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<span class="kw">let </span><font color="Maroon" title="c1">C</font>, <font color="Maroon" title="c2">D</font>, <font color="Maroon" title="c3">E</font> be   <a href="cat_1.html#NM4" title="CAT_1:NM.4">Category</a>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> for <font color="Olive" title="b1">F</font> being   <a href="cat_1.html#M2" title="CAT_1:mode.2">Functor</a> of <font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c3">E</font><br/> for <font color="Olive" title="b2">G</font> being   <a href="cat_1.html#M2" title="CAT_1:mode.2">Functor</a> of <font color="Maroon" title="c2">D</font>,<font color="Maroon" title="c3">E</font><br/> for <font color="Olive" title="b3">k</font> being   <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="Olive" title="b1">F</font>,<font color="Olive" title="b2">G</font>  st  ex <font color="Olive" title="b4">c</font> being  <a href="cat_1.html#NM1" title="CAT_1:NM.1">Object</a> of <font color="Maroon" title="c1">C</font> ex <font color="Olive" title="b5">d</font> being  <a href="cat_1.html#NM1" title="CAT_1:NM.1">Object</a> of <font color="Maroon" title="c2">D</font> ex <font color="Olive" title="b6">f</font> being  <a href="cat_1.html#NM2" title="CAT_1:NM.2">Morphism</a> of <font color="Maroon" title="c3">E</font> st <font color="Olive" title="b6">f</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="cat_1.html#K3" title="CAT_1:func.3">Hom</a> <span class="p1">(<span class="default"><font color="Olive" title="b1">F</font> <a href="cat_1.html#K9" title="CAT_1:func.9">.</a> <font color="Olive" title="b4">c</font></span>)</span>,<span class="p1">(<span class="default"><font color="Olive" title="b2">G</font> <a href="cat_1.html#K9" title="CAT_1:func.9">.</a> <font color="Olive" title="b5">d</font></span>)</span> holds <br/>( <font color="Olive" title="b3">k</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"><font color="Olive" title="b3">k</font> <a href="commacat.html#K3" title="COMMACAT:func.3">`11</a> </span>)</span>,<span class="p3">(<span class="default"><font color="Olive" title="b3">k</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"><font color="Olive" title="b3">k</font> <a href="domain_1.html#K16" title="DOMAIN_1:func.16">`21</a> </span>)</span>,<span class="p3">(<span class="default"><font color="Olive" title="b3">k</font> <a href="domain_1.html#K17" title="DOMAIN_1:func.17">`22</a> </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> &amp;  <a href="graph_1.html#K1" title="GRAPH_1:func.1">dom</a> <span class="p1">(<span class="default"><font color="Olive" title="b3">k</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="Olive" title="b3">k</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="Olive" title="b3">k</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="Olive" title="b3">k</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>  &amp;  <a href="graph_1.html#K1" title="GRAPH_1:func.1">dom</a> <span class="p1">(<span class="default"><font color="Olive" title="b3">k</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="Olive" title="b3">k</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>  &amp;  <a href="graph_1.html#K2" title="GRAPH_1:func.2">cod</a> <span class="p1">(<span class="default"><font color="Olive" title="b3">k</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="Olive" title="b3">k</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>  &amp; <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Olive" title="b3">k</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="Olive" title="b1">F</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <span class="p2">(<span class="default"><font color="Olive" title="b3">k</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="Olive" title="b2">G</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <span class="p2">(<span class="default"><font color="Olive" title="b3">k</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="Olive" title="b3">k</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><br/><span class="kw">let </span><font color="Maroon" title="c4">F</font> be    <a href="cat_1.html#M2" title="CAT_1:mode.2">Functor</a> of <font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c3">E</font>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> for <font color="Olive" title="b1">G</font> being   <a href="cat_1.html#M2" title="CAT_1:mode.2">Functor</a> of <font color="Maroon" title="c2">D</font>,<font color="Maroon" title="c3">E</font><br/> for <font color="Olive" title="b2">k</font> being   <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="Olive" title="b1">G</font>  st  ex <font color="Olive" title="b3">c</font> being  <a href="cat_1.html#NM1" title="CAT_1:NM.1">Object</a> of <font color="Maroon" title="c1">C</font> ex <font color="Olive" title="b4">d</font> being  <a href="cat_1.html#NM1" title="CAT_1:NM.1">Object</a> of <font color="Maroon" title="c2">D</font> ex <font color="Olive" title="b5">f</font> being  <a href="cat_1.html#NM2" title="CAT_1:NM.2">Morphism</a> of <font color="Maroon" title="c3">E</font> st <font color="Olive" title="b5">f</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="cat_1.html#K3" title="CAT_1:func.3">Hom</a> <span class="p1">(<span class="default"><font color="Maroon" title="c4">F</font> <a href="cat_1.html#K9" title="CAT_1:func.9">.</a> <font color="Olive" title="b3">c</font></span>)</span>,<span class="p1">(<span class="default"><font color="Olive" title="b1">G</font> <a href="cat_1.html#K9" title="CAT_1:func.9">.</a> <font color="Olive" title="b4">d</font></span>)</span> holds <br/>( <font color="Olive" title="b2">k</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"><font color="Olive" title="b2">k</font> <a href="commacat.html#K3" title="COMMACAT:func.3">`11</a> </span>)</span>,<span class="p3">(<span class="default"><font color="Olive" title="b2">k</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"><font color="Olive" title="b2">k</font> <a href="domain_1.html#K16" title="DOMAIN_1:func.16">`21</a> </span>)</span>,<span class="p3">(<span class="default"><font color="Olive" title="b2">k</font> <a href="domain_1.html#K17" title="DOMAIN_1:func.17">`22</a> </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> &amp;  <a href="graph_1.html#K1" title="GRAPH_1:func.1">dom</a> <span class="p1">(<span class="default"><font color="Olive" title="b2">k</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="Olive" title="b2">k</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="Olive" title="b2">k</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="Olive" title="b2">k</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>  &amp;  <a href="graph_1.html#K1" title="GRAPH_1:func.1">dom</a> <span class="p1">(<span class="default"><font color="Olive" title="b2">k</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="Olive" title="b2">k</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>  &amp;  <a href="graph_1.html#K2" title="GRAPH_1:func.2">cod</a> <span class="p1">(<span class="default"><font color="Olive" title="b2">k</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="Olive" title="b2">k</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>  &amp; <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Olive" title="b2">k</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="Olive" title="b2">k</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="Olive" title="b1">G</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <span class="p2">(<span class="default"><font color="Olive" title="b2">k</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="Olive" title="b2">k</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><br/><span class="kw">let </span><font color="Maroon" title="c5">G</font> be    <a href="cat_1.html#M2" title="CAT_1:mode.2">Functor</a> of <font color="Maroon" title="c2">D</font>,<font color="Maroon" title="c3">E</font>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> for <font color="Olive" title="b1">k</font> being   <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>  st  ex <font color="Olive" title="b2">c</font> being  <a href="cat_1.html#NM1" title="CAT_1:NM.1">Object</a> of <font color="Maroon" title="c1">C</font> ex <font color="Olive" title="b3">d</font> being  <a href="cat_1.html#NM1" title="CAT_1:NM.1">Object</a> of <font color="Maroon" title="c2">D</font> ex <font color="Olive" title="b4">f</font> being  <a href="cat_1.html#NM2" title="CAT_1:NM.2">Morphism</a> of <font color="Maroon" title="c3">E</font> st <font color="Olive" title="b4">f</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="cat_1.html#K3" title="CAT_1:func.3">Hom</a> <span class="p1">(<span class="default"><font color="Maroon" title="c4">F</font> <a href="cat_1.html#K9" title="CAT_1:func.9">.</a> <font color="Olive" title="b2">c</font></span>)</span>,<span class="p1">(<span class="default"><font color="Maroon" title="c5">G</font> <a href="cat_1.html#K9" title="CAT_1:func.9">.</a> <font color="Olive" title="b3">d</font></span>)</span> holds <br/>( <font color="Olive" title="b1">k</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"><font color="Olive" title="b1">k</font> <a href="commacat.html#K3" title="COMMACAT:func.3">`11</a> </span>)</span>,<span class="p3">(<span class="default"><font color="Olive" title="b1">k</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"><font color="Olive" title="b1">k</font> <a href="domain_1.html#K16" title="DOMAIN_1:func.16">`21</a> </span>)</span>,<span class="p3">(<span class="default"><font color="Olive" title="b1">k</font> <a href="domain_1.html#K17" title="DOMAIN_1:func.17">`22</a> </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> &amp;  <a href="graph_1.html#K1" title="GRAPH_1:func.1">dom</a> <span class="p1">(<span class="default"><font color="Olive" title="b1">k</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="Olive" title="b1">k</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="Olive" title="b1">k</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="Olive" title="b1">k</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>  &amp;  <a href="graph_1.html#K1" title="GRAPH_1:func.1">dom</a> <span class="p1">(<span class="default"><font color="Olive" title="b1">k</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="Olive" title="b1">k</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>  &amp;  <a href="graph_1.html#K2" title="GRAPH_1:func.2">cod</a> <span class="p1">(<span class="default"><font color="Olive" title="b1">k</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="Olive" title="b1">k</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>  &amp; <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Olive" title="b1">k</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="Olive" title="b1">k</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="Olive" title="b1">k</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="Olive" title="b1">k</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><br/><span class="kw">let </span><font color="Maroon" title="c6">k</font> be    <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"> (  ex <font color="Olive" title="b1">c</font> being  <a href="cat_1.html#NM1" title="CAT_1:NM.1">Object</a> of <font color="Maroon" title="c1">C</font> ex <font color="Olive" title="b2">d</font> being  <a href="cat_1.html#NM1" title="CAT_1:NM.1">Object</a> of <font color="Maroon" title="c2">D</font> ex <font color="Olive" title="b3">f</font> being  <a href="cat_1.html#NM2" title="CAT_1:NM.2">Morphism</a> of <font color="Maroon" title="c3">E</font> st <font color="Olive" title="b3">f</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="cat_1.html#K3" title="CAT_1:func.3">Hom</a> <span class="p1">(<span class="default"><font color="Maroon" title="c4">F</font> <a href="cat_1.html#K9" title="CAT_1:func.9">.</a> <font color="Olive" title="b1">c</font></span>)</span>,<span class="p1">(<span class="default"><font color="Maroon" title="c5">G</font> <a href="cat_1.html#K9" title="CAT_1:func.9">.</a> <font color="Olive" title="b2">d</font></span>)</span> implies ( <font color="Maroon" title="c6">k</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"><font color="Maroon" title="c6">k</font> <a href="commacat.html#K3" title="COMMACAT:func.3">`11</a> </span>)</span>,<span class="p3">(<span class="default"><font color="Maroon" title="c6">k</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"><font color="Maroon" title="c6">k</font> <a href="domain_1.html#K16" title="DOMAIN_1:func.16">`21</a> </span>)</span>,<span class="p3">(<span class="default"><font color="Maroon" title="c6">k</font> <a href="domain_1.html#K17" title="DOMAIN_1:func.17">`22</a> </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> &amp;  <a href="graph_1.html#K1" title="GRAPH_1:func.1">dom</a> <span class="p1">(<span class="default"><font color="Maroon" title="c6">k</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">k</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="c6">k</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">k</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>  &amp;  <a href="graph_1.html#K1" title="GRAPH_1:func.1">dom</a> <span class="p1">(<span class="default"><font color="Maroon" title="c6">k</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">k</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>  &amp;  <a href="graph_1.html#K2" title="GRAPH_1:func.2">cod</a> <span class="p1">(<span class="default"><font color="Maroon" title="c6">k</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">k</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>  &amp; <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c6">k</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">k</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">k</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">k</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><br/>











<span class="kw">assume </span><a NAME="E1:7"/>
 ex <font color="Olive" title="b1">c</font> being  <a href="cat_1.html#NM1" title="CAT_1:NM.1">Object</a> of <font color="Maroon" title="c1">C</font> ex <font color="Olive" title="b2">d</font> being  <a href="cat_1.html#NM1" title="CAT_1:NM.1">Object</a> of <font color="Maroon" title="c2">D</font> ex <font color="Olive" title="b3">f</font> being  <a href="cat_1.html#NM2" title="CAT_1:NM.2">Morphism</a> of <font color="Maroon" title="c3">E</font> st <font color="Olive" title="b3">f</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="cat_1.html#K3" title="CAT_1:func.3">Hom</a> <span class="p1">(<span class="default"><font color="Maroon" title="c4">F</font> <a href="cat_1.html#K9" title="CAT_1:func.9">.</a> <font color="Olive" title="b1">c</font></span>)</span>,<span class="p1">(<span class="default"><font color="Maroon" title="c5">G</font> <a href="cat_1.html#K9" title="CAT_1:func.9">.</a> <font color="Olive" title="b2">d</font></span>)</span>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> ( <font color="Maroon" title="c6">k</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"><font color="Maroon" title="c6">k</font> <a href="commacat.html#K3" title="COMMACAT:func.3">`11</a> </span>)</span>,<span class="p3">(<span class="default"><font color="Maroon" title="c6">k</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"><font color="Maroon" title="c6">k</font> <a href="domain_1.html#K16" title="DOMAIN_1:func.16">`21</a> </span>)</span>,<span class="p3">(<span class="default"><font color="Maroon" title="c6">k</font> <a href="domain_1.html#K17" title="DOMAIN_1:func.17">`22</a> </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> &amp;  <a href="graph_1.html#K1" title="GRAPH_1:func.1">dom</a> <span class="p1">(<span class="default"><font color="Maroon" title="c6">k</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">k</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="c6">k</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">k</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>  &amp;  <a href="graph_1.html#K1" title="GRAPH_1:func.1">dom</a> <span class="p1">(<span class="default"><font color="Maroon" title="c6">k</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">k</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>  &amp;  <a href="graph_1.html#K2" title="GRAPH_1:func.2">cod</a> <span class="p1">(<span class="default"><font color="Maroon" title="c6">k</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">k</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>  &amp; <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c6">k</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">k</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">k</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">k</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><br/>

<a NAME="E2:7"/><span class="kw">then </span><span class="lab"><font color="Green" title="E5">A1</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="ref" href="commacat.html#D6" target="_self" title="COMMACAT:def.6">Def6</a></span>;<br/>
<a NAME="E3:7"/>
<font color="Maroon" title="c6">k</font> <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>
 
;<br/>
<span class="kw">then </span><span class="kw">consider </span><font color="Maroon" title="c7">g</font> being   <a href="cat_1.html#NM2" title="CAT_1:NM.2">Morphism</a> of <font color="Maroon" title="c1">C</font>, <font color="Maroon" title="c8">h</font> being   <a href="cat_1.html#NM2" title="CAT_1:NM.2">Morphism</a> of <font color="Maroon" title="c2">D</font>, <font color="Maroon" title="c9">o1</font>, <font color="Maroon" title="c10">o2</font> being    <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><span class="kw"> such that </span><br/><a NAME="E5:7"/><span class="lab"><font color="Green" title="E6">A2</font></span>: 
<font color="Maroon" title="c6">k</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"><font color="Maroon" title="c9">o1</font>,<font color="Maroon" title="c10">o2</font></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"><font color="Maroon" title="c7">g</font>,<font color="Maroon" title="c8">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>
 <span class="kw">and </span><br/><a NAME="E6:7"/><span class="lab"><font color="Green" title="E7">A3</font></span>: 
(  <a href="graph_1.html#K1" title="GRAPH_1:func.1">dom</a> <font color="Maroon" title="c7">g</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c9">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="Maroon" title="c7">g</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c10">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="Maroon" title="c8">h</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c9">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="Maroon" title="c8">h</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c10">o2</font> <a href="domain_1.html#K15" title="DOMAIN_1:func.15">`12</a>  &amp; <span class="p1">(<span class="default"><font color="Maroon" title="c10">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="Maroon" title="c7">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="Maroon" title="c8">h</font></span>)</span> <a href="cat_1.html#K1" title="CAT_1:func.1">*</a> <span class="p1">(<span class="default"><font color="Maroon" title="c9">o1</font> <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="#E2:7"><span class="lab"><font color="Green" title="E5">A1</font></span></a></span>;<br/>
<a NAME="E7:7"/><span class="lab"><font color="Green" title="E8">A4</font></span>: 
<font color="Maroon" title="c6">k</font> <a href="domain_1.html#K16" title="DOMAIN_1:func.16">`21</a>  <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c7">g</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E5:7"><span class="lab"><font color="Green" title="E6">A2</font></span></a>, <a class="ref" href="mcart_1.html#T89" title="MCART_1:th.89">MCART_1:89</a></span>;<br/>
<a NAME="E8:7"/>
( <font color="Maroon" title="c6">k</font> <a href="commacat.html#K3" title="COMMACAT:func.3">`11</a>  <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c9">o1</font> &amp; <font color="Maroon" title="c6">k</font> <a href="commacat.html#K4" title="COMMACAT:func.4">`12</a>  <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c10">o2</font> )
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E5:7"><span class="lab"><font color="Green" title="E6">A2</font></span></a>, <a class="ref" href="mcart_1.html#T89" title="MCART_1:th.89">MCART_1:89</a></span>;<br/>
<span class="kw">hence </span><a NAME="E9:7"/>
( <font color="Maroon" title="c6">k</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"><font color="Maroon" title="c6">k</font> <a href="commacat.html#K3" title="COMMACAT:func.3">`11</a> </span>)</span>,<span class="p3">(<span class="default"><font color="Maroon" title="c6">k</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"><font color="Maroon" title="c6">k</font> <a href="domain_1.html#K16" title="DOMAIN_1:func.16">`21</a> </span>)</span>,<span class="p3">(<span class="default"><font color="Maroon" title="c6">k</font> <a href="domain_1.html#K17" title="DOMAIN_1:func.17">`22</a> </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> &amp;  <a href="graph_1.html#K1" title="GRAPH_1:func.1">dom</a> <span class="p1">(<span class="default"><font color="Maroon" title="c6">k</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">k</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="c6">k</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">k</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>  &amp;  <a href="graph_1.html#K1" title="GRAPH_1:func.1">dom</a> <span class="p1">(<span class="default"><font color="Maroon" title="c6">k</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">k</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>  &amp;  <a href="graph_1.html#K2" title="GRAPH_1:func.2">cod</a> <span class="p1">(<span class="default"><font color="Maroon" title="c6">k</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">k</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>  &amp; <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c6">k</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">k</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">k</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">k</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="#E5:7"><span class="lab"><font color="Green" title="E6">A2</font></span></a>, <a class="txt" href="#E6:7"><span class="lab"><font color="Green" title="E7">A3</font></span></a>, <a class="txt" href="#E7:7"><span class="lab"><font color="Green" title="E8">A4</font></span></a>, <a class="ref" href="mcart_1.html#T89" title="MCART_1:th.89">MCART_1:89</a></span>; <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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