<?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_0.html#NM8">LATTICE</a>;<br/><b>let </b><font color="Maroon">c<sub>2</sub></font> be  <a href="tex_2.html#V1">proper</a> <a href="waybel_0.html#NM4">Filter</a> of <span class="p1">(<span class="default"><a href="yellow_1.html#K3">BoolePoset</a> <span class="p2">(<span class="default"><a href="pre_topc.html#K2">[#]</a> <font color="Maroon">c<sub>1</sub></font></span>)</span></span>)</span>;<br/><b>let </b><font color="Maroon">c<sub>3</sub></font> be   <a href="struct_0.html#NM2">Subset</a> of <font color="Maroon">c<sub>1</sub></font>;<br/>





<b>assume </b><a NAME="E1:25"/><i><font color="Green">E16</font></i>: 
<font color="Maroon">c<sub>3</sub></font> <a href="hidden.html#R2">in</a> <font color="Maroon">c<sub>2</sub></font>
 ;<br/>

<b>let </b><font color="Maroon">c<sub>4</sub></font> be   <a href="struct_0.html#NM1">Element</a> of <span class="p1">(<span class="default"><a href="yellow19.html#K3">a_net</a> <font color="Maroon">c<sub>2</sub></font></span>)</span>;<br/>

<b>assume </b><a NAME="E2:25"/><i><font color="Green">E17</font></i>: 
<font color="Maroon">c<sub>4</sub></font> <a href="mcart_1.html#K2">`2</a>  <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>3</sub></font>
 ;<br/>

<i><font color="Green">E18</font></i>:  <a href="waybel_9.html#K2">inf</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="yellow19.html#K3">a_net</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="waybel_9.html#K6">|</a> <font color="Maroon">c<sub>4</sub></font></span>)</span> = 
 <a href="yellow_2.html#NK7" target="_self">Inf</a> 
<b>by </b><i><a class="ref" href="waybel_9.html#D2">WAYBEL_9:def 2</a></i>
<br/>.= 
 <a href="yellow_0.html#K2">"/\"</a> <span class="p1">(<span class="default"><a href="relset_1.html#K5">rng</a> the <a href="waybel_0.html#U1">mapping</a> of <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="yellow19.html#K3">a_net</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="waybel_9.html#K6">|</a> <font color="Maroon">c<sub>4</sub></font></span>)</span></span>)</span>,<font color="Maroon">c<sub>1</sub></font>
<b>by </b><i><a class="ref" href="yellow_2.html#D6">YELLOW_2:def 6</a></i>
;<br/>
<a NAME="E4:25"/>
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>  <a href="relset_1.html#K5">rng</a> the <a href="waybel_0.html#U1">mapping</a> of <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="yellow19.html#K3">a_net</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="waybel_9.html#K6">|</a> <font color="Maroon">c<sub>4</sub></font></span>)</span> holds <br/><font color="Olive">b<sub>1</sub></font> <a href="hidden.html#R2">in</a> <font color="Maroon">c<sub>3</sub></font>
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="25_2"><b>proof </b></a><div class="add">

<b>let </b><font color="Maroon">c<sub>5</sub></font> be    <a href="hidden.html#M1">set</a> ;<br/>

<b>assume </b><a NAME="E1:25_2"/>
<font color="Maroon">c<sub>5</sub></font> <a href="hidden.html#R2">in</a>  <a href="relset_1.html#K5">rng</a> the <a href="waybel_0.html#U1">mapping</a> of <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="yellow19.html#K3">a_net</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="waybel_9.html#K6">|</a> <font color="Maroon">c<sub>4</sub></font></span>)</span>
 ;<br/>

<a NAME="E2:25_2"/><b>then </b>
<font color="Maroon">c<sub>5</sub></font> <a href="hidden.html#R2">in</a> <span class="p1">{<span class="default"> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="yellow19.html#K3">a_net</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="waybel_9.html#K6">|</a> <font color="Maroon">c<sub>4</sub></font></span>)</span> <a href="waybel_0.html#K2">.</a> <font color="Olive">b<sub>1</sub></font></span>)</span> where B is    <a href="subset_1.html#M1">Element</a> of the <a href="struct_0.html#U1">carrier</a> of <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="yellow19.html#K3">a_net</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="waybel_9.html#K6">|</a> <font color="Maroon">c<sub>4</sub></font></span>)</span> : verum </span>}</span> 
 
<b>by </b><i><a class="ref" href="waybel11.html#T19">WAYBEL11:19</a></i>;<br/>
<b>then consider </b><font color="Maroon">c<sub>6</sub></font> being   <a href="struct_0.html#NM1">Element</a> of <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="yellow19.html#K3">a_net</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="waybel_9.html#K6">|</a> <font color="Maroon">c<sub>4</sub></font></span>)</span><b> such that </b><br/><a NAME="E4:25_2"/><i><font color="Green">E19</font></i>: 
<font color="Maroon">c<sub>5</sub></font> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="yellow19.html#K3">a_net</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="waybel_9.html#K6">|</a> <font color="Maroon">c<sub>4</sub></font></span>)</span> <a href="waybel_0.html#K2">.</a> <font color="Maroon">c<sub>6</sub></font>
 ;<br/>
<a NAME="E5:25_2"/><i><font color="Green">E20</font></i>: 
the <a href="struct_0.html#U1">carrier</a> of <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="yellow19.html#K3">a_net</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="waybel_9.html#K6">|</a> <font color="Maroon">c<sub>4</sub></font></span>)</span> <a href="tarski.html#R1">c=</a> the <a href="struct_0.html#U1">carrier</a> of <span class="p1">(<span class="default"><a href="yellow19.html#K3">a_net</a> <font color="Maroon">c<sub>2</sub></font></span>)</span>
 
<b>by </b><i><a class="ref" href="waybel_9.html#T13">WAYBEL_9:13</a></i>;<br/>
<a NAME="E6:25_2"/><b>then </b><i><font color="Green">E21</font></i>: 
<font color="Maroon">c<sub>6</sub></font> <a href="hidden.html#R2">in</a> the <a href="struct_0.html#U1">carrier</a> of <span class="p1">(<span class="default"><a href="yellow19.html#K3">a_net</a> <font color="Maroon">c<sub>2</sub></font></span>)</span>
 
<b>by </b><i><a class="ref" href="tarski.html#D3">TARSKI:def 3</a></i>;<br/>
<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#NM1">Element</a> of <span class="p1">(<span class="default"><a href="yellow19.html#K3">a_net</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> <b>by </b><i><a class="txt" href="waybel33.html#E5:25_2"><i><font color="Green">E20</font></i></a>, <a class="ref" href="tarski.html#D3">TARSKI:def 3</a></i>;<br/>
<a NAME="E8:25_2"/>
<font color="Maroon">c<sub>6</sub></font> <a href="hidden.html#R2">in</a> <span class="p1">{<span class="default"> <span class="p2"><a href="domain_1.html#K1">[</a><span class="default"><font color="Olive">b<sub>1</sub></font>,<font color="Olive">b<sub>2</sub></font></span><a href="domain_1.html#K1">]</a></span> where B is   <a href="struct_0.html#NM1">Element</a> of <font color="Maroon">c<sub>1</sub></font>, B is    <a href="struct_0.html#M1">Element</a> of <font color="Maroon">c<sub>2</sub></font> : <font color="Olive">b<sub>1</sub></font> <a href="hidden.html#R2">in</a> <font color="Olive">b<sub>2</sub></font> </span>}</span> 
 
<b>by </b><i><a class="txt" href="waybel33.html#E6:25_2"><i><font color="Green">E21</font></i></a>, <a class="ref" href="yellow19.html#D4">YELLOW19:def 4</a></i>;<br/>
<b>then consider </b><font color="Maroon">c<sub>8</sub></font> being   <a href="struct_0.html#NM1">Element</a> of <font color="Maroon">c<sub>1</sub></font>, <font color="Maroon">c<sub>9</sub></font> being    <a href="struct_0.html#M1">Element</a> of <font color="Maroon">c<sub>2</sub></font><b> such that </b><br/><a NAME="E10:25_2"/><i><font color="Green">E22</font></i>: 
( <font color="Maroon">c<sub>6</sub></font> <a href="hidden.html#R1">=</a> <span class="p1"><a href="domain_1.html#K1">[</a><span class="default"><font color="Maroon">c<sub>8</sub></font>,<font color="Maroon">c<sub>9</sub></font></span><a href="domain_1.html#K1">]</a></span> &amp; <font color="Maroon">c<sub>8</sub></font> <a href="hidden.html#R2">in</a> <font color="Maroon">c<sub>9</sub></font> )
 ;<br/>
<a NAME="E11:25_2"/><i><font color="Green">E23</font></i>: 
( <font color="Maroon">c<sub>6</sub></font> <a href="mcart_1.html#K1">`1</a>  <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>8</sub></font> &amp; <font color="Maroon">c<sub>6</sub></font> <a href="mcart_1.html#K2">`2</a>  <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>9</sub></font> )
 
<b>by </b><i><a class="txt" href="waybel33.html#E10:25_2"><i><font color="Green">E22</font></i></a>, <a class="ref" href="mcart_1.html#D1">MCART_1:def 1</a>, <a class="ref" href="mcart_1.html#D2">MCART_1:def 2</a></i>;<br/>
<a NAME="E12:25_2"/>
<font color="Maroon">c<sub>6</sub></font> <a href="hidden.html#R2">in</a> the <a href="struct_0.html#U1">carrier</a> of <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="yellow19.html#K3">a_net</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="waybel_9.html#K6">|</a> <font color="Maroon">c<sub>4</sub></font></span>)</span>
 
;<br/>
<a NAME="E13:25_2"/><b>then </b>
<font color="Maroon">c<sub>6</sub></font> <a href="hidden.html#R2">in</a> <span class="p1">{<span class="default"> <font color="Olive">b<sub>1</sub></font> where B is   <a href="struct_0.html#NM1">Element</a> of <span class="p1">(<span class="default"><a href="yellow19.html#K3">a_net</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> : <font color="Maroon">c<sub>4</sub></font> <a href="orders_2.html#R3">&lt;=</a> <font color="Olive">b<sub>1</sub></font> </span>}</span> 
 
<b>by </b><i><a class="ref" href="waybel_9.html#T12">WAYBEL_9:12</a></i>;<br/>
<b>then consider </b><font color="Maroon">c<sub>10</sub></font> being   <a href="struct_0.html#NM1">Element</a> of <span class="p1">(<span class="default"><a href="yellow19.html#K3">a_net</a> <font color="Maroon">c<sub>2</sub></font></span>)</span><b> such that </b><br/><a NAME="E15:25_2"/><i><font color="Green">E24</font></i>: 
( <font color="Maroon">c<sub>6</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>10</sub></font> &amp; <font color="Maroon">c<sub>4</sub></font> <a href="orders_2.html#R3">&lt;=</a> <font color="Maroon">c<sub>10</sub></font> )
 ;<br/>
<a NAME="E16:25_2"/><i><font color="Green">E25</font></i>: 
<font color="Maroon">c<sub>7</sub></font> <a href="mcart_1.html#K2">`2</a>  <a href="tarski.html#R1">c=</a> <font color="Maroon">c<sub>3</sub></font>
 
<b>by </b><i><a class="txt" href="waybel33.html#E2:25"><i><font color="Green">E17</font></i></a>, <a class="txt" href="waybel33.html#E15:25_2"><i><font color="Green">E24</font></i></a>, <a class="ref" href="yellow19.html#D4">YELLOW19:def 4</a></i>;<br/>
<b>reconsider </b><font color="Maroon">c<sub>11</sub></font> = <font color="Maroon">c<sub>6</sub></font> as   <a href="struct_0.html#NM1">Element</a> of <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="yellow19.html#K3">a_net</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="waybel_9.html#K6">|</a> <font color="Maroon">c<sub>4</sub></font></span>)</span> ;<br/>
<a NAME="E18:25_2"/>
<span class="p1">(<span class="default"><a href="yellow19.html#K3">a_net</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="waybel_0.html#K2">.</a> <font color="Maroon">c<sub>7</sub></font> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="yellow19.html#K3">a_net</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="waybel_9.html#K6">|</a> <font color="Maroon">c<sub>4</sub></font></span>)</span> <a href="waybel_0.html#K2">.</a> <font color="Maroon">c<sub>11</sub></font>
 
<b>by </b><i><a class="ref" href="waybel_9.html#T16">WAYBEL_9:16</a></i>;<br/>
<a NAME="E19:25_2"/><b>then </b>
<font color="Maroon">c<sub>5</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>7</sub></font> <a href="mcart_1.html#K1">`1</a> 
 
<b>by </b><i><a class="txt" href="waybel33.html#E4:25_2"><i><font color="Green">E19</font></i></a>, <a class="ref" href="yellow19.html#D4">YELLOW19:def 4</a></i>;<br/>
<b>hence </b><a NAME="E20:25_2"/>
<font color="Maroon">c<sub>5</sub></font> <a href="hidden.html#R2">in</a> <font color="Maroon">c<sub>3</sub></font>
 <b>by </b><i><a class="txt" href="waybel33.html#E10:25_2"><i><font color="Green">E22</font></i></a>, <a class="txt" href="waybel33.html#E11:25_2"><i><font color="Green">E23</font></i></a>, <a class="txt" href="waybel33.html#E16:25_2"><i><font color="Green">E25</font></i></a></i>;<br/>


</div><b>end;</b></div>
<a NAME="E5:25"/><b>then </b><i><font color="Green">E19</font></i>: 
 <a href="relset_1.html#K5">rng</a> the <a href="waybel_0.html#U1">mapping</a> of <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="yellow19.html#K3">a_net</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="waybel_9.html#K6">|</a> <font color="Maroon">c<sub>4</sub></font></span>)</span> <a href="tarski.html#R1">c=</a> <font color="Maroon">c<sub>3</sub></font>
 
<b>by </b><i><a class="ref" href="tarski.html#D3">TARSKI:def 3</a></i>;<br/>
<a NAME="E6:25"/>
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>3</sub></font> holds <br/><font color="Olive">b<sub>1</sub></font> <a href="hidden.html#R2">in</a>  <a href="relset_1.html#K5">rng</a> the <a href="waybel_0.html#U1">mapping</a> of <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="yellow19.html#K3">a_net</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="waybel_9.html#K6">|</a> <font color="Maroon">c<sub>4</sub></font></span>)</span>
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="25_3"><b>proof </b></a><div class="add">

<b>let </b><font color="Maroon">c<sub>5</sub></font> be    <a href="hidden.html#M1">set</a> ;<br/>

<b>assume </b><a NAME="E1:25_3"/><i><font color="Green">E20</font></i>: 
<font color="Maroon">c<sub>5</sub></font> <a href="hidden.html#R2">in</a> <font color="Maroon">c<sub>3</sub></font>
 ;<br/>

<b>then reconsider </b><font color="Maroon">c<sub>6</sub></font> = <font color="Maroon">c<sub>5</sub></font> as   <a href="struct_0.html#NM1">Element</a> of <font color="Maroon">c<sub>1</sub></font> ;<br/>
<b>reconsider </b><font color="Maroon">c<sub>7</sub></font> = <font color="Maroon">c<sub>3</sub></font> as    <a href="struct_0.html#M1">Element</a> of <font color="Maroon">c<sub>2</sub></font> <b>by </b><i><a class="txt" href="waybel33.html#E1:25"><i><font color="Green">E16</font></i></a></i>;<br/>
<a NAME="E4:25_3"/>
<span class="p1"><a href="domain_1.html#K1">[</a><span class="default"><font color="Maroon">c<sub>6</sub></font>,<font color="Maroon">c<sub>7</sub></font></span><a href="domain_1.html#K1">]</a></span> <a href="hidden.html#R2">in</a> <span class="p1">{<span class="default"> <span class="p2"><a href="domain_1.html#K1">[</a><span class="default"><font color="Olive">b<sub>1</sub></font>,<font color="Olive">b<sub>2</sub></font></span><a href="domain_1.html#K1">]</a></span> where B is   <a href="struct_0.html#NM1">Element</a> of <font color="Maroon">c<sub>1</sub></font>, B is    <a href="struct_0.html#M1">Element</a> of <font color="Maroon">c<sub>2</sub></font> : <font color="Olive">b<sub>1</sub></font> <a href="hidden.html#R2">in</a> <font color="Olive">b<sub>2</sub></font> </span>}</span> 
 
<b>by </b><i><a class="txt" href="waybel33.html#E1:25_3"><i><font color="Green">E20</font></i></a></i>;<br/>
<b>then reconsider </b><font color="Maroon">c<sub>8</sub></font> = <span class="p1"><a href="domain_1.html#K1">[</a><span class="default"><font color="Maroon">c<sub>6</sub></font>,<font color="Maroon">c<sub>7</sub></font></span><a href="domain_1.html#K1">]</a></span> as   <a href="struct_0.html#NM1">Element</a> of <span class="p1">(<span class="default"><a href="yellow19.html#K3">a_net</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> <b>by </b><i><a class="ref" href="yellow19.html#D4">YELLOW19:def 4</a></i>;<br/>
<a NAME="E6:25_3"/>
( <font color="Maroon">c<sub>8</sub></font> <a href="mcart_1.html#K2">`2</a>  <a href="tarski.html#R1">c=</a> <font color="Maroon">c<sub>4</sub></font> <a href="mcart_1.html#K2">`2</a>  &amp; <font color="Maroon">c<sub>8</sub></font> <a href="mcart_1.html#K1">`1</a>  <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>6</sub></font> )
 
<b>by </b><i><a class="txt" href="waybel33.html#E2:25"><i><font color="Green">E17</font></i></a>, <a class="ref" href="mcart_1.html#D1">MCART_1:def 1</a>, <a class="ref" href="mcart_1.html#D2">MCART_1:def 2</a></i>;<br/>
<a NAME="E7:25_3"/><b>then </b><i><font color="Green">E21</font></i>: 
( <font color="Maroon">c<sub>6</sub></font> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><a href="yellow19.html#K3">a_net</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="waybel_0.html#K2">.</a> <font color="Maroon">c<sub>8</sub></font> &amp; <font color="Maroon">c<sub>4</sub></font> <a href="orders_2.html#R3">&lt;=</a> <font color="Maroon">c<sub>8</sub></font> )
 
<b>by </b><i><a class="ref" href="yellow19.html#D4">YELLOW19:def 4</a></i>;<br/>
<b>reconsider </b><font color="Maroon">c<sub>9</sub></font> = <font color="Maroon">c<sub>8</sub></font> as   <a href="struct_0.html#NM1">Element</a> of <span class="p1">(<span class="default"><a href="yellow19.html#K3">a_net</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> ;<br/>
<a NAME="E9:25_3"/>
<font color="Maroon">c<sub>9</sub></font> <a href="hidden.html#R2">in</a> <span class="p1">{<span class="default"> <font color="Olive">b<sub>1</sub></font> where B is   <a href="struct_0.html#NM1">Element</a> of <span class="p1">(<span class="default"><a href="yellow19.html#K3">a_net</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> : <font color="Maroon">c<sub>4</sub></font> <a href="orders_2.html#R3">&lt;=</a> <font color="Olive">b<sub>1</sub></font> </span>}</span> 
 
<b>by </b><i><a class="txt" href="waybel33.html#E7:25_3"><i><font color="Green">E21</font></i></a></i>;<br/>
<b>then reconsider </b><font color="Maroon">c<sub>10</sub></font> = <font color="Maroon">c<sub>8</sub></font> as   <a href="struct_0.html#NM1">Element</a> of <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="yellow19.html#K3">a_net</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="waybel_9.html#K6">|</a> <font color="Maroon">c<sub>4</sub></font></span>)</span> <b>by </b><i><a class="ref" href="waybel_9.html#T12">WAYBEL_9:12</a></i>;<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#NM1">Element</a> of <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="yellow19.html#K3">a_net</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="waybel_9.html#K6">|</a> <font color="Maroon">c<sub>4</sub></font></span>)</span> ;<br/>
<a NAME="E12:25_3"/>
<span class="p1">(<span class="default"><a href="yellow19.html#K3">a_net</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="waybel_0.html#K2">.</a> <font color="Maroon">c<sub>9</sub></font> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="yellow19.html#K3">a_net</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="waybel_9.html#K6">|</a> <font color="Maroon">c<sub>4</sub></font></span>)</span> <a href="waybel_0.html#K2">.</a> <font color="Maroon">c<sub>11</sub></font>
 
<b>by </b><i><a class="ref" href="waybel_9.html#T16">WAYBEL_9:16</a></i>;<br/>
<a NAME="E13:25_3"/><b>then </b>
<font color="Maroon">c<sub>6</sub></font> <a href="hidden.html#R2">in</a> <span class="p1">{<span class="default"> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="yellow19.html#K3">a_net</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="waybel_9.html#K6">|</a> <font color="Maroon">c<sub>4</sub></font></span>)</span> <a href="waybel_0.html#K2">.</a> <font color="Olive">b<sub>1</sub></font></span>)</span> where B is    <a href="subset_1.html#M1">Element</a> of the <a href="struct_0.html#U1">carrier</a> of <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="yellow19.html#K3">a_net</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="waybel_9.html#K6">|</a> <font color="Maroon">c<sub>4</sub></font></span>)</span> : verum </span>}</span> 
 
<b>by </b><i><a class="txt" href="waybel33.html#E7:25_3"><i><font color="Green">E21</font></i></a></i>;<br/>
<b>hence </b><a NAME="E14:25_3"/>
<font color="Maroon">c<sub>5</sub></font> <a href="hidden.html#R2">in</a>  <a href="relset_1.html#K5">rng</a> the <a href="waybel_0.html#U1">mapping</a> of <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="yellow19.html#K3">a_net</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="waybel_9.html#K6">|</a> <font color="Maroon">c<sub>4</sub></font></span>)</span>
 <b>by </b><i><a class="ref" href="waybel11.html#T19">WAYBEL11:19</a></i>;<br/>


</div><b>end;</b></div>
<a NAME="E7:25"/><b>then </b>
<font color="Maroon">c<sub>3</sub></font> <a href="tarski.html#R1">c=</a>  <a href="relset_1.html#K5">rng</a> the <a href="waybel_0.html#U1">mapping</a> of <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="yellow19.html#K3">a_net</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="waybel_9.html#K6">|</a> <font color="Maroon">c<sub>4</sub></font></span>)</span>
 
<b>by </b><i><a class="ref" href="tarski.html#D3">TARSKI:def 3</a></i>;<br/>
<b>hence </b><a NAME="E8:25"/>
 <a href="yellow_0.html#NK4" target="_self">inf</a> <font color="Maroon">c<sub>3</sub></font> <a href="hidden.html#R1">=</a>  <a href="waybel_9.html#K2">inf</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="yellow19.html#K3">a_net</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="waybel_9.html#K6">|</a> <font color="Maroon">c<sub>4</sub></font></span>)</span>
 <b>by </b><i><a class="txt" href="waybel33.html#E3:25"><i><font color="Green">E18</font></i></a>, <a class="txt" href="waybel33.html#E5:25"><i><font color="Green">E19</font></i></a>, <a class="ref" href="xboole_0.html#D10">XBOOLE_0:def 10</a></i>;<br/>


</div>
