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

<span class="kw">set </span><font color="Maroon" title="c11">k22</font> = <span class="p1">(<span class="default"><font color="Maroon" title="c7">k2</font> <a href="domain_1.html#K17" title="DOMAIN_1:func.17">`22</a> </span>)</span> <a href="cat_1.html#K1" title="CAT_1:func.1">*</a> <span class="p1">(<span class="default"><font color="Maroon" title="c6">k1</font> <a href="domain_1.html#K17" title="DOMAIN_1:func.17">`22</a> </span>)</span>;<br/>
<span class="kw">set </span><font color="Maroon" title="c12">k21</font> = <span class="p1">(<span class="default"><font color="Maroon" title="c7">k2</font> <a href="domain_1.html#K16" title="DOMAIN_1:func.16">`21</a> </span>)</span> <a href="cat_1.html#K1" title="CAT_1:func.1">*</a> <span class="p1">(<span class="default"><font color="Maroon" title="c6">k1</font> <a href="domain_1.html#K16" title="DOMAIN_1:func.16">`21</a> </span>)</span>;<br/>
<a NAME="E1:8_1_1"/><span class="lab"><font color="Green" title="E7">A3</font></span>: 
( <font color="Maroon" title="c4">F</font> <a href="cat_1.html#K9" title="CAT_1:func.9">.</a> <span class="p1">(<span class="default"><a href="graph_1.html#K2" title="GRAPH_1:func.2">cod</a> <span class="p2">(<span class="default"><font color="Maroon" title="c7">k2</font> <a href="domain_1.html#K16" title="DOMAIN_1:func.16">`21</a> </span>)</span></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="graph_1.html#K2" title="GRAPH_1:func.2">cod</a> <span class="p1">(<span class="default"><font color="Maroon" title="c4">F</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <span class="p2">(<span class="default"><font color="Maroon" title="c7">k2</font> <a href="domain_1.html#K16" title="DOMAIN_1:func.16">`21</a> </span>)</span></span>)</span> &amp;  <a href="graph_1.html#K1" title="GRAPH_1:func.1">dom</a> <span class="p1">(<span class="default"><font color="Maroon" title="c4">F</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <span class="p2">(<span class="default"><font color="Maroon" title="c7">k2</font> <a href="domain_1.html#K16" title="DOMAIN_1:func.16">`21</a> </span>)</span></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c4">F</font> <a href="cat_1.html#K9" title="CAT_1:func.9">.</a> <span class="p1">(<span class="default"><a href="graph_1.html#K1" title="GRAPH_1:func.1">dom</a> <span class="p2">(<span class="default"><font color="Maroon" title="c7">k2</font> <a href="domain_1.html#K16" title="DOMAIN_1:func.16">`21</a> </span>)</span></span>)</span> )
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="cat_1.html#T109" title="CAT_1:th.109">CAT_1:109</a></span>;<br/>
<a NAME="E2:8_1_1"/><span class="lab"><font color="Green" title="E8">A4</font></span>: 
 <a href="graph_1.html#K2" title="GRAPH_1:func.2">cod</a> <span class="p1">(<span class="default"><font color="Maroon" title="c4">F</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <span class="p2">(<span class="default"><font color="Maroon" title="c6">k1</font> <a href="domain_1.html#K16" title="DOMAIN_1:func.16">`21</a> </span>)</span></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c4">F</font> <a href="cat_1.html#K9" title="CAT_1:func.9">.</a> <span class="p1">(<span class="default"><a href="graph_1.html#K2" title="GRAPH_1:func.2">cod</a> <span class="p2">(<span class="default"><font color="Maroon" title="c6">k1</font> <a href="domain_1.html#K16" title="DOMAIN_1:func.16">`21</a> </span>)</span></span>)</span>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="cat_1.html#T109" title="CAT_1:th.109">CAT_1:109</a></span>;<br/>
<a NAME="E3:8_1_1"/><span class="lab"><font color="Green" title="E9">A5</font></span>: 
 <a href="graph_1.html#K2" title="GRAPH_1:func.2">cod</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c6">k1</font> <a href="commacat.html#K4" title="COMMACAT:func.4">`12</a> </span>)</span> <a href="domain_1.html#K3" title="DOMAIN_1:func.3">`2</a> </span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c5">G</font> <a href="cat_1.html#K9" title="CAT_1:func.9">.</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c6">k1</font> <a href="commacat.html#K4" title="COMMACAT:func.4">`12</a> </span>)</span> <a href="domain_1.html#K15" title="DOMAIN_1:func.15">`12</a> </span>)</span>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:8"><span class="lab"><font color="Green" title="E5">A1</font></span></a>, <a class="ref" href="commacat.html#T2" target="_self" title="COMMACAT:th.2">Th2</a></span>;<br/>
<a NAME="E4:8_1_1"/><span class="lab"><font color="Green" title="E10">A6</font></span>: 
 <a href="graph_1.html#K1" title="GRAPH_1:func.1">dom</a> <span class="p1">(<span class="default"><font color="Maroon" title="c6">k1</font> <a href="domain_1.html#K17" title="DOMAIN_1:func.17">`22</a> </span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><font color="Maroon" title="c6">k1</font> <a href="commacat.html#K3" title="COMMACAT:func.3">`11</a> </span>)</span> <a href="domain_1.html#K15" title="DOMAIN_1:func.15">`12</a> 
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:8"><span class="lab"><font color="Green" title="E5">A1</font></span></a>, <a class="ref" href="commacat.html#T3" target="_self" title="COMMACAT:th.3">Th3</a></span>;<br/>
<a NAME="E5:8_1_1"/><span class="lab"><font color="Green" title="E11">A7</font></span>: 
( <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c7">k2</font> <a href="commacat.html#K4" title="COMMACAT:func.4">`12</a> </span>)</span> <a href="domain_1.html#K3" title="DOMAIN_1:func.3">`2</a> </span>)</span> <a href="cat_1.html#K1" title="CAT_1:func.1">*</a> <span class="p1">(<span class="default"><font color="Maroon" title="c4">F</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <span class="p2">(<span class="default"><font color="Maroon" title="c7">k2</font> <a href="domain_1.html#K16" title="DOMAIN_1:func.16">`21</a> </span>)</span></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><font color="Maroon" title="c5">G</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <span class="p2">(<span class="default"><font color="Maroon" title="c7">k2</font> <a href="domain_1.html#K17" title="DOMAIN_1:func.17">`22</a> </span>)</span></span>)</span> <a href="cat_1.html#K1" title="CAT_1:func.1">*</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c7">k2</font> <a href="commacat.html#K3" title="COMMACAT:func.3">`11</a> </span>)</span> <a href="domain_1.html#K3" title="DOMAIN_1:func.3">`2</a> </span>)</span> &amp;  <a href="graph_1.html#K1" title="GRAPH_1:func.1">dom</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c7">k2</font> <a href="commacat.html#K4" title="COMMACAT:func.4">`12</a> </span>)</span> <a href="domain_1.html#K3" title="DOMAIN_1:func.3">`2</a> </span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c4">F</font> <a href="cat_1.html#K9" title="CAT_1:func.9">.</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c7">k2</font> <a href="commacat.html#K4" title="COMMACAT:func.4">`12</a> </span>)</span> <a href="domain_1.html#K14" title="DOMAIN_1:func.14">`11</a> </span>)</span> )
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:8"><span class="lab"><font color="Green" title="E5">A1</font></span></a>, <a class="ref" href="commacat.html#T2" target="_self" title="COMMACAT:th.2">Th2</a>, <a class="ref" href="commacat.html#T3" target="_self" title="COMMACAT:th.3">Th3</a></span>;<br/>
<a NAME="E6:8_1_1"/><span class="lab"><font color="Green" title="E12">A8</font></span>: 
 <a href="graph_1.html#K2" title="GRAPH_1:func.2">cod</a> <span class="p1">(<span class="default"><font color="Maroon" title="c5">G</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <span class="p2">(<span class="default"><font color="Maroon" title="c6">k1</font> <a href="domain_1.html#K17" title="DOMAIN_1:func.17">`22</a> </span>)</span></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c5">G</font> <a href="cat_1.html#K9" title="CAT_1:func.9">.</a> <span class="p1">(<span class="default"><a href="graph_1.html#K2" title="GRAPH_1:func.2">cod</a> <span class="p2">(<span class="default"><font color="Maroon" title="c6">k1</font> <a href="domain_1.html#K17" title="DOMAIN_1:func.17">`22</a> </span>)</span></span>)</span>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="cat_1.html#T109" title="CAT_1:th.109">CAT_1:109</a></span>;<br/>
<a NAME="E7:8_1_1"/><span class="lab"><font color="Green" title="E13">A9</font></span>: 
( <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c6">k1</font> <a href="commacat.html#K4" title="COMMACAT:func.4">`12</a> </span>)</span> <a href="domain_1.html#K3" title="DOMAIN_1:func.3">`2</a> </span>)</span> <a href="cat_1.html#K1" title="CAT_1:func.1">*</a> <span class="p1">(<span class="default"><font color="Maroon" title="c4">F</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <span class="p2">(<span class="default"><font color="Maroon" title="c6">k1</font> <a href="domain_1.html#K16" title="DOMAIN_1:func.16">`21</a> </span>)</span></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><font color="Maroon" title="c5">G</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <span class="p2">(<span class="default"><font color="Maroon" title="c6">k1</font> <a href="domain_1.html#K17" title="DOMAIN_1:func.17">`22</a> </span>)</span></span>)</span> <a href="cat_1.html#K1" title="CAT_1:func.1">*</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c6">k1</font> <a href="commacat.html#K3" title="COMMACAT:func.3">`11</a> </span>)</span> <a href="domain_1.html#K3" title="DOMAIN_1:func.3">`2</a> </span>)</span> &amp;  <a href="graph_1.html#K1" title="GRAPH_1:func.1">dom</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c6">k1</font> <a href="commacat.html#K4" title="COMMACAT:func.4">`12</a> </span>)</span> <a href="domain_1.html#K3" title="DOMAIN_1:func.3">`2</a> </span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c4">F</font> <a href="cat_1.html#K9" title="CAT_1:func.9">.</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c6">k1</font> <a href="commacat.html#K4" title="COMMACAT:func.4">`12</a> </span>)</span> <a href="domain_1.html#K14" title="DOMAIN_1:func.14">`11</a> </span>)</span> )
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:8"><span class="lab"><font color="Green" title="E5">A1</font></span></a>, <a class="ref" href="commacat.html#T2" target="_self" title="COMMACAT:th.2">Th2</a>, <a class="ref" href="commacat.html#T3" target="_self" title="COMMACAT:th.3">Th3</a></span>;<br/>
<a NAME="E8:8_1_1"/><span class="lab"><font color="Green" title="E14">A10</font></span>: 
 <a href="graph_1.html#K1" title="GRAPH_1:func.1">dom</a> <span class="p1">(<span class="default"><font color="Maroon" title="c5">G</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <span class="p2">(<span class="default"><font color="Maroon" title="c7">k2</font> <a href="domain_1.html#K17" title="DOMAIN_1:func.17">`22</a> </span>)</span></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c5">G</font> <a href="cat_1.html#K9" title="CAT_1:func.9">.</a> <span class="p1">(<span class="default"><a href="graph_1.html#K1" title="GRAPH_1:func.1">dom</a> <span class="p2">(<span class="default"><font color="Maroon" title="c7">k2</font> <a href="domain_1.html#K17" title="DOMAIN_1:func.17">`22</a> </span>)</span></span>)</span>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="cat_1.html#T109" title="CAT_1:th.109">CAT_1:109</a></span>;<br/>
<a NAME="E9:8_1_1"/><span class="lab"><font color="Green" title="E15">A11</font></span>: 
(  <a href="graph_1.html#K2" title="GRAPH_1:func.2">cod</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c6">k1</font> <a href="commacat.html#K3" title="COMMACAT:func.3">`11</a> </span>)</span> <a href="domain_1.html#K3" title="DOMAIN_1:func.3">`2</a> </span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c5">G</font> <a href="cat_1.html#K9" title="CAT_1:func.9">.</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c6">k1</font> <a href="commacat.html#K3" title="COMMACAT:func.3">`11</a> </span>)</span> <a href="domain_1.html#K15" title="DOMAIN_1:func.15">`12</a> </span>)</span> &amp;  <a href="graph_1.html#K1" title="GRAPH_1:func.1">dom</a> <span class="p1">(<span class="default"><font color="Maroon" title="c5">G</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <span class="p2">(<span class="default"><font color="Maroon" title="c6">k1</font> <a href="domain_1.html#K17" title="DOMAIN_1:func.17">`22</a> </span>)</span></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c5">G</font> <a href="cat_1.html#K9" title="CAT_1:func.9">.</a> <span class="p1">(<span class="default"><a href="graph_1.html#K1" title="GRAPH_1:func.1">dom</a> <span class="p2">(<span class="default"><font color="Maroon" title="c6">k1</font> <a href="domain_1.html#K17" title="DOMAIN_1:func.17">`22</a> </span>)</span></span>)</span> )
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:8"><span class="lab"><font color="Green" title="E5">A1</font></span></a>, <a class="ref" href="commacat.html#T2" target="_self" title="COMMACAT:th.2">Th2</a>, <a class="ref" href="cat_1.html#T109" title="CAT_1:th.109">CAT_1:109</a></span>;<br/>
<a NAME="E10:8_1_1"/><span class="lab"><font color="Green" title="E16">A12</font></span>: 
 <a href="graph_1.html#K2" title="GRAPH_1:func.2">cod</a> <span class="p1">(<span class="default"><font color="Maroon" title="c7">k2</font> <a href="domain_1.html#K16" title="DOMAIN_1:func.16">`21</a> </span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><font color="Maroon" title="c7">k2</font> <a href="commacat.html#K4" title="COMMACAT:func.4">`12</a> </span>)</span> <a href="domain_1.html#K14" title="DOMAIN_1:func.14">`11</a> 
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:8"><span class="lab"><font color="Green" title="E5">A1</font></span></a>, <a class="ref" href="commacat.html#T3" target="_self" title="COMMACAT:th.3">Th3</a></span>;<br/>
<a NAME="E11:8_1_1"/><span class="lab"><font color="Green" title="E17">A13</font></span>: 
 <a href="commacat.html#K2" title="COMMACAT:func.2">commaMorphs</a> <font color="Maroon" title="c4">F</font>,<font color="Maroon" title="c5">G</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">{<span class="default"> <span class="p2"><a href="domain_1.html#K1" title="DOMAIN_1:func.1">[</a><span class="default"><span class="p3"><a href="domain_1.html#K1" title="DOMAIN_1:func.1">[</a><span class="default"><font color="Olive" title="b3">o1</font>,<font color="Olive" title="b4">o2</font></span><a href="domain_1.html#K1" title="DOMAIN_1:func.1">]</a></span>,<span class="p3"><a href="domain_1.html#K1" title="DOMAIN_1:func.1">[</a><span class="default"><font color="Olive" title="b1">g</font>,<font color="Olive" title="b2">h</font></span><a href="domain_1.html#K1" title="DOMAIN_1:func.1">]</a></span></span><a href="domain_1.html#K1" title="DOMAIN_1:func.1">]</a></span> where <font color="Olive" title="b1">g</font> is   <a href="cat_1.html#NM2" title="CAT_1:NM.2">Morphism</a> of <font color="Maroon" title="c1">C</font>, <font color="Olive" title="b2">h</font> is   <a href="cat_1.html#NM2" title="CAT_1:NM.2">Morphism</a> of <font color="Maroon" title="c2">D</font>, <font color="Olive" title="b3">o1</font>, <font color="Olive" title="b4">o2</font> is    <a href="subset_1.html#M2" title="SUBSET_1:mode.2">Element</a> of  <a href="commacat.html#K1" title="COMMACAT:func.1">commaObjs</a> <font color="Maroon" title="c4">F</font>,<font color="Maroon" title="c5">G</font> : (  <a href="graph_1.html#K1" title="GRAPH_1:func.1">dom</a> <font color="Olive" title="b1">g</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b3">o1</font> <a href="domain_1.html#K14" title="DOMAIN_1:func.14">`11</a>  &amp;  <a href="graph_1.html#K2" title="GRAPH_1:func.2">cod</a> <font color="Olive" title="b1">g</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b4">o2</font> <a href="domain_1.html#K14" title="DOMAIN_1:func.14">`11</a>  &amp;  <a href="graph_1.html#K1" title="GRAPH_1:func.1">dom</a> <font color="Olive" title="b2">h</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b3">o1</font> <a href="domain_1.html#K15" title="DOMAIN_1:func.15">`12</a>  &amp;  <a href="graph_1.html#K2" title="GRAPH_1:func.2">cod</a> <font color="Olive" title="b2">h</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b4">o2</font> <a href="domain_1.html#K15" title="DOMAIN_1:func.15">`12</a>  &amp; <span class="p1">(<span class="default"><font color="Olive" title="b4">o2</font> <a href="domain_1.html#K3" title="DOMAIN_1:func.3">`2</a> </span>)</span> <a href="cat_1.html#K1" title="CAT_1:func.1">*</a> <span class="p1">(<span class="default"><font color="Maroon" title="c4">F</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Olive" title="b1">g</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><font color="Maroon" title="c5">G</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Olive" title="b2">h</font></span>)</span> <a href="cat_1.html#K1" title="CAT_1:func.1">*</a> <span class="p1">(<span class="default"><font color="Olive" title="b3">o1</font> <a href="domain_1.html#K3" title="DOMAIN_1:func.3">`2</a> </span>)</span> ) </span>}</span> 
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:8"><span class="lab"><font color="Green" title="E5">A1</font></span></a>, <a class="ref" href="commacat.html#D6" target="_self" title="COMMACAT:def.6">Def6</a></span>;<br/>
<a NAME="E12:8_1_1"/><span class="lab"><font color="Green" title="E18">A14</font></span>: 
 <a href="graph_1.html#K1" title="GRAPH_1:func.1">dom</a> <span class="p1">(<span class="default"><font color="Maroon" title="c7">k2</font> <a href="domain_1.html#K17" title="DOMAIN_1:func.17">`22</a> </span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><font color="Maroon" title="c7">k2</font> <a href="commacat.html#K3" title="COMMACAT:func.3">`11</a> </span>)</span> <a href="domain_1.html#K15" title="DOMAIN_1:func.15">`12</a> 
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:8"><span class="lab"><font color="Green" title="E5">A1</font></span></a>, <a class="ref" href="commacat.html#T3" target="_self" title="COMMACAT:th.3">Th3</a></span>;<br/>
<a NAME="E13:8_1_1"/><span class="lab"><font color="Green" title="E19">A15</font></span>: 
 <a href="graph_1.html#K2" title="GRAPH_1:func.2">cod</a> <span class="p1">(<span class="default"><font color="Maroon" title="c6">k1</font> <a href="domain_1.html#K17" title="DOMAIN_1:func.17">`22</a> </span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><font color="Maroon" title="c6">k1</font> <a href="commacat.html#K4" title="COMMACAT:func.4">`12</a> </span>)</span> <a href="domain_1.html#K15" title="DOMAIN_1:func.15">`12</a> 
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:8"><span class="lab"><font color="Green" title="E5">A1</font></span></a>, <a class="ref" href="commacat.html#T3" target="_self" title="COMMACAT:th.3">Th3</a></span>;<br/>
<a NAME="E14:8_1_1"/><span class="kw">then </span><span class="lab"><font color="Green" title="E20">A16</font></span>: 
(  <a href="graph_1.html#K1" title="GRAPH_1:func.1">dom</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c7">k2</font> <a href="domain_1.html#K17" title="DOMAIN_1:func.17">`22</a> </span>)</span> <a href="cat_1.html#K1" title="CAT_1:func.1">*</a> <span class="p2">(<span class="default"><font color="Maroon" title="c6">k1</font> <a href="domain_1.html#K17" title="DOMAIN_1:func.17">`22</a> </span>)</span></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="graph_1.html#K1" title="GRAPH_1:func.1">dom</a> <span class="p1">(<span class="default"><font color="Maroon" title="c6">k1</font> <a href="domain_1.html#K17" title="DOMAIN_1:func.17">`22</a> </span>)</span> &amp;  <a href="graph_1.html#K2" title="GRAPH_1:func.2">cod</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c7">k2</font> <a href="domain_1.html#K17" title="DOMAIN_1:func.17">`22</a> </span>)</span> <a href="cat_1.html#K1" title="CAT_1:func.1">*</a> <span class="p2">(<span class="default"><font color="Maroon" title="c6">k1</font> <a href="domain_1.html#K17" title="DOMAIN_1:func.17">`22</a> </span>)</span></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="graph_1.html#K2" title="GRAPH_1:func.2">cod</a> <span class="p1">(<span class="default"><font color="Maroon" title="c7">k2</font> <a href="domain_1.html#K17" title="DOMAIN_1:func.17">`22</a> </span>)</span> )
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E3:8"><span class="lab"><font color="Green" title="E6">A2</font></span></a>, <a class="txt" href="#E12:8_1_1"><span class="lab"><font color="Green" title="E18">A14</font></span></a>, <a class="ref" href="cat_1.html#T42" title="CAT_1:th.42">CAT_1:42</a></span>;<br/>
<a NAME="E15:8_1_1"/><span class="lab"><font color="Green" title="E21">A17</font></span>: 
(  <a href="graph_1.html#K1" title="GRAPH_1:func.1">dom</a> <span class="p1">(<span class="default"><font color="Maroon" title="c6">k1</font> <a href="domain_1.html#K16" title="DOMAIN_1:func.16">`21</a> </span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><font color="Maroon" title="c6">k1</font> <a href="commacat.html#K3" title="COMMACAT:func.3">`11</a> </span>)</span> <a href="domain_1.html#K14" title="DOMAIN_1:func.14">`11</a>  &amp;  <a href="graph_1.html#K2" title="GRAPH_1:func.2">cod</a> <span class="p1">(<span class="default"><font color="Maroon" title="c7">k2</font> <a href="domain_1.html#K17" title="DOMAIN_1:func.17">`22</a> </span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><font color="Maroon" title="c7">k2</font> <a href="commacat.html#K4" title="COMMACAT:func.4">`12</a> </span>)</span> <a href="domain_1.html#K15" title="DOMAIN_1:func.15">`12</a>  )
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:8"><span class="lab"><font color="Green" title="E5">A1</font></span></a>, <a class="ref" href="commacat.html#T3" target="_self" title="COMMACAT:th.3">Th3</a></span>;<br/>
<a NAME="E16:8_1_1"/><span class="lab"><font color="Green" title="E22">A18</font></span>: 
 <a href="graph_1.html#K2" title="GRAPH_1:func.2">cod</a> <span class="p1">(<span class="default"><font color="Maroon" title="c6">k1</font> <a href="domain_1.html#K16" title="DOMAIN_1:func.16">`21</a> </span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><font color="Maroon" title="c6">k1</font> <a href="commacat.html#K4" title="COMMACAT:func.4">`12</a> </span>)</span> <a href="domain_1.html#K14" title="DOMAIN_1:func.14">`11</a> 
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:8"><span class="lab"><font color="Green" title="E5">A1</font></span></a>, <a class="ref" href="commacat.html#T3" target="_self" title="COMMACAT:th.3">Th3</a></span>;<br/>
<a NAME="E17:8_1_1"/><span class="lab"><font color="Green" title="E23">A19</font></span>: 
 <a href="graph_1.html#K1" title="GRAPH_1:func.1">dom</a> <span class="p1">(<span class="default"><font color="Maroon" title="c7">k2</font> <a href="domain_1.html#K16" title="DOMAIN_1:func.16">`21</a> </span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><font color="Maroon" title="c7">k2</font> <a href="commacat.html#K3" title="COMMACAT:func.3">`11</a> </span>)</span> <a href="domain_1.html#K14" title="DOMAIN_1:func.14">`11</a> 
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:8"><span class="lab"><font color="Green" title="E5">A1</font></span></a>, <a class="ref" href="commacat.html#T3" target="_self" title="COMMACAT:th.3">Th3</a></span>;<br/>
<a NAME="E18:8_1_1"/><span class="kw">then </span><span class="lab"><font color="Green" title="E24">A20</font></span>: 
(  <a href="graph_1.html#K1" title="GRAPH_1:func.1">dom</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c7">k2</font> <a href="domain_1.html#K16" title="DOMAIN_1:func.16">`21</a> </span>)</span> <a href="cat_1.html#K1" title="CAT_1:func.1">*</a> <span class="p2">(<span class="default"><font color="Maroon" title="c6">k1</font> <a href="domain_1.html#K16" title="DOMAIN_1:func.16">`21</a> </span>)</span></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="graph_1.html#K1" title="GRAPH_1:func.1">dom</a> <span class="p1">(<span class="default"><font color="Maroon" title="c6">k1</font> <a href="domain_1.html#K16" title="DOMAIN_1:func.16">`21</a> </span>)</span> &amp;  <a href="graph_1.html#K2" title="GRAPH_1:func.2">cod</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c7">k2</font> <a href="domain_1.html#K16" title="DOMAIN_1:func.16">`21</a> </span>)</span> <a href="cat_1.html#K1" title="CAT_1:func.1">*</a> <span class="p2">(<span class="default"><font color="Maroon" title="c6">k1</font> <a href="domain_1.html#K16" title="DOMAIN_1:func.16">`21</a> </span>)</span></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="graph_1.html#K2" title="GRAPH_1:func.2">cod</a> <span class="p1">(<span class="default"><font color="Maroon" title="c7">k2</font> <a href="domain_1.html#K16" title="DOMAIN_1:func.16">`21</a> </span>)</span> )
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E3:8"><span class="lab"><font color="Green" title="E6">A2</font></span></a>, <a class="txt" href="#E16:8_1_1"><span class="lab"><font color="Green" title="E22">A18</font></span></a>, <a class="ref" href="cat_1.html#T42" title="CAT_1:th.42">CAT_1:42</a></span>;<br/>
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c7">k2</font> <a href="commacat.html#K4" title="COMMACAT:func.4">`12</a> </span>)</span> <a href="domain_1.html#K3" title="DOMAIN_1:func.3">`2</a> </span>)</span> <a href="cat_1.html#K1" title="CAT_1:func.1">*</a> <span class="p1">(<span class="default"><font color="Maroon" title="c4">F</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon" title="c7">k2</font> <a href="domain_1.html#K16" title="DOMAIN_1:func.16">`21</a> </span>)</span> <a href="cat_1.html#K1" title="CAT_1:func.1">*</a> <span class="p3">(<span class="default"><font color="Maroon" title="c6">k1</font> <a href="domain_1.html#K16" title="DOMAIN_1:func.16">`21</a> </span>)</span></span>)</span></span>)</span> = 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c7">k2</font> <a href="commacat.html#K4" title="COMMACAT:func.4">`12</a> </span>)</span> <a href="domain_1.html#K3" title="DOMAIN_1:func.3">`2</a> </span>)</span> <a href="cat_1.html#K1" title="CAT_1:func.1">*</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c4">F</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <span class="p3">(<span class="default"><font color="Maroon" title="c7">k2</font> <a href="domain_1.html#K16" title="DOMAIN_1:func.16">`21</a> </span>)</span></span>)</span> <a href="cat_1.html#K1" title="CAT_1:func.1">*</a> <span class="p2">(<span class="default"><font color="Maroon" title="c4">F</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <span class="p3">(<span class="default"><font color="Maroon" title="c6">k1</font> <a href="domain_1.html#K16" title="DOMAIN_1:func.16">`21</a> </span>)</span></span>)</span></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E3:8"><span class="lab"><font color="Green" title="E6">A2</font></span></a>, <a class="txt" href="#E16:8_1_1"><span class="lab"><font color="Green" title="E22">A18</font></span></a>, <a class="txt" href="#E17:8_1_1"><span class="lab"><font color="Green" title="E23">A19</font></span></a>, <a class="ref" href="cat_1.html#T99" title="CAT_1:th.99">CAT_1:99</a></span>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c5">G</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <span class="p3">(<span class="default"><font color="Maroon" title="c7">k2</font> <a href="domain_1.html#K17" title="DOMAIN_1:func.17">`22</a> </span>)</span></span>)</span> <a href="cat_1.html#K1" title="CAT_1:func.1">*</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon" title="c7">k2</font> <a href="commacat.html#K3" title="COMMACAT:func.3">`11</a> </span>)</span> <a href="domain_1.html#K3" title="DOMAIN_1:func.3">`2</a> </span>)</span></span>)</span> <a href="cat_1.html#K1" title="CAT_1:func.1">*</a> <span class="p1">(<span class="default"><font color="Maroon" title="c4">F</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <span class="p2">(<span class="default"><font color="Maroon" title="c6">k1</font> <a href="domain_1.html#K16" title="DOMAIN_1:func.16">`21</a> </span>)</span></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E3:8"><span class="lab"><font color="Green" title="E6">A2</font></span></a>, <a class="txt" href="#E16:8_1_1"><span class="lab"><font color="Green" title="E22">A18</font></span></a>, <a class="txt" href="#E17:8_1_1"><span class="lab"><font color="Green" title="E23">A19</font></span></a>, <a class="txt" href="#E10:8_1_1"><span class="lab"><font color="Green" title="E16">A12</font></span></a>, <a class="txt" href="#E5:8_1_1"><span class="lab"><font color="Green" title="E11">A7</font></span></a>, <a class="txt" href="#E1:8_1_1"><span class="lab"><font color="Green" title="E7">A3</font></span></a>, <a class="txt" href="#E2:8_1_1"><span class="lab"><font color="Green" title="E8">A4</font></span></a>, <a class="ref" href="cat_1.html#T43" title="CAT_1:th.43">CAT_1:43</a></span>
<br/>.= 
<span class="p1">(<span class="default"><font color="Maroon" title="c5">G</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <span class="p2">(<span class="default"><font color="Maroon" title="c7">k2</font> <a href="domain_1.html#K17" title="DOMAIN_1:func.17">`22</a> </span>)</span></span>)</span> <a href="cat_1.html#K1" title="CAT_1:func.1">*</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c5">G</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <span class="p3">(<span class="default"><font color="Maroon" title="c6">k1</font> <a href="domain_1.html#K17" title="DOMAIN_1:func.17">`22</a> </span>)</span></span>)</span> <a href="cat_1.html#K1" title="CAT_1:func.1">*</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon" title="c6">k1</font> <a href="commacat.html#K3" title="COMMACAT:func.3">`11</a> </span>)</span> <a href="domain_1.html#K3" title="DOMAIN_1:func.3">`2</a> </span>)</span></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E3:8"><span class="lab"><font color="Green" title="E6">A2</font></span></a>, <a class="txt" href="#E16:8_1_1"><span class="lab"><font color="Green" title="E22">A18</font></span></a>, <a class="txt" href="#E12:8_1_1"><span class="lab"><font color="Green" title="E18">A14</font></span></a>, <a class="txt" href="#E7:8_1_1"><span class="lab"><font color="Green" title="E13">A9</font></span></a>, <a class="txt" href="#E3:8_1_1"><span class="lab"><font color="Green" title="E9">A5</font></span></a>, <a class="txt" href="#E2:8_1_1"><span class="lab"><font color="Green" title="E8">A4</font></span></a>, <a class="txt" href="#E8:8_1_1"><span class="lab"><font color="Green" title="E14">A10</font></span></a>, <a class="ref" href="cat_1.html#T43" title="CAT_1:th.43">CAT_1:43</a></span>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c5">G</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <span class="p3">(<span class="default"><font color="Maroon" title="c7">k2</font> <a href="domain_1.html#K17" title="DOMAIN_1:func.17">`22</a> </span>)</span></span>)</span> <a href="cat_1.html#K1" title="CAT_1:func.1">*</a> <span class="p2">(<span class="default"><font color="Maroon" title="c5">G</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <span class="p3">(<span class="default"><font color="Maroon" title="c6">k1</font> <a href="domain_1.html#K17" title="DOMAIN_1:func.17">`22</a> </span>)</span></span>)</span></span>)</span> <a href="cat_1.html#K1" title="CAT_1:func.1">*</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c6">k1</font> <a href="commacat.html#K3" title="COMMACAT:func.3">`11</a> </span>)</span> <a href="domain_1.html#K3" title="DOMAIN_1:func.3">`2</a> </span>)</span>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E3:8"><span class="lab"><font color="Green" title="E6">A2</font></span></a>, <a class="txt" href="#E4:8_1_1"><span class="lab"><font color="Green" title="E10">A6</font></span></a>, <a class="txt" href="#E13:8_1_1"><span class="lab"><font color="Green" title="E19">A15</font></span></a>, <a class="txt" href="#E12:8_1_1"><span class="lab"><font color="Green" title="E18">A14</font></span></a>, <a class="txt" href="#E8:8_1_1"><span class="lab"><font color="Green" title="E14">A10</font></span></a>, <a class="txt" href="#E9:8_1_1"><span class="lab"><font color="Green" title="E15">A11</font></span></a>, <a class="txt" href="#E6:8_1_1"><span class="lab"><font color="Green" title="E12">A8</font></span></a>, <a class="ref" href="cat_1.html#T43" title="CAT_1:th.43">CAT_1:43</a></span>
<br/>.= 
<span class="p1">(<span class="default"><font color="Maroon" title="c5">G</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon" title="c7">k2</font> <a href="domain_1.html#K17" title="DOMAIN_1:func.17">`22</a> </span>)</span> <a href="cat_1.html#K1" title="CAT_1:func.1">*</a> <span class="p3">(<span class="default"><font color="Maroon" title="c6">k1</font> <a href="domain_1.html#K17" title="DOMAIN_1:func.17">`22</a> </span>)</span></span>)</span></span>)</span> <a href="cat_1.html#K1" title="CAT_1:func.1">*</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c6">k1</font> <a href="commacat.html#K3" title="COMMACAT:func.3">`11</a> </span>)</span> <a href="domain_1.html#K3" title="DOMAIN_1:func.3">`2</a> </span>)</span>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E3:8"><span class="lab"><font color="Green" title="E6">A2</font></span></a>, <a class="txt" href="#E13:8_1_1"><span class="lab"><font color="Green" title="E19">A15</font></span></a>, <a class="txt" href="#E12:8_1_1"><span class="lab"><font color="Green" title="E18">A14</font></span></a>, <a class="ref" href="cat_1.html#T99" title="CAT_1:th.99">CAT_1:99</a></span>
;<br/>
<a NAME="E20:8_1_1"/><span class="kw">then </span>
<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"><font color="Maroon" title="c6">k1</font> <a href="commacat.html#K3" title="COMMACAT:func.3">`11</a> </span>)</span>,<span class="p3">(<span class="default"><font color="Maroon" title="c7">k2</font> <a href="commacat.html#K4" title="COMMACAT:func.4">`12</a> </span>)</span></span><a href="domain_1.html#K1" title="DOMAIN_1:func.1">]</a></span>,<span class="p2"><a href="domain_1.html#K1" title="DOMAIN_1:func.1">[</a><span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon" title="c7">k2</font> <a href="domain_1.html#K16" title="DOMAIN_1:func.16">`21</a> </span>)</span> <a href="cat_1.html#K1" title="CAT_1:func.1">*</a> <span class="p4">(<span class="default"><font color="Maroon" title="c6">k1</font> <a href="domain_1.html#K16" title="DOMAIN_1:func.16">`21</a> </span>)</span></span>)</span>,<span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon" title="c7">k2</font> <a href="domain_1.html#K17" title="DOMAIN_1:func.17">`22</a> </span>)</span> <a href="cat_1.html#K1" title="CAT_1:func.1">*</a> <span class="p4">(<span class="default"><font color="Maroon" title="c6">k1</font> <a href="domain_1.html#K17" title="DOMAIN_1:func.17">`22</a> </span>)</span></span>)</span></span><a href="domain_1.html#K1" title="DOMAIN_1:func.1">]</a></span></span><a href="domain_1.html#K1" title="DOMAIN_1:func.1">]</a></span> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="commacat.html#K2" title="COMMACAT:func.2">commaMorphs</a> <font color="Maroon" title="c4">F</font>,<font color="Maroon" title="c5">G</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E4:8_1_1"><span class="lab"><font color="Green" title="E10">A6</font></span></a>, <a class="txt" href="#E10:8_1_1"><span class="lab"><font color="Green" title="E16">A12</font></span></a>, <a class="txt" href="#E15:8_1_1"><span class="lab"><font color="Green" title="E21">A17</font></span></a>, <a class="txt" href="#E11:8_1_1"><span class="lab"><font color="Green" title="E17">A13</font></span></a>, <a class="txt" href="#E18:8_1_1"><span class="lab"><font color="Green" title="E24">A20</font></span></a>, <a class="txt" href="#E14:8_1_1"><span class="lab"><font color="Green" title="E20">A16</font></span></a></span>;<br/>
<span class="kw">hence </span><a NAME="E21:8_1_1"/>
<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"><font color="Maroon" title="c6">k1</font> <a href="commacat.html#K3" title="COMMACAT:func.3">`11</a> </span>)</span>,<span class="p3">(<span class="default"><font color="Maroon" title="c7">k2</font> <a href="commacat.html#K4" title="COMMACAT:func.4">`12</a> </span>)</span></span><a href="domain_1.html#K1" title="DOMAIN_1:func.1">]</a></span>,<span class="p2"><a href="domain_1.html#K1" title="DOMAIN_1:func.1">[</a><span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon" title="c7">k2</font> <a href="domain_1.html#K16" title="DOMAIN_1:func.16">`21</a> </span>)</span> <a href="cat_1.html#K1" title="CAT_1:func.1">*</a> <span class="p4">(<span class="default"><font color="Maroon" title="c6">k1</font> <a href="domain_1.html#K16" title="DOMAIN_1:func.16">`21</a> </span>)</span></span>)</span>,<span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon" title="c7">k2</font> <a href="domain_1.html#K17" title="DOMAIN_1:func.17">`22</a> </span>)</span> <a href="cat_1.html#K1" title="CAT_1:func.1">*</a> <span class="p4">(<span class="default"><font color="Maroon" title="c6">k1</font> <a href="domain_1.html#K17" title="DOMAIN_1:func.17">`22</a> </span>)</span></span>)</span></span><a href="domain_1.html#K1" title="DOMAIN_1:func.1">]</a></span></span><a href="domain_1.html#K1" title="DOMAIN_1:func.1">]</a></span> is    <a href="subset_1.html#M2" title="SUBSET_1:mode.2">Element</a> of  <a href="commacat.html#K2" title="COMMACAT:func.2">commaMorphs</a> <font color="Maroon" title="c4">F</font>,<font color="Maroon" title="c5">G</font>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> verum</span><br/>


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