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<b>let </b><font color="Maroon" title="c1">C1</font>, <font color="Maroon" title="c2">C2</font> be   <a href="cat_1.html#NM4" title="CAT_1:NM.4">Category</a>; <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> being   <a href="cat_1.html#M2" title="CAT_1:mode.2">Functor</a> of <font color="Maroon" title="c1">C1</font>,<font color="Maroon" title="c2">C2</font><br/> for <font color="Olive" title="b2">a</font>, <font color="Olive" title="b3">b</font> being  <a href="cat_1.html#NM1" title="CAT_1:NM.1">Object</a> of <font color="Maroon" title="c1">C1</font> holds  <span class="p1">(<span class="default"><a href="catalg_1.html#K11" title="CATALG_1:func.11">Upsilon</a> <font color="Olive" title="b1">F</font></span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <span class="p1">(<span class="default"><a href="catalg_1.html#K9" title="CATALG_1:func.9">homsym</a> <font color="Olive" title="b2">a</font>,<font color="Olive" title="b3">b</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="catalg_1.html#K9" title="CATALG_1:func.9">homsym</a> <span class="p1">(<span class="default"><font color="Olive" title="b1">F</font> <a href="cat_1.html#K13" title="CAT_1:func.13">.</a> <font color="Olive" title="b2">a</font></span>)</span>,<span class="p1">(<span class="default"><font color="Olive" title="b1">F</font> <a href="cat_1.html#K13" title="CAT_1:func.13">.</a> <font color="Olive" title="b3">b</font></span>)</span></span><br/><b>let </b><font color="Maroon" title="c3">F</font> be    <a href="cat_1.html#M2" title="CAT_1:mode.2">Functor</a> of <font color="Maroon" title="c1">C1</font>,<font color="Maroon" title="c2">C2</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">a</font>, <font color="Olive" title="b2">b</font> being  <a href="cat_1.html#NM1" title="CAT_1:NM.1">Object</a> of <font color="Maroon" title="c1">C1</font> holds  <span class="p1">(<span class="default"><a href="catalg_1.html#K11" title="CATALG_1:func.11">Upsilon</a> <font color="Maroon" title="c3">F</font></span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <span class="p1">(<span class="default"><a href="catalg_1.html#K9" title="CATALG_1:func.9">homsym</a> <font color="Olive" title="b1">a</font>,<font color="Olive" title="b2">b</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="catalg_1.html#K9" title="CATALG_1:func.9">homsym</a> <span class="p1">(<span class="default"><font color="Maroon" title="c3">F</font> <a href="cat_1.html#K13" title="CAT_1:func.13">.</a> <font color="Olive" title="b1">a</font></span>)</span>,<span class="p1">(<span class="default"><font color="Maroon" title="c3">F</font> <a href="cat_1.html#K13" title="CAT_1:func.13">.</a> <font color="Olive" title="b2">b</font></span>)</span></span><br/><b>let </b><font color="Maroon" title="c4">a</font>, <font color="Maroon" title="c5">b</font> be   <a href="cat_1.html#NM1" title="CAT_1:NM.1">Object</a> of <font color="Maroon" title="c1">C1</font>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> <span class="p1">(<span class="default"><a href="catalg_1.html#K11" title="CATALG_1:func.11">Upsilon</a> <font color="Maroon" title="c3">F</font></span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <span class="p1">(<span class="default"><a href="catalg_1.html#K9" title="CATALG_1:func.9">homsym</a> <font color="Maroon" title="c4">a</font>,<font color="Maroon" title="c5">b</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="catalg_1.html#K9" title="CATALG_1:func.9">homsym</a> <span class="p1">(<span class="default"><font color="Maroon" title="c3">F</font> <a href="cat_1.html#K13" title="CAT_1:func.13">.</a> <font color="Maroon" title="c4">a</font></span>)</span>,<span class="p1">(<span class="default"><font color="Maroon" title="c3">F</font> <a href="cat_1.html#K13" title="CAT_1:func.13">.</a> <font color="Maroon" title="c5">b</font></span>)</span></span><br/>





<a NAME="E1:63"/><i><font color="Green" title="E30">A1</font></i>: 
 <a href="relset_1.html#K4" title="RELSET_1:func.4">dom</a> <span class="p1">(<span class="default"><a href="cat_1.html#K12" title="CAT_1:func.12">Obj</a> <font color="Maroon" title="c3">F</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> the <a href="graph_1.html#U1" title="GRAPH_1:sel.1">Vertices</a> of <font color="Maroon" title="c1">C1</font>
 
<b>by </b><i><a class="ref" href="funct_2.html#D1" title="FUNCT_2:def.1">FUNCT_2:def 1</a></i>;<br/>
<b>thus </b><span class="p1">(<span class="default"><a href="catalg_1.html#K11" title="CATALG_1:func.11">Upsilon</a> <font color="Maroon" title="c3">F</font></span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <span class="p1">(<span class="default"><a href="catalg_1.html#K9" title="CATALG_1:func.9">homsym</a> <font color="Maroon" title="c4">a</font>,<font color="Maroon" title="c5">b</font></span>)</span> = 
<span class="p1"><a href="tarski.html#K4" title="TARSKI:func.4">[</a><span class="default"><a href="numbers.html#K6" title="NUMBERS:func.6">0</a> ,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="cat_1.html#K12" title="CAT_1:func.12">Obj</a> <font color="Maroon" title="c3">F</font></span>)</span> <a href="funct_1.html#NK3" title="FUNCT_1:NK.3">*</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="catalg_1.html#K9" title="CATALG_1:func.9">homsym</a> <font color="Maroon" title="c4">a</font>,<font color="Maroon" title="c5">b</font></span>)</span> <a href="mcart_1.html#K2" title="MCART_1:func.2">`2</a> </span>)</span></span>)</span></span><a href="tarski.html#K4" title="TARSKI:func.4">]</a></span>
<b>by </b><i><a class="ref" href="catalg_1.html#D13" target="_self" title="CATALG_1:def.13">Def13</a></i>
<br/>.= 
<span class="p1"><a href="tarski.html#K4" title="TARSKI:func.4">[</a><span class="default"><a href="numbers.html#K6" title="NUMBERS:func.6">0</a> ,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="cat_1.html#K12" title="CAT_1:func.12">Obj</a> <font color="Maroon" title="c3">F</font></span>)</span> <a href="partfun1.html#K1" title="PARTFUN1:func.1">*</a> <span class="p3"><a href="finseq_4.html#K2" title="FINSEQ_4:func.2">&lt;*</a><span class="default"><font color="Maroon" title="c4">a</font>,<font color="Maroon" title="c5">b</font></span><a href="finseq_4.html#K2" title="FINSEQ_4:func.2">*&gt;</a></span></span>)</span></span><a href="tarski.html#K4" title="TARSKI:func.4">]</a></span>
<b>by </b><i><a class="ref" href="mcart_1.html#T7" title="MCART_1:th.7">MCART_1:7</a></i>
<br/>.= 
<span class="p1"><a href="tarski.html#K4" title="TARSKI:func.4">[</a><span class="default"><a href="numbers.html#K6" title="NUMBERS:func.6">0</a> ,<span class="p2"><a href="finseq_4.html#K2" title="FINSEQ_4:func.2">&lt;*</a><span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="cat_1.html#K12" title="CAT_1:func.12">Obj</a> <font color="Maroon" title="c3">F</font></span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c4">a</font></span>)</span>,<span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="cat_1.html#K12" title="CAT_1:func.12">Obj</a> <font color="Maroon" title="c3">F</font></span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c5">b</font></span>)</span></span><a href="finseq_4.html#K2" title="FINSEQ_4:func.2">*&gt;</a></span></span><a href="tarski.html#K4" title="TARSKI:func.4">]</a></span>
<b>by </b><i><a class="txt" href="catalg_1.html#E1:63"><i><font color="Green" title="E30">A1</font></i></a>, <a class="ref" href="finseq_2.html#T145" title="FINSEQ_2:th.145">FINSEQ_2:145</a></i>
<br/>.= 
<span class="p1"><a href="tarski.html#K4" title="TARSKI:func.4">[</a><span class="default"><a href="numbers.html#K6" title="NUMBERS:func.6">0</a> ,<span class="p2"><a href="finseq_4.html#K2" title="FINSEQ_4:func.2">&lt;*</a><span class="default"><span class="p3">(<span class="default"><font color="Maroon" title="c3">F</font> <a href="cat_1.html#K13" title="CAT_1:func.13">.</a> <font color="Maroon" title="c4">a</font></span>)</span>,<span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="cat_1.html#K12" title="CAT_1:func.12">Obj</a> <font color="Maroon" title="c3">F</font></span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c5">b</font></span>)</span></span><a href="finseq_4.html#K2" title="FINSEQ_4:func.2">*&gt;</a></span></span><a href="tarski.html#K4" title="TARSKI:func.4">]</a></span>
<b>by </b><i><a class="ref" href="cat_1.html#D20" title="CAT_1:def.20">CAT_1:def 20</a></i>
<br/>.= 
 <a href="catalg_1.html#K9" title="CATALG_1:func.9">homsym</a> <span class="p1">(<span class="default"><font color="Maroon" title="c3">F</font> <a href="cat_1.html#K13" title="CAT_1:func.13">.</a> <font color="Maroon" title="c4">a</font></span>)</span>,<span class="p1">(<span class="default"><font color="Maroon" title="c3">F</font> <a href="cat_1.html#K13" title="CAT_1:func.13">.</a> <font color="Maroon" title="c5">b</font></span>)</span>
<b>by </b><i><a class="ref" href="cat_1.html#D20" title="CAT_1:def.20">CAT_1:def 20</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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