<?xml version="1.0"?>
<div class="add">

<b>let </b><font color="Maroon">c<sub>1</sub></font> be  <a href="lattice3.html#V3">complete</a> <a href="waybel_2.html#V2">meet-continuous</a> <a href="waybel19.html#V2">Lawson</a> <a href="waybel_9.html#NM1">TopLattice</a>;<br/><b>let </b><font color="Maroon">c<sub>2</sub></font> be  <a href="waybel11.html#V4">Scott</a>  <a href="yellow_9.html#M1">TopAugmentation</a> of <font color="Maroon">c<sub>1</sub></font>;<br/><b>let </b><font color="Maroon">c<sub>3</sub></font> be   <a href="pre_topc.html#NM2">Point</a> of <font color="Maroon">c<sub>2</sub></font>;<br/><b>let </b><font color="Maroon">c<sub>4</sub></font> be   <a href="pre_topc.html#NM2">Point</a> of <font color="Maroon">c<sub>1</sub></font>;<br/><b>let </b><font color="Maroon">c<sub>5</sub></font> be    <a href="yellow_8.html#M1">Basis</a> of <font color="Maroon">c<sub>4</sub></font>;<br/>









<b>assume </b><a NAME="E1:30"/><i><font color="Green">E15</font></i>: 
<font color="Maroon">c<sub>3</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>4</sub></font>
 ;<br/>

<a NAME="E2:30"/><i><font color="Green">E16</font></i>: 
 <a href="orders_2.html#G1">RelStr</a>(# the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">c<sub>1</sub></font>,the <a href="orders_2.html#U1">InternalRel</a> of <font color="Maroon">c<sub>1</sub></font> #) <a href="hidden.html#R1">=</a>  <a href="orders_2.html#G1">RelStr</a>(# the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">c<sub>2</sub></font>,the <a href="orders_2.html#U1">InternalRel</a> of <font color="Maroon">c<sub>2</sub></font> #)
 
<b>by </b><i><a class="ref" href="yellow_9.html#D4">YELLOW_9:def 4</a></i>;<br/>
<b>set </b><font color="Maroon">c<sub>6</sub></font> = <span class="p1">{<span class="default"> <span class="p2">(<span class="default"><a href="waybel_0.html#K4">uparrow</a> <font color="Olive">b<sub>1</sub></font></span>)</span> where B is   <a href="struct_0.html#NM2">Subset</a> of <font color="Maroon">c<sub>1</sub></font> : <font color="Olive">b<sub>1</sub></font> <a href="hidden.html#R2">in</a> <font color="Maroon">c<sub>5</sub></font> </span>}</span> ;<br/>
<b>set </b><font color="Maroon">c<sub>7</sub></font> = <span class="p1">{<span class="default"> <span class="p2">(<span class="default"><a href="waybel_0.html#K4">uparrow</a> <font color="Olive">b<sub>1</sub></font></span>)</span> where B is   <a href="struct_0.html#NM2">Subset</a> of <font color="Maroon">c<sub>1</sub></font> : <font color="Olive">b<sub>1</sub></font> <a href="hidden.html#R2">in</a> <font color="Maroon">c<sub>5</sub></font> </span>}</span> ;<br/>
<a NAME="E3:30"/>
<span class="p1">{<span class="default"> <span class="p2">(<span class="default"><a href="waybel_0.html#K4">uparrow</a> <font color="Olive">b<sub>1</sub></font></span>)</span> where B is   <a href="struct_0.html#NM2">Subset</a> of <font color="Maroon">c<sub>1</sub></font> : <font color="Olive">b<sub>1</sub></font> <a href="hidden.html#R2">in</a> <font color="Maroon">c<sub>5</sub></font> </span>}</span>  is   <a href="struct_0.html#NM3">Subset-Family</a> of <font color="Maroon">c<sub>2</sub></font>
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="30_1"><b>proof </b></a><div class="add">

<a NAME="E1:30_1"/>
<span class="p1">{<span class="default"> <span class="p2">(<span class="default"><a href="waybel_0.html#K4">uparrow</a> <font color="Olive">b<sub>1</sub></font></span>)</span> where B is   <a href="struct_0.html#NM2">Subset</a> of <font color="Maroon">c<sub>1</sub></font> : <font color="Olive">b<sub>1</sub></font> <a href="hidden.html#R2">in</a> <font color="Maroon">c<sub>5</sub></font> </span>}</span>  <a href="tarski.html#R1">c=</a>  <a href="zfmisc_1.html#K1">bool</a> the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">c<sub>2</sub></font>
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="30_1_1"><b>proof </b></a><div class="add">

<b>let </b><font color="Maroon">c<sub>8</sub></font> be    <a href="hidden.html#M1">set</a> ; <i><font color="Red">:: according to </font></i><a class="ref" href="tarski.html#D3">TARSKI:def 3</a><br/>

<b>assume </b><a NAME="E1:30_1_1"/>
<font color="Maroon">c<sub>8</sub></font> <a href="hidden.html#R2">in</a> <span class="p1">{<span class="default"> <span class="p2">(<span class="default"><a href="waybel_0.html#K4">uparrow</a> <font color="Olive">b<sub>1</sub></font></span>)</span> where B is   <a href="struct_0.html#NM2">Subset</a> of <font color="Maroon">c<sub>1</sub></font> : <font color="Olive">b<sub>1</sub></font> <a href="hidden.html#R2">in</a> <font color="Maroon">c<sub>5</sub></font> </span>}</span> 
 ;<br/>

<b>then consider </b><font color="Maroon">c<sub>9</sub></font> being   <a href="struct_0.html#NM2">Subset</a> of <font color="Maroon">c<sub>1</sub></font><b> such that </b><br/><a NAME="E3:30_1_1"/><i><font color="Green">E17</font></i>: 
<font color="Maroon">c<sub>8</sub></font> <a href="hidden.html#R1">=</a>  <a href="waybel_0.html#K4">uparrow</a> <font color="Maroon">c<sub>9</sub></font>
 <b>and </b><br/><a NAME="E4:30_1_1"/>
<font color="Maroon">c<sub>9</sub></font> <a href="hidden.html#R2">in</a> <font color="Maroon">c<sub>5</sub></font>
 ;<br/>
<b>thus </b><a NAME="E5:30_1_1"/>
<font color="Maroon">c<sub>8</sub></font> <a href="hidden.html#R2">in</a>  <a href="zfmisc_1.html#K1">bool</a> the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">c<sub>2</sub></font>
 <b>by </b><i><a class="txt" href="waybel30.html#E2:30"><i><font color="Green">E16</font></i></a>, <a class="txt" href="waybel30.html#E3:30_1_1"><i><font color="Green">E17</font></i></a></i>;<br/>


</div><b>end;</b></div>
<b>hence </b><a NAME="E2:30_1"/>
<span class="p1">{<span class="default"> <span class="p2">(<span class="default"><a href="waybel_0.html#K4">uparrow</a> <font color="Olive">b<sub>1</sub></font></span>)</span> where B is   <a href="struct_0.html#NM2">Subset</a> of <font color="Maroon">c<sub>1</sub></font> : <font color="Olive">b<sub>1</sub></font> <a href="hidden.html#R2">in</a> <font color="Maroon">c<sub>5</sub></font> </span>}</span>  is   <a href="struct_0.html#NM3">Subset-Family</a> of <font color="Maroon">c<sub>2</sub></font>
 ;<br/>


</div><b>end;</b></div>
<b>then reconsider </b><font color="Maroon">c<sub>8</sub></font> = <span class="p1">{<span class="default"> <span class="p2">(<span class="default"><a href="waybel_0.html#K4">uparrow</a> <font color="Olive">b<sub>1</sub></font></span>)</span> where B is   <a href="struct_0.html#NM2">Subset</a> of <font color="Maroon">c<sub>1</sub></font> : <font color="Olive">b<sub>1</sub></font> <a href="hidden.html#R2">in</a> <font color="Maroon">c<sub>5</sub></font> </span>}</span>  as   <a href="struct_0.html#NM3">Subset-Family</a> of <font color="Maroon">c<sub>2</sub></font> ;<br/>
<a NAME="E5:30"/>
<font color="Maroon">c<sub>8</sub></font> is    <a href="yellow_8.html#M1">Basis</a> of <font color="Maroon">c<sub>3</sub></font>
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="30_2"><b>proof </b></a><div class="add">

<b>thus </b><a NAME="E1:30_2"/>
<font color="Maroon">c<sub>8</sub></font> <a href="tarski.html#R1">c=</a> the <a href="pre_topc.html#U1">topology</a> of <font color="Maroon">c<sub>2</sub></font>
  <i><font color="Red">:: according to </font></i><a class="ref" href="yellow_8.html#D2">YELLOW_8:def 2</a><div><a class="txt" onclick="hs2(this)" href="javascript:()" title="30_2_1"><b>proof </b></a><div class="add">

<b>let </b><font color="Maroon">c<sub>9</sub></font> be    <a href="hidden.html#M1">set</a> ; <i><font color="Red">:: according to </font></i><a class="ref" href="tarski.html#D3">TARSKI:def 3</a><br/>

<b>assume </b><a NAME="E1:30_2_1"/>
<font color="Maroon">c<sub>9</sub></font> <a href="hidden.html#R2">in</a> <font color="Maroon">c<sub>8</sub></font>
 ;<br/>

<b>then consider </b><font color="Maroon">c<sub>10</sub></font> being   <a href="struct_0.html#NM2">Subset</a> of <font color="Maroon">c<sub>1</sub></font><b> such that </b><br/><a NAME="E3:30_2_1"/><i><font color="Green">E17</font></i>: 
<font color="Maroon">c<sub>9</sub></font> <a href="hidden.html#R1">=</a>  <a href="waybel_0.html#K4">uparrow</a> <font color="Maroon">c<sub>10</sub></font>
 <b>and </b><br/><a NAME="E4:30_2_1"/><i><font color="Green">E18</font></i>: 
<font color="Maroon">c<sub>10</sub></font> <a href="hidden.html#R2">in</a> <font color="Maroon">c<sub>5</sub></font>
 ;<br/>
<b>reconsider </b><font color="Maroon">c<sub>11</sub></font> = <font color="Maroon">c<sub>10</sub></font> as   <a href="struct_0.html#NM2">Subset</a> of <font color="Maroon">c<sub>2</sub></font> <b>by </b><i><a class="txt" href="waybel30.html#E2:30"><i><font color="Green">E16</font></i></a></i>;<br/>
<a NAME="E6:30_2_1"/>
<font color="Maroon">c<sub>10</sub></font> is <a href="pre_topc.html#V3">open</a>
 
<b>by </b><i><a class="txt" href="waybel30.html#E4:30_2_1"><i><font color="Green">E18</font></i></a>, <a class="ref" href="yellow_8.html#T21">YELLOW_8:21</a></i>;<br/>
<a NAME="E7:30_2_1"/><b>then </b>
 <a href="waybel_0.html#K4">uparrow</a> <font color="Maroon">c<sub>11</sub></font> is <a href="pre_topc.html#V3">open</a>
 
<b>by </b><i><a class="ref" href="waybel30.html#T15" target="_self">Th15</a></i>;<br/>
<a NAME="E8:30_2_1"/><b>then </b>
 <a href="waybel_0.html#K4">uparrow</a> <font color="Maroon">c<sub>11</sub></font> <a href="hidden.html#R2">in</a> the <a href="pre_topc.html#U1">topology</a> of <font color="Maroon">c<sub>2</sub></font>
 
<b>by </b><i><a class="ref" href="pre_topc.html#D5">PRE_TOPC:def 5</a></i>;<br/>
<b>hence </b><a NAME="E9:30_2_1"/>
<font color="Maroon">c<sub>9</sub></font> <a href="hidden.html#R2">in</a> the <a href="pre_topc.html#U1">topology</a> of <font color="Maroon">c<sub>2</sub></font>
 <b>by </b><i><a class="txt" href="waybel30.html#E2:30"><i><font color="Green">E16</font></i></a>, <a class="txt" href="waybel30.html#E3:30_2_1"><i><font color="Green">E17</font></i></a>, <a class="ref" href="waybel_0.html#T13">WAYBEL_0:13</a></i>;<br/>


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

<a NAME="E2:30_2"/>
for <font color="Olive">b<sub>1</sub></font> being   <a href="hidden.html#M1">set</a>  st <font color="Olive">b<sub>1</sub></font> <a href="hidden.html#R2">in</a> <font color="Maroon">c<sub>8</sub></font> holds <br/><font color="Maroon">c<sub>3</sub></font> <a href="hidden.html#R2">in</a> <font color="Olive">b<sub>1</sub></font>
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="30_2_2"><b>proof </b></a><div class="add">

<b>let </b><font color="Maroon">c<sub>9</sub></font> be    <a href="hidden.html#M1">set</a> ;<br/>

<b>assume </b><a NAME="E1:30_2_2"/>
<font color="Maroon">c<sub>9</sub></font> <a href="hidden.html#R2">in</a> <font color="Maroon">c<sub>8</sub></font>
 ;<br/>

<b>then consider </b><font color="Maroon">c<sub>10</sub></font> being   <a href="struct_0.html#NM2">Subset</a> of <font color="Maroon">c<sub>1</sub></font><b> such that </b><br/><a NAME="E3:30_2_2"/><i><font color="Green">E17</font></i>: 
<font color="Maroon">c<sub>9</sub></font> <a href="hidden.html#R1">=</a>  <a href="waybel_0.html#K4">uparrow</a> <font color="Maroon">c<sub>10</sub></font>
 <b>and </b><br/><a NAME="E4:30_2_2"/><i><font color="Green">E18</font></i>: 
<font color="Maroon">c<sub>10</sub></font> <a href="hidden.html#R2">in</a> <font color="Maroon">c<sub>5</sub></font>
 ;<br/>
<a NAME="E5:30_2_2"/>
<font color="Maroon">c<sub>4</sub></font> <a href="hidden.html#R2">in</a>  <a href="setfam_1.html#K8">Intersect</a> <font color="Maroon">c<sub>5</sub></font>
 
<b>by </b><i><a class="ref" href="yellow_8.html#D2">YELLOW_8:def 2</a></i>;<br/>
<a NAME="E6:30_2_2"/><b>then </b><i><font color="Green">E19</font></i>: 
<font color="Maroon">c<sub>4</sub></font> <a href="hidden.html#R2">in</a> <font color="Maroon">c<sub>10</sub></font>
 
<b>by </b><i><a class="txt" href="waybel30.html#E4:30_2_2"><i><font color="Green">E18</font></i></a>, <a class="ref" href="setfam_1.html#T58">SETFAM_1:58</a></i>;<br/>
<a NAME="E7:30_2_2"/>
<font color="Maroon">c<sub>10</sub></font> <a href="tarski.html#R1">c=</a>  <a href="waybel_0.html#K4">uparrow</a> <font color="Maroon">c<sub>10</sub></font>
 
<b>by </b><i><a class="ref" href="waybel_0.html#T16">WAYBEL_0:16</a></i>;<br/>
<b>hence </b><a NAME="E8:30_2_2"/>
<font color="Maroon">c<sub>3</sub></font> <a href="hidden.html#R2">in</a> <font color="Maroon">c<sub>9</sub></font>
 <b>by </b><i><a class="txt" href="waybel30.html#E1:30"><i><font color="Green">E15</font></i></a>, <a class="txt" href="waybel30.html#E3:30_2_2"><i><font color="Green">E17</font></i></a>, <a class="txt" href="waybel30.html#E6:30_2_2"><i><font color="Green">E19</font></i></a></i>;<br/>


</div><b>end;</b></div>
<b>hence </b><a NAME="E3:30_2"/>
<font color="Maroon">c<sub>3</sub></font> <a href="hidden.html#R2">in</a>  <a href="setfam_1.html#K8">Intersect</a> <font color="Maroon">c<sub>8</sub></font>
 <b>by </b><i><a class="ref" href="setfam_1.html#T58">SETFAM_1:58</a></i>;<br/>

<b>let </b><font color="Maroon">c<sub>9</sub></font> be   <a href="struct_0.html#NM2">Subset</a> of <font color="Maroon">c<sub>2</sub></font>;<br/>

<b>assume </b><a NAME="E4:30_2"/><i><font color="Green">E17</font></i>: 
( <font color="Maroon">c<sub>9</sub></font> is <a href="pre_topc.html#V3">open</a> &amp; <font color="Maroon">c<sub>3</sub></font> <a href="hidden.html#R2">in</a> <font color="Maroon">c<sub>9</sub></font> )
 ;<br/>

<b>reconsider </b><font color="Maroon">c<sub>10</sub></font> = <font color="Maroon">c<sub>9</sub></font> as   <a href="struct_0.html#NM2">Subset</a> of <font color="Maroon">c<sub>1</sub></font> <b>by </b><i><a class="txt" href="waybel30.html#E2:30"><i><font color="Green">E16</font></i></a></i>;<br/>
<a NAME="E6:30_2"/>
 <a href="waybel11.html#K5">sigma</a> <font color="Maroon">c<sub>1</sub></font> <a href="tarski.html#R1">c=</a>  <a href="waybel19.html#K2">lambda</a> <font color="Maroon">c<sub>1</sub></font>
 
<b>by </b><i><a class="ref" href="waybel30.html#T10" target="_self">Th10</a></i>;<br/>
<a NAME="E7:30_2"/><b>then </b><i><font color="Green">E18</font></i>: 
 <a href="waybel11.html#K5">sigma</a> <font color="Maroon">c<sub>2</sub></font> <a href="tarski.html#R1">c=</a>  <a href="waybel19.html#K2">lambda</a> <font color="Maroon">c<sub>1</sub></font>
 
<b>by </b><i><a class="txt" href="waybel30.html#E2:30"><i><font color="Green">E16</font></i></a>, <a class="ref" href="yellow_9.html#T52">YELLOW_9:52</a></i>;<br/>
<a NAME="E8:30_2"/>
<font color="Maroon">c<sub>1</sub></font> is  <a href="pre_topc.html#V2">correct</a> <a href="waybel19.html#V2">Lawson</a>  <a href="yellow_9.html#M1">TopAugmentation</a> of <font color="Maroon">c<sub>2</sub></font>
 
<b>by </b><i><a class="txt" href="waybel30.html#E2:30"><i><font color="Green">E16</font></i></a>, <a class="ref" href="yellow_9.html#D4">YELLOW_9:def 4</a></i>;<br/>
<a NAME="E9:30_2"/><b>then </b>
<font color="Maroon">c<sub>10</sub></font> is <a href="pre_topc.html#V3">open</a>
 
<b>by </b><i><a class="txt" href="waybel30.html#E4:30_2"><i><font color="Green">E17</font></i></a>, <a class="ref" href="waybel19.html#T37">WAYBEL19:37</a></i>;<br/>
<a NAME="E10:30_2"/><b>then </b>
<font color="Maroon">c<sub>10</sub></font> <a href="hidden.html#R2">in</a>  <a href="waybel19.html#K2">lambda</a> <font color="Maroon">c<sub>1</sub></font>
 
<b>by </b><i><a class="ref" href="waybel30.html#T12" target="_self">Th12</a></i>;<br/>
<a NAME="E11:30_2"/><b>then </b>
 <a href="waybel_0.html#K4">uparrow</a> <font color="Maroon">c<sub>10</sub></font> <a href="hidden.html#R2">in</a>  <a href="waybel11.html#K5">sigma</a> <font color="Maroon">c<sub>2</sub></font>
 
<b>by </b><i><a class="ref" href="waybel30.html#T14" target="_self">Th14</a></i>;<br/>
<a NAME="E12:30_2"/><b>then </b><i><font color="Green">E19</font></i>: 
 <a href="waybel_0.html#K4">uparrow</a> <font color="Maroon">c<sub>10</sub></font> is <a href="pre_topc.html#V3">open</a>
 
<b>by </b><i><a class="txt" href="waybel30.html#E7:30_2"><i><font color="Green">E18</font></i></a>, <a class="ref" href="waybel30.html#T12" target="_self">Th12</a></i>;<br/>
<a NAME="E13:30_2"/>
<font color="Maroon">c<sub>10</sub></font> <a href="tarski.html#R1">c=</a>  <a href="waybel_0.html#K4">uparrow</a> <font color="Maroon">c<sub>10</sub></font>
 
<b>by </b><i><a class="ref" href="waybel_0.html#T16">WAYBEL_0:16</a></i>;<br/>
<b>then consider </b><font color="Maroon">c<sub>11</sub></font> being   <a href="struct_0.html#NM2">Subset</a> of <font color="Maroon">c<sub>1</sub></font><b> such that </b><br/><a NAME="E15:30_2"/><i><font color="Green">E20</font></i>: 
<font color="Maroon">c<sub>11</sub></font> <a href="hidden.html#R2">in</a> <font color="Maroon">c<sub>5</sub></font>
 <b>and </b><br/><a NAME="E16:30_2"/><i><font color="Green">E21</font></i>: 
<font color="Maroon">c<sub>11</sub></font> <a href="tarski.html#R1">c=</a>  <a href="waybel_0.html#K4">uparrow</a> <font color="Maroon">c<sub>10</sub></font>
 <b>by </b><i><a class="txt" href="waybel30.html#E1:30"><i><font color="Green">E15</font></i></a>, <a class="txt" href="waybel30.html#E4:30_2"><i><font color="Green">E17</font></i></a>, <a class="txt" href="waybel30.html#E12:30_2"><i><font color="Green">E19</font></i></a>, <a class="ref" href="yellow_8.html#D2">YELLOW_8:def 2</a></i>;<br/>
<b>reconsider </b><font color="Maroon">c<sub>12</sub></font> =  <a href="waybel_0.html#K4">uparrow</a> <font color="Maroon">c<sub>11</sub></font> as   <a href="struct_0.html#NM2">Subset</a> of <font color="Maroon">c<sub>2</sub></font> <b>by </b><i><a class="txt" href="waybel30.html#E2:30"><i><font color="Green">E16</font></i></a></i>;<br/>
<b>take </b>
<font color="Maroon">c<sub>12</sub></font>
;<br/>

<b>thus </b><a NAME="E18:30_2"/>
<font color="Maroon">c<sub>12</sub></font> <a href="hidden.html#R2">in</a> <font color="Maroon">c<sub>8</sub></font>
 <b>by </b><i><a class="txt" href="waybel30.html#E15:30_2"><i><font color="Green">E20</font></i></a></i>;<br/>

<a NAME="E19:30_2"/><i><font color="Green">E22</font></i>: 
<font color="Maroon">c<sub>9</sub></font> <a href="hidden.html#R1">=</a>  <a href="waybel_0.html#K4">uparrow</a> <font color="Maroon">c<sub>9</sub></font>
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="30_2_3"><b>proof </b></a><div class="add">

<b>thus </b><a NAME="E1:30_2_3"/>
<font color="Maroon">c<sub>9</sub></font> <a href="tarski.html#R1">c=</a>  <a href="waybel_0.html#K4">uparrow</a> <font color="Maroon">c<sub>9</sub></font>
 <b>by </b><i><a class="ref" href="waybel_0.html#T16">WAYBEL_0:16</a></i>; <i><font color="Red">:: according to </font></i><a class="ref" href="xboole_0.html#D10">XBOOLE_0:def 10</a><br/>

<a NAME="E2:30_2_3"/>
<font color="Maroon">c<sub>9</sub></font> is <a href="waybel_0.html#V13">upper</a>
 
<b>by </b><i><a class="txt" href="waybel30.html#E4:30_2"><i><font color="Green">E17</font></i></a>, <a class="ref" href="waybel11.html#D4">WAYBEL11:def 4</a></i>;<br/>
<b>hence </b><a NAME="E3:30_2_3"/>
 <a href="waybel_0.html#K4">uparrow</a> <font color="Maroon">c<sub>9</sub></font> <a href="tarski.html#R1">c=</a> <font color="Maroon">c<sub>9</sub></font>
 <b>by </b><i><a class="ref" href="waybel_0.html#T24">WAYBEL_0:24</a></i>;<br/>


</div><b>end;</b></div>
<a NAME="E20:30_2"/><i><font color="Green">E23</font></i>: 
 <a href="waybel_0.html#K4">uparrow</a> <font color="Maroon">c<sub>9</sub></font> <a href="hidden.html#R1">=</a>  <a href="waybel_0.html#K4">uparrow</a> <font color="Maroon">c<sub>10</sub></font>
 
<b>by </b><i><a class="txt" href="waybel30.html#E2:30"><i><font color="Green">E16</font></i></a>, <a class="ref" href="waybel_0.html#T13">WAYBEL_0:13</a></i>;<br/>
<a NAME="E21:30_2"/>
<font color="Maroon">c<sub>11</sub></font> <a href="yellow_4.html#R4">is_coarser_than</a>  <a href="waybel_0.html#K4">uparrow</a> <font color="Maroon">c<sub>10</sub></font>
 
<b>by </b><i><a class="txt" href="waybel30.html#E16:30_2"><i><font color="Green">E21</font></i></a>, <a class="ref" href="waybel12.html#T20">WAYBEL12:20</a></i>;<br/>
<b>hence </b><a NAME="E22:30_2"/>
<font color="Maroon">c<sub>12</sub></font> <a href="tarski.html#R1">c=</a> <font color="Maroon">c<sub>9</sub></font>
 <b>by </b><i><a class="txt" href="waybel30.html#E19:30_2"><i><font color="Green">E22</font></i></a>, <a class="txt" href="waybel30.html#E20:30_2"><i><font color="Green">E23</font></i></a>, <a class="ref" href="yellow12.html#T28">YELLOW12:28</a></i>;<br/>


</div><b>end;</b></div>
<b>hence </b><a NAME="E6:30"/>
<span class="p1">{<span class="default"> <span class="p2">(<span class="default"><a href="waybel_0.html#K4">uparrow</a> <font color="Olive">b<sub>1</sub></font></span>)</span> where B is   <a href="struct_0.html#NM2">Subset</a> of <font color="Maroon">c<sub>1</sub></font> : <font color="Olive">b<sub>1</sub></font> <a href="hidden.html#R2">in</a> <font color="Maroon">c<sub>5</sub></font> </span>}</span>  is    <a href="yellow_8.html#M1">Basis</a> of <font color="Maroon">c<sub>3</sub></font>
 ;<br/>


</div>
