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<span class="kw">set </span><font color="Maroon" title="c1">S</font> =  the   <a href="waybel_9.html#V1" title="WAYBEL_9:attr.1">strict</a>   <a href="waybel11.html#V4" title="WAYBEL11:attr.4">Scott</a>   <a href="yellow_9.html#M1" title="YELLOW_9:mode.1">TopAugmentation</a> of  <a href="yellow_1.html#K2" title="YELLOW_1:func.2">BoolePoset</a> <span class="p1"><a href="tarski.html#K1" title="TARSKI:func.1">{</a><span class="default"><a href="numbers.html#K5" title="NUMBERS:func.5">0</a></span><a href="tarski.html#K1" title="TARSKI:func.1">}</a></span>;<br/>
<a NAME="E1:11"/><span class="lab"><font color="Green" title="E5">A1</font></span>: 
 <a href="orders_2.html#G1" title="ORDERS_2:aggr.1">RelStr</a>(#  the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of  the   <a href="waybel_9.html#V1" title="WAYBEL_9:attr.1">strict</a>   <a href="waybel11.html#V4" title="WAYBEL11:attr.4">Scott</a>   <a href="yellow_9.html#M1" title="YELLOW_9:mode.1">TopAugmentation</a> of  <a href="yellow_1.html#K2" title="YELLOW_1:func.2">BoolePoset</a> <span class="p1"><a href="tarski.html#K1" title="TARSKI:func.1">{</a><span class="default"><a href="numbers.html#K5" title="NUMBERS:func.5">0</a></span><a href="tarski.html#K1" title="TARSKI:func.1">}</a></span>, the <a href="orders_2.html#U1" title="ORDERS_2:sel.1">InternalRel</a> of  the   <a href="waybel_9.html#V1" title="WAYBEL_9:attr.1">strict</a>   <a href="waybel11.html#V4" title="WAYBEL11:attr.4">Scott</a>   <a href="yellow_9.html#M1" title="YELLOW_9:mode.1">TopAugmentation</a> of  <a href="yellow_1.html#K2" title="YELLOW_1:func.2">BoolePoset</a> <span class="p1"><a href="tarski.html#K1" title="TARSKI:func.1">{</a><span class="default"><a href="numbers.html#K5" title="NUMBERS:func.5">0</a></span><a href="tarski.html#K1" title="TARSKI:func.1">}</a></span> #) <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="yellow_1.html#K2" title="YELLOW_1:func.2">BoolePoset</a> <span class="p1"><a href="tarski.html#K1" title="TARSKI:func.1">{</a><span class="default"><a href="numbers.html#K5" title="NUMBERS:func.5">0</a></span><a href="tarski.html#K1" title="TARSKI:func.1">}</a></span>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="yellow_9.html#D4" onmouseover="rs('yellow_9/D4')" onmouseout="rh()">YELLOW_9:def 4</a></span>;<br/>
<a NAME="E2:11"/>
 <a href="yellow_1.html#K2" title="YELLOW_1:func.2">BoolePoset</a> <span class="p1"><a href="tarski.html#K1" title="TARSKI:func.1">{</a><span class="default"><a href="numbers.html#K5" title="NUMBERS:func.5">0</a></span><a href="tarski.html#K1" title="TARSKI:func.1">}</a></span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="yellow_1.html#K1" title="YELLOW_1:func.1">InclPoset</a> <span class="p1">(<span class="default"><a href="setfam_1.html#K9" title="SETFAM_1:func.9">bool</a> <span class="p2"><a href="tarski.html#K1" title="TARSKI:func.1">{</a><span class="default"><a href="numbers.html#K5" title="NUMBERS:func.5">0</a></span><a href="tarski.html#K1" title="TARSKI:func.1">}</a></span></span>)</span>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="yellow_1.html#T4" onmouseover="rs('yellow_1/T4')" onmouseout="rh()">YELLOW_1:4</a></span>;<br/>
<a NAME="E3:11"/><span class="kw">then </span><span class="lab"><font color="Green" title="E6">A2</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="yellow_1.html#K2" title="YELLOW_1:func.2">BoolePoset</a> <span class="p2"><a href="tarski.html#K1" title="TARSKI:func.1">{</a><span class="default"><a href="numbers.html#K5" title="NUMBERS:func.5">0</a></span><a href="tarski.html#K1" title="TARSKI:func.1">}</a></span></span>)</span> <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="numbers.html#K5" title="NUMBERS:func.5">0</a>,1</span><a href="tarski.html#K2" title="TARSKI:func.2">}</a></span>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="yellow14.html#T1" onmouseover="rs('yellow14/T1')" onmouseout="rh()">YELLOW14:1</a>, <a class="ref" href="yellow_1.html#T1" onmouseover="rs('yellow_1/T1')" onmouseout="rh()">YELLOW_1:1</a></span>;<br/>
<a NAME="E4:11"/>
(  the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <a href="waybel18.html#K9" title="WAYBEL18:func.9">Sierpinski_Space</a> <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="numbers.html#K5" title="NUMBERS:func.5">0</a>,1</span><a href="tarski.html#K2" title="TARSKI:func.2">}</a></span> &amp;  the <a href="pre_topc.html#U1" title="PRE_TOPC:sel.1">topology</a> of  the   <a href="waybel_9.html#V1" title="WAYBEL_9:attr.1">strict</a>   <a href="waybel11.html#V4" title="WAYBEL11:attr.4">Scott</a>   <a href="yellow_9.html#M1" title="YELLOW_9:mode.1">TopAugmentation</a> of  <a href="yellow_1.html#K2" title="YELLOW_1:func.2">BoolePoset</a> <span class="p1"><a href="tarski.html#K1" title="TARSKI:func.1">{</a><span class="default"><a href="numbers.html#K5" title="NUMBERS:func.5">0</a></span><a href="tarski.html#K1" title="TARSKI:func.1">}</a></span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  the <a href="pre_topc.html#U1" title="PRE_TOPC:sel.1">topology</a> of <a href="waybel18.html#K9" title="WAYBEL18:func.9">Sierpinski_Space</a> )
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="waybel18.html#T12" onmouseover="rs('waybel18/T12')" onmouseout="rh()">WAYBEL18:12</a>, <a class="ref" href="waybel18.html#D9" onmouseover="rs('waybel18/D9')" onmouseout="rh()">WAYBEL18:def 9</a></span>;<br/>
<span class="kw">then </span> <a href="waybel25.html#K1" title="WAYBEL25:func.1">Omega</a> <a href="waybel18.html#K9" title="WAYBEL18:func.9">Sierpinski_Space</a> = 
 <a href="waybel25.html#K1" title="WAYBEL25:func.1">Omega</a>  the   <a href="waybel_9.html#V1" title="WAYBEL_9:attr.1">strict</a>   <a href="waybel11.html#V4" title="WAYBEL11:attr.4">Scott</a>   <a href="yellow_9.html#M1" title="YELLOW_9:mode.1">TopAugmentation</a> of  <a href="yellow_1.html#K2" title="YELLOW_1:func.2">BoolePoset</a> <span class="p1"><a href="tarski.html#K1" title="TARSKI:func.1">{</a><span class="default"><a href="numbers.html#K5" title="NUMBERS:func.5">0</a></span><a href="tarski.html#K1" title="TARSKI:func.1">}</a></span>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E3:11"><span class="lab"><font color="Green" title="E6">A2</font></span></a>, <a class="txt" href="#E1:11"><span class="lab"><font color="Green" title="E5">A1</font></span></a>, <a class="ref" href="waybel25.html#T13" onmouseover="rs('waybel25/T13')" onmouseout="rh()">WAYBEL25:13</a></span>
<br/>.= 
 the   <a href="waybel_9.html#V1" title="WAYBEL_9:attr.1">strict</a>   <a href="waybel11.html#V4" title="WAYBEL11:attr.4">Scott</a>   <a href="yellow_9.html#M1" title="YELLOW_9:mode.1">TopAugmentation</a> of  <a href="yellow_1.html#K2" title="YELLOW_1:func.2">BoolePoset</a> <span class="p1"><a href="tarski.html#K1" title="TARSKI:func.1">{</a><span class="default"><a href="numbers.html#K5" title="NUMBERS:func.5">0</a></span><a href="tarski.html#K1" title="TARSKI:func.1">}</a></span>
<span class="kw">by</span> <span class="lab"><a class="ref" href="waybel25.html#T15" onmouseover="rs('waybel25/T15')" onmouseout="rh()">WAYBEL25:15</a></span>
;<br/>
<span class="kw">hence </span><a NAME="E6:11"/>
 <a href="waybel25.html#K1" title="WAYBEL25:func.1">Omega</a> <a href="waybel18.html#K9" title="WAYBEL18:func.9">Sierpinski_Space</a> is    <a href="yellow_9.html#M1" title="YELLOW_9:mode.1">TopAugmentation</a> of  <a href="yellow_1.html#K2" title="YELLOW_1:func.2">BoolePoset</a> <span class="p1"><a href="tarski.html#K1" title="TARSKI:func.1">{</a><span class="default"><a href="numbers.html#K5" title="NUMBERS:func.5">0</a></span><a href="tarski.html#K1" title="TARSKI:func.1">}</a></span>
 ; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" 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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