span>)</span></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">g</font> <a href="hidden.html#R1">=</a> <font color="Maroon">F</font> <a href="funct_2.html#K3">.</a> <font color="Maroon">g</font> )
 
<b>by </b><i>, <a class="ref" href="funct_1.html#T72">FUNCT_1:72</a></i>;<br/>
<a NAME="E20:76"/>
 <a href="finseq_1.html#K4">dom</a> <span class="p1"><a href="finseq_4.html#K2">&lt;*</a><span class="default"><font color="Maroon">g</font>,<font color="Maroon">f</font></span><a href="finseq_4.html#K2">*&gt;</a></span> <a href="hidden.html#R1">=</a>  <a href="finseq_1.html#K2">Seg</a> 2
 
<b>by </b><i><a class="ref" href="finseq_3.html#T29">FINSEQ_3:29</a></i>;<br/>
<a NAME="E21:76"/><b>then </b>
( 1 <a href="hidden.html#R2">in</a>  <a href="finseq_1.html#K4">dom</a> <span class="p1"><a href="finseq_4.html#K2">&lt;*</a><span class="default"><font color="Maroon">g</font>,<font color="Maroon">f</font></span><a href="finseq_4.html#K2">*&gt;</a></span> &amp; 2 <a href="hidden.html#R2">in</a>  <a href="finseq_1.html#K4">dom</a> <span class="p1"><a href="finseq_4.html#K2">&lt;*</a><span class="default"><font color="Maroon">g</font>,<font color="Maroon">f</font></span><a href="finseq_4.html#K2">*&gt;</a></span> )
 
<b>by </b><i><a class="ref" href="finseq_1.html#T4">FINSEQ_1:4</a>, <a class="ref" href="tarski.html#D2">TARSKI:def 2</a></i>;<br/>
<a NAME="E22:76"/><b>then </b>
( <span class="p1"><a href="finseq_4.html#K2">&lt;*</a><span class="default"><font color="Maroon">g'</font>,<font color="Maroon">f'</font></span><a href="finseq_4.html#K2">*&gt;</a></span> <a href="funct_1.html#K1">.</a> 2 <a href="hidden.html#R1">=</a> <font color="Maroon">F</font> <a href="funct_2.html#K3">.</a> <font color="Maroon">f</font> &amp; <span class="p1"><a href="finseq_4.html#K2">&lt;*</a><span class="default"><font color="Maroon">g'</font>,<font color="Maroon">f'</font></span><a href="finseq_4.html#K2">*&gt;</a></span> <a href="funct_1.html#K1">.</a> 1 <a href="hidden.html#R1">=</a> <font color="Maroon">F</font> <a href="funct_2.html#K3">.</a> <font color="Maroon">g</font> &amp; <span class="p1"><a href="finseq_4.html#K2">&lt;*</a><span class="default"><font color="Maroon">g'</font>,<font color="Maroon">f'</font></span><a href="finseq_4.html#K2">*&gt;</a></span> <a href="funct_1.html#K1">.</a> 1 <a href="hidden.html#R1">=</a> <font color="Maroon">g'</font> &amp; <span class="p1"><a href="finseq_4.html#K2">&lt;*</a><span class="default"><font color="Maroon">g'</font>,<font color="Maroon">f'</font></span><a href="finseq_4.html#K2">*&gt;</a></span> <a href="funct_1.html#K1">.</a> 2 <a href="hidden.html#R1">=</a> <font color="Maroon">f'</font> )
 
<b>by </b><i>, <a class="txt" href="catalg_1.html#E5:76"><i><font color="Green">E45</font></i></a>, <a class="txt" href="catalg_1.html#E6:76"><i><font color="Green">E46</font></i></a>, , , <a class="ref" href="catalg_1.html#T5" target="_self">Th5</a>, <a class="txt" href="catalg_1.html#E8"><i><font color="Green">Lemma51</font></i></a>, , <a class="ref" href="finseq_1.html#T61">FINSEQ_1:61</a>, <a class="ref" href="msualg_3.html#T24">MSUALG_3:24</a></i>;<br/>
<b>hence </b><a NAME="E23:76"/>
<font color="Maroon">H</font> <a href="msualg_3.html#K5">#</a> <font color="Maroon">x</font> <a href="hidden.html#R1">=</a> <span class="p1"><a href="finseq_4.html#K2">&lt;*</a><span class="default"><span class="p2">(<span class="default"><font color="Maroon">F</font> <a href="funct_2.html#K3">.</a> <font color="Maroon">g</font></span>)</span>,<span class="p2">(<span class="default"><font color="Maroon">F</font> <a href="funct_2.html#K3">.</a> <font color="Maroon">f</font></span>)</span></span><a href="finseq_4.html#K2">*&gt;</a></span>
 <b>by </b><i><a class="ref" href="catalg_1.html#T5" target="_self">Th5</a></i>;<br/>


</div>
