<?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_3.html#V3">continuous</a> <a href="waybel_0.html#NM8">LATTICE</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  non <a href="struct_0.html#V3">empty</a> <a href="pre_topc.html#NM1">TopSpace</a>; <i><font color="Red">:: according to </font></i><a class="ref" href="waybel18.html#D5">WAYBEL18:def 5</a><br/><b>let </b><font color="Maroon">c<sub>4</sub></font> be   <a href="struct_0.html#NM7">Function</a> of <font color="Maroon">c<sub>3</sub></font>,<font color="Maroon">c<sub>2</sub></font>;<br/>







<b>assume </b><a NAME="E1:17"/><i><font color="Green">E9</font></i>: 
<font color="Maroon">c<sub>4</sub></font> is <a href="pre_topc.html#V5">continuous</a>
 ;<br/>

<b>let </b><font color="Maroon">c<sub>5</sub></font> be  non <a href="struct_0.html#V3">empty</a> <a href="pre_topc.html#NM1">TopSpace</a>;<br/>

<b>assume </b><a NAME="E2:17"/><i><font color="Green">E10</font></i>: 
<font color="Maroon">c<sub>3</sub></font> is    <a href="pre_topc.html#M1">SubSpace</a> of <font color="Maroon">c<sub>5</sub></font>
 ;<br/>

<b>deffunc </b><font color="Maroon">H<sub>1</sub></font>(   <a href="hidden.html#M1">set</a> ) <b>-&gt; </b>   <a href="subset_1.html#M1">Element</a> of the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">c<sub>2</sub></font> =  <a href="yellow_0.html#K1">"\/"</a> <span class="p1">{<span class="default"> <span class="p2">(<span class="default"><a href="yellow_0.html#NK4" target="_self">inf</a> <span class="p3">(<span class="default"><font color="Maroon">c<sub>4</sub></font> <a href="relset_1.html#K10">.:</a> <span class="p4">(<span class="default"><font color="Olive">b<sub>1</sub></font> <a href="subset_1.html#K8">/\</a> the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">c<sub>3</sub></font></span>)</span></span>)</span></span>)</span> where B is  <a href="pre_topc.html#V3">open</a> <a href="struct_0.html#NM2">Subset</a> of <font color="Maroon">c<sub>5</sub></font> : <font color="Maroon">a<sub>1</sub></font> <a href="hidden.html#R2">in</a> <font color="Olive">b<sub>1</sub></font> </span>}</span> ,<font color="Maroon">c<sub>2</sub></font>;<br/>
<b>consider </b><font color="Maroon">c<sub>6</sub></font> being   <a href="funct_2.html#NM1">Function</a> of the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">c<sub>5</sub></font>,the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">c<sub>2</sub></font><b> such that </b><br/><a NAME="E4:17"/><i><font color="Green">E11</font></i>: 
for <font color="Olive">b<sub>1</sub></font> being  <a href="struct_0.html#NM1">Element</a> of <font color="Maroon">c<sub>5</sub></font> holds <font color="Maroon">c<sub>6</sub></font> <a href="yellow_6.html#K3">.</a> <font color="Olive">b<sub>1</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">H<sub>1</sub></font>(<font color="Olive">b<sub>1</sub></font>)
 <b>from </b><i><a class="ref" href="funct_2.html#S4">FUNCT_2:sch 4</a>();<br/></i>
<b>reconsider </b><font color="Maroon">c<sub>7</sub></font> = <font color="Maroon">c<sub>6</sub></font> as   <a href="struct_0.html#NM7">Function</a> of <font color="Maroon">c<sub>5</sub></font>,<font color="Maroon">c<sub>2</sub></font> ;<br/>
<b>take </b>
<font color="Maroon">c<sub>7</sub></font>
;<br/>

<a NAME="E6:17"/>
for <font color="Olive">b<sub>1</sub></font> being  <a href="struct_0.html#NM2">Subset</a> of <font color="Maroon">c<sub>2</sub></font> st <font color="Olive">b<sub>1</sub></font> is <a href="pre_topc.html#V3">open</a> holds <br/><font color="Maroon">c<sub>7</sub></font> <a href="relset_1.html#K11">"</a> <font color="Olive">b<sub>1</sub></font> is <a href="pre_topc.html#V3">open</a>
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="17_1"><b>proof </b></a><div class="add">

<b>let </b><font color="Maroon">c<sub>8</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="E1:17_1"/>
<font color="Maroon">c<sub>8</sub></font> is <a href="pre_topc.html#V3">open</a>
 ;<br/>

<b>then reconsider </b><font color="Maroon">c<sub>9</sub></font> = <font color="Maroon">c<sub>8</sub></font> as  <a href="pre_topc.html#V3">open</a> <a href="struct_0.html#NM2">Subset</a> of <font color="Maroon">c<sub>2</sub></font> ;<br/>
<a NAME="E3:17_1"/>
for <font color="Olive">b<sub>1</sub></font> being   <a href="hidden.html#M1">set</a>  holds <br/>( <font color="Olive">b<sub>1</sub></font> <a href="hidden.html#R2">in</a> <font color="Maroon">c<sub>7</sub></font> <a href="relset_1.html#K11">"</a> <font color="Maroon">c<sub>9</sub></font> iff ex <font color="Olive">b<sub>2</sub></font> being  <a href="struct_0.html#NM2">Subset</a> of <font color="Maroon">c<sub>5</sub></font> st <br/>( <font color="Olive">b<sub>2</sub></font> is <a href="pre_topc.html#V3">open</a> &amp; <font color="Olive">b<sub>2</sub></font> <a href="tarski.html#R1">c=</a> <font color="Maroon">c<sub>7</sub></font> <a href="relset_1.html#K11">"</a> <font color="Maroon">c<sub>9</sub></font> &amp; <font color="Olive">b<sub>1</sub></font> <a href="hidden.html#R2">in</a> <font color="Olive">b<sub>2</sub></font> ) )
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="17_1_1"><b>proof </b></a><div class="add">

<b>let </b><font color="Maroon">c<sub>10</sub></font> be    <a href="hidden.html#M1">set</a> ;<br/>

<b>thus </b><a NAME="E1:17_1_1"/>
( <font color="Maroon">c<sub>10</sub></font> <a href="hidden.html#R2">in</a> <font color="Maroon">c<sub>7</sub></font> <a href="relset_1.html#K11">"</a> <font color="Maroon">c<sub>9</sub></font> implies ex <font color="Olive">b<sub>1</sub></font> being  <a href="struct_0.html#NM2">Subset</a> of <font color="Maroon">c<sub>5</sub></font> st <br/>( <font color="Olive">b<sub>1</sub></font> is <a href="pre_topc.html#V3">open</a> &amp; <font color="Olive">b<sub>1</sub></font> <a href="tarski.html#R1">c=</a> <font color="Maroon">c<sub>7</sub></font> <a href="relset_1.html#K11">"</a> <font color="Maroon">c<sub>9</sub></font> &amp; <font color="Maroon">c<sub>10</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="17_1_1_1"><b>proof </b></a><div class="add">

<b>assume </b><a NAME="E1:17_1_1_1"/><i><font color="Green">E12</font></i>: 
<font color="Maroon">c<sub>10</sub></font> <a href="hidden.html#R2">in</a> <font color="Maroon">c<sub>7</sub></font> <a href="relset_1.html#K11">"</a> <font color="Maroon">c<sub>9</sub></font>
 ;<br/>

<b>then reconsider </b><font color="Maroon">c<sub>11</sub></font> = <font color="Maroon">c<sub>10</sub></font> as   <a href="pre_topc.html#NM2">Point</a> of <font color="Maroon">c<sub>5</sub></font> ;<br/>
<a NAME="E3:17_1_1_1"/><i><font color="Green">E13</font></i>: 
<font color="Maroon">c<sub>7</sub></font> <a href="yellow_6.html#K3">.</a> <font color="Maroon">c<sub>11</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="waybel25.html#E1:17_1_1_1"><i><font color="Green">E12</font></i></a>, <a class="ref" href="funct_2.html#T46">FUNCT_2:46</a></i>;<br/>
<b>set </b><font color="Maroon">c<sub>12</sub></font> = <span class="p1">{<span class="default"> <span class="p2">(<span class="default"><a href="yellow_0.html#NK4" target="_self">inf</a> <span class="p3">(<span class="default"><font color="Maroon">c<sub>4</sub></font> <a href="relset_1.html#K10">.:</a> <span class="p4">(<span class="default"><font color="Olive">b<sub>1</sub></font> <a href="subset_1.html#K8">/\</a> the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">c<sub>3</sub></font></span>)</span></span>)</span></span>)</span> where B is  <a href="pre_topc.html#V3">open</a> <a href="struct_0.html#NM2">Subset</a> of <font color="Maroon">c<sub>5</sub></font> : <font color="Maroon">c<sub>11</sub></font> <a href="hidden.html#R2">in</a> <font color="Olive">b<sub>1</sub></font> </span>}</span> ;<br/>
<a NAME="E4:17_1_1_1"/>
<span class="p1">{<span class="default"> <span class="p2">(<span class="default"><a href="yellow_0.html#NK4" target="_self">inf</a> <span class="p3">(<span class="default"><font color="Maroon">c<sub>4</sub></font> <a href="relset_1.html#K10">.:</a> <span class="p4">(<span class="default"><font color="Olive">b<sub>1</sub></font> <a href="subset_1.html#K8">/\</a> the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">c<sub>3</sub></font></span>)</span></span>)</span></span>)</span> where B is  <a href="pre_topc.html#V3">open</a> <a href="struct_0.html#NM2">Subset</a> of <font color="Maroon">c<sub>5</sub></font> : <font color="Maroon">c<sub>11</sub></font> <a href="hidden.html#R2">in</a> <font color="Olive">b<sub>1</sub></font> </span>}</span>  <a href="tarski.html#R1">c=</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="17_1_1_1_1"><b>proof </b></a><div class="add">

<b>let </b><font color="Maroon">c<sub>13</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="E1:17_1_1_1_1"/>
<font color="Maroon">c<sub>13</sub></font> <a href="hidden.html#R2">in</a> <span class="p1">{<span class="default"> <span class="p2">(<span class="default"><a href="yellow_0.html#NK4" target="_self">inf</a> <span class="p3">(<span class="default"><font color="Maroon">c<sub>4</sub></font> <a href="relset_1.html#K10">.:</a> <span class="p4">(<span class="default"><font color="Olive">b<sub>1</sub></font> <a href="subset_1.html#K8">/\</a> the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">c<sub>3</sub></font></span>)</span></span>)</span></span>)</span> where B is  <a href="pre_topc.html#V3">open</a> <a href="struct_0.html#NM2">Subset</a> of <font color="Maroon">c<sub>5</sub></font> : <font color="Maroon">c<sub>11</sub></font> <a href="hidden.html#R2">in</a> <font color="Olive">b<sub>1</sub></font> </span>}</span> 
 ;<br/>

<a NAME="E2:17_1_1_1_1"/><b>then </b>
ex <font color="Olive">b<sub>1</sub></font> being <a href="pre_topc.html#V3">open</a> <a href="struct_0.html#NM2">Subset</a> of <font color="Maroon">c<sub>5</sub></font> st <br/>( <font color="Maroon">c<sub>13</sub></font> <a href="hidden.html#R1">=</a>  <a href="yellow_0.html#NK4" target="_self">inf</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>4</sub></font> <a href="relset_1.html#K10">.:</a> <span class="p2">(<span class="default"><font color="Olive">b<sub>1</sub></font> <a href="subset_1.html#K8">/\</a> the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">c<sub>3</sub></font></span>)</span></span>)</span> &amp; <font color="Maroon">c<sub>11</sub></font> <a href="hidden.html#R2">in</a> <font color="Olive">b<sub>1</sub></font> )
 
;<br/>
<b>hence </b><a NAME="E3:17_1_1_1_1"/>
<font color="Maroon">c<sub>13</sub></font> <a href="hidden.html#R2">in</a> the <a href="struct_0.html#U1">carrier</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>13</sub></font> = <span class="p1">{<span class="default"> <span class="p2">(<span class="default"><a href="yellow_0.html#NK4" target="_self">inf</a> <span class="p3">(<span class="default"><font color="Maroon">c<sub>4</sub></font> <a href="relset_1.html#K10">.:</a> <span class="p4">(<span class="default"><font color="Olive">b<sub>1</sub></font> <a href="subset_1.html#K8">/\</a> the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">c<sub>3</sub></font></span>)</span></span>)</span></span>)</span> where B is  <a href="pre_topc.html#V3">open</a> <a href="struct_0.html#NM2">Subset</a> of <font color="Maroon">c<sub>5</sub></font> : <font color="Maroon">c<sub>11</sub></font> <a href="hidden.html#R2">in</a> <font color="Olive">b<sub>1</sub></font> </span>}</span>  as   <a href="struct_0.html#NM2">Subset</a> of <font color="Maroon">c<sub>2</sub></font> ;<br/>
<a NAME="E6:17_1_1_1"/><i><font color="Green">E14</font></i>: 
<font color="Maroon">c<sub>7</sub></font> <a href="yellow_6.html#K3">.</a> <font color="Maroon">c<sub>11</sub></font> <a href="hidden.html#R1">=</a>  <a href="yellow_0.html#NK3" target="_self">sup</a> <font color="Maroon">c<sub>13</sub></font>
 
<b>by </b><i><a class="txt" href="waybel25.html#E4:17"><i><font color="Green">E11</font></i></a></i>;<br/>
<a NAME="E7:17_1_1_1"/><i><font color="Green">E15</font></i>: 
 <a href="yellow_0.html#NK4" target="_self">inf</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>4</sub></font> <a href="relset_1.html#K10">.:</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="pre_topc.html#K2">[#]</a> <font color="Maroon">c<sub>5</sub></font></span>)</span> <a href="subset_1.html#K8">/\</a> the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">c<sub>3</sub></font></span>)</span></span>)</span> <a href="hidden.html#R2">in</a> <font color="Maroon">c<sub>13</sub></font>
 
;<br/>
<a NAME="E8:17_1_1_1"/>
<font color="Maroon">c<sub>13</sub></font> is <a href="waybel_0.html#V1">directed</a>
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="17_1_1_1_2"><b>proof </b></a><div class="add">

<b>let </b><font color="Maroon">c<sub>14</sub></font>, <font color="Maroon">c<sub>15</sub></font> be   <a href="struct_0.html#NM1">Element</a> of <font color="Maroon">c<sub>2</sub></font>; <i><font color="Red">:: according to </font></i><a class="ref" href="waybel_0.html#D1">WAYBEL_0:def 1</a><br/>

<b>assume </b><a NAME="E1:17_1_1_1_2"/>
<font color="Maroon">c<sub>14</sub></font> <a href="hidden.html#R2">in</a> <font color="Maroon">c<sub>13</sub></font>
 ;<br/>

<b>then consider </b><font color="Maroon">c<sub>16</sub></font> being  <a href="pre_topc.html#V3">open</a> <a href="struct_0.html#NM2">Subset</a> of <font color="Maroon">c<sub>5</sub></font><b> such that </b><br/><a NAME="E3:17_1_1_1_2"/><i><font color="Green">E16</font></i>: 
<font color="Maroon">c<sub>14</sub></font> <a href="hidden.html#R1">=</a>  <a href="yellow_0.html#NK4" target="_self">inf</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>4</sub></font> <a href="relset_1.html#K10">.:</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>16</sub></font> <a href="subset_1.html#K8">/\</a> the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">c<sub>3</sub></font></span>)</span></span>)</span>
 <b>and </b><br/><a NAME="E4:17_1_1_1_2"/><i><font color="Green">E17</font></i>: 
<font color="Maroon">c<sub>11</sub></font> <a href="hidden.html#R2">in</a> <font color="Maroon">c<sub>16</sub></font>
 ;<br/>
<b>assume </b><a NAME="E5:17_1_1_1_2"/>
<font color="Maroon">c<sub>15</sub></font> <a href="hidden.html#R2">in</a> <font color="Maroon">c<sub>13</sub></font>
 ;<br/>

<b>then consider </b><font color="Maroon">c<sub>17</sub></font> being  <a href="pre_topc.html#V3">open</a> <a href="struct_0.html#NM2">Subset</a> of <font color="Maroon">c<sub>5</sub></font><b> such that </b><br/><a NAME="E7:17_1_1_1_2"/><i><font color="Green">E18</font></i>: 
<font color="Maroon">c<sub>15</sub></font> <a href="hidden.html#R1">=</a>  <a href="yellow_0.html#NK4" target="_self">inf</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>4</sub></font> <a href="relset_1.html#K10">.:</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>17</sub></font> <a href="subset_1.html#K8">/\</a> the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">c<sub>3</sub></font></span>)</span></span>)</span>
 <b>and </b><br/><a NAME="E8:17_1_1_1_2"/><i><font color="Green">E19</font></i>: 
<font color="Maroon">c<sub>11</sub></font> <a href="hidden.html#R2">in</a> <font color="Maroon">c<sub>17</sub></font>
 ;<br/>
<b>take </b>
 <a href="yellow_0.html#NK4" target="_self">inf</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>4</sub></font> <a href="relset_1.html#K10">.:</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">c<sub>16</sub></font> <a href="subset_1.html#K9">/\</a> <font color="Maroon">c<sub>17</sub></font></span>)</span> <a href="subset_1.html#K8">/\</a> the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">c<sub>3</sub></font></span>)</span></span>)</span>
;<br/>

<a NAME="E9:17_1_1_1_2"/><i><font color="Green">E20</font></i>: 
<font color="Maroon">c<sub>16</sub></font> <a href="subset_1.html#K9">/\</a> <font color="Maroon">c<sub>17</sub></font> is <a href="pre_topc.html#V3">open</a>
 
<b>by </b><i><a class="ref" href="tops_1.html#T38">TOPS_1:38</a></i>;<br/>
<a NAME="E10:17_1_1_1_2"/>
<font color="Maroon">c<sub>11</sub></font> <a href="hidden.html#R2">in</a> <font color="Maroon">c<sub>16</sub></font> <a href="subset_1.html#K9">/\</a> <font color="Maroon">c<sub>17</sub></font>
 
<b>by </b><i><a class="txt" href="waybel25.html#E4:17_1_1_1_2"><i><font color="Green">E17</font></i></a>, <a class="txt" href="waybel25.html#E8:17_1_1_1_2"><i><font color="Green">E19</font></i></a>, <a class="ref" href="xboole_0.html#D3">XBOOLE_0:def 3</a></i>;<br/>
<b>hence </b><a NAME="E11:17_1_1_1_2"/>
 <a href="yellow_0.html#NK4" target="_self">inf</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>4</sub></font> <a href="relset_1.html#K10">.:</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">c<sub>16</sub></font> <a href="subset_1.html#K9">/\</a> <font color="Maroon">c<sub>17</sub></font></span>)</span> <a href="subset_1.html#K8">/\</a> the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">c<sub>3</sub></font></span>)</span></span>)</span> <a href="hidden.html#R2">in</a> <font color="Maroon">c<sub>13</sub></font>
 <b>by </b><i><a class="txt" href="waybel25.html#E9:17_1_1_1_2"><i><font color="Green">E20</font></i></a></i>;<br/>

<a NAME="E12:17_1_1_1_2"/>
( <font color="Maroon">c<sub>16</sub></font> <a href="subset_1.html#K9">/\</a> <font color="Maroon">c<sub>17</sub></font> <a href="tarski.html#R1">c=</a> <font color="Maroon">c<sub>16</sub></font> &amp; <font color="Maroon">c<sub>16</sub></font> <a href="subset_1.html#K9">/\</a> <font color="Maroon">c<sub>17</sub></font> <a href="tarski.html#R1">c=</a> <font color="Maroon">c<sub>17</sub></font> )
 
<b>by </b><i><a class="ref" href="xboole_1.html#T17">XBOOLE_1:17</a></i>;<br/>
<a NAME="E13:17_1_1_1_2"/><b>then </b>
( <span class="p1">(<span class="default"><font color="Maroon">c<sub>16</sub></font> <a href="subset_1.html#K9">/\</a> <font color="Maroon">c<sub>17</sub></font></span>)</span> <a href="subset_1.html#K8">/\</a> the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">c<sub>3</sub></font> <a href="tarski.html#R1">c=</a> <font color="Maroon">c<sub>16</sub></font> <a href="subset_1.html#K8">/\</a> the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">c<sub>3</sub></font> &amp; <span class="p1">(<span class="default"><font color="Maroon">c<sub>16</sub></font> <a href="subset_1.html#K9">/\</a> <font color="Maroon">c<sub>17</sub></font></span>)</span> <a href="subset_1.html#K8">/\</a> the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">c<sub>3</sub></font> <a href="tarski.html#R1">c=</a> <font color="Maroon">c<sub>17</sub></font> <a href="subset_1.html#K8">/\</a> the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">c<sub>3</sub></font> )
 
<b>by </b><i><a class="ref" href="xboole_1.html#T26">XBOOLE_1:26</a></i>;<br/>
<a NAME="E14:17_1_1_1_2"/><b>then </b>
( <font color="Maroon">c<sub>4</sub></font> <a href="relset_1.html#K10">.:</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>16</sub></font> <a href="subset_1.html#K9">/\</a> <font color="Maroon">c<sub>17</sub></font></span>)</span> <a href="subset_1.html#K8">/\</a> the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">c<sub>3</sub></font></span>)</span> <a href="tarski.html#R1">c=</a> <font color="Maroon">c<sub>4</sub></font> <a href="relset_1.html#K10">.:</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>16</sub></font> <a href="subset_1.html#K8">/\</a> the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">c<sub>3</sub></font></span>)</span> &amp; <font color="Maroon">c<sub>4</sub></font> <a href="relset_1.html#K10">.:</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>16</sub></font> <a href="subset_1.html#K9">/\</a> <font color="Maroon">c<sub>17</sub></font></span>)</span> <a href="subset_1.html#K8">/\</a> the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">c<sub>3</sub></font></span>)</span> <a href="tarski.html#R1">c=</a> <font color="Maroon">c<sub>4</sub></font> <a href="relset_1.html#K10">.:</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>17</sub></font> <a href="subset_1.html#K8">/\</a> the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">c<sub>3</sub></font></span>)</span> )
 
<b>by </b><i><a class="ref" href="relat_1.html#T156">RELAT_1:156</a></i>;<br/>
<b>hence </b><a NAME="E15:17_1_1_1_2"/>
( <font color="Maroon">c<sub>14</sub></font> <a href="orders_2.html#R1">&lt;=</a>  <a href="yellow_0.html#NK4" target="_self">inf</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>4</sub></font> <a href="relset_1.html#K10">.:</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">c<sub>16</sub></font> <a href="subset_1.html#K9">/\</a> <font color="Maroon">c<sub>17</sub></font></span>)</span> <a href="subset_1.html#K8">/\</a> the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">c<sub>3</sub></font></span>)</span></span>)</span> &amp; <font color="Maroon">c<sub>15</sub></font> <a href="orders_2.html#R1">&lt;=</a>  <a href="yellow_0.html#NK4" target="_self">inf</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>4</sub></font> <a href="relset_1.html#K10">.:</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">c<sub>16</sub></font> <a href="subset_1.html#K9">/\</a> <font color="Maroon">c<sub>17</sub></font></span>)</span> <a href="subset_1.html#K8">/\</a> the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">c<sub>3</sub></font></span>)</span></span>)</span> )
 <b>by </b><i><a class="txt" href="waybel25.html#E3:17_1_1_1_2"><i><font color="Green">E16</font></i></a>, <a class="txt" href="waybel25.html#E7:17_1_1_1_2"><i><font color="Green">E18</font></i></a>, <a class="ref" href="waybel_7.html#T3">WAYBEL_7:3</a></i>;<br/>


</div><b>end;</b></div>
<a NAME="E9:17_1_1_1"/><b>then </b>
<font color="Maroon">c<sub>13</sub></font> <a href="xboole_0.html#NR5" target="_self">meets</a> <font color="Maroon">c<sub>9</sub></font>
 
<b>by </b><i><a class="txt" href="waybel25.html#E3:17_1_1_1"><i><font color="Green">E13</font></i></a>, <a class="txt" href="waybel25.html#E6:17_1_1_1"><i><font color="Green">E14</font></i></a>, <a class="txt" href="waybel25.html#E7:17_1_1_1"><i><font color="Green">E15</font></i></a>, <a class="ref" href="waybel11.html#D1">WAYBEL11:def 1</a></i>;<br/>
<b>then consider </b><font color="Maroon">c<sub>14</sub></font> being    <a href="hidden.html#M1">set</a> <b> such that </b><br/><a NAME="E11:17_1_1_1"/><i><font color="Green">E16</font></i>: 
<font color="Maroon">c<sub>14</sub></font> <a href="hidden.html#R2">in</a> <font color="Maroon">c<sub>13</sub></font>
 <b>and </b><br/><a NAME="E12:17_1_1_1"/><i><font color="Green">E17</font></i>: 
<font color="Maroon">c<sub>14</sub></font> <a href="hidden.html#R2">in</a> <font color="Maroon">c<sub>9</sub></font>
 <b>by </b><i><a class="ref" href="xboole_0.html#T3">XBOOLE_0:3</a></i>;<br/>
<b>consider </b><font color="Maroon">c<sub>15</sub></font> being  <a href="pre_topc.html#V3">open</a> <a href="struct_0.html#NM2">Subset</a> of <font color="Maroon">c<sub>5</sub></font><b> such that </b><br/><a NAME="E14:17_1_1_1"/><i><font color="Green">E18</font></i>: 
<font color="Maroon">c<sub>14</sub></font> <a href="hidden.html#R1">=</a>  <a href="yellow_0.html#NK4" target="_self">inf</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>4</sub></font> <a href="relset_1.html#K10">.:</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>15</sub></font> <a href="subset_1.html#K8">/\</a> the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">c<sub>3</sub></font></span>)</span></span>)</span>
 <b>and </b><br/><a NAME="E15:17_1_1_1"/><i><font color="Green">E19</font></i>: 
<font color="Maroon">c<sub>11</sub></font> <a href="hidden.html#R2">in</a> <font color="Maroon">c<sub>15</sub></font>
 <b>by </b><i><a class="txt" href="waybel25.html#E11:17_1_1_1"><i><font color="Green">E16</font></i></a></i>;<br/>
<b>reconsider </b><font color="Maroon">c<sub>16</sub></font> = <font color="Maroon">c<sub>14</sub></font> as   <a href="struct_0.html#NM1">Element</a> of <font color="Maroon">c<sub>2</sub></font> <b>by </b><i><a class="txt" href="waybel25.html#E14:17_1_1_1"><i><font color="Green">E18</font></i></a></i>;<br/>
<b>take </b>
<font color="Maroon">c<sub>15</sub></font>
;<br/>

<b>thus </b><a NAME="E17:17_1_1_1"/>
<font color="Maroon">c<sub>15</sub></font> is <a href="pre_topc.html#V3">open</a>
 ;<br/>

<b>thus </b><a NAME="E18:17_1_1_1"/>
<font color="Maroon">c<sub>15</sub></font> <a href="tarski.html#R1">c=</a> <font color="Maroon">c<sub>7</sub></font> <a href="relset_1.html#K11">"</a> <font color="Maroon">c<sub>9</sub></font>
 <div><a class="txt" onclick="hs2(this)" href="javascript:()" title="17_1_1_1_3"><b>proof </b></a><div class="add">

<b>let </b><font color="Maroon">c<sub>17</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="E1:17_1_1_1_3"/><i><font color="Green">E20</font></i>: 
<font color="Maroon">c<sub>17</sub></font> <a href="hidden.html#R2">in</a> <font color="Maroon">c<sub>15</sub></font>
 ;<br/>

<b>then reconsider </b><font color="Maroon">c<sub>18</sub></font> = <font color="Maroon">c<sub>17</sub></font> as   <a href="pre_topc.html#NM2">Point</a> of <font color="Maroon">c<sub>5</sub></font> ;<br/>
<a NAME="E3:17_1_1_1_3"/><i><font color="Green">E21</font></i>: 
<font color="Maroon">c<sub>7</sub></font> <a href="yellow_6.html#K3">.</a> <font color="Maroon">c<sub>18</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">H<sub>1</sub></font>(<font color="Maroon">c<sub>18</sub></font>)
 
<b>by </b><i><a class="txt" href="waybel25.html#E4:17"><i><font color="Green">E11</font></i></a></i>;<br/>
<a NAME="E4:17_1_1_1_3"/>
<font color="Maroon">c<sub>16</sub></font> <a href="hidden.html#R2">in</a> <span class="p1">{<span class="default"> <span class="p2">(<span class="default"><a href="yellow_0.html#NK4" target="_self">inf</a> <span class="p3">(<span class="default"><font color="Maroon">c<sub>4</sub></font> <a href="relset_1.html#K10">.:</a> <span class="p4">(<span class="default"><font color="Olive">b<sub>1</sub></font> <a href="subset_1.html#K8">/\</a> the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">c<sub>3</sub></font></span>)</span></span>)</span></span>)</span> where B is  <a href="pre_topc.html#V3">open</a> <a href="struct_0.html#NM2">Subset</a> of <font color="Maroon">c<sub>5</sub></font> : <font color="Maroon">c<sub>18</sub></font> <a href="hidden.html#R2">in</a> <font color="Olive">b<sub>1</sub></font> </span>}</span> 
 
<b>by </b><i><a class="txt" href="waybel25.html#E14:17_1_1_1"><i><font color="Green">E18</font></i></a>, <a class="txt" href="waybel25.html#E1:17_1_1_1_3"><i><font color="Green">E20</font></i></a></i>;<br/>
<a NAME="E5:17_1_1_1_3"/><b>then </b>
<font color="Maroon">c<sub>16</sub></font> <a href="orders_2.html#R3">&lt;=</a> <font color="Maroon">c<sub>7</sub></font> <a href="yellow_6.html#K3">.</a> <font color="Maroon">c<sub>18</sub></font>
 
<b>by </b><i><a class="txt" href="waybel25.html#E3:17_1_1_1_3"><i><font color="Green">E21</font></i></a>, <a class="ref" href="yellow_2.html#T24">YELLOW_2:24</a></i>;<br/>
<a NAME="E6:17_1_1_1_3"/><b>then </b>
<font color="Maroon">c<sub>7</sub></font> <a href="yellow_6.html#K3">.</a> <font color="Maroon">c<sub>18</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="waybel25.html#E12:17_1_1_1"><i><font color="Green">E17</font></i></a>, <a class="ref" href="waybel_0.html#D20">WAYBEL_0:def 20</a></i>;<br/>
<b>hence </b><a NAME="E7:17_1_1_1_3"/>
<font color="Maroon">c<sub>17</sub></font> <a href="hidden.html#R2">in</a> <font color="Maroon">c<sub>7</sub></font> <a href="relset_1.html#K11">"</a> <font color="Maroon">c<sub>9</sub></font>
 <b>by </b><i><a class="ref" href="funct_2.html#T46">FUNCT_2:46</a></i>;<br/>


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

<b>thus </b><a NAME="E19:17_1_1_1"/>
<font color="Maroon">c<sub>10</sub></font> <a href="hidden.html#R2">in</a> <font color="Maroon">c<sub>15</sub></font>
 <b>by </b><i><a class="txt" href="waybel25.html#E15:17_1_1_1"><i><font color="Green">E19</font></i></a></i>;<br/>


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

<b>thus </b><a NAME="E2:17_1_1"/>
( ex <font color="Olive">b<sub>1</sub></font> being  <a href="struct_0.html#NM2">Subset</a> of <font color="Maroon">c<sub>5</sub></font> st <br/>( <font color="Olive">b<sub>1</sub></font> is <a href="pre_topc.html#V3">open</a> &amp; <font color="Olive">b<sub>1</sub></font> <a href="tarski.html#R1">c=</a> <font color="Maroon">c<sub>7</sub></font> <a href="relset_1.html#K11">"</a> <font color="Maroon">c<sub>9</sub></font> &amp; <font color="Maroon">c<sub>10</sub></font> <a href="hidden.html#R2">in</a> <font color="Olive">b<sub>1</sub></font> ) implies <font color="Maroon">c<sub>10</sub></font> <a href="hidden.html#R2">in</a> <font color="Maroon">c<sub>7</sub></font> <a href="relset_1.html#K11">"</a> <font color="Maroon">c<sub>9</sub></font> )
 ;<br/>


</div><b>end;</b></div>
<b>hence </b><a NAME="E4:17_1"/>
<font color="Maroon">c<sub>7</sub></font> <a href="relset_1.html#K11">"</a> <font color="Maroon">c<sub>8</sub></font> is <a href="pre_topc.html#V3">open</a>
 <b>by </b><i><a class="ref" href="tops_1.html#T57">TOPS_1:57</a></i>;<br/>


</div><b>end;</b></div>
<b>hence </b><a NAME="E7:17"/>
<font color="Maroon">c<sub>7</sub></font> is <a href="pre_topc.html#V5">continuous</a>
 <b>by </b><i><a class="ref" href="tops_2.html#T55">TOPS_2:55</a></i>;<br/>

<b>set </b><font color="Maroon">c<sub>8</sub></font> = <font color="Maroon">c<sub>7</sub></font> <a href="partfun1.html#K2">|</a> the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">c<sub>3</sub></font>;<br/>
<a NAME="E8:17"/><i><font color="Green">E12</font></i>: 
the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">c<sub>3</sub></font> <a href="tarski.html#R1">c=</a> the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">c<sub>5</sub></font>
 
<b>by </b><i><a class="txt" href="waybel25.html#E2:17"><i><font color="Green">E10</font></i></a>, <a class="ref" href="borsuk_1.html#T35">BORSUK_1:35</a></i>;<br/>
<i><font color="Green">E13</font></i>:  <a href="relset_1.html#K4">dom</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>7</sub></font> <a href="partfun1.html#K2">|</a> the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">c<sub>3</sub></font></span>)</span> = 
<span class="p1">(<span class="default"><a href="relset_1.html#K4">dom</a> <font color="Maroon">c<sub>7</sub></font></span>)</span> <a href="subset_1.html#K8">/\</a> the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">c<sub>3</sub></font>
<b>by </b><i><a class="ref" href="relat_1.html#T90">RELAT_1:90</a></i>
<br/>.= 
the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">c<sub>5</sub></font> <a href="xboole_0.html#K3">/\</a> the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">c<sub>3</sub></font>
<b>by </b><i><a class="ref" href="funct_2.html#D1">FUNCT_2:def 1</a></i>
<br/>.= 
the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">c<sub>3</sub></font>
<b>by </b><i><a class="txt" href="waybel25.html#E8:17"><i><font color="Green">E12</font></i></a>, <a class="ref" href="xboole_1.html#T28">XBOOLE_1:28</a></i>
;<br/>
<a NAME="E10:17"/><i><font color="Green">E14</font></i>: 
 <a href="relset_1.html#K4">dom</a> <font color="Maroon">c<sub>4</sub></font> <a href="hidden.html#R1">=</a> the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">c<sub>3</sub></font>
 
<b>by </b><i><a class="ref" href="funct_2.html#D1">FUNCT_2:def 1</a></i>;<br/>
<a NAME="E11:17"/>
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> the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">c<sub>3</sub></font> holds <br/><span class="p1">(<span class="default"><font color="Maroon">c<sub>7</sub></font> <a href="partfun1.html#K2">|</a> the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">c<sub>3</sub></font></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Olive">b<sub>1</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>4</sub></font> <a href="funct_1.html#K1">.</a> <font color="Olive">b<sub>1</sub></font>
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="17_3"><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="E1:17_3"/><i><font color="Green">E15</font></i>: 
<font color="Maroon">c<sub>9</sub></font> <a href="hidden.html#R2">in</a> the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">c<sub>3</sub></font>
 ;<br/>

<b>then reconsider </b><font color="Maroon">c<sub>10</sub></font> = <font color="Maroon">c<sub>9</sub></font> as   <a href="pre_topc.html#NM2">Point</a> of <font color="Maroon">c<sub>3</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="pre_topc.html#NM2">Point</a> of <font color="Maroon">c<sub>5</sub></font> <b>by </b><i><a class="txt" href="waybel25.html#E8:17"><i><font color="Green">E12</font></i></a>, <a class="txt" href="waybel25.html#E1:17_3"><i><font color="Green">E15</font></i></a></i>;<br/>
<b>set </b><font color="Maroon">c<sub>12</sub></font> = <span class="p1">{<span class="default"> <span class="p2">(<span class="default"><a href="yellow_0.html#NK4" target="_self">inf</a> <span class="p3">(<span class="default"><font color="Maroon">c<sub>4</sub></font> <a href="relset_1.html#K10">.:</a> <span class="p4">(<span class="default"><font color="Olive">b<sub>1</sub></font> <a href="subset_1.html#K8">/\</a> the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">c<sub>3</sub></font></span>)</span></span>)</span></span>)</span> where B is  <a href="pre_topc.html#V3">open</a> <a href="struct_0.html#NM2">Subset</a> of <font color="Maroon">c<sub>5</sub></font> : <font color="Maroon">c<sub>11</sub></font> <a href="hidden.html#R2">in</a> <font color="Olive">b<sub>1</sub></font> </span>}</span> ;<br/>
<a NAME="E4:17_3"/>
<span class="p1">{<span class="default"> <span class="p2">(<span class="default"><a href="yellow_0.html#NK4" target="_self">inf</a> <span class="p3">(<span class="default"><font color="Maroon">c<sub>4</sub></font> <a href="relset_1.html#K10">.:</a> <span class="p4">(<span class="default"><font color="Olive">b<sub>1</sub></font> <a href="subset_1.html#K8">/\</a> the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">c<sub>3</sub></font></span>)</span></span>)</span></span>)</span> where B is  <a href="pre_topc.html#V3">open</a> <a href="struct_0.html#NM2">Subset</a> of <font color="Maroon">c<sub>5</sub></font> : <font color="Maroon">c<sub>11</sub></font> <a href="hidden.html#R2">in</a> <font color="Olive">b<sub>1</sub></font> </span>}</span>  <a href="tarski.html#R1">c=</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="17_3_1"><b>proof </b></a><div class="add">

<b>let </b><font color="Maroon">c<sub>13</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="E1:17_3_1"/>
<font color="Maroon">c<sub>13</sub></font> <a href="hidden.html#R2">in</a> <span class="p1">{<span class="default"> <span class="p2">(<span class="default"><a href="yellow_0.html#NK4" target="_self">inf</a> <span class="p3">(<span class="default"><font color="Maroon">c<sub>4</sub></font> <a href="relset_1.html#K10">.:</a> <span class="p4">(<span class="default"><font color="Olive">b<sub>1</sub></font> <a href="subset_1.html#K8">/\</a> the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">c<sub>3</sub></font></span>)</span></span>)</span></span>)</span> where B is  <a href="pre_topc.html#V3">open</a> <a href="struct_0.html#NM2">Subset</a> of <font color="Maroon">c<sub>5</sub></font> : <font color="Maroon">c<sub>11</sub></font> <a href="hidden.html#R2">in</a> <font color="Olive">b<sub>1</sub></font> </span>}</span> 
 ;<br/>

<a NAME="E2:17_3_1"/><b>then </b>
ex <font color="Olive">b<sub>1</sub></font> being <a href="pre_topc.html#V3">open</a> <a href="struct_0.html#NM2">Subset</a> of <font color="Maroon">c<sub>5</sub></font> st <br/>( <font color="Maroon">c<sub>13</sub></font> <a href="hidden.html#R1">=</a>  <a href="yellow_0.html#NK4" target="_self">inf</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>4</sub></font> <a href="relset_1.html#K10">.:</a> <span class="p2">(<span class="default"><font color="Olive">b<sub>1</sub></font> <a href="subset_1.html#K8">/\</a> the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">c<sub>3</sub></font></span>)</span></span>)</span> &amp; <font color="Maroon">c<sub>11</sub></font> <a href="hidden.html#R2">in</a> <font color="Olive">b<sub>1</sub></font> )
 
;<br/>
<b>hence </b><a NAME="E3:17_3_1"/>
<font color="Maroon">c<sub>13</sub></font> <a href="hidden.html#R2">in</a> the <a href="struct_0.html#U1">carrier</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>13</sub></font> = <span class="p1">{<span class="default"> <span class="p2">(<span class="default"><a href="yellow_0.html#NK4" target="_self">inf</a> <span class="p3">(<span class="default"><font color="Maroon">c<sub>4</sub></font> <a href="relset_1.html#K10">.:</a> <span class="p4">(<span class="default"><font color="Olive">b<sub>1</sub></font> <a href="subset_1.html#K8">/\</a> the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">c<sub>3</sub></font></span>)</span></span>)</span></span>)</span> where B is  <a href="pre_topc.html#V3">open</a> <a href="struct_0.html#NM2">Subset</a> of <font color="Maroon">c<sub>5</sub></font> : <font color="Maroon">c<sub>11</sub></font> <a href="hidden.html#R2">in</a> <font color="Olive">b<sub>1</sub></font> </span>}</span>  as   <a href="struct_0.html#NM2">Subset</a> of <font color="Maroon">c<sub>2</sub></font> ;<br/>
<a NAME="E6:17_3"/><i><font color="Green">E16</font></i>: 
<font color="Maroon">c<sub>4</sub></font> <a href="yellow_6.html#K3">.</a> <font color="Maroon">c<sub>10</sub></font> <a href="lattice3.html#NR4" target="_self">is_&gt;=_than</a> <font color="Maroon">c<sub>13</sub></font>
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="17_3_2"><b>proof </b></a><div class="add">

<b>let </b><font color="Maroon">c<sub>14</sub></font> be   <a href="struct_0.html#NM1">Element</a> of <font color="Maroon">c<sub>2</sub></font>; <i><font color="Red">:: according to </font></i><a class="ref" href="lattice3.html#D9">LATTICE3:def 9</a><br/>

<b>assume </b><a NAME="E1:17_3_2"/>
<font color="Maroon">c<sub>14</sub></font> <a href="hidden.html#R2">in</a> <font color="Maroon">c<sub>13</sub></font>
 ;<br/>

<b>then consider </b><font color="Maroon">c<sub>15</sub></font> being  <a href="pre_topc.html#V3">open</a> <a href="struct_0.html#NM2">Subset</a> of <font color="Maroon">c<sub>5</sub></font><b> such that </b><br/><a NAME="E3:17_3_2"/><i><font color="Green">E17</font></i>: 
<font color="Maroon">c<sub>14</sub></font> <a href="hidden.html#R1">=</a>  <a href="yellow_0.html#NK4" target="_self">inf</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>4</sub></font> <a href="relset_1.html#K10">.:</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>15</sub></font> <a href="subset_1.html#K8">/\</a> the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">c<sub>3</sub></font></span>)</span></span>)</span>
 <b>and </b><br/><a NAME="E4:17_3_2"/><i><font color="Green">E18</font></i>: 
<font color="Maroon">c<sub>11</sub></font> <a href="hidden.html#R2">in</a> <font color="Maroon">c<sub>15</sub></font>
 ;<br/>
<a NAME="E5:17_3_2"/><i><font color="Green">E19</font></i>: 
 <a href="yellow_0.html#R2">ex_inf_of</a> <font color="Maroon">c<sub>4</sub></font> <a href="relset_1.html#K10">.:</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>15</sub></font> <a href="subset_1.html#K8">/\</a> the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">c<sub>3</sub></font></span>)</span>,<font color="Maroon">c<sub>2</sub></font>
 
<b>by </b><i><a class="ref" href="yellow_0.html#T17">YELLOW_0:17</a></i>;<br/>
<a NAME="E6:17_3_2"/>
<font color="Maroon">c<sub>11</sub></font> <a href="hidden.html#R2">in</a> <font color="Maroon">c<sub>15</sub></font> <a href="subset_1.html#K8">/\</a> the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">c<sub>3</sub></font>
 
<b>by </b><i><a class="txt" href="waybel25.html#E4:17_3_2"><i><font color="Green">E18</font></i></a>, <a class="ref" href="xboole_0.html#D3">XBOOLE_0:def 3</a></i>;<br/>
<a NAME="E7:17_3_2"/><b>then </b>
<font color="Maroon">c<sub>4</sub></font> <a href="yellow_6.html#K3">.</a> <font color="Maroon">c<sub>10</sub></font> <a href="hidden.html#R2">in</a> <font color="Maroon">c<sub>4</sub></font> <a href="relset_1.html#K10">.:</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>15</sub></font> <a href="subset_1.html#K8">/\</a> the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">c<sub>3</sub></font></span>)</span>
 
<b>by </b><i><a class="ref" href="funct_2.html#T43">FUNCT_2:43</a></i>;<br/>
<b>hence </b><a NAME="E8:17_3_2"/>
<font color="Maroon">c<sub>14</sub></font> <a href="orders_2.html#R3">&lt;=</a> <font color="Maroon">c<sub>4</sub></font> <a href="yellow_6.html#K3">.</a> <font color="Maroon">c<sub>10</sub></font>
 <b>by </b><i><a class="txt" href="waybel25.html#E3:17_3_2"><i><font color="Green">E17</font></i></a>, <a class="txt" href="waybel25.html#E5:17_3_2"><i><font color="Green">E19</font></i></a>, <a class="ref" href="yellow_4.html#T2">YELLOW_4:2</a></i>;<br/>


</div><b>end;</b></div>
<a NAME="E7:17_3"/><i><font color="Green">E17</font></i>: 
for <font color="Olive">b<sub>1</sub></font> being  <a href="struct_0.html#NM1">Element</a> of <font color="Maroon">c<sub>2</sub></font> st <font color="Olive">b<sub>1</sub></font> <a href="lattice3.html#NR4" target="_self">is_&gt;=_than</a> <font color="Maroon">c<sub>13</sub></font> holds <br/><font color="Maroon">c<sub>4</sub></font> <a href="yellow_6.html#K3">.</a> <font color="Maroon">c<sub>10</sub></font> <a href="orders_2.html#R3">&lt;=</a> <font color="Olive">b<sub>1</sub></font>
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="17_3_3"><b>proof </b></a><div class="add">

<b>let </b><font color="Maroon">c<sub>14</sub></font> be   <a href="struct_0.html#NM1">Element</a> of <font color="Maroon">c<sub>2</sub></font>;<br/>

<b>assume </b><a NAME="E1:17_3_3"/><i><font color="Green">E18</font></i>: 
for <font color="Olive">b<sub>1</sub></font> being  <a href="struct_0.html#NM1">Element</a> of <font color="Maroon">c<sub>2</sub></font> st <font color="Olive">b<sub>1</sub></font> <a href="hidden.html#R2">in</a> <font color="Maroon">c<sub>13</sub></font> holds <br/><font color="Olive">b<sub>1</sub></font> <a href="orders_2.html#R3">&lt;=</a> <font color="Maroon">c<sub>14</sub></font>
 ; <i><font color="Red">:: according to </font></i><a class="ref" href="lattice3.html#D9">LATTICE3:def 9</a><br/>

<a NAME="E2:17_3_3"/><i><font color="Green">E19</font></i>: 
for <font color="Olive">b<sub>1</sub></font> being <a href="pre_topc.html#V3">open</a> <a href="struct_0.html#NM2">Subset</a> of <font color="Maroon">c<sub>3</sub></font> st <font color="Maroon">c<sub>10</sub></font> <a href="hidden.html#R2">in</a> <font color="Olive">b<sub>1</sub></font> holds <br/> <a href="yellow_0.html#NK4" target="_self">inf</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>4</sub></font> <a href="relset_1.html#K10">.:</a> <font color="Olive">b<sub>1</sub></font></span>)</span> <a href="orders_2.html#R3">&lt;=</a> <font color="Maroon">c<sub>14</sub></font>
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="17_3_3_1"><b>proof </b></a><div class="add">

<b>let </b><font color="Maroon">c<sub>15</sub></font> be  <a href="pre_topc.html#V3">open</a> <a href="struct_0.html#NM2">Subset</a> of <font color="Maroon">c<sub>3</sub></font>;<br/>

<b>assume </b><a NAME="E1:17_3_3_1"/><i><font color="Green">E20</font></i>: 
<font color="Maroon">c<sub>10</sub></font> <a href="hidden.html#R2">in</a> <font color="Maroon">c<sub>15</sub></font>
 ;<br/>

<a NAME="E2:17_3_3_1"/>
<font color="Maroon">c<sub>15</sub></font> <a href="hidden.html#R2">in</a> the <a href="pre_topc.html#U1">topology</a> of <font color="Maroon">c<sub>3</sub></font>
 
<b>by </b><i><a class="ref" href="pre_topc.html#D5">PRE_TOPC:def 5</a></i>;<br/>
<b>then consider </b><font color="Maroon">c<sub>16</sub></font> being   <a href="struct_0.html#NM2">Subset</a> of <font color="Maroon">c<sub>5</sub></font><b> such that </b><br/><a NAME="E4:17_3_3_1"/><i><font color="Green">E21</font></i>: 
<font color="Maroon">c<sub>16</sub></font> <a href="hidden.html#R2">in</a> the <a href="pre_topc.html#U1">topology</a> of <font color="Maroon">c<sub>5</sub></font>
 <b>and </b><br/><a NAME="E5:17_3_3_1"/><i><font color="Green">E22</font></i>: 
<font color="Maroon">c<sub>15</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>16</sub></font> <a href="subset_1.html#K9">/\</a> <span class="p1">(<span class="default"><a href="pre_topc.html#K2">[#]</a> <font color="Maroon">c<sub>3</sub></font></span>)</span>
 <b>by </b><i><a class="txt" href="waybel25.html#E2:17"><i><font color="Green">E10</font></i></a>, <a class="ref" href="pre_topc.html#D9">PRE_TOPC:def 9</a></i>;<br/>
<b>reconsider </b><font color="Maroon">c<sub>17</sub></font> = <font color="Maroon">c<sub>16</sub></font> as  <a href="pre_topc.html#V3">open</a> <a href="struct_0.html#NM2">Subset</a> of <font color="Maroon">c<sub>5</sub></font> <b>by </b><i><a class="txt" href="waybel25.html#E4:17_3_3_1"><i><font color="Green">E21</font></i></a>, <a class="ref" href="pre_topc.html#D5">PRE_TOPC:def 5</a></i>;<br/>
<a NAME="E7:17_3_3_1"/><i><font color="Green">E23</font></i>: 
<font color="Maroon">c<sub>11</sub></font> <a href="hidden.html#R2">in</a> <font color="Maroon">c<sub>17</sub></font>
 
<b>by </b><i><a class="txt" href="waybel25.html#E1:17_3_3_1"><i><font color="Green">E20</font></i></a>, <a class="txt" href="waybel25.html#E5:17_3_3_1"><i><font color="Green">E22</font></i></a>, <a class="ref" href="xboole_0.html#D3">XBOOLE_0:def 3</a></i>;<br/>
<a NAME="E8:17_3_3_1"/><i><font color="Green">E24</font></i>: 
<font color="Maroon">c<sub>15</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>17</sub></font> <a href="subset_1.html#K8">/\</a> the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">c<sub>3</sub></font>
 
<b>by </b><i><a class="txt" href="waybel25.html#E5:17_3_3_1"><i><font color="Green">E22</font></i></a></i>;<br/>
<a NAME="E9:17_3_3_1"/>
 <a href="yellow_0.html#NK4" target="_self">inf</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>4</sub></font> <a href="relset_1.html#K10">.:</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>17</sub></font> <a href="subset_1.html#K8">/\</a> the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">c<sub>3</sub></font></span>)</span></span>)</span> <a href="hidden.html#R2">in</a> <font color="Maroon">c<sub>13</sub></font>
 
<b>by </b><i><a class="txt" href="waybel25.html#E7:17_3_3_1"><i><font color="Green">E23</font></i></a></i>;<br/>
<b>hence </b><a NAME="E10:17_3_3_1"/>
 <a href="yellow_0.html#NK4" target="_self">inf</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>4</sub></font> <a href="relset_1.html#K10">.:</a> <font color="Maroon">c<sub>15</sub></font></span>)</span> <a href="orders_2.html#R3">&lt;=</a> <font color="Maroon">c<sub>14</sub></font>
 <b>by </b><i><a class="txt" href="waybel25.html#E1:17_3_3"><i><font color="Green">E18</font></i></a>, <a class="txt" href="waybel25.html#E8:17_3_3_1"><i><font color="Green">E24</font></i></a></i>;<br/>


</div><b>end;</b></div>
<a NAME="E3:17_3_3"/><i><font color="Green">E20</font></i>: 
<font color="Maroon">c<sub>14</sub></font> <a href="lattice3.html#NR4" target="_self">is_&gt;=_than</a>  <a href="waybel_3.html#K1">waybelow</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>4</sub></font> <a href="yellow_6.html#K3">.</a> <font color="Maroon">c<sub>10</sub></font></span>)</span>
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="17_3_3_2"><b>proof </b></a><div class="add">

<b>let </b><font color="Maroon">c<sub>15</sub></font> be   <a href="struct_0.html#NM1">Element</a> of <font color="Maroon">c<sub>2</sub></font>; <i><font color="Red">:: according to </font></i><a class="ref" href="lattice3.html#D9">LATTICE3:def 9</a><br/>

<b>assume </b><a NAME="E1:17_3_3_2"/>
<font color="Maroon">c<sub>15</sub></font> <a href="hidden.html#R2">in</a>  <a href="waybel_3.html#K1">waybelow</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>4</sub></font> <a href="yellow_6.html#K3">.</a> <font color="Maroon">c<sub>10</sub></font></span>)</span>
 ;<br/>

<a NAME="E2:17_3_3_2"/><b>then </b>
<font color="Maroon">c<sub>15</sub></font> <a href="waybel_3.html#NR2" target="_self">&lt;&lt;</a> <font color="Maroon">c<sub>4</sub></font> <a href="yellow_6.html#K3">.</a> <font color="Maroon">c<sub>10</sub></font>
 
<b>by </b><i><a class="ref" href="waybel_3.html#T7">WAYBEL_3:7</a></i>;<br/>
<a NAME="E3:17_3_3_2"/><b>then </b>
<font color="Maroon">c<sub>4</sub></font> <a href="yellow_6.html#K3">.</a> <font color="Maroon">c<sub>10</sub></font> <a href="hidden.html#R2">in</a>  <a href="waybel_3.html#K2">wayabove</a> <font color="Maroon">c<sub>15</sub></font>
 
<b>by </b><i><a class="ref" href="waybel_3.html#T8">WAYBEL_3:8</a></i>;<br/>
<a NAME="E4:17_3_3_2"/><b>then </b><i><font color="Green">E21</font></i>: 
<font color="Maroon">c<sub>10</sub></font> <a href="hidden.html#R2">in</a> <font color="Maroon">c<sub>4</sub></font> <a href="relset_1.html#K11">"</a> <span class="p1">(<span class="default"><a href="waybel_3.html#K2">wayabove</a> <font color="Maroon">c<sub>15</sub></font></span>)</span>
 
<b>by </b><i><a class="ref" href="funct_2.html#T46">FUNCT_2:46</a></i>;<br/>
<a NAME="E5:17_3_3_2"/>
 <a href="waybel_3.html#K2">wayabove</a> <font color="Maroon">c<sub>15</sub></font> is <a href="pre_topc.html#V3">open</a>
 
<b>by </b><i><a class="ref" href="waybel11.html#T36">WAYBEL11:36</a></i>;<br/>
<a NAME="E6:17_3_3_2"/><b>then </b>
<font color="Maroon">c<sub>4</sub></font> <a href="relset_1.html#K11">"</a> <span class="p1">(<span class="default"><a href="waybel_3.html#K2">wayabove</a> <font color="Maroon">c<sub>15</sub></font></span>)</span> is <a href="pre_topc.html#V3">open</a>
 
<b>by </b><i><a class="txt" href="waybel25.html#E1:17"><i><font color="Green">E9</font></i></a>, <a class="ref" href="tops_2.html#T55">TOPS_2:55</a></i>;<br/>
<a NAME="E7:17_3_3_2"/><b>then </b><i><font color="Green">E22</font></i>: 
 <a href="yellow_0.html#NK4" target="_self">inf</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>4</sub></font> <a href="relset_1.html#K10">.:</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>4</sub></font> <a href="relset_1.html#K11">"</a> <span class="p3">(<span class="default"><a href="waybel_3.html#K2">wayabove</a> <font color="Maroon">c<sub>15</sub></font></span>)</span></span>)</span></span>)</span> <a href="orders_2.html#R3">&lt;=</a> <font color="Maroon">c<sub>14</sub></font>
 
<b>by </b><i><a class="txt" href="waybel25.html#E2:17_3_3"><i><font color="Green">E19</font></i></a>, <a class="txt" href="waybel25.html#E4:17_3_3_2"><i><font color="Green">E21</font></i></a></i>;<br/>
<a NAME="E8:17_3_3_2"/><i><font color="Green">E23</font></i>: 
(  <a href="yellow_0.html#R2">ex_inf_of</a>  <a href="waybel_3.html#K2">wayabove</a> <font color="Maroon">c<sub>15</sub></font>,<font color="Maroon">c<sub>2</sub></font> &amp;  <a href="yellow_0.html#R2">ex_inf_of</a> <font color="Maroon">c<sub>4</sub></font> <a href="relset_1.html#K10">.:</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>4</sub></font> <a href="relset_1.html#K11">"</a> <span class="p2">(<span class="default"><a href="waybel_3.html#K2">wayabove</a> <font color="Maroon">c<sub>15</sub></font></span>)</span></span>)</span>,<font color="Maroon">c<sub>2</sub></font> )
 
<b>by </b><i><a class="ref" href="yellow_0.html#T17">YELLOW_0:17</a></i>;<br/>
<a NAME="E9:17_3_3_2"/>
<font color="Maroon">c<sub>4</sub></font> <a href="relset_1.html#K10">.:</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>4</sub></font> <a href="relset_1.html#K11">"</a> <span class="p2">(<span class="default"><a href="waybel_3.html#K2">wayabove</a> <font color="Maroon">c<sub>15</sub></font></span>)</span></span>)</span> <a href="tarski.html#R1">c=</a>  <a href="waybel_3.html#K2">wayabove</a> <font color="Maroon">c<sub>15</sub></font>
 
<b>by </b><i><a class="ref" href="funct_1.html#T145">FUNCT_1:145</a></i>;<br/>
<a NAME="E10:17_3_3_2"/><b>then </b><i><font color="Green">E24</font></i>: 
 <a href="yellow_0.html#NK4" target="_self">inf</a> <span class="p1">(<span class="default"><a href="waybel_3.html#K2">wayabove</a> <font color="Maroon">c<sub>15</sub></font></span>)</span> <a href="orders_2.html#R3">&lt;=</a>  <a href="yellow_0.html#NK4" target="_self">inf</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>4</sub></font> <a href="relset_1.html#K10">.:</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>4</sub></font> <a href="relset_1.html#K11">"</a> <span class="p3">(<span class="default"><a href="waybel_3.html#K2">wayabove</a> <font color="Maroon">c<sub>15</sub></font></span>)</span></span>)</span></span>)</span>
 
<b>by </b><i><a class="txt" href="waybel25.html#E8:17_3_3_2"><i><font color="Green">E23</font></i></a>, <a class="ref" href="yellow_0.html#T35">YELLOW_0:35</a></i>;<br/>
<a NAME="E11:17_3_3_2"/>
<font color="Maroon">c<sub>15</sub></font> <a href="orders_2.html#R3">&lt;=</a>  <a href="yellow_0.html#NK4" target="_self">inf</a> <span class="p1">(<span class="default"><a href="waybel_3.html#K2">wayabove</a> <font color="Maroon">c<sub>15</sub></font></span>)</span>
 
<b>by </b><i><a class="ref" href="waybel14.html#T9">WAYBEL14:9</a></i>;<br/>
<a NAME="E12:17_3_3_2"/><b>then </b>
<font color="Maroon">c<sub>15</sub></font> <a href="orders_2.html#R3">&lt;=</a>  <a href="yellow_0.html#NK4" target="_self">inf</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>4</sub></font> <a href="relset_1.html#K10">.:</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>4</sub></font> <a href="relset_1.html#K11">"</a> <span class="p3">(<span class="default"><a href="waybel_3.html#K2">wayabove</a> <font color="Maroon">c<sub>15</sub></font></span>)</span></span>)</span></span>)</span>
 
<b>by </b><i><a class="txt" href="waybel25.html#E10:17_3_3_2"><i><font color="Green">E24</font></i></a>, <a class="ref" href="orders_2.html#T26">ORDERS_2:26</a></i>;<br/>
<b>hence </b><a NAME="E13:17_3_3_2"/>
<font color="Maroon">c<sub>15</sub></font> <a href="orders_2.html#R3">&lt;=</a> <font color="Maroon">c<sub>14</sub></font>
 <b>by </b><i><a class="txt" href="waybel25.html#E7:17_3_3_2"><i><font color="Green">E22</font></i></a>, <a class="ref" href="orders_2.html#T26">ORDERS_2:26</a></i>;<br/>


</div><b>end;</b></div>
<a NAME="E4:17_3_3"/>
<font color="Maroon">c<sub>4</sub></font> <a href="yellow_6.html#K3">.</a> <font color="Maroon">c<sub>10</sub></font> <a href="hidden.html#R1">=</a>  <a href="yellow_0.html#NK3" target="_self">sup</a> <span class="p1">(<span class="default"><a href="waybel_3.html#K1">waybelow</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>4</sub></font> <a href="yellow_6.html#K3">.</a> <font color="Maroon">c<sub>10</sub></font></span>)</span></span>)</span>
 
<b>by </b><i><a class="ref" href="waybel_3.html#D5">WAYBEL_3:def 5</a></i>;<br/>
<b>hence </b><a NAME="E5:17_3_3"/>
<font color="Maroon">c<sub>4</sub></font> <a href="yellow_6.html#K3">.</a> <font color="Maroon">c<sub>10</sub></font> <a href="orders_2.html#R3">&lt;=</a> <font color="Maroon">c<sub>14</sub></font>
 <b>by </b><i><a class="txt" href="waybel25.html#E3:17_3_3"><i><font color="Green">E20</font></i></a>, <a class="ref" href="yellow_0.html#T32">YELLOW_0:32</a></i>;<br/>


</div><b>end;</b></div>
<b>thus </b><span class="p1">(<span class="default"><font color="Maroon">c<sub>7</sub></font> <a href="partfun1.html#K2">|</a> the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">c<sub>3</sub></font></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">c<sub>9</sub></font> = 
<font color="Maroon">c<sub>7</sub></font> <a href="yellow_6.html#K3">.</a> <font color="Maroon">c<sub>11</sub></font>
<b>by </b><i><a class="ref" href="funct_1.html#T72">FUNCT_1:72</a></i>
<br/>.= 
<font color="Maroon">H<sub>1</sub></font>(<font color="Maroon">c<sub>11</sub></font>)
<b>by </b><i><a class="txt" href="waybel25.html#E4:17"><i><font color="Green">E11</font></i></a></i>
<br/>.= 
<font color="Maroon">c<sub>4</sub></font> <a href="funct_1.html#K1">.</a> <font color="Maroon">c<sub>9</sub></font>
<b>by </b><i><a class="txt" href="waybel25.html#E6:17_3"><i><font color="Green">E16</font></i></a>, <a class="txt" href="waybel25.html#E7:17_3"><i><font color="Green">E17</font></i></a>, <a class="ref" href="yellow_0.html#T30">YELLOW_0:30</a></i>
;<br/>


</div><b>end;</b></div>
<b>hence </b><a NAME="E12:17"/>
<font color="Maroon">c<sub>7</sub></font> <a href="partfun1.html#K2">|</a> the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">c<sub>3</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>4</sub></font>
 <b>by </b><i><a class="txt" href="waybel25.html#E9:17"><i><font color="Green">E13</font></i></a>, <a class="txt" href="waybel25.html#E10:17"><i><font color="Green">E14</font></i></a>, <a class="ref" href="funct_1.html#T9">FUNCT_1:9</a></i>;<br/>


</div>
