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<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="Red">::  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> is    <a href="cat_2.html#M3" title="CAT_2:mode.3">Subcategory</a> of <font color="Olive" title="b1">C1</font> &amp; <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> is    <a href="cat_2.html#M3" title="CAT_2:mode.3">Subcategory</a> of <font color="Olive" title="b2">C2</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="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="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> is    <a href="cat_2.html#M3" title="CAT_2:mode.3">Subcategory</a> of <font color="Maroon" title="c2">C1</font> &amp; <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> is    <a href="cat_2.html#M3" title="CAT_2:mode.3">Subcategory</a> of <font color="Maroon" title="c3">C2</font> ) )</span><br/>





<span class="kw">assume </span><a NAME="E1:15"/><span class="lab"><font color="Green" title="E9">A1</font></span>: 
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>
 ; <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="c2">C1</font> <a href="cat_5.html#K6" title="CAT_5:func.6">/\</a> <font color="Maroon" title="c3">C2</font> is    <a href="cat_2.html#M3" title="CAT_2:mode.3">Subcategory</a> of <font color="Maroon" title="c2">C1</font> &amp; <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> is    <a href="cat_2.html#M3" title="CAT_2:mode.3">Subcategory</a> of <font color="Maroon" title="c3">C2</font> )</span><br/>

<a NAME="E2:15"/><span class="kw">then </span><span class="lab"><font color="Green" title="E10">A2</font></span>: 
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="kw">by</span> <span class="lab"><a class="ref" href="xboole_0.html#D7" title="XBOOLE_0:def.7">XBOOLE_0:def 7</a></span>;<br/>
<a NAME="E3:15"/><span class="lab"><font color="Green" title="E11">A3</font></span>: 
<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="#E1:15"><span class="lab"><font color="Green" title="E9">A1</font></span></a>, <a class="ref" href="cat_5.html#T5" target="_self" title="CAT_5:th.5">Th5</a></span>;<br/>
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="15_1"><span class="kw">now </span></a><div class="add"><span class="kw">let </span><font color="Maroon" title="c4">C1</font>, <font color="Maroon" title="c5">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="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="c4">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="c5">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>  implies <font color="Maroon" title="c4">C1</font> <a href="cat_5.html#K6" title="CAT_5:func.6">/\</a> <font color="Maroon" title="c5">C2</font> is    <a href="cat_2.html#M3" title="CAT_2:mode.3">Subcategory</a> of <font color="Maroon" title="c4">C1</font> )</span><br/><span class="kw">assume </span><a NAME="E1:15_1"/><span class="lab"><font color="Green" title="E12">A4</font></span>: 
the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c4">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="c5">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> 
 ; <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="c4">C1</font> <a href="cat_5.html#K6" title="CAT_5:func.6">/\</a> <font color="Maroon" title="c5">C2</font> is    <a href="cat_2.html#M3" title="CAT_2:mode.3">Subcategory</a> of <font color="Maroon" title="c4">C1</font></span><br/><a NAME="E2:15_1"/><span class="lab"><font color="Green" title="E13">A5</font></span>: 
the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c4">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="c5">C2</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c4">C1</font>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="xboole_1.html#T17" title="XBOOLE_1:th.17">XBOOLE_1:17</a></span>;<br/><a NAME="E3:15_1"/><span class="lab"><font color="Green" title="E14">A6</font></span>: 
the <a href="struct_0.html#U4" title="STRUCT_0:sel.4">carrier'</a> of <font color="Maroon" title="c4">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="c5">C2</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> the <a href="struct_0.html#U4" title="STRUCT_0:sel.4">carrier'</a> of <font color="Maroon" title="c4">C1</font>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="xboole_1.html#T17" title="XBOOLE_1:th.17">XBOOLE_1:17</a></span>;<br/><span class="kw">reconsider </span><font color="Maroon" title="c6">O</font> = the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c4">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="c5">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>  <span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:15_1"><span class="lab"><font color="Green" title="E12">A4</font></span></a></span>;<br/><span class="kw">consider </span><font color="Maroon" title="c7">o</font> being    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of <font color="Maroon" title="c6">O</font>;<br/><a NAME="E6:15_1"/><span class="lab"><font color="Green" title="E15">A7</font></span>: 
<font color="Maroon" title="c7">o</font> is   <a href="cat_1.html#NM1" title="CAT_1:NM.1">Object</a> of <font color="Maroon" title="c4">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="E7:15_1"/><span class="lab"><font color="Green" title="E16">A8</font></span>: 
<font color="Maroon" title="c7">o</font> is   <a href="cat_1.html#NM1" title="CAT_1:NM.1">Object</a> of <font color="Maroon" title="c5">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="E8:15_1"/><span class="kw">then </span><span class="lab"><font color="Green" title="E17">A9</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="c4">C1</font> <a href="cat_5.html#K6" title="CAT_5:func.6">/\</a> <font color="Maroon" title="c5">C2</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c4">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="c5">C2</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E6:15_1"><span class="lab"><font color="Green" title="E15">A7</font></span></a>, <a class="ref" href="cat_5.html#D2" target="_self" title="CAT_5:def.2">Def2</a></span>;<br/><a NAME="E9:15_1"/><span class="lab"><font color="Green" title="E18">A10</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="c4">C1</font> <a href="cat_5.html#K6" title="CAT_5:func.6">/\</a> <font color="Maroon" title="c5">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="c4">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="c5">C2</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E6:15_1"><span class="lab"><font color="Green" title="E15">A7</font></span></a>, <a class="txt" href="#E7:15_1"><span class="lab"><font color="Green" title="E16">A8</font></span></a>, <a class="ref" href="cat_5.html#D2" target="_self" title="CAT_5:def.2">Def2</a></span>;<br/><a NAME="E10:15_1"/><span class="lab"><font color="Green" title="E19">A11</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="c4">C1</font> <a href="cat_5.html#K6" title="CAT_5:func.6">/\</a> <font color="Maroon" title="c5">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="c4">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="c5">C2</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E6:15_1"><span class="lab"><font color="Green" title="E15">A7</font></span></a>, <a class="txt" href="#E7:15_1"><span class="lab"><font color="Green" title="E16">A8</font></span></a>, <a class="ref" href="cat_5.html#D2" target="_self" title="CAT_5:def.2">Def2</a></span>;<br/><a NAME="E11:15_1"/><span class="lab"><font color="Green" title="E20">A12</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="c4">C1</font> <a href="cat_5.html#K6" title="CAT_5:func.6">/\</a> <font color="Maroon" title="c5">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="c4">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="c5">C2</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E6:15_1"><span class="lab"><font color="Green" title="E15">A7</font></span></a>, <a class="txt" href="#E7:15_1"><span class="lab"><font color="Green" title="E16">A8</font></span></a>, <a class="ref" href="cat_5.html#D2" target="_self" title="CAT_5:def.2">Def2</a></span>;<br/><a NAME="E12:15_1"/><span class="lab"><font color="Green" title="E21">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="c4">C1</font> <a href="cat_5.html#K6" title="CAT_5:func.6">/\</a> <font color="Maroon" title="c5">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="c4">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="c5">C2</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E6:15_1"><span class="lab"><font color="Green" title="E15">A7</font></span></a>, <a class="txt" href="#E7:15_1"><span class="lab"><font color="Green" title="E16">A8</font></span></a>, <a class="ref" href="cat_5.html#D2" target="_self" title="CAT_5:def.2">Def2</a></span>;<br/><a NAME="E13:15_1"/><span class="lab"><font color="Green" title="E22">A14</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="c4">C1</font> <a href="cat_5.html#K6" title="CAT_5:func.6">/\</a> <font color="Maroon" title="c5">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="c4">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="c5">C2</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E6:15_1"><span class="lab"><font color="Green" title="E15">A7</font></span></a>, <a class="txt" href="#E7:15_1"><span class="lab"><font color="Green" title="E16">A8</font></span></a>, <a class="ref" href="cat_5.html#D2" target="_self" title="CAT_5:def.2">Def2</a></span>;<br/><a NAME="E14:15_1"/><span class="lab"><font color="Green" title="E23">A15</font></span>: 
the <a href="graph_1.html#U1" title="GRAPH_1:sel.1">Source</a> of <font color="Maroon" title="c4">C1</font> <a href="relset_1.html#R2" title="RELSET_1:pred.2">=</a> the <a href="graph_1.html#U1" title="GRAPH_1:sel.1">Source</a> of <font color="Maroon" title="c4">C1</font> <a href="partfun1.html#K2" title="PARTFUN1:func.2">|</a> <span class="p1">(<span class="default"><a href="relset_1.html#K1" title="RELSET_1:func.1">dom</a> the <a href="graph_1.html#U1" title="GRAPH_1:sel.1">Source</a> of <font color="Maroon" title="c4">C1</font></span>)</span>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="relat_1.html#T97" title="RELAT_1:th.97">RELAT_1:97</a></span>;<br/><a NAME="E15:15_1"/>
 <a href="relset_1.html#K1" title="RELSET_1:func.1">dom</a> the <a href="graph_1.html#U1" title="GRAPH_1:sel.1">Source</a> of <font color="Maroon" title="c4">C1</font> <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="c4">C1</font>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="funct_2.html#D1" title="FUNCT_2:def.1">FUNCT_2:def 1</a></span>;<br/><a NAME="E16:15_1"/><span class="kw">then </span><span class="lab"><font color="Green" title="E24">A16</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="c4">C1</font> <a href="cat_5.html#K6" title="CAT_5:func.6">/\</a> <font color="Maroon" title="c5">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="c4">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 <span class="p1">(<span class="default"><font color="Maroon" title="c4">C1</font> <a href="cat_5.html#K6" title="CAT_5:func.6">/\</a> <font color="Maroon" title="c5">C2</font></span>)</span>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E9:15_1"><span class="lab"><font color="Green" title="E18">A10</font></span></a>, <a class="txt" href="#E10:15_1"><span class="lab"><font color="Green" title="E19">A11</font></span></a>, <a class="txt" href="#E14:15_1"><span class="lab"><font color="Green" title="E23">A15</font></span></a>, <a class="ref" href="relat_1.html#T100" title="RELAT_1:th.100">RELAT_1:100</a></span>;<br/><a NAME="E17:15_1"/><span class="lab"><font color="Green" title="E25">A17</font></span>: 
the <a href="graph_1.html#U2" title="GRAPH_1:sel.2">Target</a> of <font color="Maroon" title="c4">C1</font> <a href="relset_1.html#R2" title="RELSET_1:pred.2">=</a> the <a href="graph_1.html#U2" title="GRAPH_1:sel.2">Target</a> of <font color="Maroon" title="c4">C1</font> <a href="partfun1.html#K2" title="PARTFUN1:func.2">|</a> <span class="p1">(<span class="default"><a href="relset_1.html#K1" title="RELSET_1:func.1">dom</a> the <a href="graph_1.html#U2" title="GRAPH_1:sel.2">Target</a> of <font color="Maroon" title="c4">C1</font></span>)</span>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="relat_1.html#T97" title="RELAT_1:th.97">RELAT_1:97</a></span>;<br/><a NAME="E18:15_1"/>
 <a href="relset_1.html#K1" title="RELSET_1:func.1">dom</a> the <a href="graph_1.html#U2" title="GRAPH_1:sel.2">Target</a> of <font color="Maroon" title="c4">C1</font> <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="c4">C1</font>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="funct_2.html#D1" title="FUNCT_2:def.1">FUNCT_2:def 1</a></span>;<br/><a NAME="E19:15_1"/><span class="kw">then </span><span class="lab"><font color="Green" title="E26">A18</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="c4">C1</font> <a href="cat_5.html#K6" title="CAT_5:func.6">/\</a> <font color="Maroon" title="c5">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="c4">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 <span class="p1">(<span class="default"><font color="Maroon" title="c4">C1</font> <a href="cat_5.html#K6" title="CAT_5:func.6">/\</a> <font color="Maroon" title="c5">C2</font></span>)</span>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E9:15_1"><span class="lab"><font color="Green" title="E18">A10</font></span></a>, <a class="txt" href="#E11:15_1"><span class="lab"><font color="Green" title="E20">A12</font></span></a>, <a class="txt" href="#E17:15_1"><span class="lab"><font color="Green" title="E25">A17</font></span></a>, <a class="ref" href="relat_1.html#T100" title="RELAT_1:th.100">RELAT_1:100</a></span>;<br/><a NAME="E20:15_1"/><span class="lab"><font color="Green" title="E27">A19</font></span>: 
the <a href="cat_1.html#U2" title="CAT_1:sel.2">Id</a> of <font color="Maroon" title="c4">C1</font> <a href="relset_1.html#R2" title="RELSET_1:pred.2">=</a> the <a href="cat_1.html#U2" title="CAT_1:sel.2">Id</a> of <font color="Maroon" title="c4">C1</font> <a href="partfun1.html#K2" title="PARTFUN1:func.2">|</a> <span class="p1">(<span class="default"><a href="relset_1.html#K1" title="RELSET_1:func.1">dom</a> the <a href="cat_1.html#U2" title="CAT_1:sel.2">Id</a> of <font color="Maroon" title="c4">C1</font></span>)</span>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="relat_1.html#T97" title="RELAT_1:th.97">RELAT_1:97</a></span>;<br/><a NAME="E21:15_1"/>
 <a href="relset_1.html#K1" title="RELSET_1:func.1">dom</a> the <a href="cat_1.html#U2" title="CAT_1:sel.2">Id</a> of <font color="Maroon" title="c4">C1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c4">C1</font>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="funct_2.html#D1" title="FUNCT_2:def.1">FUNCT_2:def 1</a></span>;<br/><a NAME="E22:15_1"/><span class="kw">then </span><span class="lab"><font color="Green" title="E28">A20</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="c4">C1</font> <a href="cat_5.html#K6" title="CAT_5:func.6">/\</a> <font color="Maroon" title="c5">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="c4">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 <span class="p1">(<span class="default"><font color="Maroon" title="c4">C1</font> <a href="cat_5.html#K6" title="CAT_5:func.6">/\</a> <font color="Maroon" title="c5">C2</font></span>)</span>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E8:15_1"><span class="lab"><font color="Green" title="E17">A9</font></span></a>, <a class="txt" href="#E13:15_1"><span class="lab"><font color="Green" title="E22">A14</font></span></a>, <a class="txt" href="#E20:15_1"><span class="lab"><font color="Green" title="E27">A19</font></span></a>, <a class="ref" href="relat_1.html#T100" title="RELAT_1:th.100">RELAT_1:100</a></span>;<br/><a NAME="E23:15_1"/>
 <a href="relset_1.html#K1" title="RELSET_1:func.1">dom</a> the <a href="cat_1.html#U1" title="CAT_1:sel.1">Comp</a> of <font color="Maroon" title="c4">C1</font> <a href="relset_1.html#R1" title="RELSET_1:pred.1">c=</a> <span class="p1"><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="c4">C1</font>,the <a href="struct_0.html#U4" title="STRUCT_0:sel.4">carrier'</a> of <font color="Maroon" title="c4">C1</font></span><a href="zfmisc_1.html#K2" title="ZFMISC_1:func.2">:]</a></span>
 ;<br/><a NAME="E24:15_1"/><span class="kw">then </span>
the <a href="cat_1.html#U1" title="CAT_1:sel.1">Comp</a> of <font color="Maroon" title="c4">C1</font> <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="c4">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="c4">C1</font>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="relat_1.html#T97" title="RELAT_1:th.97">RELAT_1:97</a></span>;<br/><a NAME="E25:15_1"/><span class="kw">then </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="c4">C1</font> <a href="cat_5.html#K6" title="CAT_5:func.6">/\</a> <font color="Maroon" title="c5">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="c4">C1</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="c4">C1</font>,the <a href="struct_0.html#U4" title="STRUCT_0:sel.4">carrier'</a> of <font color="Maroon" title="c4">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="c5">C2</font>,the <a href="struct_0.html#U4" title="STRUCT_0:sel.4">carrier'</a> of <font color="Maroon" title="c5">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="txt" href="#E12:15_1"><span class="lab"><font color="Green" title="E21">A13</font></span></a>, <a class="ref" href="relat_1.html#T100" title="RELAT_1:th.100">RELAT_1:100</a></span>;<br/><a NAME="E26:15_1"/><span class="kw">then </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="c4">C1</font> <a href="cat_5.html#K6" title="CAT_5:func.6">/\</a> <font color="Maroon" title="c5">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="c4">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 <span class="p1">(<span class="default"><font color="Maroon" title="c4">C1</font> <a href="cat_5.html#K6" title="CAT_5:func.6">/\</a> <font color="Maroon" title="c5">C2</font></span>)</span>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E9:15_1"><span class="lab"><font color="Green" title="E18">A10</font></span></a>, <a class="ref" href="zfmisc_1.html#T123" title="ZFMISC_1:th.123">ZFMISC_1:123</a></span>;<br/><span class="kw">hence </span><a NAME="E27:15_1"/>
<font color="Maroon" title="c4">C1</font> <a href="cat_5.html#K6" title="CAT_5:func.6">/\</a> <font color="Maroon" title="c5">C2</font> is    <a href="cat_2.html#M3" title="CAT_2:mode.3">Subcategory</a> of <font color="Maroon" title="c4">C1</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:15_1"><span class="lab"><font color="Green" title="E13">A5</font></span></a>, <a class="txt" href="#E3:15_1"><span class="lab"><font color="Green" title="E14">A6</font></span></a>, <a class="txt" href="#E8:15_1"><span class="lab"><font color="Green" title="E17">A9</font></span></a>, <a class="txt" href="#E9:15_1"><span class="lab"><font color="Green" title="E18">A10</font></span></a>, <a class="txt" href="#E16:15_1"><span class="lab"><font color="Green" title="E24">A16</font></span></a>, <a class="txt" href="#E19:15_1"><span class="lab"><font color="Green" title="E26">A18</font></span></a>, <a class="txt" href="#E22:15_1"><span class="lab"><font color="Green" title="E28">A20</font></span></a>, <a class="ref" href="nattra_1.html#T9" title="NATTRA_1:th.9">NATTRA_1:9</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>
<span class="kw">hence </span><a NAME="E5:15"/>
( <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> is    <a href="cat_2.html#M3" title="CAT_2:mode.3">Subcategory</a> of <font color="Maroon" title="c2">C1</font> &amp; <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> is    <a href="cat_2.html#M3" title="CAT_2:mode.3">Subcategory</a> of <font color="Maroon" title="c3">C2</font> )
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:15"><span class="lab"><font color="Green" title="E10">A2</font></span></a>, <a class="txt" href="#E3:15"><span class="lab"><font color="Green" title="E11">A3</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>
