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

<b>set </b><font color="Maroon" title="c2">X</font> = the <a href="graph_1.html#U2" title="GRAPH_1:sel.2">Edges</a> of <span class="p1"><a href="cat_2.html#K11" title="CAT_2:func.11">[:</a><span class="default"><font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c1">C</font></span><a href="cat_2.html#K11" title="CAT_2:func.11">:]</a></span>;<br/>
<b>set </b><font color="Maroon" title="c3">Y</font> =  <a href="ens_1.html#K2" title="ENS_1:func.2">Maps</a> <span class="p1">(<span class="default"><a href="ens_1.html#K17" title="ENS_1:func.17">Hom</a> <font color="Maroon" title="c1">C</font></span>)</span>;<br/>
<b>defpred </b><font color="Maroon">S<sub>1</sub></font>[   <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a> ,   <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a> ] <b>means </b>for <font color="Olive" title="b1">f</font>, <font color="Olive" title="b2">g</font> being  <a href="cat_1.html#NM2" title="CAT_1:NM.2">Morphism</a> of <font color="Maroon" title="c1">C</font>  st $1 <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1"><a href="cat_2.html#K13" title="CAT_2:func.13">[</a><span class="default"><font color="Olive" title="b1">f</font>,<font color="Olive" title="b2">g</font></span><a href="cat_2.html#K13" title="CAT_2:func.13">]</a></span> holds <br/>$2 <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1"><a href="domain_1.html#K1" title="DOMAIN_1:func.1">[</a><span class="default"><span class="p2"><a href="domain_1.html#K1" title="DOMAIN_1:func.1">[</a><span class="default"><span class="p3">(<span class="default"><a href="cat_1.html#K7" title="CAT_1:func.7">Hom</a> <span class="p4">(<span class="default"><a href="cat_1.html#K4" title="CAT_1:func.4">cod</a> <font color="Olive" title="b1">f</font></span>)</span>,<span class="p4">(<span class="default"><a href="cat_1.html#K3" title="CAT_1:func.3">dom</a> <font color="Olive" title="b2">g</font></span>)</span></span>)</span>,<span class="p3">(<span class="default"><a href="cat_1.html#K7" title="CAT_1:func.7">Hom</a> <span class="p4">(<span class="default"><a href="cat_1.html#K3" title="CAT_1:func.3">dom</a> <font color="Olive" title="b1">f</font></span>)</span>,<span class="p4">(<span class="default"><a href="cat_1.html#K4" title="CAT_1:func.4">cod</a> <font color="Olive" title="b2">g</font></span>)</span></span>)</span></span><a href="domain_1.html#K1" title="DOMAIN_1:func.1">]</a></span>,<span class="p2">(<span class="default"><a href="ens_1.html#K22" title="ENS_1:func.22">hom</a> <font color="Olive" title="b1">f</font>,<font color="Olive" title="b2">g</font></span>)</span></span><a href="domain_1.html#K1" title="DOMAIN_1:func.1">]</a></span>;<br/>
<a NAME="E1:81_1_1"/><i><font color="Green" title="E56">A1</font></i>: 
for <font color="Olive" title="b1">x</font> being   <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a>   st <font color="Olive" title="b1">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> the <a href="graph_1.html#U2" title="GRAPH_1:sel.2">Edges</a> of <span class="p1"><a href="cat_2.html#K11" title="CAT_2:func.11">[:</a><span class="default"><font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c1">C</font></span><a href="cat_2.html#K11" title="CAT_2:func.11">:]</a></span> holds <br/> ex <font color="Olive" title="b2">y</font> being   <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a>  st <br/>( <font color="Olive" title="b2">y</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="ens_1.html#K2" title="ENS_1:func.2">Maps</a> <span class="p1">(<span class="default"><a href="ens_1.html#K17" title="ENS_1:func.17">Hom</a> <font color="Maroon" title="c1">C</font></span>)</span> &amp; <font color="Maroon">S<sub>1</sub></font>[<font color="Olive" title="b1">x</font>,<font color="Olive" title="b2">y</font>] )
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="81_1_1_1"><b>proof </b></a><div class="add">

<b>let </b><font color="Maroon" title="c4">x</font> be    <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a> ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> ( <font color="Maroon" title="c4">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> the <a href="graph_1.html#U2" title="GRAPH_1:sel.2">Edges</a> of <span class="p1"><a href="cat_2.html#K11" title="CAT_2:func.11">[:</a><span class="default"><font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c1">C</font></span><a href="cat_2.html#K11" title="CAT_2:func.11">:]</a></span> implies  ex <font color="Olive" title="b1">y</font> being   <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a>  st <br/>( <font color="Olive" title="b1">y</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="ens_1.html#K2" title="ENS_1:func.2">Maps</a> <span class="p1">(<span class="default"><a href="ens_1.html#K17" title="ENS_1:func.17">Hom</a> <font color="Maroon" title="c1">C</font></span>)</span> &amp; <font color="Maroon">S<sub>1</sub></font>[<font color="Maroon" title="c4">x</font>,<font color="Olive" title="b1">y</font>] ) )</span><br/>

<b>assume </b><a NAME="E1:81_1_1_1"/>
<font color="Maroon" title="c4">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> the <a href="graph_1.html#U2" title="GRAPH_1:sel.2">Edges</a> of <span class="p1"><a href="cat_2.html#K11" title="CAT_2:func.11">[:</a><span class="default"><font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c1">C</font></span><a href="cat_2.html#K11" title="CAT_2:func.11">:]</a></span>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide">  ex <font color="Olive" title="b1">y</font> being   <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a>  st <br/>( <font color="Olive" title="b1">y</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="ens_1.html#K2" title="ENS_1:func.2">Maps</a> <span class="p1">(<span class="default"><a href="ens_1.html#K17" title="ENS_1:func.17">Hom</a> <font color="Maroon" title="c1">C</font></span>)</span> &amp; <font color="Maroon">S<sub>1</sub></font>[<font color="Maroon" title="c4">x</font>,<font color="Olive" title="b1">y</font>] )</span><br/>

<b>then consider </b><font color="Maroon" title="c5">f</font>, <font color="Maroon" title="c6">g</font> being   <a href="cat_1.html#NM2" title="CAT_1:NM.2">Morphism</a> of <font color="Maroon" title="c1">C</font><b> such that </b><br/><a NAME="E3:81_1_1_1"/><i><font color="Green" title="E57">A2</font></i>: 
<font color="Maroon" title="c4">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1"><a href="cat_2.html#K13" title="CAT_2:func.13">[</a><span class="default"><font color="Maroon" title="c5">f</font>,<font color="Maroon" title="c6">g</font></span><a href="cat_2.html#K13" title="CAT_2:func.13">]</a></span>
 <b>by </b><i><a class="ref" href="domain_1.html#T9" title="DOMAIN_1:th.9">DOMAIN_1:9</a></i>;<br/>
<b>take </b><font color="Maroon" title="c7">y</font> = <span class="p1"><a href="domain_1.html#K1" title="DOMAIN_1:func.1">[</a><span class="default"><span class="p2"><a href="domain_1.html#K1" title="DOMAIN_1:func.1">[</a><span class="default"><span class="p3">(<span class="default"><a href="cat_1.html#K7" title="CAT_1:func.7">Hom</a> <span class="p4">(<span class="default"><a href="cat_1.html#K4" title="CAT_1:func.4">cod</a> <font color="Maroon" title="c5">f</font></span>)</span>,<span class="p4">(<span class="default"><a href="cat_1.html#K3" title="CAT_1:func.3">dom</a> <font color="Maroon" title="c6">g</font></span>)</span></span>)</span>,<span class="p3">(<span class="default"><a href="cat_1.html#K7" title="CAT_1:func.7">Hom</a> <span class="p4">(<span class="default"><a href="cat_1.html#K3" title="CAT_1:func.3">dom</a> <font color="Maroon" title="c5">f</font></span>)</span>,<span class="p4">(<span class="default"><a href="cat_1.html#K4" title="CAT_1:func.4">cod</a> <font color="Maroon" title="c6">g</font></span>)</span></span>)</span></span><a href="domain_1.html#K1" title="DOMAIN_1:func.1">]</a></span>,<span class="p2">(<span class="default"><a href="ens_1.html#K22" title="ENS_1:func.22">hom</a> <font color="Maroon" title="c5">f</font>,<font color="Maroon" title="c6">g</font></span>)</span></span><a href="domain_1.html#K1" title="DOMAIN_1:func.1">]</a></span>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> ( <font color="Maroon" title="c7">y</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="ens_1.html#K2" title="ENS_1:func.2">Maps</a> <span class="p1">(<span class="default"><a href="ens_1.html#K17" title="ENS_1:func.17">Hom</a> <font color="Maroon" title="c1">C</font></span>)</span> &amp; <font color="Maroon">S<sub>1</sub></font>[<font color="Maroon" title="c4">x</font>,<font color="Maroon" title="c7">y</font>] )</span><br/>

<a NAME="E4:81_1_1_1"/>
<font color="Maroon" title="c7">y</font> is    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of  <a href="ens_1.html#K2" title="ENS_1:func.2">Maps</a> <span class="p1">(<span class="default"><a href="ens_1.html#K17" title="ENS_1:func.17">Hom</a> <font color="Maroon" title="c1">C</font></span>)</span>
 
<b>by </b><i><a class="ref" href="ens_1.html#T52" target="_self" title="ENS_1:th.52">Th52</a></i>;<br/>
<b>hence </b><a NAME="E5:81_1_1_1"/>
<font color="Maroon" title="c7">y</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="ens_1.html#K2" title="ENS_1:func.2">Maps</a> <span class="p1">(<span class="default"><a href="ens_1.html#K17" title="ENS_1:func.17">Hom</a> <font color="Maroon" title="c1">C</font></span>)</span>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> <font color="Maroon">S<sub>1</sub></font>[<font color="Maroon" title="c4">x</font>,<font color="Maroon" title="c7">y</font>]</span><br/>

<b>let </b><font color="Maroon" title="c8">f'</font>, <font color="Maroon" title="c9">g'</font> be   <a href="cat_1.html#NM2" title="CAT_1:NM.2">Morphism</a> of <font color="Maroon" title="c1">C</font>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> ( <font color="Maroon" title="c4">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1"><a href="cat_2.html#K13" title="CAT_2:func.13">[</a><span class="default"><font color="Maroon" title="c8">f'</font>,<font color="Maroon" title="c9">g'</font></span><a href="cat_2.html#K13" title="CAT_2:func.13">]</a></span> implies <font color="Maroon" title="c7">y</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1"><a href="domain_1.html#K1" title="DOMAIN_1:func.1">[</a><span class="default"><span class="p2"><a href="domain_1.html#K1" title="DOMAIN_1:func.1">[</a><span class="default"><span class="p3">(<span class="default"><a href="cat_1.html#K7" title="CAT_1:func.7">Hom</a> <span class="p4">(<span class="default"><a href="cat_1.html#K4" title="CAT_1:func.4">cod</a> <font color="Maroon" title="c8">f'</font></span>)</span>,<span class="p4">(<span class="default"><a href="cat_1.html#K3" title="CAT_1:func.3">dom</a> <font color="Maroon" title="c9">g'</font></span>)</span></span>)</span>,<span class="p3">(<span class="default"><a href="cat_1.html#K7" title="CAT_1:func.7">Hom</a> <span class="p4">(<span class="default"><a href="cat_1.html#K3" title="CAT_1:func.3">dom</a> <font color="Maroon" title="c8">f'</font></span>)</span>,<span class="p4">(<span class="default"><a href="cat_1.html#K4" title="CAT_1:func.4">cod</a> <font color="Maroon" title="c9">g'</font></span>)</span></span>)</span></span><a href="domain_1.html#K1" title="DOMAIN_1:func.1">]</a></span>,<span class="p2">(<span class="default"><a href="ens_1.html#K22" title="ENS_1:func.22">hom</a> <font color="Maroon" title="c8">f'</font>,<font color="Maroon" title="c9">g'</font></span>)</span></span><a href="domain_1.html#K1" title="DOMAIN_1:func.1">]</a></span> )</span><br/>



<b>assume </b><a NAME="E6:81_1_1_1"/>
<font color="Maroon" title="c4">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1"><a href="cat_2.html#K13" title="CAT_2:func.13">[</a><span class="default"><font color="Maroon" title="c8">f'</font>,<font color="Maroon" title="c9">g'</font></span><a href="cat_2.html#K13" title="CAT_2:func.13">]</a></span>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> <font color="Maroon" title="c7">y</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1"><a href="domain_1.html#K1" title="DOMAIN_1:func.1">[</a><span class="default"><span class="p2"><a href="domain_1.html#K1" title="DOMAIN_1:func.1">[</a><span class="default"><span class="p3">(<span class="default"><a href="cat_1.html#K7" title="CAT_1:func.7">Hom</a> <span class="p4">(<span class="default"><a href="cat_1.html#K4" title="CAT_1:func.4">cod</a> <font color="Maroon" title="c8">f'</font></span>)</span>,<span class="p4">(<span class="default"><a href="cat_1.html#K3" title="CAT_1:func.3">dom</a> <font color="Maroon" title="c9">g'</font></span>)</span></span>)</span>,<span class="p3">(<span class="default"><a href="cat_1.html#K7" title="CAT_1:func.7">Hom</a> <span class="p4">(<span class="default"><a href="cat_1.html#K3" title="CAT_1:func.3">dom</a> <font color="Maroon" title="c8">f'</font></span>)</span>,<span class="p4">(<span class="default"><a href="cat_1.html#K4" title="CAT_1:func.4">cod</a> <font color="Maroon" title="c9">g'</font></span>)</span></span>)</span></span><a href="domain_1.html#K1" title="DOMAIN_1:func.1">]</a></span>,<span class="p2">(<span class="default"><a href="ens_1.html#K22" title="ENS_1:func.22">hom</a> <font color="Maroon" title="c8">f'</font>,<font color="Maroon" title="c9">g'</font></span>)</span></span><a href="domain_1.html#K1" title="DOMAIN_1:func.1">]</a></span></span><br/>

<a NAME="E7:81_1_1_1"/><b>then </b>
( <font color="Maroon" title="c8">f'</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c5">f</font> &amp; <font color="Maroon" title="c9">g'</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c6">g</font> )
 
<b>by </b><i><a class="txt" href="ens_1.html#E3:81_1_1_1"><i><font color="Green" title="E57">A2</font></i></a>, <a class="ref" href="zfmisc_1.html#T33" title="ZFMISC_1:th.33">ZFMISC_1:33</a></i>;<br/>
<b>hence </b><a NAME="E8:81_1_1_1"/>
<font color="Maroon" title="c7">y</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1"><a href="domain_1.html#K1" title="DOMAIN_1:func.1">[</a><span class="default"><span class="p2"><a href="domain_1.html#K1" title="DOMAIN_1:func.1">[</a><span class="default"><span class="p3">(<span class="default"><a href="cat_1.html#K7" title="CAT_1:func.7">Hom</a> <span class="p4">(<span class="default"><a href="cat_1.html#K4" title="CAT_1:func.4">cod</a> <font color="Maroon" title="c8">f'</font></span>)</span>,<span class="p4">(<span class="default"><a href="cat_1.html#K3" title="CAT_1:func.3">dom</a> <font color="Maroon" title="c9">g'</font></span>)</span></span>)</span>,<span class="p3">(<span class="default"><a href="cat_1.html#K7" title="CAT_1:func.7">Hom</a> <span class="p4">(<span class="default"><a href="cat_1.html#K3" title="CAT_1:func.3">dom</a> <font color="Maroon" title="c8">f'</font></span>)</span>,<span class="p4">(<span class="default"><a href="cat_1.html#K4" title="CAT_1:func.4">cod</a> <font color="Maroon" title="c9">g'</font></span>)</span></span>)</span></span><a href="domain_1.html#K1" title="DOMAIN_1:func.1">]</a></span>,<span class="p2">(<span class="default"><a href="ens_1.html#K22" title="ENS_1:func.22">hom</a> <font color="Maroon" title="c8">f'</font>,<font color="Maroon" title="c9">g'</font></span>)</span></span><a href="domain_1.html#K1" title="DOMAIN_1:func.1">]</a></span>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> verum</span><br/>


</div><b>end;</b></div>
<b>consider </b><font color="Maroon" title="c4">h</font> being   <a href="funct_1.html#NM1" title="FUNCT_1:NM.1">Function</a><b> such that </b><br/><a NAME="E3:81_1_1"/><i><font color="Green" title="E57">A3</font></i>: 
(  <a href="relat_1.html#NK2" title="RELAT_1:NK.2">dom</a> <font color="Maroon" title="c4">h</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> the <a href="graph_1.html#U2" title="GRAPH_1:sel.2">Edges</a> of <span class="p1"><a href="cat_2.html#K11" title="CAT_2:func.11">[:</a><span class="default"><font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c1">C</font></span><a href="cat_2.html#K11" title="CAT_2:func.11">:]</a></span> &amp;  <a href="relat_1.html#K2" title="RELAT_1:func.2">rng</a> <font color="Maroon" title="c4">h</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a>  <a href="ens_1.html#K2" title="ENS_1:func.2">Maps</a> <span class="p1">(<span class="default"><a href="ens_1.html#K17" title="ENS_1:func.17">Hom</a> <font color="Maroon" title="c1">C</font></span>)</span> )
 <b>and </b><br/><a NAME="E4:81_1_1"/><i><font color="Green" title="E58">A4</font></i>: 
for <font color="Olive" title="b1">x</font> being   <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a>   st <font color="Olive" title="b1">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> the <a href="graph_1.html#U2" title="GRAPH_1:sel.2">Edges</a> of <span class="p1"><a href="cat_2.html#K11" title="CAT_2:func.11">[:</a><span class="default"><font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c1">C</font></span><a href="cat_2.html#K11" title="CAT_2:func.11">:]</a></span> holds <br/><font color="Maroon">S<sub>1</sub></font>[<font color="Olive" title="b1">x</font>,<font color="Maroon" title="c4">h</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Olive" title="b1">x</font>]
 <b>from </b><i><a class="ref" href="wellord2.html#S1" title="WELLORD2:sch.1">WELLORD2:sch 1</a>(<a class="txt" href="ens_1.html#E1:81_1_1"><i><font color="Green" title="E56">A1</font></i></a>);<br/></i>
<b>reconsider </b><font color="Maroon" title="c5">h</font> = <font color="Maroon" title="c4">h</font> as   <a href="funct_2.html#NM1" title="FUNCT_2:NM.1">Function</a> of the <a href="graph_1.html#U2" title="GRAPH_1:sel.2">Edges</a> of <span class="p1"><a href="cat_2.html#K11" title="CAT_2:func.11">[:</a><span class="default"><font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c1">C</font></span><a href="cat_2.html#K11" title="CAT_2:func.11">:]</a></span>, <a href="ens_1.html#K2" title="ENS_1:func.2">Maps</a> <span class="p1">(<span class="default"><a href="ens_1.html#K17" title="ENS_1:func.17">Hom</a> <font color="Maroon" title="c1">C</font></span>)</span> <b>by </b><i><a class="txt" href="ens_1.html#E3:81_1_1"><i><font color="Green" title="E57">A3</font></i></a>, <a class="ref" href="funct_2.html#D1" title="FUNCT_2:def.1">FUNCT_2:def 1</a>, <a class="ref" href="relset_1.html#T11" title="RELSET_1:th.11">RELSET_1:11</a></i>;<br/>
<b>take </b>
<font color="Maroon" title="c5">h</font>
; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> for <font color="Olive" title="b1">f</font>, <font color="Olive" title="b2">g</font> being  <a href="cat_1.html#NM2" title="CAT_1:NM.2">Morphism</a> of <font color="Maroon" title="c1">C</font> holds  <font color="Maroon" title="c5">h</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <span class="p1"><a href="cat_2.html#K13" title="CAT_2:func.13">[</a><span class="default"><font color="Olive" title="b1">f</font>,<font color="Olive" title="b2">g</font></span><a href="cat_2.html#K13" title="CAT_2:func.13">]</a></span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1"><a href="domain_1.html#K1" title="DOMAIN_1:func.1">[</a><span class="default"><span class="p2"><a href="domain_1.html#K1" title="DOMAIN_1:func.1">[</a><span class="default"><span class="p3">(<span class="default"><a href="cat_1.html#K7" title="CAT_1:func.7">Hom</a> <span class="p4">(<span class="default"><a href="cat_1.html#K4" title="CAT_1:func.4">cod</a> <font color="Olive" title="b1">f</font></span>)</span>,<span class="p4">(<span class="default"><a href="cat_1.html#K3" title="CAT_1:func.3">dom</a> <font color="Olive" title="b2">g</font></span>)</span></span>)</span>,<span class="p3">(<span class="default"><a href="cat_1.html#K7" title="CAT_1:func.7">Hom</a> <span class="p4">(<span class="default"><a href="cat_1.html#K3" title="CAT_1:func.3">dom</a> <font color="Olive" title="b1">f</font></span>)</span>,<span class="p4">(<span class="default"><a href="cat_1.html#K4" title="CAT_1:func.4">cod</a> <font color="Olive" title="b2">g</font></span>)</span></span>)</span></span><a href="domain_1.html#K1" title="DOMAIN_1:func.1">]</a></span>,<span class="p2">(<span class="default"><a href="ens_1.html#K22" title="ENS_1:func.22">hom</a> <font color="Olive" title="b1">f</font>,<font color="Olive" title="b2">g</font></span>)</span></span><a href="domain_1.html#K1" title="DOMAIN_1:func.1">]</a></span></span><br/>

<b>thus </b><a NAME="E6:81_1_1"/>
for <font color="Olive" title="b1">f</font>, <font color="Olive" title="b2">g</font> being  <a href="cat_1.html#NM2" title="CAT_1:NM.2">Morphism</a> of <font color="Maroon" title="c1">C</font> holds  <font color="Maroon" title="c5">h</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <span class="p1"><a href="cat_2.html#K13" title="CAT_2:func.13">[</a><span class="default"><font color="Olive" title="b1">f</font>,<font color="Olive" title="b2">g</font></span><a href="cat_2.html#K13" title="CAT_2:func.13">]</a></span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1"><a href="domain_1.html#K1" title="DOMAIN_1:func.1">[</a><span class="default"><span class="p2"><a href="domain_1.html#K1" title="DOMAIN_1:func.1">[</a><span class="default"><span class="p3">(<span class="default"><a href="cat_1.html#K7" title="CAT_1:func.7">Hom</a> <span class="p4">(<span class="default"><a href="cat_1.html#K4" title="CAT_1:func.4">cod</a> <font color="Olive" title="b1">f</font></span>)</span>,<span class="p4">(<span class="default"><a href="cat_1.html#K3" title="CAT_1:func.3">dom</a> <font color="Olive" title="b2">g</font></span>)</span></span>)</span>,<span class="p3">(<span class="default"><a href="cat_1.html#K7" title="CAT_1:func.7">Hom</a> <span class="p4">(<span class="default"><a href="cat_1.html#K3" title="CAT_1:func.3">dom</a> <font color="Olive" title="b1">f</font></span>)</span>,<span class="p4">(<span class="default"><a href="cat_1.html#K4" title="CAT_1:func.4">cod</a> <font color="Olive" title="b2">g</font></span>)</span></span>)</span></span><a href="domain_1.html#K1" title="DOMAIN_1:func.1">]</a></span>,<span class="p2">(<span class="default"><a href="ens_1.html#K22" title="ENS_1:func.22">hom</a> <font color="Olive" title="b1">f</font>,<font color="Olive" title="b2">g</font></span>)</span></span><a href="domain_1.html#K1" title="DOMAIN_1:func.1">]</a></span>
 <b>by </b><i><a class="txt" href="ens_1.html#E4:81_1_1"><i><font color="Green" title="E58">A4</font></i></a></i>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> verum</span><br/>


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