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<div class="add">

<b>let </b><font color="Maroon" title="c1">A</font>, <font color="Maroon" title="c2">B</font> be   <a href="cat_1.html#NM4" title="CAT_1:NM.4">Category</a>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide">  <a href="nattra_1.html#K13" title="NATTRA_1:func.13">IdCat</a> <span class="p1"><a href="cat_2.html#K11" title="CAT_2:func.11">[:</a><span class="default"><font color="Maroon" title="c1">A</font>,<font color="Maroon" title="c2">B</font></span><a href="cat_2.html#K11" title="CAT_2:func.11">:]</a></span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1"><a href="cat_2.html#K11" title="CAT_2:func.11">[:</a><span class="default"><span class="p2">(<span class="default"><a href="nattra_1.html#K13" title="NATTRA_1:func.13">IdCat</a> <font color="Maroon" title="c1">A</font></span>)</span>,<span class="p2">(<span class="default"><a href="nattra_1.html#K13" title="NATTRA_1:func.13">IdCat</a> <font color="Maroon" title="c2">B</font></span>)</span></span><a href="cat_2.html#K11" title="CAT_2:func.11">:]</a></span></span><br/>



<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="76_1"><b>now </b></a><div class="add"><a NAME="E1:76_1"/>
( the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <span class="p1">(<span class="default"><a href="nattra_1.html#K13" title="NATTRA_1:func.13">IdCat</a> <font color="Maroon" title="c1">A</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="c1">A</font> &amp; the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <span class="p1">(<span class="default"><a href="nattra_1.html#K13" title="NATTRA_1:func.13">IdCat</a> <font color="Maroon" title="c2">B</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="c2">B</font> )
 <b>by </b><i><a class="ref" href="nattra_1.html#D20" target="_self" title="NATTRA_1:def.20">Def20</a></i>;<br/><b>hence </b><a NAME="E2:76_1"/><i><font color="Green" title="E58">A1</font></i>: 
<span class="p1"><a href="zfmisc_1.html#K2" title="ZFMISC_1:func.2">[:</a><span class="default">the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <span class="p2">(<span class="default"><a href="nattra_1.html#K13" title="NATTRA_1:func.13">IdCat</a> <font color="Maroon" title="c1">A</font></span>)</span>,the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <span class="p2">(<span class="default"><a href="nattra_1.html#K13" title="NATTRA_1:func.13">IdCat</a> <font color="Maroon" title="c2">B</font></span>)</span></span><a href="zfmisc_1.html#K2" title="ZFMISC_1:func.2">:]</a></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 <span class="p1">(<span class="default"><a href="nattra_1.html#K13" title="NATTRA_1:func.13">IdCat</a> <span class="p2"><a href="cat_2.html#K11" title="CAT_2:func.11">[:</a><span class="default"><font color="Maroon" title="c1">A</font>,<font color="Maroon" title="c2">B</font></span><a href="cat_2.html#K11" title="CAT_2:func.11">:]</a></span></span>)</span>
 <b>by </b><i><a class="ref" href="nattra_1.html#D20" target="_self" title="NATTRA_1:def.20">Def20</a></i>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> ( the <a href="struct_0.html#U4" title="STRUCT_0:sel.4">carrier'</a> of <span class="p1">(<span class="default"><a href="nattra_1.html#K13" title="NATTRA_1:func.13">IdCat</a> <span class="p2"><a href="cat_2.html#K11" title="CAT_2:func.11">[:</a><span class="default"><font color="Maroon" title="c1">A</font>,<font color="Maroon" title="c2">B</font></span><a href="cat_2.html#K11" title="CAT_2:func.11">:]</a></span></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</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 <span class="p2">(<span class="default"><a href="nattra_1.html#K13" title="NATTRA_1:func.13">IdCat</a> <font color="Maroon" title="c1">A</font></span>)</span>,the <a href="struct_0.html#U4" title="STRUCT_0:sel.4">carrier'</a> of <span class="p2">(<span class="default"><a href="nattra_1.html#K13" title="NATTRA_1:func.13">IdCat</a> <font color="Maroon" title="c2">B</font></span>)</span></span><a href="zfmisc_1.html#K2" title="ZFMISC_1:func.2">:]</a></span> &amp; <span class="p1"><a href="cat_2.html#K9" title="CAT_2:func.9">[:</a><span class="default">the <a href="graph_1.html#U1" title="GRAPH_1:sel.1">Source</a> of <span class="p2">(<span class="default"><a href="nattra_1.html#K13" title="NATTRA_1:func.13">IdCat</a> <font color="Maroon" title="c1">A</font></span>)</span>,the <a href="graph_1.html#U1" title="GRAPH_1:sel.1">Source</a> of <span class="p2">(<span class="default"><a href="nattra_1.html#K13" title="NATTRA_1:func.13">IdCat</a> <font color="Maroon" title="c2">B</font></span>)</span></span><a href="cat_2.html#K9" title="CAT_2:func.9">:]</a></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 <span class="p1">(<span class="default"><a href="nattra_1.html#K13" title="NATTRA_1:func.13">IdCat</a> <span class="p2"><a href="cat_2.html#K11" title="CAT_2:func.11">[:</a><span class="default"><font color="Maroon" title="c1">A</font>,<font color="Maroon" title="c2">B</font></span><a href="cat_2.html#K11" title="CAT_2:func.11">:]</a></span></span>)</span> &amp; <span class="p1"><a href="cat_2.html#K9" title="CAT_2:func.9">[:</a><span class="default">the <a href="graph_1.html#U2" title="GRAPH_1:sel.2">Target</a> of <span class="p2">(<span class="default"><a href="nattra_1.html#K13" title="NATTRA_1:func.13">IdCat</a> <font color="Maroon" title="c1">A</font></span>)</span>,the <a href="graph_1.html#U2" title="GRAPH_1:sel.2">Target</a> of <span class="p2">(<span class="default"><a href="nattra_1.html#K13" title="NATTRA_1:func.13">IdCat</a> <font color="Maroon" title="c2">B</font></span>)</span></span><a href="cat_2.html#K9" title="CAT_2:func.9">:]</a></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 <span class="p1">(<span class="default"><a href="nattra_1.html#K13" title="NATTRA_1:func.13">IdCat</a> <span class="p2"><a href="cat_2.html#K11" title="CAT_2:func.11">[:</a><span class="default"><font color="Maroon" title="c1">A</font>,<font color="Maroon" title="c2">B</font></span><a href="cat_2.html#K11" title="CAT_2:func.11">:]</a></span></span>)</span> &amp; <span class="p1"><a href="cat_2.html#K10" title="CAT_2:func.10">|:</a><span class="default">the <a href="cat_1.html#U1" title="CAT_1:sel.1">Comp</a> of <span class="p2">(<span class="default"><a href="nattra_1.html#K13" title="NATTRA_1:func.13">IdCat</a> <font color="Maroon" title="c1">A</font></span>)</span>,the <a href="cat_1.html#U1" title="CAT_1:sel.1">Comp</a> of <span class="p2">(<span class="default"><a href="nattra_1.html#K13" title="NATTRA_1:func.13">IdCat</a> <font color="Maroon" title="c2">B</font></span>)</span></span><a href="cat_2.html#K10" title="CAT_2:func.10">:|</a></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 <span class="p1">(<span class="default"><a href="nattra_1.html#K13" title="NATTRA_1:func.13">IdCat</a> <span class="p2"><a href="cat_2.html#K11" title="CAT_2:func.11">[:</a><span class="default"><font color="Maroon" title="c1">A</font>,<font color="Maroon" title="c2">B</font></span><a href="cat_2.html#K11" title="CAT_2:func.11">:]</a></span></span>)</span> &amp; <span class="p1"><a href="cat_2.html#K9" title="CAT_2:func.9">[:</a><span class="default">the <a href="cat_1.html#U2" title="CAT_1:sel.2">Id</a> of <span class="p2">(<span class="default"><a href="nattra_1.html#K13" title="NATTRA_1:func.13">IdCat</a> <font color="Maroon" title="c1">A</font></span>)</span>,the <a href="cat_1.html#U2" title="CAT_1:sel.2">Id</a> of <span class="p2">(<span class="default"><a href="nattra_1.html#K13" title="NATTRA_1:func.13">IdCat</a> <font color="Maroon" title="c2">B</font></span>)</span></span><a href="cat_2.html#K9" title="CAT_2:func.9">:]</a></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 <span class="p1">(<span class="default"><a href="nattra_1.html#K13" title="NATTRA_1:func.13">IdCat</a> <span class="p2"><a href="cat_2.html#K11" title="CAT_2:func.11">[:</a><span class="default"><font color="Maroon" title="c1">A</font>,<font color="Maroon" title="c2">B</font></span><a href="cat_2.html#K11" title="CAT_2:func.11">:]</a></span></span>)</span> )</span><br/><b>set </b><font color="Maroon" title="c3">AB</font> = <span class="p1">{<span class="default"> <span class="p2">(<span class="default"><a href="cat_1.html#K6" title="CAT_1:func.6">id</a> <font color="Olive" title="b1">c</font></span>)</span> where <font color="Olive" title="b1">c</font> is   <a href="cat_1.html#NM1" title="CAT_1:NM.1">Object</a> of <span class="p1"><a href="cat_2.html#K11" title="CAT_2:func.11">[:</a><span class="default"><font color="Maroon" title="c1">A</font>,<font color="Maroon" title="c2">B</font></span><a href="cat_2.html#K11" title="CAT_2:func.11">:]</a></span> : verum </span>}</span> ;<br/><b>set </b><font color="Maroon" title="c4">MA</font> = <span class="p1">{<span class="default"> <span class="p2">(<span class="default"><a href="cat_1.html#K6" title="CAT_1:func.6">id</a> <font color="Olive" title="b1">a</font></span>)</span> where <font color="Olive" title="b1">a</font> is   <a href="cat_1.html#NM1" title="CAT_1:NM.1">Object</a> of <font color="Maroon" title="c1">A</font> : verum </span>}</span> ;<br/><b>set </b><font color="Maroon" title="c5">MB</font> = <span class="p1">{<span class="default"> <span class="p2">(<span class="default"><a href="cat_1.html#K6" title="CAT_1:func.6">id</a> <font color="Olive" title="b1">b</font></span>)</span> where <font color="Olive" title="b1">b</font> is   <a href="cat_1.html#NM1" title="CAT_1:NM.1">Object</a> of <font color="Maroon" title="c2">B</font> : verum </span>}</span> ;<br/><a NAME="E3:76_1"/><i><font color="Green" title="E59">A2</font></i>: 
<span class="p1">{<span class="default"> <span class="p2">(<span class="default"><a href="cat_1.html#K6" title="CAT_1:func.6">id</a> <font color="Olive" title="b1">c</font></span>)</span> where <font color="Olive" title="b1">c</font> is   <a href="cat_1.html#NM1" title="CAT_1:NM.1">Object</a> of <span class="p1"><a href="cat_2.html#K11" title="CAT_2:func.11">[:</a><span class="default"><font color="Maroon" title="c1">A</font>,<font color="Maroon" title="c2">B</font></span><a href="cat_2.html#K11" title="CAT_2:func.11">:]</a></span> : verum </span>}</span>  <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1"><a href="zfmisc_1.html#K2" title="ZFMISC_1:func.2">[:</a><span class="default"><span class="p2">{<span class="default"> <span class="p3">(<span class="default"><a href="cat_1.html#K6" title="CAT_1:func.6">id</a> <font color="Olive" title="b1">a</font></span>)</span> where <font color="Olive" title="b1">a</font> is   <a href="cat_1.html#NM1" title="CAT_1:NM.1">Object</a> of <font color="Maroon" title="c1">A</font> : verum </span>}</span> ,<span class="p2">{<span class="default"> <span class="p3">(<span class="default"><a href="cat_1.html#K6" title="CAT_1:func.6">id</a> <font color="Olive" title="b1">b</font></span>)</span> where <font color="Olive" title="b1">b</font> is   <a href="cat_1.html#NM1" title="CAT_1:NM.1">Object</a> of <font color="Maroon" title="c2">B</font> : verum </span>}</span> </span><a href="zfmisc_1.html#K2" title="ZFMISC_1:func.2">:]</a></span>
 <div><a class="txt" onclick="hs2(this)" href="javascript:()" title="76_1_1"><b>proof </b></a><div class="add">

<b>thus </b><a NAME="E1:76_1_1"/>
<span class="p1">{<span class="default"> <span class="p2">(<span class="default"><a href="cat_1.html#K6" title="CAT_1:func.6">id</a> <font color="Olive" title="b1">c</font></span>)</span> where <font color="Olive" title="b1">c</font> is   <a href="cat_1.html#NM1" title="CAT_1:NM.1">Object</a> of <span class="p1"><a href="cat_2.html#K11" title="CAT_2:func.11">[:</a><span class="default"><font color="Maroon" title="c1">A</font>,<font color="Maroon" title="c2">B</font></span><a href="cat_2.html#K11" title="CAT_2:func.11">:]</a></span> : verum </span>}</span>  <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <span class="p1"><a href="zfmisc_1.html#K2" title="ZFMISC_1:func.2">[:</a><span class="default"><span class="p2">{<span class="default"> <span class="p3">(<span class="default"><a href="cat_1.html#K6" title="CAT_1:func.6">id</a> <font color="Olive" title="b1">a</font></span>)</span> where <font color="Olive" title="b1">a</font> is   <a href="cat_1.html#NM1" title="CAT_1:NM.1">Object</a> of <font color="Maroon" title="c1">A</font> : verum </span>}</span> ,<span class="p2">{<span class="default"> <span class="p3">(<span class="default"><a href="cat_1.html#K6" title="CAT_1:func.6">id</a> <font color="Olive" title="b1">b</font></span>)</span> where <font color="Olive" title="b1">b</font> is   <a href="cat_1.html#NM1" title="CAT_1:NM.1">Object</a> of <font color="Maroon" title="c2">B</font> : verum </span>}</span> </span><a href="zfmisc_1.html#K2" title="ZFMISC_1:func.2">:]</a></span>
  <i><font color="Red">:: according to </font></i><a class="ref" href="xboole_0.html#D10" title="XBOOLE_0:def.10">XBOOLE_0:def 10</a> <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> <span class="p1"><a href="zfmisc_1.html#K2" title="ZFMISC_1:func.2">[:</a><span class="default"><span class="p2">{<span class="default"> <span class="p3">(<span class="default"><a href="cat_1.html#K6" title="CAT_1:func.6">id</a> <font color="Olive" title="b1">a</font></span>)</span> where <font color="Olive" title="b1">a</font> is   <a href="cat_1.html#NM1" title="CAT_1:NM.1">Object</a> of <font color="Maroon" title="c1">A</font> : verum </span>}</span> ,<span class="p2">{<span class="default"> <span class="p3">(<span class="default"><a href="cat_1.html#K6" title="CAT_1:func.6">id</a> <font color="Olive" title="b1">b</font></span>)</span> where <font color="Olive" title="b1">b</font> is   <a href="cat_1.html#NM1" title="CAT_1:NM.1">Object</a> of <font color="Maroon" title="c2">B</font> : verum </span>}</span> </span><a href="zfmisc_1.html#K2" title="ZFMISC_1:func.2">:]</a></span> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <span class="p1">{<span class="default"> <span class="p2">(<span class="default"><a href="cat_1.html#K6" title="CAT_1:func.6">id</a> <font color="Olive" title="b1">c</font></span>)</span> where <font color="Olive" title="b1">c</font> is   <a href="cat_1.html#NM1" title="CAT_1:NM.1">Object</a> of <span class="p1"><a href="cat_2.html#K11" title="CAT_2:func.11">[:</a><span class="default"><font color="Maroon" title="c1">A</font>,<font color="Maroon" title="c2">B</font></span><a href="cat_2.html#K11" title="CAT_2:func.11">:]</a></span> : verum </span>}</span> </span><div><a class="txt" onclick="hs2(this)" href="javascript:()" title="76_1_1_1"><b>proof </b></a><div class="add">

<b>let </b><font color="Maroon" title="c6">x</font> be    <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a> ; <i><font color="Red">:: according to </font></i><a class="ref" href="tarski.html#D3" title="TARSKI:def.3">TARSKI:def 3</a> <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> (  not <font color="Maroon" title="c6">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <span class="p1">{<span class="default"> <span class="p2">(<span class="default"><a href="cat_1.html#K6" title="CAT_1:func.6">id</a> <font color="Olive" title="b1">c</font></span>)</span> where <font color="Olive" title="b1">c</font> is   <a href="cat_1.html#NM1" title="CAT_1:NM.1">Object</a> of <span class="p1"><a href="cat_2.html#K11" title="CAT_2:func.11">[:</a><span class="default"><font color="Maroon" title="c1">A</font>,<font color="Maroon" title="c2">B</font></span><a href="cat_2.html#K11" title="CAT_2:func.11">:]</a></span> : verum </span>}</span>  or <font color="Maroon" title="c6">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <span class="p1"><a href="zfmisc_1.html#K2" title="ZFMISC_1:func.2">[:</a><span class="default"><span class="p2">{<span class="default"> <span class="p3">(<span class="default"><a href="cat_1.html#K6" title="CAT_1:func.6">id</a> <font color="Olive" title="b1">a</font></span>)</span> where <font color="Olive" title="b1">a</font> is   <a href="cat_1.html#NM1" title="CAT_1:NM.1">Object</a> of <font color="Maroon" title="c1">A</font> : verum </span>}</span> ,<span class="p2">{<span class="default"> <span class="p3">(<span class="default"><a href="cat_1.html#K6" title="CAT_1:func.6">id</a> <font color="Olive" title="b1">b</font></span>)</span> where <font color="Olive" title="b1">b</font> is   <a href="cat_1.html#NM1" title="CAT_1:NM.1">Object</a> of <font color="Maroon" title="c2">B</font> : verum </span>}</span> </span><a href="zfmisc_1.html#K2" title="ZFMISC_1:func.2">:]</a></span> )</span><br/>

<b>assume </b><a NAME="E1:76_1_1_1"/>
<font color="Maroon" title="c6">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <span class="p1">{<span class="default"> <span class="p2">(<span class="default"><a href="cat_1.html#K6" title="CAT_1:func.6">id</a> <font color="Olive" title="b1">c</font></span>)</span> where <font color="Olive" title="b1">c</font> is   <a href="cat_1.html#NM1" title="CAT_1:NM.1">Object</a> of <span class="p1"><a href="cat_2.html#K11" title="CAT_2:func.11">[:</a><span class="default"><font color="Maroon" title="c1">A</font>,<font color="Maroon" title="c2">B</font></span><a href="cat_2.html#K11" title="CAT_2:func.11">:]</a></span> : verum </span>}</span> 
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> <font color="Maroon" title="c6">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <span class="p1"><a href="zfmisc_1.html#K2" title="ZFMISC_1:func.2">[:</a><span class="default"><span class="p2">{<span class="default"> <span class="p3">(<span class="default"><a href="cat_1.html#K6" title="CAT_1:func.6">id</a> <font color="Olive" title="b1">a</font></span>)</span> where <font color="Olive" title="b1">a</font> is   <a href="cat_1.html#NM1" title="CAT_1:NM.1">Object</a> of <font color="Maroon" title="c1">A</font> : verum </span>}</span> ,<span class="p2">{<span class="default"> <span class="p3">(<span class="default"><a href="cat_1.html#K6" title="CAT_1:func.6">id</a> <font color="Olive" title="b1">b</font></span>)</span> where <font color="Olive" title="b1">b</font> is   <a href="cat_1.html#NM1" title="CAT_1:NM.1">Object</a> of <font color="Maroon" title="c2">B</font> : verum </span>}</span> </span><a href="zfmisc_1.html#K2" title="ZFMISC_1:func.2">:]</a></span></span><br/>

<b>then consider </b><font color="Maroon" title="c7">c</font> being   <a href="cat_1.html#NM1" title="CAT_1:NM.1">Object</a> of <span class="p1"><a href="cat_2.html#K11" title="CAT_2:func.11">[:</a><span class="default"><font color="Maroon" title="c1">A</font>,<font color="Maroon" title="c2">B</font></span><a href="cat_2.html#K11" title="CAT_2:func.11">:]</a></span><b> such that </b><br/><a NAME="E3:76_1_1_1"/><i><font color="Green" title="E60">A3</font></i>: 
<font color="Maroon" title="c6">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="cat_1.html#K6" title="CAT_1:func.6">id</a> <font color="Maroon" title="c7">c</font>
 ;<br/>
<b>consider </b><font color="Maroon" title="c8">c1</font> being   <a href="cat_1.html#NM1" title="CAT_1:NM.1">Object</a> of <font color="Maroon" title="c1">A</font>, <font color="Maroon" title="c9">c2</font> being   <a href="cat_1.html#NM1" title="CAT_1:NM.1">Object</a> of <font color="Maroon" title="c2">B</font><b> such that </b><br/><a NAME="E5:76_1_1_1"/><i><font color="Green" title="E61">A4</font></i>: 
<font color="Maroon" title="c7">c</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1"><a href="cat_2.html#K12" title="CAT_2:func.12">[</a><span class="default"><font color="Maroon" title="c8">c1</font>,<font color="Maroon" title="c9">c2</font></span><a href="cat_2.html#K12" title="CAT_2:func.12">]</a></span>
 <b>by </b><i><a class="ref" href="domain_1.html#T9" title="DOMAIN_1:th.9">DOMAIN_1:9</a></i>;<br/>
<a NAME="E6:76_1_1_1"/><i><font color="Green" title="E62">A5</font></i>: 
 <a href="cat_1.html#K6" title="CAT_1:func.6">id</a> <font color="Maroon" title="c7">c</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">(<span class="default"><a href="cat_1.html#K6" title="CAT_1:func.6">id</a> <font color="Maroon" title="c8">c1</font></span>)</span>,<span class="p2">(<span class="default"><a href="cat_1.html#K6" title="CAT_1:func.6">id</a> <font color="Maroon" title="c9">c2</font></span>)</span></span><a href="cat_2.html#K13" title="CAT_2:func.13">]</a></span>
 
<b>by </b><i><a class="txt" href="#E5:76_1_1_1"><i><font color="Green" title="E61">A4</font></i></a>, <a class="ref" href="cat_2.html#T41" title="CAT_2:th.41">CAT_2:41</a></i>;<br/>
<a NAME="E7:76_1_1_1"/>
(  <a href="cat_1.html#K6" title="CAT_1:func.6">id</a> <font color="Maroon" title="c8">c1</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <span class="p1">{<span class="default"> <span class="p2">(<span class="default"><a href="cat_1.html#K6" title="CAT_1:func.6">id</a> <font color="Olive" title="b1">a</font></span>)</span> where <font color="Olive" title="b1">a</font> is   <a href="cat_1.html#NM1" title="CAT_1:NM.1">Object</a> of <font color="Maroon" title="c1">A</font> : verum </span>}</span>  &amp;  <a href="cat_1.html#K6" title="CAT_1:func.6">id</a> <font color="Maroon" title="c9">c2</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <span class="p1">{<span class="default"> <span class="p2">(<span class="default"><a href="cat_1.html#K6" title="CAT_1:func.6">id</a> <font color="Olive" title="b1">b</font></span>)</span> where <font color="Olive" title="b1">b</font> is   <a href="cat_1.html#NM1" title="CAT_1:NM.1">Object</a> of <font color="Maroon" title="c2">B</font> : verum </span>}</span>  )
 
;<br/>
<b>hence </b><a NAME="E8:76_1_1_1"/>
<font color="Maroon" title="c6">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <span class="p1"><a href="zfmisc_1.html#K2" title="ZFMISC_1:func.2">[:</a><span class="default"><span class="p2">{<span class="default"> <span class="p3">(<span class="default"><a href="cat_1.html#K6" title="CAT_1:func.6">id</a> <font color="Olive" title="b1">a</font></span>)</span> where <font color="Olive" title="b1">a</font> is   <a href="cat_1.html#NM1" title="CAT_1:NM.1">Object</a> of <font color="Maroon" title="c1">A</font> : verum </span>}</span> ,<span class="p2">{<span class="default"> <span class="p3">(<span class="default"><a href="cat_1.html#K6" title="CAT_1:func.6">id</a> <font color="Olive" title="b1">b</font></span>)</span> where <font color="Olive" title="b1">b</font> is   <a href="cat_1.html#NM1" title="CAT_1:NM.1">Object</a> of <font color="Maroon" title="c2">B</font> : verum </span>}</span> </span><a href="zfmisc_1.html#K2" title="ZFMISC_1:func.2">:]</a></span>
 <b>by </b><i><a class="txt" href="#E3:76_1_1_1"><i><font color="Green" title="E60">A3</font></i></a>, <a class="txt" href="#E6:76_1_1_1"><i><font color="Green" title="E62">A5</font></i></a>, <a class="ref" href="zfmisc_1.html#T106" title="ZFMISC_1:th.106">ZFMISC_1:106</a></i>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> verum</span><br/>


</div><b>end;</b></div>

<b>let </b><font color="Maroon" title="c6">x</font> be    <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a> ; <i><font color="Red">:: according to </font></i><a class="ref" href="tarski.html#D3" title="TARSKI:def.3">TARSKI:def 3</a> <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> (  not <font color="Maroon" title="c6">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <span class="p1"><a href="zfmisc_1.html#K2" title="ZFMISC_1:func.2">[:</a><span class="default"><span class="p2">{<span class="default"> <span class="p3">(<span class="default"><a href="cat_1.html#K6" title="CAT_1:func.6">id</a> <font color="Olive" title="b1">a</font></span>)</span> where <font color="Olive" title="b1">a</font> is   <a href="cat_1.html#NM1" title="CAT_1:NM.1">Object</a> of <font color="Maroon" title="c1">A</font> : verum </span>}</span> ,<span class="p2">{<span class="default"> <span class="p3">(<span class="default"><a href="cat_1.html#K6" title="CAT_1:func.6">id</a> <font color="Olive" title="b1">b</font></span>)</span> where <font color="Olive" title="b1">b</font> is   <a href="cat_1.html#NM1" title="CAT_1:NM.1">Object</a> of <font color="Maroon" title="c2">B</font> : verum </span>}</span> </span><a href="zfmisc_1.html#K2" title="ZFMISC_1:func.2">:]</a></span> or <font color="Maroon" title="c6">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <span class="p1">{<span class="default"> <span class="p2">(<span class="default"><a href="cat_1.html#K6" title="CAT_1:func.6">id</a> <font color="Olive" title="b1">c</font></span>)</span> where <font color="Olive" title="b1">c</font> is   <a href="cat_1.html#NM1" title="CAT_1:NM.1">Object</a> of <span class="p1"><a href="cat_2.html#K11" title="CAT_2:func.11">[:</a><span class="default"><font color="Maroon" title="c1">A</font>,<font color="Maroon" title="c2">B</font></span><a href="cat_2.html#K11" title="CAT_2:func.11">:]</a></span> : verum </span>}</span>  )</span><br/>

<b>assume </b><a NAME="E2:76_1_1"/>
<font color="Maroon" title="c6">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <span class="p1"><a href="zfmisc_1.html#K2" title="ZFMISC_1:func.2">[:</a><span class="default"><span class="p2">{<span class="default"> <span class="p3">(<span class="default"><a href="cat_1.html#K6" title="CAT_1:func.6">id</a> <font color="Olive" title="b1">a</font></span>)</span> where <font color="Olive" title="b1">a</font> is   <a href="cat_1.html#NM1" title="CAT_1:NM.1">Object</a> of <font color="Maroon" title="c1">A</font> : verum </span>}</span> ,<span class="p2">{<span class="default"> <span class="p3">(<span class="default"><a href="cat_1.html#K6" title="CAT_1:func.6">id</a> <font color="Olive" title="b1">b</font></span>)</span> where <font color="Olive" title="b1">b</font> is   <a href="cat_1.html#NM1" title="CAT_1:NM.1">Object</a> of <font color="Maroon" title="c2">B</font> : verum </span>}</span> </span><a href="zfmisc_1.html#K2" title="ZFMISC_1:func.2">:]</a></span>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> <font color="Maroon" title="c6">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <span class="p1">{<span class="default"> <span class="p2">(<span class="default"><a href="cat_1.html#K6" title="CAT_1:func.6">id</a> <font color="Olive" title="b1">c</font></span>)</span> where <font color="Olive" title="b1">c</font> is   <a href="cat_1.html#NM1" title="CAT_1:NM.1">Object</a> of <span class="p1"><a href="cat_2.html#K11" title="CAT_2:func.11">[:</a><span class="default"><font color="Maroon" title="c1">A</font>,<font color="Maroon" title="c2">B</font></span><a href="cat_2.html#K11" title="CAT_2:func.11">:]</a></span> : verum </span>}</span> </span><br/>

<b>then consider </b><font color="Maroon" title="c7">x1</font>, <font color="Maroon" title="c8">x2</font> being    <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a> <b> such that </b><br/><a NAME="E4:76_1_1"/><i><font color="Green" title="E60">A6</font></i>: 
( <font color="Maroon" title="c7">x1</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <span class="p1">{<span class="default"> <span class="p2">(<span class="default"><a href="cat_1.html#K6" title="CAT_1:func.6">id</a> <font color="Olive" title="b1">a</font></span>)</span> where <font color="Olive" title="b1">a</font> is   <a href="cat_1.html#NM1" title="CAT_1:NM.1">Object</a> of <font color="Maroon" title="c1">A</font> : verum </span>}</span>  &amp; <font color="Maroon" title="c8">x2</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <span class="p1">{<span class="default"> <span class="p2">(<span class="default"><a href="cat_1.html#K6" title="CAT_1:func.6">id</a> <font color="Olive" title="b1">b</font></span>)</span> where <font color="Olive" title="b1">b</font> is   <a href="cat_1.html#NM1" title="CAT_1:NM.1">Object</a> of <font color="Maroon" title="c2">B</font> : verum </span>}</span>  )
 <b>and </b><br/><a NAME="E5:76_1_1"/><i><font color="Green" title="E61">A7</font></i>: 
<font color="Maroon" title="c6">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1"><a href="tarski.html#K4" title="TARSKI:func.4">[</a><span class="default"><font color="Maroon" title="c7">x1</font>,<font color="Maroon" title="c8">x2</font></span><a href="tarski.html#K4" title="TARSKI:func.4">]</a></span>
 <b>by </b><i><a class="ref" href="zfmisc_1.html#T103" title="ZFMISC_1:th.103">ZFMISC_1:103</a></i>;<br/>
<b>consider </b><font color="Maroon" title="c9">a</font> being   <a href="cat_1.html#NM1" title="CAT_1:NM.1">Object</a> of <font color="Maroon" title="c1">A</font><b> such that </b><br/><a NAME="E7:76_1_1"/><i><font color="Green" title="E62">A8</font></i>: 
<font color="Maroon" title="c7">x1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="cat_1.html#K6" title="CAT_1:func.6">id</a> <font color="Maroon" title="c9">a</font>
 <b>by </b><i><a class="txt" href="#E4:76_1_1"><i><font color="Green" title="E60">A6</font></i></a></i>;<br/>
<b>consider </b><font color="Maroon" title="c10">b</font> being   <a href="cat_1.html#NM1" title="CAT_1:NM.1">Object</a> of <font color="Maroon" title="c2">B</font><b> such that </b><br/><a NAME="E9:76_1_1"/><i><font color="Green" title="E63">A9</font></i>: 
<font color="Maroon" title="c8">x2</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="cat_1.html#K6" title="CAT_1:func.6">id</a> <font color="Maroon" title="c10">b</font>
 <b>by </b><i><a class="txt" href="#E4:76_1_1"><i><font color="Green" title="E60">A6</font></i></a></i>;<br/>
<a NAME="E10:76_1_1"/>
 <a href="cat_1.html#K6" title="CAT_1:func.6">id</a> <span class="p1"><a href="cat_2.html#K12" title="CAT_2:func.12">[</a><span class="default"><font color="Maroon" title="c9">a</font>,<font color="Maroon" title="c10">b</font></span><a href="cat_2.html#K12" title="CAT_2:func.12">]</a></span> <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">(<span class="default"><a href="cat_1.html#K6" title="CAT_1:func.6">id</a> <font color="Maroon" title="c9">a</font></span>)</span>,<span class="p2">(<span class="default"><a href="cat_1.html#K6" title="CAT_1:func.6">id</a> <font color="Maroon" title="c10">b</font></span>)</span></span><a href="cat_2.html#K13" title="CAT_2:func.13">]</a></span>
 
<b>by </b><i><a class="ref" href="cat_2.html#T41" title="CAT_2:th.41">CAT_2:41</a></i>;<br/>
<b>hence </b><a NAME="E11:76_1_1"/>
<font color="Maroon" title="c6">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <span class="p1">{<span class="default"> <span class="p2">(<span class="default"><a href="cat_1.html#K6" title="CAT_1:func.6">id</a> <font color="Olive" title="b1">c</font></span>)</span> where <font color="Olive" title="b1">c</font> is   <a href="cat_1.html#NM1" title="CAT_1:NM.1">Object</a> of <span class="p1"><a href="cat_2.html#K11" title="CAT_2:func.11">[:</a><span class="default"><font color="Maroon" title="c1">A</font>,<font color="Maroon" title="c2">B</font></span><a href="cat_2.html#K11" title="CAT_2:func.11">:]</a></span> : verum </span>}</span> 
 <b>by </b><i><a class="txt" href="#E5:76_1_1"><i><font color="Green" title="E61">A7</font></i></a>, <a class="txt" href="#E7:76_1_1"><i><font color="Green" title="E62">A8</font></i></a>, <a class="txt" href="#E9:76_1_1"><i><font color="Green" title="E63">A9</font></i></a></i>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> verum</span><br/>


</div><b>end;</b></div><a NAME="E4:76_1"/>
( the <a href="struct_0.html#U4" title="STRUCT_0:sel.4">carrier'</a> of <span class="p1">(<span class="default"><a href="nattra_1.html#K13" title="NATTRA_1:func.13">IdCat</a> <font color="Maroon" title="c1">A</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">{<span class="default"> <span class="p2">(<span class="default"><a href="cat_1.html#K6" title="CAT_1:func.6">id</a> <font color="Olive" title="b1">a</font></span>)</span> where <font color="Olive" title="b1">a</font> is   <a href="cat_1.html#NM1" title="CAT_1:NM.1">Object</a> of <font color="Maroon" title="c1">A</font> : verum </span>}</span>  &amp; the <a href="struct_0.html#U4" title="STRUCT_0:sel.4">carrier'</a> of <span class="p1">(<span class="default"><a href="nattra_1.html#K13" title="NATTRA_1:func.13">IdCat</a> <font color="Maroon" title="c2">B</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">{<span class="default"> <span class="p2">(<span class="default"><a href="cat_1.html#K6" title="CAT_1:func.6">id</a> <font color="Olive" title="b1">b</font></span>)</span> where <font color="Olive" title="b1">b</font> is   <a href="cat_1.html#NM1" title="CAT_1:NM.1">Object</a> of <font color="Maroon" title="c2">B</font> : verum </span>}</span>  )
 <b>by </b><i><a class="ref" href="nattra_1.html#D20" target="_self" title="NATTRA_1:def.20">Def20</a></i>;<br/><b>hence </b><a NAME="E5:76_1"/><i><font color="Green" title="E60">A10</font></i>: 
the <a href="struct_0.html#U4" title="STRUCT_0:sel.4">carrier'</a> of <span class="p1">(<span class="default"><a href="nattra_1.html#K13" title="NATTRA_1:func.13">IdCat</a> <span class="p2"><a href="cat_2.html#K11" title="CAT_2:func.11">[:</a><span class="default"><font color="Maroon" title="c1">A</font>,<font color="Maroon" title="c2">B</font></span><a href="cat_2.html#K11" title="CAT_2:func.11">:]</a></span></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</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 <span class="p2">(<span class="default"><a href="nattra_1.html#K13" title="NATTRA_1:func.13">IdCat</a> <font color="Maroon" title="c1">A</font></span>)</span>,the <a href="struct_0.html#U4" title="STRUCT_0:sel.4">carrier'</a> of <span class="p2">(<span class="default"><a href="nattra_1.html#K13" title="NATTRA_1:func.13">IdCat</a> <font color="Maroon" title="c2">B</font></span>)</span></span><a href="zfmisc_1.html#K2" title="ZFMISC_1:func.2">:]</a></span>
 <b>by </b><i><a class="txt" href="#E3:76_1"><i><font color="Green" title="E59">A2</font></i></a>, <a class="ref" href="nattra_1.html#D20" target="_self" title="NATTRA_1:def.20">Def20</a></i>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> ( <span class="p1"><a href="cat_2.html#K9" title="CAT_2:func.9">[:</a><span class="default">the <a href="graph_1.html#U1" title="GRAPH_1:sel.1">Source</a> of <span class="p2">(<span class="default"><a href="nattra_1.html#K13" title="NATTRA_1:func.13">IdCat</a> <font color="Maroon" title="c1">A</font></span>)</span>,the <a href="graph_1.html#U1" title="GRAPH_1:sel.1">Source</a> of <span class="p2">(<span class="default"><a href="nattra_1.html#K13" title="NATTRA_1:func.13">IdCat</a> <font color="Maroon" title="c2">B</font></span>)</span></span><a href="cat_2.html#K9" title="CAT_2:func.9">:]</a></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 <span class="p1">(<span class="default"><a href="nattra_1.html#K13" title="NATTRA_1:func.13">IdCat</a> <span class="p2"><a href="cat_2.html#K11" title="CAT_2:func.11">[:</a><span class="default"><font color="Maroon" title="c1">A</font>,<font color="Maroon" title="c2">B</font></span><a href="cat_2.html#K11" title="CAT_2:func.11">:]</a></span></span>)</span> &amp; <span class="p1"><a href="cat_2.html#K9" title="CAT_2:func.9">[:</a><span class="default">the <a href="graph_1.html#U2" title="GRAPH_1:sel.2">Target</a> of <span class="p2">(<span class="default"><a href="nattra_1.html#K13" title="NATTRA_1:func.13">IdCat</a> <font color="Maroon" title="c1">A</font></span>)</span>,the <a href="graph_1.html#U2" title="GRAPH_1:sel.2">Target</a> of <span class="p2">(<span class="default"><a href="nattra_1.html#K13" title="NATTRA_1:func.13">IdCat</a> <font color="Maroon" title="c2">B</font></span>)</span></span><a href="cat_2.html#K9" title="CAT_2:func.9">:]</a></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 <span class="p1">(<span class="default"><a href="nattra_1.html#K13" title="NATTRA_1:func.13">IdCat</a> <span class="p2"><a href="cat_2.html#K11" title="CAT_2:func.11">[:</a><span class="default"><font color="Maroon" title="c1">A</font>,<font color="Maroon" title="c2">B</font></span><a href="cat_2.html#K11" title="CAT_2:func.11">:]</a></span></span>)</span> &amp; <span class="p1"><a href="cat_2.html#K10" title="CAT_2:func.10">|:</a><span class="default">the <a href="cat_1.html#U1" title="CAT_1:sel.1">Comp</a> of <span class="p2">(<span class="default"><a href="nattra_1.html#K13" title="NATTRA_1:func.13">IdCat</a> <font color="Maroon" title="c1">A</font></span>)</span>,the <a href="cat_1.html#U1" title="CAT_1:sel.1">Comp</a> of <span class="p2">(<span class="default"><a href="nattra_1.html#K13" title="NATTRA_1:func.13">IdCat</a> <font color="Maroon" title="c2">B</font></span>)</span></span><a href="cat_2.html#K10" title="CAT_2:func.10">:|</a></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 <span class="p1">(<span class="default"><a href="nattra_1.html#K13" title="NATTRA_1:func.13">IdCat</a> <span class="p2"><a href="cat_2.html#K11" title="CAT_2:func.11">[:</a><span class="default"><font color="Maroon" title="c1">A</font>,<font color="Maroon" title="c2">B</font></span><a href="cat_2.html#K11" title="CAT_2:func.11">:]</a></span></span>)</span> &amp; <span class="p1"><a href="cat_2.html#K9" title="CAT_2:func.9">[:</a><span class="default">the <a href="cat_1.html#U2" title="CAT_1:sel.2">Id</a> of <span class="p2">(<span class="default"><a href="nattra_1.html#K13" title="NATTRA_1:func.13">IdCat</a> <font color="Maroon" title="c1">A</font></span>)</span>,the <a href="cat_1.html#U2" title="CAT_1:sel.2">Id</a> of <span class="p2">(<span class="default"><a href="nattra_1.html#K13" title="NATTRA_1:func.13">IdCat</a> <font color="Maroon" title="c2">B</font></span>)</span></span><a href="cat_2.html#K9" title="CAT_2:func.9">:]</a></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 <span class="p1">(<span class="default"><a href="nattra_1.html#K13" title="NATTRA_1:func.13">IdCat</a> <span class="p2"><a href="cat_2.html#K11" title="CAT_2:func.11">[:</a><span class="default"><font color="Maroon" title="c1">A</font>,<font color="Maroon" title="c2">B</font></span><a href="cat_2.html#K11" title="CAT_2:func.11">:]</a></span></span>)</span> )</span><br/><b>reconsider </b><font color="Maroon" title="c6">MA</font> = the <a href="struct_0.html#U4" title="STRUCT_0:sel.4">carrier'</a> of <span class="p1">(<span class="default"><a href="nattra_1.html#K13" title="NATTRA_1:func.13">IdCat</a> <font color="Maroon" title="c1">A</font></span>)</span> as  non <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a> <a href="subset_1.html#NM2" title="SUBSET_1:NM.2">Subset</a> of the <a href="struct_0.html#U4" title="STRUCT_0:sel.4">carrier'</a> of <font color="Maroon" title="c1">A</font> <b>by </b><i><a class="ref" href="cat_2.html#T13" title="CAT_2:th.13">CAT_2:13</a></i>;<br/><b>reconsider </b><font color="Maroon" title="c7">MB</font> = the <a href="struct_0.html#U4" title="STRUCT_0:sel.4">carrier'</a> of <span class="p1">(<span class="default"><a href="nattra_1.html#K13" title="NATTRA_1:func.13">IdCat</a> <font color="Maroon" title="c2">B</font></span>)</span> as  non <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a> <a href="subset_1.html#NM2" title="SUBSET_1:NM.2">Subset</a> of the <a href="struct_0.html#U4" title="STRUCT_0:sel.4">carrier'</a> of <font color="Maroon" title="c2">B</font> <b>by </b><i><a class="ref" href="cat_2.html#T13" title="CAT_2:th.13">CAT_2:13</a></i>;<br/><a NAME="E8:76_1"/>
( the <a href="graph_1.html#U1" title="GRAPH_1:sel.1">Source</a> of <span class="p1">(<span class="default"><a href="nattra_1.html#K13" title="NATTRA_1:func.13">IdCat</a> <font color="Maroon" title="c1">A</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="c1">A</font> <a href="relat_1.html#K7" title="RELAT_1:func.7">|</a> the <a href="struct_0.html#U4" title="STRUCT_0:sel.4">carrier'</a> of <span class="p1">(<span class="default"><a href="nattra_1.html#K13" title="NATTRA_1:func.13">IdCat</a> <font color="Maroon" title="c1">A</font></span>)</span> &amp; the <a href="graph_1.html#U1" title="GRAPH_1:sel.1">Source</a> of <span class="p1">(<span class="default"><a href="nattra_1.html#K13" title="NATTRA_1:func.13">IdCat</a> <font color="Maroon" title="c2">B</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">B</font> <a href="relat_1.html#K7" title="RELAT_1:func.7">|</a> the <a href="struct_0.html#U4" title="STRUCT_0:sel.4">carrier'</a> of <span class="p1">(<span class="default"><a href="nattra_1.html#K13" title="NATTRA_1:func.13">IdCat</a> <font color="Maroon" title="c2">B</font></span>)</span> )
 <b>by </b><i><a class="ref" href="nattra_1.html#T8" target="_self" title="NATTRA_1:th.8">Th8</a></i>;<br/><b>hence </b><span class="p1"><a href="cat_2.html#K9" title="CAT_2:func.9">[:</a><span class="default">the <a href="graph_1.html#U1" title="GRAPH_1:sel.1">Source</a> of <span class="p2">(<span class="default"><a href="nattra_1.html#K13" title="NATTRA_1:func.13">IdCat</a> <font color="Maroon" title="c1">A</font></span>)</span>,the <a href="graph_1.html#U1" title="GRAPH_1:sel.1">Source</a> of <span class="p2">(<span class="default"><a href="nattra_1.html#K13" title="NATTRA_1:func.13">IdCat</a> <font color="Maroon" title="c2">B</font></span>)</span></span><a href="cat_2.html#K9" title="CAT_2:func.9">:]</a></span> = 
<span class="p1"><a href="cat_2.html#K9" title="CAT_2:func.9">[:</a><span class="default">the <a href="graph_1.html#U1" title="GRAPH_1:sel.1">Source</a> of <font color="Maroon" title="c1">A</font>,the <a href="graph_1.html#U1" title="GRAPH_1:sel.1">Source</a> of <font color="Maroon" title="c2">B</font></span><a href="cat_2.html#K9" title="CAT_2:func.9">:]</a></span> <a href="nattra_1.html#K1" title="NATTRA_1:func.1">|</a> <span class="p1"><a href="mcart_1.html#K12" title="MCART_1:func.12">[:</a><span class="default"><font color="Maroon" title="c6">MA</font>,<font color="Maroon" title="c7">MB</font></span><a href="mcart_1.html#K12" title="MCART_1:func.12">:]</a></span>
<b>by </b><i><a class="ref" href="nattra_1.html#T1" target="_self" title="NATTRA_1:th.1">Th1</a></i>
<br/>.= 
the <a href="graph_1.html#U1" title="GRAPH_1:sel.1">Source</a> of <span class="p1">(<span class="default"><a href="nattra_1.html#K13" title="NATTRA_1:func.13">IdCat</a> <span class="p2"><a href="cat_2.html#K11" title="CAT_2:func.11">[:</a><span class="default"><font color="Maroon" title="c1">A</font>,<font color="Maroon" title="c2">B</font></span><a href="cat_2.html#K11" title="CAT_2:func.11">:]</a></span></span>)</span>
<b>by </b><i><a class="txt" href="#E5:76_1"><i><font color="Green" title="E60">A10</font></i></a>, <a class="ref" href="nattra_1.html#T8" target="_self" title="NATTRA_1:th.8">Th8</a></i>
;<br/> <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> ( <span class="p1"><a href="cat_2.html#K9" title="CAT_2:func.9">[:</a><span class="default">the <a href="graph_1.html#U2" title="GRAPH_1:sel.2">Target</a> of <span class="p2">(<span class="default"><a href="nattra_1.html#K13" title="NATTRA_1:func.13">IdCat</a> <font color="Maroon" title="c1">A</font></span>)</span>,the <a href="graph_1.html#U2" title="GRAPH_1:sel.2">Target</a> of <span class="p2">(<span class="default"><a href="nattra_1.html#K13" title="NATTRA_1:func.13">IdCat</a> <font color="Maroon" title="c2">B</font></span>)</span></span><a href="cat_2.html#K9" title="CAT_2:func.9">:]</a></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 <span class="p1">(<span class="default"><a href="nattra_1.html#K13" title="NATTRA_1:func.13">IdCat</a> <span class="p2"><a href="cat_2.html#K11" title="CAT_2:func.11">[:</a><span class="default"><font color="Maroon" title="c1">A</font>,<font color="Maroon" title="c2">B</font></span><a href="cat_2.html#K11" title="CAT_2:func.11">:]</a></span></span>)</span> &amp; <span class="p1"><a href="cat_2.html#K10" title="CAT_2:func.10">|:</a><span class="default">the <a href="cat_1.html#U1" title="CAT_1:sel.1">Comp</a> of <span class="p2">(<span class="default"><a href="nattra_1.html#K13" title="NATTRA_1:func.13">IdCat</a> <font color="Maroon" title="c1">A</font></span>)</span>,the <a href="cat_1.html#U1" title="CAT_1:sel.1">Comp</a> of <span class="p2">(<span class="default"><a href="nattra_1.html#K13" title="NATTRA_1:func.13">IdCat</a> <font color="Maroon" title="c2">B</font></span>)</span></span><a href="cat_2.html#K10" title="CAT_2:func.10">:|</a></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 <span class="p1">(<span class="default"><a href="nattra_1.html#K13" title="NATTRA_1:func.13">IdCat</a> <span class="p2"><a href="cat_2.html#K11" title="CAT_2:func.11">[:</a><span class="default"><font color="Maroon" title="c1">A</font>,<font color="Maroon" title="c2">B</font></span><a href="cat_2.html#K11" title="CAT_2:func.11">:]</a></span></span>)</span> &amp; <span class="p1"><a href="cat_2.html#K9" title="CAT_2:func.9">[:</a><span class="default">the <a href="cat_1.html#U2" title="CAT_1:sel.2">Id</a> of <span class="p2">(<span class="default"><a href="nattra_1.html#K13" title="NATTRA_1:func.13">IdCat</a> <font color="Maroon" title="c1">A</font></span>)</span>,the <a href="cat_1.html#U2" title="CAT_1:sel.2">Id</a> of <span class="p2">(<span class="default"><a href="nattra_1.html#K13" title="NATTRA_1:func.13">IdCat</a> <font color="Maroon" title="c2">B</font></span>)</span></span><a href="cat_2.html#K9" title="CAT_2:func.9">:]</a></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 <span class="p1">(<span class="default"><a href="nattra_1.html#K13" title="NATTRA_1:func.13">IdCat</a> <span class="p2"><a href="cat_2.html#K11" title="CAT_2:func.11">[:</a><span class="default"><font color="Maroon" title="c1">A</font>,<font color="Maroon" title="c2">B</font></span><a href="cat_2.html#K11" title="CAT_2:func.11">:]</a></span></span>)</span> )</span><br/><a NAME="E10:76_1"/>
( the <a href="graph_1.html#U2" title="GRAPH_1:sel.2">Target</a> of <span class="p1">(<span class="default"><a href="nattra_1.html#K13" title="NATTRA_1:func.13">IdCat</a> <font color="Maroon" title="c1">A</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="c1">A</font> <a href="relat_1.html#K7" title="RELAT_1:func.7">|</a> the <a href="struct_0.html#U4" title="STRUCT_0:sel.4">carrier'</a> of <span class="p1">(<span class="default"><a href="nattra_1.html#K13" title="NATTRA_1:func.13">IdCat</a> <font color="Maroon" title="c1">A</font></span>)</span> &amp; the <a href="graph_1.html#U2" title="GRAPH_1:sel.2">Target</a> of <span class="p1">(<span class="default"><a href="nattra_1.html#K13" title="NATTRA_1:func.13">IdCat</a> <font color="Maroon" title="c2">B</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">B</font> <a href="relat_1.html#K7" title="RELAT_1:func.7">|</a> the <a href="struct_0.html#U4" title="STRUCT_0:sel.4">carrier'</a> of <span class="p1">(<span class="default"><a href="nattra_1.html#K13" title="NATTRA_1:func.13">IdCat</a> <font color="Maroon" title="c2">B</font></span>)</span> )
 <b>by </b><i><a class="ref" href="nattra_1.html#T8" target="_self" title="NATTRA_1:th.8">Th8</a></i>;<br/><b>hence </b><span class="p1"><a href="cat_2.html#K9" title="CAT_2:func.9">[:</a><span class="default">the <a href="graph_1.html#U2" title="GRAPH_1:sel.2">Target</a> of <span class="p2">(<span class="default"><a href="nattra_1.html#K13" title="NATTRA_1:func.13">IdCat</a> <font color="Maroon" title="c1">A</font></span>)</span>,the <a href="graph_1.html#U2" title="GRAPH_1:sel.2">Target</a> of <span class="p2">(<span class="default"><a href="nattra_1.html#K13" title="NATTRA_1:func.13">IdCat</a> <font color="Maroon" title="c2">B</font></span>)</span></span><a href="cat_2.html#K9" title="CAT_2:func.9">:]</a></span> = 
<span class="p1"><a href="cat_2.html#K9" title="CAT_2:func.9">[:</a><span class="default">the <a href="graph_1.html#U2" title="GRAPH_1:sel.2">Target</a> of <font color="Maroon" title="c1">A</font>,the <a href="graph_1.html#U2" title="GRAPH_1:sel.2">Target</a> of <font color="Maroon" title="c2">B</font></span><a href="cat_2.html#K9" title="CAT_2:func.9">:]</a></span> <a href="nattra_1.html#K1" title="NATTRA_1:func.1">|</a> <span class="p1"><a href="mcart_1.html#K12" title="MCART_1:func.12">[:</a><span class="default"><font color="Maroon" title="c6">MA</font>,<font color="Maroon" title="c7">MB</font></span><a href="mcart_1.html#K12" title="MCART_1:func.12">:]</a></span>
<b>by </b><i><a class="ref" href="nattra_1.html#T1" target="_self" title="NATTRA_1:th.1">Th1</a></i>
<br/>.= 
the <a href="graph_1.html#U2" title="GRAPH_1:sel.2">Target</a> of <span class="p1">(<span class="default"><a href="nattra_1.html#K13" title="NATTRA_1:func.13">IdCat</a> <span class="p2"><a href="cat_2.html#K11" title="CAT_2:func.11">[:</a><span class="default"><font color="Maroon" title="c1">A</font>,<font color="Maroon" title="c2">B</font></span><a href="cat_2.html#K11" title="CAT_2:func.11">:]</a></span></span>)</span>
<b>by </b><i><a class="txt" href="#E5:76_1"><i><font color="Green" title="E60">A10</font></i></a>, <a class="ref" href="nattra_1.html#T8" target="_self" title="NATTRA_1:th.8">Th8</a></i>
;<br/> <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> ( <span class="p1"><a href="cat_2.html#K10" title="CAT_2:func.10">|:</a><span class="default">the <a href="cat_1.html#U1" title="CAT_1:sel.1">Comp</a> of <span class="p2">(<span class="default"><a href="nattra_1.html#K13" title="NATTRA_1:func.13">IdCat</a> <font color="Maroon" title="c1">A</font></span>)</span>,the <a href="cat_1.html#U1" title="CAT_1:sel.1">Comp</a> of <span class="p2">(<span class="default"><a href="nattra_1.html#K13" title="NATTRA_1:func.13">IdCat</a> <font color="Maroon" title="c2">B</font></span>)</span></span><a href="cat_2.html#K10" title="CAT_2:func.10">:|</a></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 <span class="p1">(<span class="default"><a href="nattra_1.html#K13" title="NATTRA_1:func.13">IdCat</a> <span class="p2"><a href="cat_2.html#K11" title="CAT_2:func.11">[:</a><span class="default"><font color="Maroon" title="c1">A</font>,<font color="Maroon" title="c2">B</font></span><a href="cat_2.html#K11" title="CAT_2:func.11">:]</a></span></span>)</span> &amp; <span class="p1"><a href="cat_2.html#K9" title="CAT_2:func.9">[:</a><span class="default">the <a href="cat_1.html#U2" title="CAT_1:sel.2">Id</a> of <span class="p2">(<span class="default"><a href="nattra_1.html#K13" title="NATTRA_1:func.13">IdCat</a> <font color="Maroon" title="c1">A</font></span>)</span>,the <a href="cat_1.html#U2" title="CAT_1:sel.2">Id</a> of <span class="p2">(<span class="default"><a href="nattra_1.html#K13" title="NATTRA_1:func.13">IdCat</a> <font color="Maroon" title="c2">B</font></span>)</span></span><a href="cat_2.html#K9" title="CAT_2:func.9">:]</a></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 <span class="p1">(<span class="default"><a href="nattra_1.html#K13" title="NATTRA_1:func.13">IdCat</a> <span class="p2"><a href="cat_2.html#K11" title="CAT_2:func.11">[:</a><span class="default"><font color="Maroon" title="c1">A</font>,<font color="Maroon" title="c2">B</font></span><a href="cat_2.html#K11" title="CAT_2:func.11">:]</a></span></span>)</span> )</span><br/><a NAME="E12:76_1"/><i><font color="Green" title="E61">A11</font></i>: 
<span class="p1"><a href="cat_2.html#K10" title="CAT_2:func.10">|:</a><span class="default">the <a href="cat_1.html#U1" title="CAT_1:sel.1">Comp</a> of <font color="Maroon" title="c1">A</font>,the <a href="cat_1.html#U1" title="CAT_1:sel.1">Comp</a> of <font color="Maroon" title="c2">B</font></span><a href="cat_2.html#K10" title="CAT_2:func.10">:|</a></span> <a href="realset1.html#K1" title="REALSET1:func.1">||</a> <span class="p1"><a href="mcart_1.html#K12" title="MCART_1:func.12">[:</a><span class="default"><font color="Maroon" title="c6">MA</font>,<font color="Maroon" title="c7">MB</font></span><a href="mcart_1.html#K12" title="MCART_1:func.12">:]</a></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 <span class="p1">(<span class="default"><a href="nattra_1.html#K13" title="NATTRA_1:func.13">IdCat</a> <span class="p2"><a href="cat_2.html#K11" title="CAT_2:func.11">[:</a><span class="default"><font color="Maroon" title="c1">A</font>,<font color="Maroon" title="c2">B</font></span><a href="cat_2.html#K11" title="CAT_2:func.11">:]</a></span></span>)</span>
 <b>by </b><i><a class="txt" href="#E5:76_1"><i><font color="Green" title="E60">A10</font></i></a>, <a class="ref" href="nattra_1.html#T8" target="_self" title="NATTRA_1:th.8">Th8</a></i>;<br/><a NAME="E13:76_1"/>
( the <a href="cat_1.html#U1" title="CAT_1:sel.1">Comp</a> of <span class="p1">(<span class="default"><a href="nattra_1.html#K13" title="NATTRA_1:func.13">IdCat</a> <font color="Maroon" title="c1">A</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="c1">A</font> <a href="realset1.html#K1" title="REALSET1:func.1">||</a> <font color="Maroon" title="c6">MA</font> &amp; the <a href="cat_1.html#U1" title="CAT_1:sel.1">Comp</a> of <span class="p1">(<span class="default"><a href="nattra_1.html#K13" title="NATTRA_1:func.13">IdCat</a> <font color="Maroon" title="c2">B</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">B</font> <a href="realset1.html#K1" title="REALSET1:func.1">||</a> <font color="Maroon" title="c7">MB</font> )
 <b>by </b><i><a class="ref" href="nattra_1.html#T8" target="_self" title="NATTRA_1:th.8">Th8</a></i>;<br/><b>hence </b><a NAME="E14:76_1"/>
<span class="p1"><a href="cat_2.html#K10" title="CAT_2:func.10">|:</a><span class="default">the <a href="cat_1.html#U1" title="CAT_1:sel.1">Comp</a> of <span class="p2">(<span class="default"><a href="nattra_1.html#K13" title="NATTRA_1:func.13">IdCat</a> <font color="Maroon" title="c1">A</font></span>)</span>,the <a href="cat_1.html#U1" title="CAT_1:sel.1">Comp</a> of <span class="p2">(<span class="default"><a href="nattra_1.html#K13" title="NATTRA_1:func.13">IdCat</a> <font color="Maroon" title="c2">B</font></span>)</span></span><a href="cat_2.html#K10" title="CAT_2:func.10">:|</a></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 <span class="p1">(<span class="default"><a href="nattra_1.html#K13" title="NATTRA_1:func.13">IdCat</a> <span class="p2"><a href="cat_2.html#K11" title="CAT_2:func.11">[:</a><span class="default"><font color="Maroon" title="c1">A</font>,<font color="Maroon" title="c2">B</font></span><a href="cat_2.html#K11" title="CAT_2:func.11">:]</a></span></span>)</span>
 <b>by </b><i><a class="txt" href="#E12:76_1"><i><font color="Green" title="E61">A11</font></i></a>, <a class="ref" href="nattra_1.html#T2" target="_self" title="NATTRA_1:th.2">Th2</a></i>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> <span class="p1"><a href="cat_2.html#K9" title="CAT_2:func.9">[:</a><span class="default">the <a href="cat_1.html#U2" title="CAT_1:sel.2">Id</a> of <span class="p2">(<span class="default"><a href="nattra_1.html#K13" title="NATTRA_1:func.13">IdCat</a> <font color="Maroon" title="c1">A</font></span>)</span>,the <a href="cat_1.html#U2" title="CAT_1:sel.2">Id</a> of <span class="p2">(<span class="default"><a href="nattra_1.html#K13" title="NATTRA_1:func.13">IdCat</a> <font color="Maroon" title="c2">B</font></span>)</span></span><a href="cat_2.html#K9" title="CAT_2:func.9">:]</a></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 <span class="p1">(<span class="default"><a href="nattra_1.html#K13" title="NATTRA_1:func.13">IdCat</a> <span class="p2"><a href="cat_2.html#K11" title="CAT_2:func.11">[:</a><span class="default"><font color="Maroon" title="c1">A</font>,<font color="Maroon" title="c2">B</font></span><a href="cat_2.html#K11" title="CAT_2:func.11">:]</a></span></span>)</span></span><br/><b>reconsider </b><font color="Maroon" title="c8">OA</font> = the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <span class="p1">(<span class="default"><a href="nattra_1.html#K13" title="NATTRA_1:func.13">IdCat</a> <font color="Maroon" title="c1">A</font></span>)</span> as  non <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a> <a href="subset_1.html#NM2" title="SUBSET_1:NM.2">Subset</a> of the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c1">A</font> <b>by </b><i><a class="ref" href="cat_2.html#D4" title="CAT_2:def.4">CAT_2:def 4</a></i>;<br/><b>reconsider </b><font color="Maroon" title="c9">OB</font> = the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <span class="p1">(<span class="default"><a href="nattra_1.html#K13" title="NATTRA_1:func.13">IdCat</a> <font color="Maroon" title="c2">B</font></span>)</span> as  non <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a> <a href="subset_1.html#NM2" title="SUBSET_1:NM.2">Subset</a> of the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c2">B</font> <b>by </b><i><a class="ref" href="cat_2.html#D4" title="CAT_2:def.4">CAT_2:def 4</a></i>;<br/><a NAME="E17:76_1"/>
( the <a href="cat_1.html#U2" title="CAT_1:sel.2">Id</a> of <span class="p1">(<span class="default"><a href="nattra_1.html#K13" title="NATTRA_1:func.13">IdCat</a> <font color="Maroon" title="c1">A</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="c1">A</font> <a href="relat_1.html#K7" title="RELAT_1:func.7">|</a> the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <span class="p1">(<span class="default"><a href="nattra_1.html#K13" title="NATTRA_1:func.13">IdCat</a> <font color="Maroon" title="c1">A</font></span>)</span> &amp; the <a href="cat_1.html#U2" title="CAT_1:sel.2">Id</a> of <span class="p1">(<span class="default"><a href="nattra_1.html#K13" title="NATTRA_1:func.13">IdCat</a> <font color="Maroon" title="c2">B</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">B</font> <a href="relat_1.html#K7" title="RELAT_1:func.7">|</a> the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <span class="p1">(<span class="default"><a href="nattra_1.html#K13" title="NATTRA_1:func.13">IdCat</a> <font color="Maroon" title="c2">B</font></span>)</span> )
 <b>by </b><i><a class="ref" href="nattra_1.html#T8" target="_self" title="NATTRA_1:th.8">Th8</a></i>;<br/><b>hence </b><span class="p1"><a href="cat_2.html#K9" title="CAT_2:func.9">[:</a><span class="default">the <a href="cat_1.html#U2" title="CAT_1:sel.2">Id</a> of <span class="p2">(<span class="default"><a href="nattra_1.html#K13" title="NATTRA_1:func.13">IdCat</a> <font color="Maroon" title="c1">A</font></span>)</span>,the <a href="cat_1.html#U2" title="CAT_1:sel.2">Id</a> of <span class="p2">(<span class="default"><a href="nattra_1.html#K13" title="NATTRA_1:func.13">IdCat</a> <font color="Maroon" title="c2">B</font></span>)</span></span><a href="cat_2.html#K9" title="CAT_2:func.9">:]</a></span> = 
<span class="p1"><a href="cat_2.html#K9" title="CAT_2:func.9">[:</a><span class="default">the <a href="cat_1.html#U2" title="CAT_1:sel.2">Id</a> of <font color="Maroon" title="c1">A</font>,the <a href="cat_1.html#U2" title="CAT_1:sel.2">Id</a> of <font color="Maroon" title="c2">B</font></span><a href="cat_2.html#K9" title="CAT_2:func.9">:]</a></span> <a href="nattra_1.html#K1" title="NATTRA_1:func.1">|</a> <span class="p1"><a href="mcart_1.html#K12" title="MCART_1:func.12">[:</a><span class="default"><font color="Maroon" title="c8">OA</font>,<font color="Maroon" title="c9">OB</font></span><a href="mcart_1.html#K12" title="MCART_1:func.12">:]</a></span>
<b>by </b><i><a class="ref" href="nattra_1.html#T1" target="_self" title="NATTRA_1:th.1">Th1</a></i>
<br/>.= 
the <a href="cat_1.html#U2" title="CAT_1:sel.2">Id</a> of <span class="p1">(<span class="default"><a href="nattra_1.html#K13" title="NATTRA_1:func.13">IdCat</a> <span class="p2"><a href="cat_2.html#K11" title="CAT_2:func.11">[:</a><span class="default"><font color="Maroon" title="c1">A</font>,<font color="Maroon" title="c2">B</font></span><a href="cat_2.html#K11" title="CAT_2:func.11">:]</a></span></span>)</span>
<b>by </b><i><a class="txt" href="#E2:76_1"><i><font color="Green" title="E58">A1</font></i></a>, <a class="ref" href="nattra_1.html#T8" target="_self" title="NATTRA_1:th.8">Th8</a></i>
;<br/> <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> verum</span><br/></div><b>end;</b></div>
<b>hence </b><a NAME="E2:76"/>
 <a href="nattra_1.html#K13" title="NATTRA_1:func.13">IdCat</a> <span class="p1"><a href="cat_2.html#K11" title="CAT_2:func.11">[:</a><span class="default"><font color="Maroon" title="c1">A</font>,<font color="Maroon" title="c2">B</font></span><a href="cat_2.html#K11" title="CAT_2:func.11">:]</a></span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1"><a href="cat_2.html#K11" title="CAT_2:func.11">[:</a><span class="default"><span class="p2">(<span class="default"><a href="nattra_1.html#K13" title="NATTRA_1:func.13">IdCat</a> <font color="Maroon" title="c1">A</font></span>)</span>,<span class="p2">(<span class="default"><a href="nattra_1.html#K13" title="NATTRA_1:func.13">IdCat</a> <font color="Maroon" title="c2">B</font></span>)</span></span><a href="cat_2.html#K11" title="CAT_2:func.11">:]</a></span>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> verum</span><br/>


</div>
