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<b>let </b><font color="Maroon" title="c1">tau</font> be   <a href="setfam_1.html#NM1" title="SETFAM_1:NM.1">Subset-Family</a> of <span class="p1"><a href="tarski.html#K1" title="TARSKI:func.1">{</a><span class="default"><a href="numbers.html#K6" title="NUMBERS:func.6">0</a> </span><a href="tarski.html#K1" title="TARSKI:func.1">}</a></span>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> for <font color="Olive" title="b1">r</font> being  <a href="relset_1.html#NM3" title="RELSET_1:NM.3">Relation</a> of <span class="p1"><a href="tarski.html#K1" title="TARSKI:func.1">{</a><span class="default"><a href="numbers.html#K6" title="NUMBERS:func.6">0</a> </span><a href="tarski.html#K1" title="TARSKI:func.1">}</a></span>  st <font color="Maroon" title="c1">tau</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1"><a href="tarski.html#K2" title="TARSKI:func.2">{</a><span class="default"><a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a> ,<span class="p2"><a href="tarski.html#K1" title="TARSKI:func.1">{</a><span class="default"><a href="numbers.html#K6" title="NUMBERS:func.6">0</a> </span><a href="tarski.html#K1" title="TARSKI:func.1">}</a></span></span><a href="tarski.html#K2" title="TARSKI:func.2">}</a></span> &amp; <font color="Olive" title="b1">r</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1"><a href="tarski.html#K1" title="TARSKI:func.1">{</a><span class="default"><span class="p2"><a href="tarski.html#K4" title="TARSKI:func.4">[</a><span class="default"><a href="numbers.html#K6" title="NUMBERS:func.6">0</a> ,<a href="numbers.html#K6" title="NUMBERS:func.6">0</a> </span><a href="tarski.html#K4" title="TARSKI:func.4">]</a></span></span><a href="tarski.html#K1" title="TARSKI:func.1">}</a></span> holds <br/>(  <a href="waybel_9.html#G1" title="WAYBEL_9:aggr.1">TopRelStr</a>(# <span class="p1"><a href="tarski.html#K1" title="TARSKI:func.1">{</a><span class="default"><a href="numbers.html#K6" title="NUMBERS:func.6">0</a> </span><a href="tarski.html#K1" title="TARSKI:func.1">}</a></span>,<font color="Olive" title="b1">r</font>,<font color="Maroon" title="c1">tau</font> #) is <a href="struct_0.html#V7" title="STRUCT_0:attr.7">trivial</a> &amp;  <a href="waybel_9.html#G1" title="WAYBEL_9:aggr.1">TopRelStr</a>(# <span class="p1"><a href="tarski.html#K1" title="TARSKI:func.1">{</a><span class="default"><a href="numbers.html#K6" title="NUMBERS:func.6">0</a> </span><a href="tarski.html#K1" title="TARSKI:func.1">}</a></span>,<font color="Olive" title="b1">r</font>,<font color="Maroon" title="c1">tau</font> #) is <a href="orders_2.html#V3" title="ORDERS_2:attr.3">reflexive</a> &amp; not  <a href="waybel_9.html#G1" title="WAYBEL_9:aggr.1">TopRelStr</a>(# <span class="p1"><a href="tarski.html#K1" title="TARSKI:func.1">{</a><span class="default"><a href="numbers.html#K6" title="NUMBERS:func.6">0</a> </span><a href="tarski.html#K1" title="TARSKI:func.1">}</a></span>,<font color="Olive" title="b1">r</font>,<font color="Maroon" title="c1">tau</font> #) is <a href="struct_0.html#V2" title="STRUCT_0:attr.2">empty</a> &amp;  <a href="waybel_9.html#G1" title="WAYBEL_9:aggr.1">TopRelStr</a>(# <span class="p1"><a href="tarski.html#K1" title="TARSKI:func.1">{</a><span class="default"><a href="numbers.html#K6" title="NUMBERS:func.6">0</a> </span><a href="tarski.html#K1" title="TARSKI:func.1">}</a></span>,<font color="Olive" title="b1">r</font>,<font color="Maroon" title="c1">tau</font> #) is <a href="tdlat_3.html#V1" title="TDLAT_3:attr.1">discrete</a> &amp;  <a href="waybel_9.html#G1" title="WAYBEL_9:aggr.1">TopRelStr</a>(# <span class="p1"><a href="tarski.html#K1" title="TARSKI:func.1">{</a><span class="default"><a href="numbers.html#K6" title="NUMBERS:func.6">0</a> </span><a href="tarski.html#K1" title="TARSKI:func.1">}</a></span>,<font color="Olive" title="b1">r</font>,<font color="Maroon" title="c1">tau</font> #) is <a href="struct_0.html#V8" title="STRUCT_0:attr.8">finite</a> )</span><br/><b>let </b><font color="Maroon" title="c2">r</font> be   <a href="relset_1.html#NM3" title="RELSET_1:NM.3">Relation</a> of <span class="p1"><a href="tarski.html#K1" title="TARSKI:func.1">{</a><span class="default"><a href="numbers.html#K6" title="NUMBERS:func.6">0</a> </span><a href="tarski.html#K1" title="TARSKI:func.1">}</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="c1">tau</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1"><a href="tarski.html#K2" title="TARSKI:func.2">{</a><span class="default"><a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a> ,<span class="p2"><a href="tarski.html#K1" title="TARSKI:func.1">{</a><span class="default"><a href="numbers.html#K6" title="NUMBERS:func.6">0</a> </span><a href="tarski.html#K1" title="TARSKI:func.1">}</a></span></span><a href="tarski.html#K2" title="TARSKI:func.2">}</a></span> &amp; <font color="Maroon" title="c2">r</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1"><a href="tarski.html#K1" title="TARSKI:func.1">{</a><span class="default"><span class="p2"><a href="tarski.html#K4" title="TARSKI:func.4">[</a><span class="default"><a href="numbers.html#K6" title="NUMBERS:func.6">0</a> ,<a href="numbers.html#K6" title="NUMBERS:func.6">0</a> </span><a href="tarski.html#K4" title="TARSKI:func.4">]</a></span></span><a href="tarski.html#K1" title="TARSKI:func.1">}</a></span> implies (  <a href="waybel_9.html#G1" title="WAYBEL_9:aggr.1">TopRelStr</a>(# <span class="p1"><a href="tarski.html#K1" title="TARSKI:func.1">{</a><span class="default"><a href="numbers.html#K6" title="NUMBERS:func.6">0</a> </span><a href="tarski.html#K1" title="TARSKI:func.1">}</a></span>,<font color="Maroon" title="c2">r</font>,<font color="Maroon" title="c1">tau</font> #) is <a href="struct_0.html#V7" title="STRUCT_0:attr.7">trivial</a> &amp;  <a href="waybel_9.html#G1" title="WAYBEL_9:aggr.1">TopRelStr</a>(# <span class="p1"><a href="tarski.html#K1" title="TARSKI:func.1">{</a><span class="default"><a href="numbers.html#K6" title="NUMBERS:func.6">0</a> </span><a href="tarski.html#K1" title="TARSKI:func.1">}</a></span>,<font color="Maroon" title="c2">r</font>,<font color="Maroon" title="c1">tau</font> #) is <a href="orders_2.html#V3" title="ORDERS_2:attr.3">reflexive</a> &amp; not  <a href="waybel_9.html#G1" title="WAYBEL_9:aggr.1">TopRelStr</a>(# <span class="p1"><a href="tarski.html#K1" title="TARSKI:func.1">{</a><span class="default"><a href="numbers.html#K6" title="NUMBERS:func.6">0</a> </span><a href="tarski.html#K1" title="TARSKI:func.1">}</a></span>,<font color="Maroon" title="c2">r</font>,<font color="Maroon" title="c1">tau</font> #) is <a href="struct_0.html#V2" title="STRUCT_0:attr.2">empty</a> &amp;  <a href="waybel_9.html#G1" title="WAYBEL_9:aggr.1">TopRelStr</a>(# <span class="p1"><a href="tarski.html#K1" title="TARSKI:func.1">{</a><span class="default"><a href="numbers.html#K6" title="NUMBERS:func.6">0</a> </span><a href="tarski.html#K1" title="TARSKI:func.1">}</a></span>,<font color="Maroon" title="c2">r</font>,<font color="Maroon" title="c1">tau</font> #) is <a href="tdlat_3.html#V1" title="TDLAT_3:attr.1">discrete</a> &amp;  <a href="waybel_9.html#G1" title="WAYBEL_9:aggr.1">TopRelStr</a>(# <span class="p1"><a href="tarski.html#K1" title="TARSKI:func.1">{</a><span class="default"><a href="numbers.html#K6" title="NUMBERS:func.6">0</a> </span><a href="tarski.html#K1" title="TARSKI:func.1">}</a></span>,<font color="Maroon" title="c2">r</font>,<font color="Maroon" title="c1">tau</font> #) is <a href="struct_0.html#V8" title="STRUCT_0:attr.8">finite</a> ) )</span><br/>



<b>assume </b><b>that </b><br/><a NAME="E1:68"/><i><font color="Green" title="E26">A1</font></i>: 
<font color="Maroon" title="c1">tau</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1"><a href="tarski.html#K2" title="TARSKI:func.2">{</a><span class="default"><a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a> ,<span class="p2"><a href="tarski.html#K1" title="TARSKI:func.1">{</a><span class="default"><a href="numbers.html#K6" title="NUMBERS:func.6">0</a> </span><a href="tarski.html#K1" title="TARSKI:func.1">}</a></span></span><a href="tarski.html#K2" title="TARSKI:func.2">}</a></span>
 <b>and </b><br/><a NAME="E2:68"/><i><font color="Green" title="E27">A2</font></i>: 
<font color="Maroon" title="c2">r</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1"><a href="tarski.html#K1" title="TARSKI:func.1">{</a><span class="default"><span class="p2"><a href="tarski.html#K4" title="TARSKI:func.4">[</a><span class="default"><a href="numbers.html#K6" title="NUMBERS:func.6">0</a> ,<a href="numbers.html#K6" title="NUMBERS:func.6">0</a> </span><a href="tarski.html#K4" title="TARSKI:func.4">]</a></span></span><a href="tarski.html#K1" title="TARSKI:func.1">}</a></span>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> (  <a href="waybel_9.html#G1" title="WAYBEL_9:aggr.1">TopRelStr</a>(# <span class="p1"><a href="tarski.html#K1" title="TARSKI:func.1">{</a><span class="default"><a href="numbers.html#K6" title="NUMBERS:func.6">0</a> </span><a href="tarski.html#K1" title="TARSKI:func.1">}</a></span>,<font color="Maroon" title="c2">r</font>,<font color="Maroon" title="c1">tau</font> #) is <a href="struct_0.html#V7" title="STRUCT_0:attr.7">trivial</a> &amp;  <a href="waybel_9.html#G1" title="WAYBEL_9:aggr.1">TopRelStr</a>(# <span class="p1"><a href="tarski.html#K1" title="TARSKI:func.1">{</a><span class="default"><a href="numbers.html#K6" title="NUMBERS:func.6">0</a> </span><a href="tarski.html#K1" title="TARSKI:func.1">}</a></span>,<font color="Maroon" title="c2">r</font>,<font color="Maroon" title="c1">tau</font> #) is <a href="orders_2.html#V3" title="ORDERS_2:attr.3">reflexive</a> &amp; not  <a href="waybel_9.html#G1" title="WAYBEL_9:aggr.1">TopRelStr</a>(# <span class="p1"><a href="tarski.html#K1" title="TARSKI:func.1">{</a><span class="default"><a href="numbers.html#K6" title="NUMBERS:func.6">0</a> </span><a href="tarski.html#K1" title="TARSKI:func.1">}</a></span>,<font color="Maroon" title="c2">r</font>,<font color="Maroon" title="c1">tau</font> #) is <a href="struct_0.html#V2" title="STRUCT_0:attr.2">empty</a> &amp;  <a href="waybel_9.html#G1" title="WAYBEL_9:aggr.1">TopRelStr</a>(# <span class="p1"><a href="tarski.html#K1" title="TARSKI:func.1">{</a><span class="default"><a href="numbers.html#K6" title="NUMBERS:func.6">0</a> </span><a href="tarski.html#K1" title="TARSKI:func.1">}</a></span>,<font color="Maroon" title="c2">r</font>,<font color="Maroon" title="c1">tau</font> #) is <a href="tdlat_3.html#V1" title="TDLAT_3:attr.1">discrete</a> &amp;  <a href="waybel_9.html#G1" title="WAYBEL_9:aggr.1">TopRelStr</a>(# <span class="p1"><a href="tarski.html#K1" title="TARSKI:func.1">{</a><span class="default"><a href="numbers.html#K6" title="NUMBERS:func.6">0</a> </span><a href="tarski.html#K1" title="TARSKI:func.1">}</a></span>,<font color="Maroon" title="c2">r</font>,<font color="Maroon" title="c1">tau</font> #) is <a href="struct_0.html#V8" title="STRUCT_0:attr.8">finite</a> )</span><br/>

<b>set </b><font color="Maroon" title="c3">T</font> =  <a href="waybel_9.html#G1" title="WAYBEL_9:aggr.1">TopRelStr</a>(# <span class="p1"><a href="tarski.html#K1" title="TARSKI:func.1">{</a><span class="default"><a href="numbers.html#K6" title="NUMBERS:func.6">0</a> </span><a href="tarski.html#K1" title="TARSKI:func.1">}</a></span>,<font color="Maroon" title="c2">r</font>,<font color="Maroon" title="c1">tau</font> #);<br/>
<b>thus </b><a NAME="E3:68"/>
 <a href="waybel_9.html#G1" title="WAYBEL_9:aggr.1">TopRelStr</a>(# <span class="p1"><a href="tarski.html#K1" title="TARSKI:func.1">{</a><span class="default"><a href="numbers.html#K6" title="NUMBERS:func.6">0</a> </span><a href="tarski.html#K1" title="TARSKI:func.1">}</a></span>,<font color="Maroon" title="c2">r</font>,<font color="Maroon" title="c1">tau</font> #) is <a href="struct_0.html#V7" title="STRUCT_0:attr.7">trivial</a>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> (  <a href="waybel_9.html#G1" title="WAYBEL_9:aggr.1">TopRelStr</a>(# <span class="p1"><a href="tarski.html#K1" title="TARSKI:func.1">{</a><span class="default"><a href="numbers.html#K6" title="NUMBERS:func.6">0</a> </span><a href="tarski.html#K1" title="TARSKI:func.1">}</a></span>,<font color="Maroon" title="c2">r</font>,<font color="Maroon" title="c1">tau</font> #) is <a href="orders_2.html#V3" title="ORDERS_2:attr.3">reflexive</a> &amp; not  <a href="waybel_9.html#G1" title="WAYBEL_9:aggr.1">TopRelStr</a>(# <span class="p1"><a href="tarski.html#K1" title="TARSKI:func.1">{</a><span class="default"><a href="numbers.html#K6" title="NUMBERS:func.6">0</a> </span><a href="tarski.html#K1" title="TARSKI:func.1">}</a></span>,<font color="Maroon" title="c2">r</font>,<font color="Maroon" title="c1">tau</font> #) is <a href="struct_0.html#V2" title="STRUCT_0:attr.2">empty</a> &amp;  <a href="waybel_9.html#G1" title="WAYBEL_9:aggr.1">TopRelStr</a>(# <span class="p1"><a href="tarski.html#K1" title="TARSKI:func.1">{</a><span class="default"><a href="numbers.html#K6" title="NUMBERS:func.6">0</a> </span><a href="tarski.html#K1" title="TARSKI:func.1">}</a></span>,<font color="Maroon" title="c2">r</font>,<font color="Maroon" title="c1">tau</font> #) is <a href="tdlat_3.html#V1" title="TDLAT_3:attr.1">discrete</a> &amp;  <a href="waybel_9.html#G1" title="WAYBEL_9:aggr.1">TopRelStr</a>(# <span class="p1"><a href="tarski.html#K1" title="TARSKI:func.1">{</a><span class="default"><a href="numbers.html#K6" title="NUMBERS:func.6">0</a> </span><a href="tarski.html#K1" title="TARSKI:func.1">}</a></span>,<font color="Maroon" title="c2">r</font>,<font color="Maroon" title="c1">tau</font> #) is <a href="struct_0.html#V8" title="STRUCT_0:attr.8">finite</a> )</span><br/>

<b>thus </b><a NAME="E4:68"/>
 <a href="waybel_9.html#G1" title="WAYBEL_9:aggr.1">TopRelStr</a>(# <span class="p1"><a href="tarski.html#K1" title="TARSKI:func.1">{</a><span class="default"><a href="numbers.html#K6" title="NUMBERS:func.6">0</a> </span><a href="tarski.html#K1" title="TARSKI:func.1">}</a></span>,<font color="Maroon" title="c2">r</font>,<font color="Maroon" title="c1">tau</font> #) is <a href="orders_2.html#V3" title="ORDERS_2:attr.3">reflexive</a>
  <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> ( not  <a href="waybel_9.html#G1" title="WAYBEL_9:aggr.1">TopRelStr</a>(# <span class="p1"><a href="tarski.html#K1" title="TARSKI:func.1">{</a><span class="default"><a href="numbers.html#K6" title="NUMBERS:func.6">0</a> </span><a href="tarski.html#K1" title="TARSKI:func.1">}</a></span>,<font color="Maroon" title="c2">r</font>,<font color="Maroon" title="c1">tau</font> #) is <a href="struct_0.html#V2" title="STRUCT_0:attr.2">empty</a> &amp;  <a href="waybel_9.html#G1" title="WAYBEL_9:aggr.1">TopRelStr</a>(# <span class="p1"><a href="tarski.html#K1" title="TARSKI:func.1">{</a><span class="default"><a href="numbers.html#K6" title="NUMBERS:func.6">0</a> </span><a href="tarski.html#K1" title="TARSKI:func.1">}</a></span>,<font color="Maroon" title="c2">r</font>,<font color="Maroon" title="c1">tau</font> #) is <a href="tdlat_3.html#V1" title="TDLAT_3:attr.1">discrete</a> &amp;  <a href="waybel_9.html#G1" title="WAYBEL_9:aggr.1">TopRelStr</a>(# <span class="p1"><a href="tarski.html#K1" title="TARSKI:func.1">{</a><span class="default"><a href="numbers.html#K6" title="NUMBERS:func.6">0</a> </span><a href="tarski.html#K1" title="TARSKI:func.1">}</a></span>,<font color="Maroon" title="c2">r</font>,<font color="Maroon" title="c1">tau</font> #) is <a href="struct_0.html#V8" title="STRUCT_0:attr.8">finite</a> )</span><div><a class="txt" onclick="hs2(this)" href="javascript:()" title="68_1"><b>proof </b></a><div class="add">

<b>let </b><font color="Maroon" title="c4">x</font> be   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <a href="waybel_9.html#G1" title="WAYBEL_9:aggr.1">TopRelStr</a>(# <span class="p1"><a href="tarski.html#K1" title="TARSKI:func.1">{</a><span class="default"><a href="numbers.html#K6" title="NUMBERS:func.6">0</a> </span><a href="tarski.html#K1" title="TARSKI:func.1">}</a></span>,<font color="Maroon" title="c2">r</font>,<font color="Maroon" title="c1">tau</font> #); <i><font color="Red">:: according to </font></i><a class="ref" href="yellow_0.html#D1" title="YELLOW_0:def.1">YELLOW_0:def 1</a> <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> <font color="Maroon" title="c4">x</font> <a href="orders_2.html#R1" title="ORDERS_2:pred.1">&lt;=</a> <font color="Maroon" title="c4">x</font></span><br/>

<a NAME="E1:68_1"/>
<font color="Maroon" title="c4">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="numbers.html#K6" title="NUMBERS:func.6">0</a> 
 
<b>by </b><i><a class="ref" href="tarski.html#D1" title="TARSKI:def.1">TARSKI:def 1</a></i>;<br/>
<a NAME="E2:68_1"/><b>then </b>
<span class="p1"><a href="domain_1.html#K1" title="DOMAIN_1:func.1">[</a><span class="default"><font color="Maroon" title="c4">x</font>,<font color="Maroon" title="c4">x</font></span><a href="domain_1.html#K1" title="DOMAIN_1:func.1">]</a></span> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <span class="p1"><a href="tarski.html#K1" title="TARSKI:func.1">{</a><span class="default"><span class="p2"><a href="tarski.html#K4" title="TARSKI:func.4">[</a><span class="default"><a href="numbers.html#K6" title="NUMBERS:func.6">0</a> ,<a href="numbers.html#K6" title="NUMBERS:func.6">0</a> </span><a href="tarski.html#K4" title="TARSKI:func.4">]</a></span></span><a href="tarski.html#K1" title="TARSKI:func.1">}</a></span>
 
<b>by </b><i><a class="ref" href="tarski.html#D1" title="TARSKI:def.1">TARSKI:def 1</a></i>;<br/>
<b>hence </b><a NAME="E3:68_1"/>
<font color="Maroon" title="c4">x</font> <a href="orders_2.html#R1" title="ORDERS_2:pred.1">&lt;=</a> <font color="Maroon" title="c4">x</font>
 <b>by </b><i><a class="txt" href="#E2:68"><i><font color="Green" title="E27">A2</font></i></a>, <a class="ref" href="orders_2.html#D9" title="ORDERS_2:def.9">ORDERS_2:def 9</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>thus </b><a NAME="E5:68"/>
not  <a href="waybel_9.html#G1" title="WAYBEL_9:aggr.1">TopRelStr</a>(# <span class="p1"><a href="tarski.html#K1" title="TARSKI:func.1">{</a><span class="default"><a href="numbers.html#K6" title="NUMBERS:func.6">0</a> </span><a href="tarski.html#K1" title="TARSKI:func.1">}</a></span>,<font color="Maroon" title="c2">r</font>,<font color="Maroon" title="c1">tau</font> #) is <a href="struct_0.html#V2" title="STRUCT_0:attr.2">empty</a>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> (  <a href="waybel_9.html#G1" title="WAYBEL_9:aggr.1">TopRelStr</a>(# <span class="p1"><a href="tarski.html#K1" title="TARSKI:func.1">{</a><span class="default"><a href="numbers.html#K6" title="NUMBERS:func.6">0</a> </span><a href="tarski.html#K1" title="TARSKI:func.1">}</a></span>,<font color="Maroon" title="c2">r</font>,<font color="Maroon" title="c1">tau</font> #) is <a href="tdlat_3.html#V1" title="TDLAT_3:attr.1">discrete</a> &amp;  <a href="waybel_9.html#G1" title="WAYBEL_9:aggr.1">TopRelStr</a>(# <span class="p1"><a href="tarski.html#K1" title="TARSKI:func.1">{</a><span class="default"><a href="numbers.html#K6" title="NUMBERS:func.6">0</a> </span><a href="tarski.html#K1" title="TARSKI:func.1">}</a></span>,<font color="Maroon" title="c2">r</font>,<font color="Maroon" title="c1">tau</font> #) is <a href="struct_0.html#V8" title="STRUCT_0:attr.8">finite</a> )</span><br/>

<a NAME="E6:68"/>
the <a href="pre_topc.html#U1" title="PRE_TOPC:sel.1">topology</a> of <a href="waybel_9.html#G1" title="WAYBEL_9:aggr.1">TopRelStr</a>(# <span class="p1"><a href="tarski.html#K1" title="TARSKI:func.1">{</a><span class="default"><a href="numbers.html#K6" title="NUMBERS:func.6">0</a> </span><a href="tarski.html#K1" title="TARSKI:func.1">}</a></span>,<font color="Maroon" title="c2">r</font>,<font color="Maroon" title="c1">tau</font> #) <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="pcomps_1.html#K1" title="PCOMPS_1:func.1">bool</a> the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <a href="waybel_9.html#G1" title="WAYBEL_9:aggr.1">TopRelStr</a>(# <span class="p1"><a href="tarski.html#K1" title="TARSKI:func.1">{</a><span class="default"><a href="numbers.html#K6" title="NUMBERS:func.6">0</a> </span><a href="tarski.html#K1" title="TARSKI:func.1">}</a></span>,<font color="Maroon" title="c2">r</font>,<font color="Maroon" title="c1">tau</font> #)
 
<b>by </b><i><a class="txt" href="#E1:68"><i><font color="Green" title="E26">A1</font></i></a>, <a class="ref" href="zfmisc_1.html#T30" title="ZFMISC_1:th.30">ZFMISC_1:30</a></i>;<br/>
<b>hence </b><a NAME="E7:68"/>
 <a href="waybel_9.html#G1" title="WAYBEL_9:aggr.1">TopRelStr</a>(# <span class="p1"><a href="tarski.html#K1" title="TARSKI:func.1">{</a><span class="default"><a href="numbers.html#K6" title="NUMBERS:func.6">0</a> </span><a href="tarski.html#K1" title="TARSKI:func.1">}</a></span>,<font color="Maroon" title="c2">r</font>,<font color="Maroon" title="c1">tau</font> #) is <a href="tdlat_3.html#V1" title="TDLAT_3:attr.1">discrete</a>
 <b>by </b><i><a class="ref" href="tdlat_3.html#D1" title="TDLAT_3:def.1">TDLAT_3:def 1</a></i>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide">  <a href="waybel_9.html#G1" title="WAYBEL_9:aggr.1">TopRelStr</a>(# <span class="p1"><a href="tarski.html#K1" title="TARSKI:func.1">{</a><span class="default"><a href="numbers.html#K6" title="NUMBERS:func.6">0</a> </span><a href="tarski.html#K1" title="TARSKI:func.1">}</a></span>,<font color="Maroon" title="c2">r</font>,<font color="Maroon" title="c1">tau</font> #) is <a href="struct_0.html#V8" title="STRUCT_0:attr.8">finite</a></span><br/>

<b>thus </b><a NAME="E8:68"/>
the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <a href="waybel_9.html#G1" title="WAYBEL_9:aggr.1">TopRelStr</a>(# <span class="p1"><a href="tarski.html#K1" title="TARSKI:func.1">{</a><span class="default"><a href="numbers.html#K6" title="NUMBERS:func.6">0</a> </span><a href="tarski.html#K1" title="TARSKI:func.1">}</a></span>,<font color="Maroon" title="c2">r</font>,<font color="Maroon" title="c1">tau</font> #) is <a href="finset_1.html#V1" title="FINSET_1:attr.1">finite</a>
 ; <i><font color="Red">:: according to </font></i><a class="ref" href="struct_0.html#D11" title="STRUCT_0:def.11">STRUCT_0:def 11</a> <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> verum</span><br/>


</div>
