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<b>let </b><font color="Maroon" title="c1">C</font>, <font color="Maroon" title="c2">D</font>, <font color="Maroon" title="c3">C'</font>, <font color="Maroon" title="c4">D'</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">T</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="c2">D</font><br/> for <font color="Olive" title="b2">T'</font> being   <a href="cat_1.html#M2" title="CAT_1:mode.2">Functor</a> of <font color="Maroon" title="c3">C'</font>,<font color="Maroon" title="c4">D'</font> holds  <span class="p1"><a href="cat_2.html#K9" title="CAT_2:func.9">[:</a><span class="default"><font color="Olive" title="b1">T</font>,<font color="Olive" title="b2">T'</font></span><a href="cat_2.html#K9" title="CAT_2:func.9">:]</a></span> <a href="funct_2.html#R1" title="FUNCT_2:pred.1">=</a> <span class="p1"><a href="cat_2.html#K19" title="CAT_2:func.19">&lt;:</a><span class="default"><span class="p2">(<span class="default"><font color="Olive" title="b1">T</font> <a href="cat_1.html#K14" title="CAT_1:func.14">*</a> <span class="p3">(<span class="default"><a href="cat_2.html#K17" title="CAT_2:func.17">pr1</a> <font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c3">C'</font></span>)</span></span>)</span>,<span class="p2">(<span class="default"><font color="Olive" title="b2">T'</font> <a href="cat_1.html#K14" title="CAT_1:func.14">*</a> <span class="p3">(<span class="default"><a href="cat_2.html#K18" title="CAT_2:func.18">pr2</a> <font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c3">C'</font></span>)</span></span>)</span></span><a href="cat_2.html#K19" title="CAT_2:func.19">:&gt;</a></span></span><br/><b>let </b><font color="Maroon" title="c5">T</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="c2">D</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">T'</font> being   <a href="cat_1.html#M2" title="CAT_1:mode.2">Functor</a> of <font color="Maroon" title="c3">C'</font>,<font color="Maroon" title="c4">D'</font> holds  <span class="p1"><a href="cat_2.html#K9" title="CAT_2:func.9">[:</a><span class="default"><font color="Maroon" title="c5">T</font>,<font color="Olive" title="b1">T'</font></span><a href="cat_2.html#K9" title="CAT_2:func.9">:]</a></span> <a href="funct_2.html#R1" title="FUNCT_2:pred.1">=</a> <span class="p1"><a href="cat_2.html#K19" title="CAT_2:func.19">&lt;:</a><span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c5">T</font> <a href="cat_1.html#K14" title="CAT_1:func.14">*</a> <span class="p3">(<span class="default"><a href="cat_2.html#K17" title="CAT_2:func.17">pr1</a> <font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c3">C'</font></span>)</span></span>)</span>,<span class="p2">(<span class="default"><font color="Olive" title="b1">T'</font> <a href="cat_1.html#K14" title="CAT_1:func.14">*</a> <span class="p3">(<span class="default"><a href="cat_2.html#K18" title="CAT_2:func.18">pr2</a> <font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c3">C'</font></span>)</span></span>)</span></span><a href="cat_2.html#K19" title="CAT_2:func.19">:&gt;</a></span></span><br/><b>let </b><font color="Maroon" title="c6">T'</font> be    <a href="cat_1.html#M2" title="CAT_1:mode.2">Functor</a> of <font color="Maroon" title="c3">C'</font>,<font color="Maroon" title="c4">D'</font>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> <span class="p1"><a href="cat_2.html#K9" title="CAT_2:func.9">[:</a><span class="default"><font color="Maroon" title="c5">T</font>,<font color="Maroon" title="c6">T'</font></span><a href="cat_2.html#K9" title="CAT_2:func.9">:]</a></span> <a href="funct_2.html#R1" title="FUNCT_2:pred.1">=</a> <span class="p1"><a href="cat_2.html#K19" title="CAT_2:func.19">&lt;:</a><span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c5">T</font> <a href="cat_1.html#K14" title="CAT_1:func.14">*</a> <span class="p3">(<span class="default"><a href="cat_2.html#K17" title="CAT_2:func.17">pr1</a> <font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c3">C'</font></span>)</span></span>)</span>,<span class="p2">(<span class="default"><font color="Maroon" title="c6">T'</font> <a href="cat_1.html#K14" title="CAT_1:func.14">*</a> <span class="p3">(<span class="default"><a href="cat_2.html#K18" title="CAT_2:func.18">pr2</a> <font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c3">C'</font></span>)</span></span>)</span></span><a href="cat_2.html#K19" title="CAT_2:func.19">:&gt;</a></span></span><br/>











<a NAME="E1:65"/>
(  <a href="cat_2.html#K17" title="CAT_2:func.17">pr1</a> <font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c3">C'</font> <a href="funct_2.html#R1" title="FUNCT_2:pred.1">=</a>  <a href="funct_3.html#K9" title="FUNCT_3:func.9">pr1</a> the <a href="graph_1.html#U2" title="GRAPH_1:sel.2">Edges</a> of <font color="Maroon" title="c1">C</font>,the <a href="graph_1.html#U2" title="GRAPH_1:sel.2">Edges</a> of <font color="Maroon" title="c3">C'</font> &amp;  <a href="cat_2.html#K18" title="CAT_2:func.18">pr2</a> <font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c3">C'</font> <a href="funct_2.html#R1" title="FUNCT_2:pred.1">=</a>  <a href="funct_3.html#K10" title="FUNCT_3:func.10">pr2</a> the <a href="graph_1.html#U2" title="GRAPH_1:sel.2">Edges</a> of <font color="Maroon" title="c1">C</font>,the <a href="graph_1.html#U2" title="GRAPH_1:sel.2">Edges</a> of <font color="Maroon" title="c3">C'</font> &amp;  <a href="relat_1.html#NK2" title="RELAT_1:NK.2">dom</a> <font color="Maroon" title="c5">T</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> the <a href="graph_1.html#U2" title="GRAPH_1:sel.2">Edges</a> of <font color="Maroon" title="c1">C</font> &amp;  <a href="relat_1.html#NK2" title="RELAT_1:NK.2">dom</a> <font color="Maroon" title="c6">T'</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> the <a href="graph_1.html#U2" title="GRAPH_1:sel.2">Edges</a> of <font color="Maroon" title="c3">C'</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>hence </b><a NAME="E2:65"/>
<span class="p1"><a href="cat_2.html#K9" title="CAT_2:func.9">[:</a><span class="default"><font color="Maroon" title="c5">T</font>,<font color="Maroon" title="c6">T'</font></span><a href="cat_2.html#K9" title="CAT_2:func.9">:]</a></span> <a href="funct_2.html#R1" title="FUNCT_2:pred.1">=</a> <span class="p1"><a href="cat_2.html#K19" title="CAT_2:func.19">&lt;:</a><span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c5">T</font> <a href="cat_1.html#K14" title="CAT_1:func.14">*</a> <span class="p3">(<span class="default"><a href="cat_2.html#K17" title="CAT_2:func.17">pr1</a> <font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c3">C'</font></span>)</span></span>)</span>,<span class="p2">(<span class="default"><font color="Maroon" title="c6">T'</font> <a href="cat_1.html#K14" title="CAT_1:func.14">*</a> <span class="p3">(<span class="default"><a href="cat_2.html#K18" title="CAT_2:func.18">pr2</a> <font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c3">C'</font></span>)</span></span>)</span></span><a href="cat_2.html#K19" title="CAT_2:func.19">:&gt;</a></span>
 <b>by </b><i><a class="ref" href="funct_3.html#T87" title="FUNCT_3:th.87">FUNCT_3:87</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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