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<span class="kw">let </span><font color="Maroon" title="c9">E1</font>, <font color="Maroon" title="c10">E2</font> be   <a href="cat_1.html#V1" title="CAT_1:attr.1">strict</a>  <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"> ( the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c9">E1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <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> &amp; the <a href="struct_0.html#U4" title="STRUCT_0:sel.4">carrier'</a> of <font color="Maroon" title="c9">E1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</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> &amp; ( 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> holds  the <a href="graph_1.html#U1" title="GRAPH_1:sel.1">Source</a> of <font color="Maroon" title="c9">E1</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Olive" title="b1">k</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b1">k</font> <a href="commacat.html#K3" title="COMMACAT:func.3">`11</a>  ) &amp; ( 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> holds  the <a href="graph_1.html#U2" title="GRAPH_1:sel.2">Target</a> of <font color="Maroon" title="c9">E1</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Olive" title="b1">k</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b1">k</font> <a href="commacat.html#K4" title="COMMACAT:func.4">`12</a>  ) &amp; ( for <font color="Olive" title="b1">o</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> holds  the <a href="cat_1.html#U2" title="CAT_1:sel.2">Id</a> of <font color="Maroon" title="c9">E1</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Olive" title="b1">o</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="Olive" title="b1">o</font>,<font color="Olive" title="b1">o</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"><span class="p3">(<span class="default"><a href="cat_1.html#K6" title="CAT_1:func.6">id</a> <span class="p4">(<span class="default"><font color="Olive" title="b1">o</font> <a href="domain_1.html#K14" title="DOMAIN_1:func.14">`11</a> </span>)</span></span>)</span>,<span class="p3">(<span class="default"><a href="cat_1.html#K6" title="CAT_1:func.6">id</a> <span class="p4">(<span class="default"><font color="Olive" title="b1">o</font> <a href="domain_1.html#K15" title="DOMAIN_1:func.15">`12</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> ) &amp; the <a href="cat_1.html#U1" title="CAT_1:sel.1">Comp</a> of <font color="Maroon" title="c9">E1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="commacat.html#K6" title="COMMACAT:func.6">commaComp</a> <font color="Maroon" title="c4">F</font>,<font color="Maroon" title="c5">G</font> &amp; the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c10">E2</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <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> &amp; the <a href="struct_0.html#U4" title="STRUCT_0:sel.4">carrier'</a> of <font color="Maroon" title="c10">E2</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</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> &amp; ( 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> holds  the <a href="graph_1.html#U1" title="GRAPH_1:sel.1">Source</a> of <font color="Maroon" title="c10">E2</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Olive" title="b1">k</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b1">k</font> <a href="commacat.html#K3" title="COMMACAT:func.3">`11</a>  ) &amp; ( 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> holds  the <a href="graph_1.html#U2" title="GRAPH_1:sel.2">Target</a> of <font color="Maroon" title="c10">E2</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Olive" title="b1">k</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b1">k</font> <a href="commacat.html#K4" title="COMMACAT:func.4">`12</a>  ) &amp; ( for <font color="Olive" title="b1">o</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> holds  the <a href="cat_1.html#U2" title="CAT_1:sel.2">Id</a> of <font color="Maroon" title="c10">E2</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Olive" title="b1">o</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="Olive" title="b1">o</font>,<font color="Olive" title="b1">o</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"><span class="p3">(<span class="default"><a href="cat_1.html#K6" title="CAT_1:func.6">id</a> <span class="p4">(<span class="default"><font color="Olive" title="b1">o</font> <a href="domain_1.html#K14" title="DOMAIN_1:func.14">`11</a> </span>)</span></span>)</span>,<span class="p3">(<span class="default"><a href="cat_1.html#K6" title="CAT_1:func.6">id</a> <span class="p4">(<span class="default"><font color="Olive" title="b1">o</font> <a href="domain_1.html#K15" title="DOMAIN_1:func.15">`12</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> ) &amp; the <a href="cat_1.html#U1" title="CAT_1:sel.1">Comp</a> of <font color="Maroon" title="c10">E2</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="commacat.html#K6" title="COMMACAT:func.6">commaComp</a> <font color="Maroon" title="c4">F</font>,<font color="Maroon" title="c5">G</font> implies <font color="Maroon" title="c9">E1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c10">E2</font> )</span><br/>

<span class="kw">assume </span><span class="kw">that </span><br/><a NAME="E1:10_1_2"/><span class="lab"><font color="Green" title="E8">A55</font></span>: 
the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c9">E1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <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">and </span><br/><a NAME="E2:10_1_2"/><span class="lab"><font color="Green" title="E9">A56</font></span>: 
the <a href="struct_0.html#U4" title="STRUCT_0:sel.4">carrier'</a> of <font color="Maroon" title="c9">E1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</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">and </span><br/><a NAME="E3:10_1_2"/><span class="lab"><font color="Green" title="E10">A57</font></span>: 
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> holds  the <a href="graph_1.html#U1" title="GRAPH_1:sel.1">Source</a> of <font color="Maroon" title="c9">E1</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Olive" title="b1">k</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b1">k</font> <a href="commacat.html#K3" title="COMMACAT:func.3">`11</a> 
 <span class="kw">and </span><br/><a NAME="E4:10_1_2"/><span class="lab"><font color="Green" title="E11">A58</font></span>: 
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> holds  the <a href="graph_1.html#U2" title="GRAPH_1:sel.2">Target</a> of <font color="Maroon" title="c9">E1</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Olive" title="b1">k</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b1">k</font> <a href="commacat.html#K4" title="COMMACAT:func.4">`12</a> 
 <span class="kw">and </span><br/><a NAME="E5:10_1_2"/><span class="lab"><font color="Green" title="E12">A59</font></span>: 
for <font color="Olive" title="b1">o</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> holds  the <a href="cat_1.html#U2" title="CAT_1:sel.2">Id</a> of <font color="Maroon" title="c9">E1</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Olive" title="b1">o</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="Olive" title="b1">o</font>,<font color="Olive" title="b1">o</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"><span class="p3">(<span class="default"><a href="cat_1.html#K6" title="CAT_1:func.6">id</a> <span class="p4">(<span class="default"><font color="Olive" title="b1">o</font> <a href="domain_1.html#K14" title="DOMAIN_1:func.14">`11</a> </span>)</span></span>)</span>,<span class="p3">(<span class="default"><a href="cat_1.html#K6" title="CAT_1:func.6">id</a> <span class="p4">(<span class="default"><font color="Olive" title="b1">o</font> <a href="domain_1.html#K15" title="DOMAIN_1:func.15">`12</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>
 <span class="kw">and </span><br/><a NAME="E6:10_1_2"/><span class="lab"><font color="Green" title="E13">A60</font></span>: 
the <a href="cat_1.html#U1" title="CAT_1:sel.1">Comp</a> of <font color="Maroon" title="c9">E1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="commacat.html#K6" title="COMMACAT:func.6">commaComp</a> <font color="Maroon" title="c4">F</font>,<font color="Maroon" title="c5">G</font>
 <span class="kw">and </span><br/><a NAME="E7:10_1_2"/><span class="lab"><font color="Green" title="E14">A61</font></span>: 
( the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c10">E2</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <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> &amp; the <a href="struct_0.html#U4" title="STRUCT_0:sel.4">carrier'</a> of <font color="Maroon" title="c10">E2</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</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">and </span><br/><a NAME="E8:10_1_2"/><span class="lab"><font color="Green" title="E15">A62</font></span>: 
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> holds  the <a href="graph_1.html#U1" title="GRAPH_1:sel.1">Source</a> of <font color="Maroon" title="c10">E2</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Olive" title="b1">k</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b1">k</font> <a href="commacat.html#K3" title="COMMACAT:func.3">`11</a> 
 <span class="kw">and </span><br/><a NAME="E9:10_1_2"/><span class="lab"><font color="Green" title="E16">A63</font></span>: 
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> holds  the <a href="graph_1.html#U2" title="GRAPH_1:sel.2">Target</a> of <font color="Maroon" title="c10">E2</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Olive" title="b1">k</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b1">k</font> <a href="commacat.html#K4" title="COMMACAT:func.4">`12</a> 
 <span class="kw">and </span><br/><a NAME="E10:10_1_2"/><span class="lab"><font color="Green" title="E17">A64</font></span>: 
for <font color="Olive" title="b1">o</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> holds  the <a href="cat_1.html#U2" title="CAT_1:sel.2">Id</a> of <font color="Maroon" title="c10">E2</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Olive" title="b1">o</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="Olive" title="b1">o</font>,<font color="Olive" title="b1">o</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"><span class="p3">(<span class="default"><a href="cat_1.html#K6" title="CAT_1:func.6">id</a> <span class="p4">(<span class="default"><font color="Olive" title="b1">o</font> <a href="domain_1.html#K14" title="DOMAIN_1:func.14">`11</a> </span>)</span></span>)</span>,<span class="p3">(<span class="default"><a href="cat_1.html#K6" title="CAT_1:func.6">id</a> <span class="p4">(<span class="default"><font color="Olive" title="b1">o</font> <a href="domain_1.html#K15" title="DOMAIN_1:func.15">`12</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>
 <span class="kw">and </span><br/><a NAME="E11:10_1_2"/><span class="lab"><font color="Green" title="E18">A65</font></span>: 
the <a href="cat_1.html#U1" title="CAT_1:sel.1">Comp</a> of <font color="Maroon" title="c10">E2</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="commacat.html#K6" title="COMMACAT:func.6">commaComp</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"> <font color="Maroon" title="c9">E1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c10">E2</font></span><br/>

<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="10_1_2_1"><span class="kw">now </span></a><div class="add"><span class="kw">let </span><font color="Maroon" title="c11">x</font> be    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of <font color="Maroon">H<sub>2</sub></font>(<font color="Maroon" title="c9">E1</font>); <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> the <a href="graph_1.html#U2" title="GRAPH_1:sel.2">Target</a> of <font color="Maroon" title="c9">E1</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c11">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> the <a href="graph_1.html#U2" title="GRAPH_1:sel.2">Target</a> of <font color="Maroon" title="c10">E2</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c11">x</font></span><br/><span class="kw">thus </span>the <a href="graph_1.html#U2" title="GRAPH_1:sel.2">Target</a> of <font color="Maroon" title="c9">E1</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c11">x</font> = 
<font color="Maroon" title="c11">x</font> <a href="mcart_1.html#K18" title="MCART_1:func.18">`12</a> 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:10_1_2"><span class="lab"><font color="Green" title="E9">A56</font></span></a>, <a class="txt" href="#E4:10_1_2"><span class="lab"><font color="Green" title="E11">A58</font></span></a></span>
<br/>.= 
the <a href="graph_1.html#U2" title="GRAPH_1:sel.2">Target</a> of <font color="Maroon" title="c10">E2</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c11">x</font>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:10_1_2"><span class="lab"><font color="Green" title="E9">A56</font></span></a>, <a class="txt" href="#E9:10_1_2"><span class="lab"><font color="Green" title="E16">A63</font></span></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/></div><span class="kw">end;</span></div>
<a NAME="E13:10_1_2"/><span class="kw">then </span><span class="lab"><font color="Green" title="E19">A66</font></span>: 
the <a href="graph_1.html#U2" title="GRAPH_1:sel.2">Target</a> of <font color="Maroon" title="c9">E1</font> <a href="funct_2.html#R1" title="FUNCT_2:pred.1">=</a> the <a href="graph_1.html#U2" title="GRAPH_1:sel.2">Target</a> of <font color="Maroon" title="c10">E2</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:10_1_2"><span class="lab"><font color="Green" title="E8">A55</font></span></a>, <a class="txt" href="#E2:10_1_2"><span class="lab"><font color="Green" title="E9">A56</font></span></a>, <a class="txt" href="#E7:10_1_2"><span class="lab"><font color="Green" title="E14">A61</font></span></a>, <a class="ref" href="funct_2.html#T113" title="FUNCT_2:th.113">FUNCT_2:113</a></span>;<br/>
<div><span class="lab"><font color="Green" title="E20">A67</font></span>: <a class="txt" onclick="hs2(this)" href="javascript:()" title="10_1_2_2"><span class="kw">now </span></a><div class="add"><span class="kw">let </span><font color="Maroon" title="c11">x</font> be   <a href="cat_1.html#NM1" title="CAT_1:NM.1">Object</a> of <font color="Maroon" title="c9">E1</font>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> the <a href="cat_1.html#U2" title="CAT_1:sel.2">Id</a> of <font color="Maroon" title="c9">E1</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c11">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> the <a href="cat_1.html#U2" title="CAT_1:sel.2">Id</a> of <font color="Maroon" title="c10">E2</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c11">x</font></span><br/><span class="kw">reconsider </span><font color="Maroon" title="c12">o</font> = <font color="Maroon" title="c11">x</font> as    <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">by</span> <span class="lab"><a class="txt" href="#E1:10_1_2"><span class="lab"><font color="Green" title="E8">A55</font></span></a></span>;<br/><span class="kw">thus </span>the <a href="cat_1.html#U2" title="CAT_1:sel.2">Id</a> of <font color="Maroon" title="c9">E1</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c11">x</font> = 
<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="c12">o</font>,<font color="Maroon" title="c12">o</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"><span class="p3">(<span class="default"><a href="cat_1.html#K6" title="CAT_1:func.6">id</a> <span class="p4">(<span class="default"><font color="Maroon" title="c12">o</font> <a href="domain_1.html#K14" title="DOMAIN_1:func.14">`11</a> </span>)</span></span>)</span>,<span class="p3">(<span class="default"><a href="cat_1.html#K6" title="CAT_1:func.6">id</a> <span class="p4">(<span class="default"><font color="Maroon" title="c12">o</font> <a href="domain_1.html#K15" title="DOMAIN_1:func.15">`12</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>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E5:10_1_2"><span class="lab"><font color="Green" title="E12">A59</font></span></a></span>
<br/>.= 
the <a href="cat_1.html#U2" title="CAT_1:sel.2">Id</a> of <font color="Maroon" title="c10">E2</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c11">x</font>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E10:10_1_2"><span class="lab"><font color="Green" title="E17">A64</font></span></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/></div><span class="kw">end;</span></div>
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="10_1_2_3"><span class="kw">now </span></a><div class="add"><span class="kw">let </span><font color="Maroon" title="c11">x</font> be    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of <font color="Maroon">H<sub>2</sub></font>(<font color="Maroon" title="c9">E1</font>); <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> the <a href="graph_1.html#U1" title="GRAPH_1:sel.1">Source</a> of <font color="Maroon" title="c9">E1</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c11">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> the <a href="graph_1.html#U1" title="GRAPH_1:sel.1">Source</a> of <font color="Maroon" title="c10">E2</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c11">x</font></span><br/><span class="kw">thus </span>the <a href="graph_1.html#U1" title="GRAPH_1:sel.1">Source</a> of <font color="Maroon" title="c9">E1</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c11">x</font> = 
<font color="Maroon" title="c11">x</font> <a href="mcart_1.html#K17" title="MCART_1:func.17">`11</a> 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:10_1_2"><span class="lab"><font color="Green" title="E9">A56</font></span></a>, <a class="txt" href="#E3:10_1_2"><span class="lab"><font color="Green" title="E10">A57</font></span></a></span>
<br/>.= 
the <a href="graph_1.html#U1" title="GRAPH_1:sel.1">Source</a> of <font color="Maroon" title="c10">E2</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c11">x</font>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:10_1_2"><span class="lab"><font color="Green" title="E9">A56</font></span></a>, <a class="txt" href="#E8:10_1_2"><span class="lab"><font color="Green" title="E15">A62</font></span></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/></div><span class="kw">end;</span></div>
<a NAME="E16:10_1_2"/><span class="kw">then </span>
the <a href="graph_1.html#U1" title="GRAPH_1:sel.1">Source</a> of <font color="Maroon" title="c9">E1</font> <a href="funct_2.html#R1" title="FUNCT_2:pred.1">=</a> the <a href="graph_1.html#U1" title="GRAPH_1:sel.1">Source</a> of <font color="Maroon" title="c10">E2</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:10_1_2"><span class="lab"><font color="Green" title="E8">A55</font></span></a>, <a class="txt" href="#E2:10_1_2"><span class="lab"><font color="Green" title="E9">A56</font></span></a>, <a class="txt" href="#E7:10_1_2"><span class="lab"><font color="Green" title="E14">A61</font></span></a>, <a class="ref" href="funct_2.html#T113" title="FUNCT_2:th.113">FUNCT_2:113</a></span>;<br/>
<span class="kw">hence </span><a NAME="E17:10_1_2"/>
<font color="Maroon" title="c9">E1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c10">E2</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:10_1_2"><span class="lab"><font color="Green" title="E8">A55</font></span></a>, <a class="txt" href="#E2:10_1_2"><span class="lab"><font color="Green" title="E9">A56</font></span></a>, <a class="txt" href="#E6:10_1_2"><span class="lab"><font color="Green" title="E13">A60</font></span></a>, <a class="txt" href="#E7:10_1_2"><span class="lab"><font color="Green" title="E14">A61</font></span></a>, <a class="txt" href="#E11:10_1_2"><span class="lab"><font color="Green" title="E18">A65</font></span></a>, <a class="txt" href="#E13:10_1_2"><span class="lab"><font color="Green" title="E19">A66</font></span></a>, <a class="txt" href="#E14:10_1_2"><span class="lab"><font color="Green" title="E20">A67</font></span></a>, <a class="ref" href="funct_2.html#T113" title="FUNCT_2:th.113">FUNCT_2:113</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/>


</div>
