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<span class="kw">let </span><font color="Maroon" title="c3">F1</font>, <font color="Maroon" title="c4">F2</font> be    <a href="cat_1.html#M2" title="CAT_1:mode.2">Functor</a> of <span class="p1">(<span class="default"><a href="graph_1.html#K2" title="GRAPH_1:func.2">cod</a> <font color="Maroon" title="c2">f</font></span>)</span> <a href="cat_5.html#K15" title="CAT_5:func.15">-SliceCat</a> <font color="Maroon" title="c1">C</font>,<span class="p1">(<span class="default"><a href="graph_1.html#K1" title="GRAPH_1:func.1">dom</a> <font color="Maroon" title="c2">f</font></span>)</span> <a href="cat_5.html#K15" title="CAT_5:func.15">-SliceCat</a> <font color="Maroon" title="c1">C</font>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> ( (  for <font color="Olive" title="b1">m</font> being   <a href="cat_1.html#NM2" title="CAT_1:NM.2">Morphism</a> of <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="graph_1.html#K2" title="GRAPH_1:func.2">cod</a> <font color="Maroon" title="c2">f</font></span>)</span> <a href="cat_5.html#K15" title="CAT_5:func.15">-SliceCat</a> <font color="Maroon" title="c1">C</font></span>)</span> holds  <font color="Maroon" title="c3">F1</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Olive" title="b1">m</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1"><a href="cat_2.html#K13" title="CAT_2:func.13">[</a><span class="default"><span class="p2"><a href="cat_2.html#K13" title="CAT_2:func.13">[</a><span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Olive" title="b1">m</font> <a href="cat_5.html#K20" title="CAT_5:func.20">`11</a></span>)</span> <a href="cat_1.html#K1" title="CAT_1:func.1">*</a> <font color="Maroon" title="c2">f</font></span>)</span>,<span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Olive" title="b1">m</font> <a href="cat_5.html#K21" title="CAT_5:func.21">`12</a></span>)</span> <a href="cat_1.html#K1" title="CAT_1:func.1">*</a> <font color="Maroon" title="c2">f</font></span>)</span></span><a href="cat_2.html#K13" title="CAT_2:func.13">]</a></span>,<span class="p2">(<span class="default"><font color="Olive" title="b1">m</font> <a href="cat_5.html#K19" title="CAT_5:func.19">`2</a></span>)</span></span><a href="cat_2.html#K13" title="CAT_2:func.13">]</a></span> ) &amp; (  for <font color="Olive" title="b1">m</font> being   <a href="cat_1.html#NM2" title="CAT_1:NM.2">Morphism</a> of <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="graph_1.html#K2" title="GRAPH_1:func.2">cod</a> <font color="Maroon" title="c2">f</font></span>)</span> <a href="cat_5.html#K15" title="CAT_5:func.15">-SliceCat</a> <font color="Maroon" title="c1">C</font></span>)</span> holds  <font color="Maroon" title="c4">F2</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Olive" title="b1">m</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1"><a href="cat_2.html#K13" title="CAT_2:func.13">[</a><span class="default"><span class="p2"><a href="cat_2.html#K13" title="CAT_2:func.13">[</a><span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Olive" title="b1">m</font> <a href="cat_5.html#K20" title="CAT_5:func.20">`11</a></span>)</span> <a href="cat_1.html#K1" title="CAT_1:func.1">*</a> <font color="Maroon" title="c2">f</font></span>)</span>,<span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Olive" title="b1">m</font> <a href="cat_5.html#K21" title="CAT_5:func.21">`12</a></span>)</span> <a href="cat_1.html#K1" title="CAT_1:func.1">*</a> <font color="Maroon" title="c2">f</font></span>)</span></span><a href="cat_2.html#K13" title="CAT_2:func.13">]</a></span>,<span class="p2">(<span class="default"><font color="Olive" title="b1">m</font> <a href="cat_5.html#K19" title="CAT_5:func.19">`2</a></span>)</span></span><a href="cat_2.html#K13" title="CAT_2:func.13">]</a></span> ) implies <font color="Maroon" title="c3">F1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c4">F2</font> )</span><br/>

<span class="kw">assume </span><span class="kw">that </span><br/><a NAME="E1:60_2_2"/><span class="lab"><font color="Green" title="E38">A99</font></span>: 
 for <font color="Olive" title="b1">m</font> being   <a href="cat_1.html#NM2" title="CAT_1:NM.2">Morphism</a> of <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="graph_1.html#K2" title="GRAPH_1:func.2">cod</a> <font color="Maroon" title="c2">f</font></span>)</span> <a href="cat_5.html#K15" title="CAT_5:func.15">-SliceCat</a> <font color="Maroon" title="c1">C</font></span>)</span> holds  <font color="Maroon" title="c3">F1</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Olive" title="b1">m</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1"><a href="cat_2.html#K13" title="CAT_2:func.13">[</a><span class="default"><span class="p2"><a href="cat_2.html#K13" title="CAT_2:func.13">[</a><span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Olive" title="b1">m</font> <a href="cat_5.html#K20" title="CAT_5:func.20">`11</a></span>)</span> <a href="cat_1.html#K1" title="CAT_1:func.1">*</a> <font color="Maroon" title="c2">f</font></span>)</span>,<span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Olive" title="b1">m</font> <a href="cat_5.html#K21" title="CAT_5:func.21">`12</a></span>)</span> <a href="cat_1.html#K1" title="CAT_1:func.1">*</a> <font color="Maroon" title="c2">f</font></span>)</span></span><a href="cat_2.html#K13" title="CAT_2:func.13">]</a></span>,<span class="p2">(<span class="default"><font color="Olive" title="b1">m</font> <a href="cat_5.html#K19" title="CAT_5:func.19">`2</a></span>)</span></span><a href="cat_2.html#K13" title="CAT_2:func.13">]</a></span>
 <span class="kw">and </span><br/><a NAME="E2:60_2_2"/><span class="lab"><font color="Green" title="E39">A100</font></span>: 
 for <font color="Olive" title="b1">m</font> being   <a href="cat_1.html#NM2" title="CAT_1:NM.2">Morphism</a> of <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="graph_1.html#K2" title="GRAPH_1:func.2">cod</a> <font color="Maroon" title="c2">f</font></span>)</span> <a href="cat_5.html#K15" title="CAT_5:func.15">-SliceCat</a> <font color="Maroon" title="c1">C</font></span>)</span> holds  <font color="Maroon" title="c4">F2</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Olive" title="b1">m</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1"><a href="cat_2.html#K13" title="CAT_2:func.13">[</a><span class="default"><span class="p2"><a href="cat_2.html#K13" title="CAT_2:func.13">[</a><span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Olive" title="b1">m</font> <a href="cat_5.html#K20" title="CAT_5:func.20">`11</a></span>)</span> <a href="cat_1.html#K1" title="CAT_1:func.1">*</a> <font color="Maroon" title="c2">f</font></span>)</span>,<span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Olive" title="b1">m</font> <a href="cat_5.html#K21" title="CAT_5:func.21">`12</a></span>)</span> <a href="cat_1.html#K1" title="CAT_1:func.1">*</a> <font color="Maroon" title="c2">f</font></span>)</span></span><a href="cat_2.html#K13" title="CAT_2:func.13">]</a></span>,<span class="p2">(<span class="default"><font color="Olive" title="b1">m</font> <a href="cat_5.html#K19" title="CAT_5:func.19">`2</a></span>)</span></span><a href="cat_2.html#K13" title="CAT_2:func.13">]</a></span>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> <font color="Maroon" title="c3">F1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c4">F2</font></span><br/>

<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="60_2_2_1"><span class="kw">now </span></a><div class="add"><span class="kw">let </span><font color="Maroon" title="c5">m</font> be   <a href="cat_1.html#NM2" title="CAT_1:NM.2">Morphism</a> of <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="graph_1.html#K2" title="GRAPH_1:func.2">cod</a> <font color="Maroon" title="c2">f</font></span>)</span> <a href="cat_5.html#K15" title="CAT_5:func.15">-SliceCat</a> <font color="Maroon" title="c1">C</font></span>)</span>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> <font color="Maroon" title="c3">F1</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c5">m</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c4">F2</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c5">m</font></span><br/><span class="kw">thus </span><font color="Maroon" title="c3">F1</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c5">m</font> = 
<span class="p1"><a href="cat_2.html#K13" title="CAT_2:func.13">[</a><span class="default"><span class="p2"><a href="cat_2.html#K13" title="CAT_2:func.13">[</a><span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon" title="c5">m</font> <a href="cat_5.html#K20" title="CAT_5:func.20">`11</a></span>)</span> <a href="cat_1.html#K1" title="CAT_1:func.1">*</a> <font color="Maroon" title="c2">f</font></span>)</span>,<span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon" title="c5">m</font> <a href="cat_5.html#K21" title="CAT_5:func.21">`12</a></span>)</span> <a href="cat_1.html#K1" title="CAT_1:func.1">*</a> <font color="Maroon" title="c2">f</font></span>)</span></span><a href="cat_2.html#K13" title="CAT_2:func.13">]</a></span>,<span class="p2">(<span class="default"><font color="Maroon" title="c5">m</font> <a href="cat_5.html#K19" title="CAT_5:func.19">`2</a></span>)</span></span><a href="cat_2.html#K13" title="CAT_2:func.13">]</a></span>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:60_2_2"><span class="lab"><font color="Green" title="E38">A99</font></span></a></span>
<br/>.= 
<font color="Maroon" title="c4">F2</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c5">m</font>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:60_2_2"><span class="lab"><font color="Green" title="E39">A100</font></span></a></span>
; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> verum</span><br/></div><span class="kw">end;</span></div>
<span class="kw">hence </span><a NAME="E4:60_2_2"/>
<font color="Maroon" title="c3">F1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c4">F2</font>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="funct_2.html#T63" title="FUNCT_2:th.63">FUNCT_2:63</a></span>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> verum</span><br/>


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