<?xml version="1.0"?>
<div class="add">

<span class="kw">let </span><font color="Maroon" title="c1">C</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="firebrick">::  thesis: </font></span></a><span class="hide">  for <font color="Olive" title="b1">C1</font>, <font color="Olive" title="b2">C2</font> being    <a href="cat_2.html#M3" title="CAT_2:mode.3">Subcategory</a> of <font color="Maroon" title="c1">C</font>  st  the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Olive" title="b1">C1</font> <a href="subset_1.html#R2" title="SUBSET_1:pred.2">meets</a>  the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Olive" title="b2">C2</font> holds <br/><font color="Olive" title="b1">C1</font> <a href="cat_5.html#K6" title="CAT_5:func.6">/\</a> <font color="Olive" title="b2">C2</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b2">C2</font> <a href="cat_5.html#K6" title="CAT_5:func.6">/\</a> <font color="Olive" title="b1">C1</font></span><br/><span class="kw">let </span><font color="Maroon" title="c2">C1</font>, <font color="Maroon" title="c3">C2</font> be    <a href="cat_2.html#M3" title="CAT_2:mode.3">Subcategory</a> of <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"> (  the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c2">C1</font> <a href="subset_1.html#R2" title="SUBSET_1:pred.2">meets</a>  the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c3">C2</font> implies <font color="Maroon" title="c2">C1</font> <a href="cat_5.html#K6" title="CAT_5:func.6">/\</a> <font color="Maroon" title="c3">C2</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c3">C2</font> <a href="cat_5.html#K6" title="CAT_5:func.6">/\</a> <font color="Maroon" title="c2">C1</font> )</span><br/>





<span class="kw">assume </span><a NAME="E1:14"/>
 the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c2">C1</font> <a href="xboole_0.html#K3" title="XBOOLE_0:func.3">/\</a>  the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c3">C2</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a>  <a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a> 
 ; <span class="comment"><font color="firebrick">:: according to </font></span><a class="ref" href="xboole_0.html#D7" title="XBOOLE_0:def.7">XBOOLE_0:def 7</a> <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="c2">C1</font> <a href="cat_5.html#K6" title="CAT_5:func.6">/\</a> <font color="Maroon" title="c3">C2</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c3">C2</font> <a href="cat_5.html#K6" title="CAT_5:func.6">/\</a> <font color="Maroon" title="c2">C1</font></span><br/>

<span class="kw">then </span><span class="kw">reconsider </span><font color="Maroon" title="c4">O</font> =  the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c2">C1</font> <a href="xboole_0.html#K3" title="XBOOLE_0:func.3">/\</a>  the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c3">C2</font> as   non  <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a>   <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a>  ;<br/>
<span class="kw">set </span><font color="Maroon" title="c5">o</font> =  the    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of <font color="Maroon" title="c4">O</font>;<br/>
<span class="kw">set </span><font color="Maroon" title="c6">C12</font> = <font color="Maroon" title="c2">C1</font> <a href="cat_5.html#K6" title="CAT_5:func.6">/\</a> <font color="Maroon" title="c3">C2</font>;<br/>
<span class="kw">set </span><font color="Maroon" title="c7">C21</font> = <font color="Maroon" title="c3">C2</font> <a href="cat_5.html#K6" title="CAT_5:func.6">/\</a> <font color="Maroon" title="c2">C1</font>;<br/>
<span class="kw">set </span><font color="Maroon" title="c8">M1</font> =  the <a href="struct_0.html#U4" title="STRUCT_0:sel.4">carrier'</a> of <font color="Maroon" title="c2">C1</font>;<br/>
<span class="kw">set </span><font color="Maroon" title="c9">M2</font> =  the <a href="struct_0.html#U4" title="STRUCT_0:sel.4">carrier'</a> of <font color="Maroon" title="c3">C2</font>;<br/>
<span class="kw">set </span><font color="Maroon" title="c10">O1</font> =  the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c2">C1</font>;<br/>
<span class="kw">set </span><font color="Maroon" title="c11">O2</font> =  the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c3">C2</font>;<br/>
<a NAME="E3:14"/><span class="lab"><font color="Green" title="E8">A1</font></span>: 
 the    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of <font color="Maroon" title="c4">O</font> is   <a href="cat_1.html#NM1" title="CAT_1:NM.1">Object</a> of <font color="Maroon" title="c2">C1</font>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="xboole_0.html#D4" title="XBOOLE_0:def.4">XBOOLE_0:def 4</a></span>;<br/>
<a NAME="E4:14"/><span class="lab"><font color="Green" title="E9">A2</font></span>: 
 the    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of <font color="Maroon" title="c4">O</font> is   <a href="cat_1.html#NM1" title="CAT_1:NM.1">Object</a> of <font color="Maroon" title="c3">C2</font>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="xboole_0.html#D4" title="XBOOLE_0:def.4">XBOOLE_0:def 4</a></span>;<br/>
<a NAME="E5:14"/><span class="kw">then </span><span class="lab"><font color="Green" title="E10">A3</font></span>: 
 the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <span class="p1">(<span class="default"><font color="Maroon" title="c2">C1</font> <a href="cat_5.html#K6" title="CAT_5:func.6">/\</a> <font color="Maroon" title="c3">C2</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c4">O</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E3:14"><span class="lab"><font color="Green" title="E8">A1</font></span></a>, <a class="ref" href="cat_5.html#D2" target="_self" title="CAT_5:def.2">Def2</a></span>;<br/>
<a NAME="E6:14"/><span class="lab"><font color="Green" title="E11">A4</font></span>: 
 the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <span class="p1">(<span class="default"><font color="Maroon" title="c3">C2</font> <a href="cat_5.html#K6" title="CAT_5:func.6">/\</a> <font color="Maroon" title="c2">C1</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c4">O</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E3:14"><span class="lab"><font color="Green" title="E8">A1</font></span></a>, <a class="txt" href="#E4:14"><span class="lab"><font color="Green" title="E9">A2</font></span></a>, <a class="ref" href="cat_5.html#D2" target="_self" title="CAT_5:def.2">Def2</a></span>;<br/>
<a NAME="E7:14"/><span class="lab"><font color="Green" title="E12">A5</font></span>: 
 the <a href="struct_0.html#U4" title="STRUCT_0:sel.4">carrier'</a> of <span class="p1">(<span class="default"><font color="Maroon" title="c2">C1</font> <a href="cat_5.html#K6" title="CAT_5:func.6">/\</a> <font color="Maroon" title="c3">C2</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  the <a href="struct_0.html#U4" title="STRUCT_0:sel.4">carrier'</a> of <font color="Maroon" title="c2">C1</font> <a href="xboole_0.html#K3" title="XBOOLE_0:func.3">/\</a>  the <a href="struct_0.html#U4" title="STRUCT_0:sel.4">carrier'</a> of <font color="Maroon" title="c3">C2</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E3:14"><span class="lab"><font color="Green" title="E8">A1</font></span></a>, <a class="txt" href="#E4:14"><span class="lab"><font color="Green" title="E9">A2</font></span></a>, <a class="ref" href="cat_5.html#D2" target="_self" title="CAT_5:def.2">Def2</a></span>;<br/>
<a NAME="E8:14"/><span class="lab"><font color="Green" title="E13">A6</font></span>: 
 the <a href="graph_1.html#U1" title="GRAPH_1:sel.1">Source</a> of <span class="p1">(<span class="default"><font color="Maroon" title="c3">C2</font> <a href="cat_5.html#K6" title="CAT_5:func.6">/\</a> <font color="Maroon" title="c2">C1</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">Source</a> of <font color="Maroon" title="c3">C2</font> <a href="partfun1.html#K2" title="PARTFUN1:func.2">|</a>  the <a href="struct_0.html#U4" title="STRUCT_0:sel.4">carrier'</a> of <font color="Maroon" title="c2">C1</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E3:14"><span class="lab"><font color="Green" title="E8">A1</font></span></a>, <a class="txt" href="#E4:14"><span class="lab"><font color="Green" title="E9">A2</font></span></a>, <a class="ref" href="cat_5.html#D2" target="_self" title="CAT_5:def.2">Def2</a></span>;<br/>
<a NAME="E9:14"/><span class="lab"><font color="Green" title="E14">A7</font></span>: 
 the <a href="graph_1.html#U1" title="GRAPH_1:sel.1">Source</a> of <span class="p1">(<span class="default"><font color="Maroon" title="c2">C1</font> <a href="cat_5.html#K6" title="CAT_5:func.6">/\</a> <font color="Maroon" title="c3">C2</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">Source</a> of <font color="Maroon" title="c2">C1</font> <a href="partfun1.html#K2" title="PARTFUN1:func.2">|</a>  the <a href="struct_0.html#U4" title="STRUCT_0:sel.4">carrier'</a> of <font color="Maroon" title="c3">C2</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E3:14"><span class="lab"><font color="Green" title="E8">A1</font></span></a>, <a class="txt" href="#E4:14"><span class="lab"><font color="Green" title="E9">A2</font></span></a>, <a class="ref" href="cat_5.html#D2" target="_self" title="CAT_5:def.2">Def2</a></span>;<br/>
<a NAME="E10:14"/><span class="lab"><font color="Green" title="E15">A8</font></span>: 
 the <a href="graph_1.html#U2" title="GRAPH_1:sel.2">Target</a> of <span class="p1">(<span class="default"><font color="Maroon" title="c3">C2</font> <a href="cat_5.html#K6" title="CAT_5:func.6">/\</a> <font color="Maroon" title="c2">C1</font></span>)</span> <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="c3">C2</font> <a href="partfun1.html#K2" title="PARTFUN1:func.2">|</a>  the <a href="struct_0.html#U4" title="STRUCT_0:sel.4">carrier'</a> of <font color="Maroon" title="c2">C1</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E3:14"><span class="lab"><font color="Green" title="E8">A1</font></span></a>, <a class="txt" href="#E4:14"><span class="lab"><font color="Green" title="E9">A2</font></span></a>, <a class="ref" href="cat_5.html#D2" target="_self" title="CAT_5:def.2">Def2</a></span>;<br/>
<a NAME="E11:14"/><span class="lab"><font color="Green" title="E16">A9</font></span>: 
 the <a href="graph_1.html#U2" title="GRAPH_1:sel.2">Target</a> of <span class="p1">(<span class="default"><font color="Maroon" title="c2">C1</font> <a href="cat_5.html#K6" title="CAT_5:func.6">/\</a> <font color="Maroon" title="c3">C2</font></span>)</span> <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="c2">C1</font> <a href="partfun1.html#K2" title="PARTFUN1:func.2">|</a>  the <a href="struct_0.html#U4" title="STRUCT_0:sel.4">carrier'</a> of <font color="Maroon" title="c3">C2</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E3:14"><span class="lab"><font color="Green" title="E8">A1</font></span></a>, <a class="txt" href="#E4:14"><span class="lab"><font color="Green" title="E9">A2</font></span></a>, <a class="ref" href="cat_5.html#D2" target="_self" title="CAT_5:def.2">Def2</a></span>;<br/>
<a NAME="E12:14"/><span class="lab"><font color="Green" title="E17">A10</font></span>: 
 the <a href="cat_1.html#U2" title="CAT_1:sel.2">Id</a> of <span class="p1">(<span class="default"><font color="Maroon" title="c3">C2</font> <a href="cat_5.html#K6" title="CAT_5:func.6">/\</a> <font color="Maroon" title="c2">C1</font></span>)</span> <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="c3">C2</font> <a href="partfun1.html#K2" title="PARTFUN1:func.2">|</a>  the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c2">C1</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E3:14"><span class="lab"><font color="Green" title="E8">A1</font></span></a>, <a class="txt" href="#E4:14"><span class="lab"><font color="Green" title="E9">A2</font></span></a>, <a class="ref" href="cat_5.html#D2" target="_self" title="CAT_5:def.2">Def2</a></span>;<br/>
<a NAME="E13:14"/><span class="lab"><font color="Green" title="E18">A11</font></span>: 
 the <a href="cat_1.html#U2" title="CAT_1:sel.2">Id</a> of <span class="p1">(<span class="default"><font color="Maroon" title="c2">C1</font> <a href="cat_5.html#K6" title="CAT_5:func.6">/\</a> <font color="Maroon" title="c3">C2</font></span>)</span> <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="c2">C1</font> <a href="partfun1.html#K2" title="PARTFUN1:func.2">|</a>  the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c3">C2</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E3:14"><span class="lab"><font color="Green" title="E8">A1</font></span></a>, <a class="txt" href="#E4:14"><span class="lab"><font color="Green" title="E9">A2</font></span></a>, <a class="ref" href="cat_5.html#D2" target="_self" title="CAT_5:def.2">Def2</a></span>;<br/>
<a NAME="E14:14"/><span class="lab"><font color="Green" title="E19">A12</font></span>: 
 the <a href="cat_1.html#U1" title="CAT_1:sel.1">Comp</a> of <span class="p1">(<span class="default"><font color="Maroon" title="c3">C2</font> <a href="cat_5.html#K6" title="CAT_5:func.6">/\</a> <font color="Maroon" title="c2">C1</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  the <a href="cat_1.html#U1" title="CAT_1:sel.1">Comp</a> of <font color="Maroon" title="c3">C2</font> <a href="realset1.html#K1" title="REALSET1:func.1">||</a>  the <a href="struct_0.html#U4" title="STRUCT_0:sel.4">carrier'</a> of <font color="Maroon" title="c2">C1</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E3:14"><span class="lab"><font color="Green" title="E8">A1</font></span></a>, <a class="txt" href="#E4:14"><span class="lab"><font color="Green" title="E9">A2</font></span></a>, <a class="ref" href="cat_5.html#D2" target="_self" title="CAT_5:def.2">Def2</a></span>;<br/>
<a NAME="E15:14"/><span class="lab"><font color="Green" title="E20">A13</font></span>: 
 the <a href="cat_1.html#U1" title="CAT_1:sel.1">Comp</a> of <span class="p1">(<span class="default"><font color="Maroon" title="c2">C1</font> <a href="cat_5.html#K6" title="CAT_5:func.6">/\</a> <font color="Maroon" title="c3">C2</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  the <a href="cat_1.html#U1" title="CAT_1:sel.1">Comp</a> of <font color="Maroon" title="c2">C1</font> <a href="realset1.html#K1" title="REALSET1:func.1">||</a>  the <a href="struct_0.html#U4" title="STRUCT_0:sel.4">carrier'</a> of <font color="Maroon" title="c3">C2</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E3:14"><span class="lab"><font color="Green" title="E8">A1</font></span></a>, <a class="txt" href="#E4:14"><span class="lab"><font color="Green" title="E9">A2</font></span></a>, <a class="ref" href="cat_5.html#D2" target="_self" title="CAT_5:def.2">Def2</a></span>;<br/>
<a NAME="E16:14"/><span class="lab"><font color="Green" title="E21">A14</font></span>: 
 the <a href="graph_1.html#U1" title="GRAPH_1:sel.1">Source</a> of <font color="Maroon" title="c2">C1</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="c1">C</font> <a href="partfun1.html#K2" title="PARTFUN1:func.2">|</a>  the <a href="struct_0.html#U4" title="STRUCT_0:sel.4">carrier'</a> of <font color="Maroon" title="c2">C1</font>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="nattra_1.html#T8" title="NATTRA_1:th.8">NATTRA_1:8</a></span>;<br/>
<a NAME="E17:14"/><span class="lab"><font color="Green" title="E22">A15</font></span>: 
 the <a href="graph_1.html#U2" title="GRAPH_1:sel.2">Target</a> of <font color="Maroon" title="c2">C1</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="c1">C</font> <a href="partfun1.html#K2" title="PARTFUN1:func.2">|</a>  the <a href="struct_0.html#U4" title="STRUCT_0:sel.4">carrier'</a> of <font color="Maroon" title="c2">C1</font>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="nattra_1.html#T8" title="NATTRA_1:th.8">NATTRA_1:8</a></span>;<br/>
<a NAME="E18:14"/><span class="lab"><font color="Green" title="E23">A16</font></span>: 
 the <a href="graph_1.html#U1" title="GRAPH_1:sel.1">Source</a> of <font color="Maroon" title="c3">C2</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="c1">C</font> <a href="partfun1.html#K2" title="PARTFUN1:func.2">|</a>  the <a href="struct_0.html#U4" title="STRUCT_0:sel.4">carrier'</a> of <font color="Maroon" title="c3">C2</font>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="nattra_1.html#T8" title="NATTRA_1:th.8">NATTRA_1:8</a></span>;<br/>
<a NAME="E19:14"/><span class="lab"><font color="Green" title="E24">A17</font></span>: 
 the <a href="graph_1.html#U2" title="GRAPH_1:sel.2">Target</a> of <font color="Maroon" title="c3">C2</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="c1">C</font> <a href="partfun1.html#K2" title="PARTFUN1:func.2">|</a>  the <a href="struct_0.html#U4" title="STRUCT_0:sel.4">carrier'</a> of <font color="Maroon" title="c3">C2</font>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="nattra_1.html#T8" title="NATTRA_1:th.8">NATTRA_1:8</a></span>;<br/>
<span class="lab"><font color="Green" title="E25">A18</font></span>:  the <a href="graph_1.html#U1" title="GRAPH_1:sel.1">Source</a> of <span class="p1">(<span class="default"><font color="Maroon" title="c2">C1</font> <a href="cat_5.html#K6" title="CAT_5:func.6">/\</a> <font color="Maroon" title="c3">C2</font></span>)</span> = 
 the <a href="graph_1.html#U1" title="GRAPH_1:sel.1">Source</a> of <font color="Maroon" title="c1">C</font> <a href="partfun1.html#K2" title="PARTFUN1:func.2">|</a> <span class="p1">(<span class="default"> the <a href="struct_0.html#U4" title="STRUCT_0:sel.4">carrier'</a> of <font color="Maroon" title="c2">C1</font> <a href="xboole_0.html#K3" title="XBOOLE_0:func.3">/\</a>  the <a href="struct_0.html#U4" title="STRUCT_0:sel.4">carrier'</a> of <font color="Maroon" title="c3">C2</font></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E9:14"><span class="lab"><font color="Green" title="E14">A7</font></span></a>, <a class="txt" href="#E16:14"><span class="lab"><font color="Green" title="E21">A14</font></span></a>, <a class="ref" href="relat_1.html#T71" title="RELAT_1:th.71">RELAT_1:71</a></span>
<br/>.= 
 the <a href="graph_1.html#U1" title="GRAPH_1:sel.1">Source</a> of <span class="p1">(<span class="default"><font color="Maroon" title="c3">C2</font> <a href="cat_5.html#K6" title="CAT_5:func.6">/\</a> <font color="Maroon" title="c2">C1</font></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E8:14"><span class="lab"><font color="Green" title="E13">A6</font></span></a>, <a class="txt" href="#E18:14"><span class="lab"><font color="Green" title="E23">A16</font></span></a>, <a class="ref" href="relat_1.html#T71" title="RELAT_1:th.71">RELAT_1:71</a></span>
;<br/>
<span class="lab"><font color="Green" title="E26">A19</font></span>:  the <a href="graph_1.html#U2" title="GRAPH_1:sel.2">Target</a> of <span class="p1">(<span class="default"><font color="Maroon" title="c2">C1</font> <a href="cat_5.html#K6" title="CAT_5:func.6">/\</a> <font color="Maroon" title="c3">C2</font></span>)</span> = 
 the <a href="graph_1.html#U2" title="GRAPH_1:sel.2">Target</a> of <font color="Maroon" title="c1">C</font> <a href="partfun1.html#K2" title="PARTFUN1:func.2">|</a> <span class="p1">(<span class="default"> the <a href="struct_0.html#U4" title="STRUCT_0:sel.4">carrier'</a> of <font color="Maroon" title="c2">C1</font> <a href="xboole_0.html#K3" title="XBOOLE_0:func.3">/\</a>  the <a href="struct_0.html#U4" title="STRUCT_0:sel.4">carrier'</a> of <font color="Maroon" title="c3">C2</font></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E11:14"><span class="lab"><font color="Green" title="E16">A9</font></span></a>, <a class="txt" href="#E17:14"><span class="lab"><font color="Green" title="E22">A15</font></span></a>, <a class="ref" href="relat_1.html#T71" title="RELAT_1:th.71">RELAT_1:71</a></span>
<br/>.= 
 the <a href="graph_1.html#U2" title="GRAPH_1:sel.2">Target</a> of <span class="p1">(<span class="default"><font color="Maroon" title="c3">C2</font> <a href="cat_5.html#K6" title="CAT_5:func.6">/\</a> <font color="Maroon" title="c2">C1</font></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E10:14"><span class="lab"><font color="Green" title="E15">A8</font></span></a>, <a class="txt" href="#E19:14"><span class="lab"><font color="Green" title="E24">A17</font></span></a>, <a class="ref" href="relat_1.html#T71" title="RELAT_1:th.71">RELAT_1:71</a></span>
;<br/>
<span class="lab"><font color="Green" title="E27">A20</font></span>:  the <a href="cat_1.html#U1" title="CAT_1:sel.1">Comp</a> of <span class="p1">(<span class="default"><font color="Maroon" title="c2">C1</font> <a href="cat_5.html#K6" title="CAT_5:func.6">/\</a> <font color="Maroon" title="c3">C2</font></span>)</span> = 
<span class="p1">(<span class="default"> the <a href="cat_1.html#U1" title="CAT_1:sel.1">Comp</a> of <font color="Maroon" title="c1">C</font> <a href="realset1.html#K1" title="REALSET1:func.1">||</a>  the <a href="struct_0.html#U4" title="STRUCT_0:sel.4">carrier'</a> of <font color="Maroon" title="c2">C1</font></span>)</span> <a href="realset1.html#K1" title="REALSET1:func.1">||</a>  the <a href="struct_0.html#U4" title="STRUCT_0:sel.4">carrier'</a> of <font color="Maroon" title="c3">C2</font>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E15:14"><span class="lab"><font color="Green" title="E20">A13</font></span></a>, <a class="ref" href="nattra_1.html#T8" title="NATTRA_1:th.8">NATTRA_1:8</a></span>
<br/>.= 
 the <a href="cat_1.html#U1" title="CAT_1:sel.1">Comp</a> of <font color="Maroon" title="c1">C</font> <a href="partfun1.html#K2" title="PARTFUN1:func.2">|</a> <span class="p1">(<span class="default"><span class="p2"><a href="zfmisc_1.html#K2" title="ZFMISC_1:func.2">[:</a><span class="default"> the <a href="struct_0.html#U4" title="STRUCT_0:sel.4">carrier'</a> of <font color="Maroon" title="c2">C1</font>, the <a href="struct_0.html#U4" title="STRUCT_0:sel.4">carrier'</a> of <font color="Maroon" title="c2">C1</font></span><a href="zfmisc_1.html#K2" title="ZFMISC_1:func.2">:]</a></span> <a href="xboole_0.html#K3" title="XBOOLE_0:func.3">/\</a> <span class="p2"><a href="zfmisc_1.html#K2" title="ZFMISC_1:func.2">[:</a><span class="default"> the <a href="struct_0.html#U4" title="STRUCT_0:sel.4">carrier'</a> of <font color="Maroon" title="c3">C2</font>, the <a href="struct_0.html#U4" title="STRUCT_0:sel.4">carrier'</a> of <font color="Maroon" title="c3">C2</font></span><a href="zfmisc_1.html#K2" title="ZFMISC_1:func.2">:]</a></span></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="ref" href="relat_1.html#T71" title="RELAT_1:th.71">RELAT_1:71</a></span>
<br/>.= 
<span class="p1">(<span class="default"> the <a href="cat_1.html#U1" title="CAT_1:sel.1">Comp</a> of <font color="Maroon" title="c1">C</font> <a href="realset1.html#K1" title="REALSET1:func.1">||</a>  the <a href="struct_0.html#U4" title="STRUCT_0:sel.4">carrier'</a> of <font color="Maroon" title="c3">C2</font></span>)</span> <a href="realset1.html#K1" title="REALSET1:func.1">||</a>  the <a href="struct_0.html#U4" title="STRUCT_0:sel.4">carrier'</a> of <font color="Maroon" title="c2">C1</font>
<span class="kw">by</span> <span class="lab"><a class="ref" href="relat_1.html#T71" title="RELAT_1:th.71">RELAT_1:71</a></span>
<br/>.= 
 the <a href="cat_1.html#U1" title="CAT_1:sel.1">Comp</a> of <span class="p1">(<span class="default"><font color="Maroon" title="c3">C2</font> <a href="cat_5.html#K6" title="CAT_5:func.6">/\</a> <font color="Maroon" title="c2">C1</font></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E14:14"><span class="lab"><font color="Green" title="E19">A12</font></span></a>, <a class="ref" href="nattra_1.html#T8" title="NATTRA_1:th.8">NATTRA_1:8</a></span>
;<br/>
 the <a href="cat_1.html#U2" title="CAT_1:sel.2">Id</a> of <span class="p1">(<span class="default"><font color="Maroon" title="c2">C1</font> <a href="cat_5.html#K6" title="CAT_5:func.6">/\</a> <font color="Maroon" title="c3">C2</font></span>)</span> = 
<span class="p1">(<span class="default"> the <a href="cat_1.html#U2" title="CAT_1:sel.2">Id</a> of <font color="Maroon" title="c1">C</font> <a href="partfun1.html#K2" title="PARTFUN1:func.2">|</a>  the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c2">C1</font></span>)</span> <a href="partfun1.html#K2" title="PARTFUN1:func.2">|</a>  the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c3">C2</font>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E13:14"><span class="lab"><font color="Green" title="E18">A11</font></span></a>, <a class="ref" href="nattra_1.html#T8" title="NATTRA_1:th.8">NATTRA_1:8</a></span>
<br/>.= 
 the <a href="cat_1.html#U2" title="CAT_1:sel.2">Id</a> of <font color="Maroon" title="c1">C</font> <a href="partfun1.html#K2" title="PARTFUN1:func.2">|</a> <span class="p1">(<span class="default"> the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c2">C1</font> <a href="xboole_0.html#K3" title="XBOOLE_0:func.3">/\</a>  the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c3">C2</font></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="ref" href="relat_1.html#T71" title="RELAT_1:th.71">RELAT_1:71</a></span>
<br/>.= 
<span class="p1">(<span class="default"> the <a href="cat_1.html#U2" title="CAT_1:sel.2">Id</a> of <font color="Maroon" title="c1">C</font> <a href="partfun1.html#K2" title="PARTFUN1:func.2">|</a>  the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c3">C2</font></span>)</span> <a href="partfun1.html#K2" title="PARTFUN1:func.2">|</a>  the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c2">C1</font>
<span class="kw">by</span> <span class="lab"><a class="ref" href="relat_1.html#T71" title="RELAT_1:th.71">RELAT_1:71</a></span>
<br/>.= 
 the <a href="cat_1.html#U2" title="CAT_1:sel.2">Id</a> of <span class="p1">(<span class="default"><font color="Maroon" title="c3">C2</font> <a href="cat_5.html#K6" title="CAT_5:func.6">/\</a> <font color="Maroon" title="c2">C1</font></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E12:14"><span class="lab"><font color="Green" title="E17">A10</font></span></a>, <a class="ref" href="nattra_1.html#T8" title="NATTRA_1:th.8">NATTRA_1:8</a></span>
;<br/>
<span class="kw">hence </span><a NAME="E24:14"/>
<font color="Maroon" title="c2">C1</font> <a href="cat_5.html#K6" title="CAT_5:func.6">/\</a> <font color="Maroon" title="c3">C2</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c3">C2</font> <a href="cat_5.html#K6" title="CAT_5:func.6">/\</a> <font color="Maroon" title="c2">C1</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E3:14"><span class="lab"><font color="Green" title="E8">A1</font></span></a>, <a class="txt" href="#E4:14"><span class="lab"><font color="Green" title="E9">A2</font></span></a>, <a class="txt" href="#E5:14"><span class="lab"><font color="Green" title="E10">A3</font></span></a>, <a class="txt" href="#E6:14"><span class="lab"><font color="Green" title="E11">A4</font></span></a>, <a class="txt" href="#E7:14"><span class="lab"><font color="Green" title="E12">A5</font></span></a>, <a class="txt" href="#E20:14"><span class="lab"><font color="Green" title="E25">A18</font></span></a>, <a class="txt" href="#E21:14"><span class="lab"><font color="Green" title="E26">A19</font></span></a>, <a class="txt" href="#E22:14"><span class="lab"><font color="Green" title="E27">A20</font></span></a>, <a class="ref" href="cat_5.html#D2" target="_self" title="CAT_5:def.2">Def2</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>
