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<div class="add">

<span class="kw">let </span><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:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></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"><span class="kw">now </span></a><div class="add"><span class="kw">reconsider </span><font color="Maroon" title="c3">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> <span class="kw">by</span> <span class="lab"><a class="ref" href="cat_2.html#D4" title="CAT_2:def.4">CAT_2:def 4</a></span>;<br/><span class="kw">set </span><font color="Maroon" title="c4">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/><span class="kw">set </span><font color="Maroon" title="c5">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/><span class="kw">set </span><font color="Maroon" title="c6">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="E2:76_1"/><span class="lab"><font color="Green" title="E58">A1</font></span>: 
<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"><span class="kw">proof </span></a><div class="add">

<span class="kw">thus </span><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>
  <span class="comment"><font color="firebrick">:: according to </font></span><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:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></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"><span class="kw">proof </span></a><div class="add">

<span class="kw">let </span><font color="Maroon" title="c7">x</font> be    <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a> ; <span class="comment"><font color="firebrick">:: according to </font></span><a class="ref" href="tarski.html#D3" title="TARSKI:def.3">TARSKI:def 3</a> <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> (  not <font color="Maroon" title="c7">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="c7">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/>

<span class="kw">assume </span><a NAME="E1:76_1_1_1"/>
<font color="Maroon" title="c7">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:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> <font color="Maroon" title="c7">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/>

<span class="kw">then </span><span class="kw">consider </span><font color="Maroon" title="c8">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><span class="kw"> such that </span><br/><a NAME="E3:76_1_1_1"/><span class="lab"><font color="Green" title="E59">A2</font></span>: 
<font color="Maroon" title="c7">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="c8">c</font>
 ;<br/>
<span class="kw">consider </span><font color="Maroon" title="c9">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="c10">c2</font> being   <a href="cat_1.html#NM1" title="CAT_1:NM.1">Object</a> of <font color="Maroon" title="c2">B</font><span class="kw"> such that </span><br/><a NAME="E5:76_1_1_1"/><span class="lab"><font color="Green" title="E60">A3</font></span>: 
<font color="Maroon" title="c8">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="c9">c1</font>,<font color="Maroon" title="c10">c2</font></span><a href="cat_2.html#K12" title="CAT_2:func.12">]</a></span>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="domain_1.html#T1" title="DOMAIN_1:th.1">DOMAIN_1:1</a></span>;<br/>
<a NAME="E6:76_1_1_1"/><span class="lab"><font color="Green" title="E61">A4</font></span>: 
 <a href="cat_1.html#K6" title="CAT_1:func.6">id</a> <font color="Maroon" title="c10">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/>
<a NAME="E7:76_1_1_1"/><span class="lab"><font color="Green" title="E62">A5</font></span>: 
 <a href="cat_1.html#K6" title="CAT_1:func.6">id</a> <font color="Maroon" title="c9">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> 
 
;<br/>
<a NAME="E8:76_1_1_1"/>
 <a href="cat_1.html#K6" title="CAT_1:func.6">id</a> <font color="Maroon" title="c8">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="c9">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="c10">c2</font></span>)</span></span><a href="cat_2.html#K13" title="CAT_2:func.13">]</a></span>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E5:76_1_1_1"><span class="lab"><font color="Green" title="E60">A3</font></span></a>, <a class="ref" href="cat_2.html#T31" title="CAT_2:th.31">CAT_2:31</a></span>;<br/>
<span class="kw">hence </span><a NAME="E9:76_1_1_1"/>
<font color="Maroon" title="c7">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 class="kw">by</span> <span class="lab"><a class="txt" href="#E3:76_1_1_1"><span class="lab"><font color="Green" title="E59">A2</font></span></a>, <a class="txt" href="#E7:76_1_1_1"><span class="lab"><font color="Green" title="E62">A5</font></span></a>, <a class="txt" href="#E6:76_1_1_1"><span class="lab"><font color="Green" title="E61">A4</font></span></a>, <a class="ref" href="zfmisc_1.html#T87" title="ZFMISC_1:th.87">ZFMISC_1:87</a></span>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> verum</span><br/>


</div><span class="kw">end;</span></div>

<span class="kw">let </span><font color="Maroon" title="c7">x</font> be    <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a> ; <span class="comment"><font color="firebrick">:: according to </font></span><a class="ref" href="tarski.html#D3" title="TARSKI:def.3">TARSKI:def 3</a> <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> (  not <font color="Maroon" title="c7">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="c7">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/>

<span class="kw">assume </span><a NAME="E2:76_1_1"/>
<font color="Maroon" title="c7">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:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> <font color="Maroon" title="c7">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/>

<span class="kw">then </span><span class="kw">consider </span><font color="Maroon" title="c8">x1</font>, <font color="Maroon" title="c9">x2</font> being    <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a> <span class="kw"> such that </span><br/><a NAME="E4:76_1_1"/><span class="lab"><font color="Green" title="E59">A6</font></span>: 
<font color="Maroon" title="c8">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> 
 <span class="kw">and </span><br/><a NAME="E5:76_1_1"/><span class="lab"><font color="Green" title="E60">A7</font></span>: 
<font color="Maroon" title="c9">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> 
 <span class="kw">and </span><br/><a NAME="E6:76_1_1"/><span class="lab"><font color="Green" title="E61">A8</font></span>: 
<font color="Maroon" title="c7">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="c8">x1</font>,<font color="Maroon" title="c9">x2</font></span><a href="tarski.html#K4" title="TARSKI:func.4">]</a></span>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="zfmisc_1.html#T84" title="ZFMISC_1:th.84">ZFMISC_1:84</a></span>;<br/>
<span class="kw">consider </span><font color="Maroon" title="c10">a</font> being   <a href="cat_1.html#NM1" title="CAT_1:NM.1">Object</a> of <font color="Maroon" title="c1">A</font><span class="kw"> such that </span><br/><a NAME="E8:76_1_1"/><span class="lab"><font color="Green" title="E62">A9</font></span>: 
<font color="Maroon" title="c8">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="c10">a</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E4:76_1_1"><span class="lab"><font color="Green" title="E59">A6</font></span></a></span>;<br/>
<span class="kw">consider </span><font color="Maroon" title="c11">b</font> being   <a href="cat_1.html#NM1" title="CAT_1:NM.1">Object</a> of <font color="Maroon" title="c2">B</font><span class="kw"> such that </span><br/><a NAME="E10:76_1_1"/><span class="lab"><font color="Green" title="E63">A10</font></span>: 
<font color="Maroon" title="c9">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="c11">b</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E5:76_1_1"><span class="lab"><font color="Green" title="E60">A7</font></span></a></span>;<br/>
<a NAME="E11:76_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="c10">a</font>,<font color="Maroon" title="c11">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="c10">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="c11">b</font></span>)</span></span><a href="cat_2.html#K13" title="CAT_2:func.13">]</a></span>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="cat_2.html#T31" title="CAT_2:th.31">CAT_2:31</a></span>;<br/>
<span class="kw">hence </span><a NAME="E12:76_1_1"/>
<font color="Maroon" title="c7">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 class="kw">by</span> <span class="lab"><a class="txt" href="#E6:76_1_1"><span class="lab"><font color="Green" title="E61">A8</font></span></a>, <a class="txt" href="#E8:76_1_1"><span class="lab"><font color="Green" title="E62">A9</font></span></a>, <a class="txt" href="#E10:76_1_1"><span class="lab"><font color="Green" title="E63">A10</font></span></a></span>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> verum</span><br/>


</div><span class="kw">end;</span></div><span class="kw">reconsider </span><font color="Maroon" title="c7">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> <span class="kw">by</span> <span class="lab"><a class="ref" href="cat_2.html#D4" title="CAT_2:def.4">CAT_2:def 4</a></span>;<br/><span class="kw">reconsider </span><font color="Maroon" title="c8">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> <span class="kw">by</span> <span class="lab"><a class="ref" href="cat_2.html#T7" title="CAT_2:th.7">CAT_2:7</a></span>;<br/><span class="kw">reconsider </span><font color="Maroon" title="c9">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> <span class="kw">by</span> <span class="lab"><a class="ref" href="cat_2.html#T7" title="CAT_2:th.7">CAT_2:7</a></span>;<br/><a NAME="E6:76_1"/><span class="lab"><font color="Green" title="E59">A11</font></span>: 
 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>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="nattra_1.html#D19" target="_self" title="NATTRA_1:def.19">Def20</a></span>;<br/><a NAME="E7:76_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>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="nattra_1.html#D19" target="_self" title="NATTRA_1:def.19">Def20</a></span>;<br/><span class="kw">hence </span><a NAME="E8:76_1"/><span class="lab"><font color="Green" title="E60">A12</font></span>: 
<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>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E6:76_1"><span class="lab"><font color="Green" title="E59">A11</font></span></a>, <a class="ref" href="nattra_1.html#D19" target="_self" title="NATTRA_1:def.19">Def20</a></span>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> (  the <a href="struct_0.html#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/><a NAME="E9:76_1"/><span class="lab"><font color="Green" title="E61">A13</font></span>: 
 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>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="nattra_1.html#T8" target="_self" title="NATTRA_1:th.8">Th8</a></span>;<br/><a NAME="E10:76_1"/><span class="lab"><font color="Green" title="E62">A14</font></span>: 
 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>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="nattra_1.html#T8" target="_self" title="NATTRA_1:th.8">Th8</a></span>;<br/><a NAME="E11:76_1"/><span class="lab"><font color="Green" title="E63">A15</font></span>: 
 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> 
 <span class="kw">by</span> <span class="lab"><a class="ref" href="nattra_1.html#D19" target="_self" title="NATTRA_1:def.19">Def20</a></span>;<br/><a NAME="E12:76_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> 
 <span class="kw">by</span> <span class="lab"><a class="ref" href="nattra_1.html#D19" target="_self" title="NATTRA_1:def.19">Def20</a></span>;<br/><span class="kw">hence </span><a NAME="E13:76_1"/><span class="lab"><font color="Green" title="E64">A16</font></span>: 
 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>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:76_1"><span class="lab"><font color="Green" title="E58">A1</font></span></a>, <a class="txt" href="#E11:76_1"><span class="lab"><font color="Green" title="E63">A15</font></span></a>, <a class="ref" href="nattra_1.html#D19" target="_self" title="NATTRA_1:def.19">Def20</a></span>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></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/><a NAME="E14:76_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>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="nattra_1.html#T8" target="_self" title="NATTRA_1:th.8">Th8</a></span>;<br/><span class="kw">hence </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 <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="c9">MA</font>,<font color="Maroon" title="c8">MB</font></span><a href="mcart_1.html#K12" title="MCART_1:func.12">:]</a></span>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E10:76_1"><span class="lab"><font color="Green" title="E62">A14</font></span></a>, <a class="ref" href="nattra_1.html#T1" target="_self" title="NATTRA_1:th.1">Th1</a></span>
<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>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E13:76_1"><span class="lab"><font color="Green" title="E64">A16</font></span></a>, <a class="ref" href="nattra_1.html#T8" target="_self" title="NATTRA_1:th.8">Th8</a></span>
;<br/> <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></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="E16:76_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>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="nattra_1.html#T8" target="_self" title="NATTRA_1:th.8">Th8</a></span>;<br/><span class="kw">hence </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 <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="c9">MA</font>,<font color="Maroon" title="c8">MB</font></span><a href="mcart_1.html#K12" title="MCART_1:func.12">:]</a></span>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E9:76_1"><span class="lab"><font color="Green" title="E61">A13</font></span></a>, <a class="ref" href="nattra_1.html#T1" target="_self" title="NATTRA_1:th.1">Th1</a></span>
<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>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E13:76_1"><span class="lab"><font color="Green" title="E64">A16</font></span></a>, <a class="ref" href="nattra_1.html#T8" target="_self" title="NATTRA_1:th.8">Th8</a></span>
;<br/> <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></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="E18:76_1"/><span class="lab"><font color="Green" title="E65">A17</font></span>: 
 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="c9">MA</font>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="nattra_1.html#T8" target="_self" title="NATTRA_1:th.8">Th8</a></span>;<br/><a NAME="E19:76_1"/><span class="lab"><font color="Green" title="E66">A18</font></span>: 
 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="c8">MB</font>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="nattra_1.html#T8" target="_self" title="NATTRA_1:th.8">Th8</a></span>;<br/><a NAME="E20:76_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 <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="c9">MA</font>,<font color="Maroon" title="c8">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>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E13:76_1"><span class="lab"><font color="Green" title="E64">A16</font></span></a>, <a class="ref" href="nattra_1.html#T8" target="_self" title="NATTRA_1:th.8">Th8</a></span>;<br/><span class="kw">hence </span><a NAME="E21:76_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>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E18:76_1"><span class="lab"><font color="Green" title="E65">A17</font></span></a>, <a class="txt" href="#E19:76_1"><span class="lab"><font color="Green" title="E66">A18</font></span></a>, <a class="ref" href="nattra_1.html#T2" target="_self" title="NATTRA_1:th.2">Th2</a></span>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></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/><a NAME="E22:76_1"/><span class="lab"><font color="Green" title="E67">A19</font></span>: 
 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>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="nattra_1.html#T8" target="_self" title="NATTRA_1:th.8">Th8</a></span>;<br/><a NAME="E23:76_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>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="nattra_1.html#T8" target="_self" title="NATTRA_1:th.8">Th8</a></span>;<br/><span class="kw">hence </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 <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="c3">OA</font>,<font color="Maroon" title="c7">OB</font></span><a href="mcart_1.html#K12" title="MCART_1:func.12">:]</a></span>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E22:76_1"><span class="lab"><font color="Green" title="E67">A19</font></span></a>, <a class="ref" href="nattra_1.html#T1" target="_self" title="NATTRA_1:th.1">Th1</a></span>
<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>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E8:76_1"><span class="lab"><font color="Green" title="E60">A12</font></span></a>, <a class="ref" href="nattra_1.html#T8" target="_self" title="NATTRA_1:th.8">Th8</a></span>
;<br/> <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> verum</span><br/></div><span class="kw">end;</span></div>
<span class="kw">hence </span><a NAME="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:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> verum</span><br/>


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