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

<b>let </b><font color="Maroon">c<sub>1</sub></font> be  <a href="yellow_0.html#V1">lower-bounded</a> <a href="waybel_8.html#V2">algebraic</a> <a href="waybel_0.html#NM7">sup-Semilattice</a>;<br/><b>let </b><font color="Maroon">c<sub>2</sub></font> be   <a href="struct_0.html#NM7">Function</a> of <font color="Maroon">c<sub>1</sub></font>,<span class="p1">(<span class="default"><a href="yellow_1.html#K2">InclPoset</a> <span class="p2">(<span class="default"><a href="waybel_0.html#K7">Ids</a> <span class="p3">(<span class="default"><a href="waybel_8.html#K1">CompactSublatt</a> <font color="Maroon">c<sub>1</sub></font></span>)</span></span>)</span></span>)</span>;<br/>



<b>assume </b><a NAME="E1:17"/><i><font color="Green">E15</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>1</sub></font> holds <font color="Maroon">c<sub>2</sub></font> <a href="funct_2.html#K3">.</a> <font color="Olive">b<sub>1</sub></font> <a href="hidden.html#R1">=</a>  <a href="waybel_8.html#K2">compactbelow</a> <font color="Olive">b<sub>1</sub></font>
 ;<br/>

<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="17_1"><b>now </b></a><div class="add"><b>let </b><font color="Maroon">c<sub>3</sub></font>, <font color="Maroon">c<sub>4</sub></font> be   <a href="struct_0.html#NM1">Element</a> of <font color="Maroon">c<sub>1</sub></font>;<br/><b>assume </b><a NAME="E1:17_1"/>
<font color="Maroon">c<sub>2</sub></font> <a href="funct_2.html#K3">.</a> <font color="Maroon">c<sub>3</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>2</sub></font> <a href="funct_2.html#K3">.</a> <font color="Maroon">c<sub>4</sub></font>
 ;<br/><a NAME="E2:17_1"/><b>then </b>
<font color="Maroon">c<sub>2</sub></font> <a href="funct_2.html#K3">.</a> <font color="Maroon">c<sub>3</sub></font> <a href="hidden.html#R1">=</a>  <a href="waybel_8.html#K2">compactbelow</a> <font color="Maroon">c<sub>4</sub></font>
 <b>by </b><i><a class="txt" href="waybel13.html#E1:17"><i><font color="Green">E15</font></i></a></i>;<br/><a NAME="E3:17_1"/><b>then </b>
 <a href="waybel_8.html#K2">compactbelow</a> <font color="Maroon">c<sub>3</sub></font> <a href="hidden.html#R1">=</a>  <a href="waybel_8.html#K2">compactbelow</a> <font color="Maroon">c<sub>4</sub></font>
 <b>by </b><i><a class="txt" href="waybel13.html#E1:17"><i><font color="Green">E15</font></i></a></i>;<br/><a NAME="E4:17_1"/><b>then </b>
 <a href="yellow_0.html#NK3" target="_self">sup</a> <span class="p1">(<span class="default"><a href="waybel_8.html#K2">compactbelow</a> <font color="Maroon">c<sub>3</sub></font></span>)</span> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>4</sub></font>
 <b>by </b><i><a class="ref" href="waybel_8.html#D3">WAYBEL_8:def 3</a></i>;<br/><b>hence </b><a NAME="E5:17_1"/>
<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="ref" href="waybel_8.html#D3">WAYBEL_8:def 3</a></i>;<br/></div><b>end;</b></div>
<a NAME="E3:17"/><b>then </b><i><font color="Green">E16</font></i>: 
<font color="Maroon">c<sub>2</sub></font> is <a href="funct_1.html#V2">one-to-one</a>
 
<b>by </b><i><a class="ref" href="waybel_1.html#D1">WAYBEL_1:def 1</a></i>;<br/>
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="17_2"><b>now </b></a><div class="add"><b>let </b><font color="Maroon">c<sub>3</sub></font> be    <a href="hidden.html#M1">set</a> ;<br/><b>assume </b><a NAME="E1:17_2"/>
<font color="Maroon">c<sub>3</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="yellow_1.html#K2">InclPoset</a> <span class="p2">(<span class="default"><a href="waybel_0.html#K7">Ids</a> <span class="p3">(<span class="default"><a href="waybel_8.html#K1">CompactSublatt</a> <font color="Maroon">c<sub>1</sub></font></span>)</span></span>)</span></span>)</span>
 ;<br/><b>then reconsider </b><font color="Maroon">c<sub>4</sub></font> = <font color="Maroon">c<sub>3</sub></font> as   <a href="waybel_0.html#NM3">Ideal</a> of <span class="p1">(<span class="default"><a href="waybel_8.html#K1">CompactSublatt</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <b>by </b><i><a class="ref" href="yellow_2.html#T43">YELLOW_2:43</a></i>;<br/><b>reconsider </b><font color="Maroon">c<sub>5</sub></font> = <font color="Maroon">c<sub>4</sub></font> as  non <a href="xboole_0.html#V1">empty</a> <a href="struct_0.html#NM2">Subset</a> of <font color="Maroon">c<sub>1</sub></font> <b>by </b><i><a class="ref" href="waybel13.html#T3" target="_self">Th3</a></i>;<br/><b>reconsider </b><font color="Maroon">c<sub>6</sub></font> = <font color="Maroon">c<sub>5</sub></font> as  non <a href="xboole_0.html#V1">empty</a> <a href="waybel_0.html#V1">directed</a> <a href="struct_0.html#NM2">Subset</a> of <font color="Maroon">c<sub>1</sub></font> <b>by </b><i><a class="ref" href="yellow_2.html#T7">YELLOW_2:7</a></i>;<br/><b>set </b><font color="Maroon">c<sub>7</sub></font> =  <a href="yellow_0.html#NK3" target="_self">sup</a> <font color="Maroon">c<sub>6</sub></font>;<br/><b>reconsider </b><font color="Maroon">c<sub>8</sub></font> =  <a href="yellow_0.html#NK3" target="_self">sup</a> <font color="Maroon">c<sub>6</sub></font> as    <a href="hidden.html#M1">set</a>  ;<br/><b>take </b><font color="Maroon">c<sub>9</sub></font> = <font color="Maroon">c<sub>8</sub></font>;<br/><b>thus </b><a NAME="E6:17_2"/>
<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>1</sub></font>
 ;<br/><a NAME="E7:17_2"/><i><font color="Green">E17</font></i>: 
<font color="Maroon">c<sub>4</sub></font> <a href="tarski.html#R1">c=</a>  <a href="waybel_8.html#K2">compactbelow</a> <span class="p1">(<span class="default"><a href="yellow_0.html#NK3" target="_self">sup</a> <font color="Maroon">c<sub>6</sub></font></span>)</span>
 <div><a class="txt" onclick="hs2(this)" href="javascript:()" title="17_2_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> ; <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_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>4</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="struct_0.html#NM1">Element</a> of <span class="p1">(<span class="default"><a href="waybel_8.html#K1">CompactSublatt</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> ;<br/>
<b>reconsider </b><font color="Maroon">c<sub>12</sub></font> = <font color="Maroon">c<sub>11</sub></font> as   <a href="struct_0.html#NM1">Element</a> of <font color="Maroon">c<sub>1</sub></font> <b>by </b><i><a class="ref" href="yellow_0.html#T59">YELLOW_0:59</a></i>;<br/>
<a NAME="E4:17_2_1"/><i><font color="Green">E19</font></i>: 
<font color="Maroon">c<sub>12</sub></font> is <a href="waybel_3.html#V1">compact</a>
 
<b>by </b><i><a class="ref" href="waybel_8.html#D1">WAYBEL_8:def 1</a></i>;<br/>
<a NAME="E5:17_2_1"/>
<font color="Maroon">c<sub>4</sub></font> <a href="lattice3.html#R2">is_&lt;=_than</a>  <a href="yellow_0.html#NK3" target="_self">sup</a> <font color="Maroon">c<sub>6</sub></font>
 
<b>by </b><i><a class="ref" href="yellow_0.html#T32">YELLOW_0:32</a></i>;<br/>
<a NAME="E6:17_2_1"/><b>then </b>
<font color="Maroon">c<sub>12</sub></font> <a href="orders_2.html#R3">&lt;=</a>  <a href="yellow_0.html#NK3" target="_self">sup</a> <font color="Maroon">c<sub>6</sub></font>
 
<b>by </b><i><a class="txt" href="waybel13.html#E1:17_2_1"><i><font color="Green">E18</font></i></a>, <a class="ref" href="lattice3.html#D9">LATTICE3:def 9</a></i>;<br/>
<b>hence </b><a NAME="E7:17_2_1"/>
<font color="Maroon">c<sub>10</sub></font> <a href="hidden.html#R2">in</a>  <a href="waybel_8.html#K2">compactbelow</a> <span class="p1">(<span class="default"><a href="yellow_0.html#NK3" target="_self">sup</a> <font color="Maroon">c<sub>6</sub></font></span>)</span>
 <b>by </b><i><a class="txt" href="waybel13.html#E4:17_2_1"><i><font color="Green">E19</font></i></a>, <a class="ref" href="waybel_8.html#T4">WAYBEL_8:4</a></i>;<br/>


</div><b>end;</b></div><a NAME="E8:17_2"/>
 <a href="waybel_8.html#K2">compactbelow</a> <span class="p1">(<span class="default"><a href="yellow_0.html#NK3" target="_self">sup</a> <font color="Maroon">c<sub>6</sub></font></span>)</span> <a href="tarski.html#R1">c=</a> <font color="Maroon">c<sub>4</sub></font>
 <div><a class="txt" onclick="hs2(this)" href="javascript:()" title="17_2_2"><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> ; <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_2_2"/>
<font color="Maroon">c<sub>10</sub></font> <a href="hidden.html#R2">in</a>  <a href="waybel_8.html#K2">compactbelow</a> <span class="p1">(<span class="default"><a href="yellow_0.html#NK3" target="_self">sup</a> <font color="Maroon">c<sub>6</sub></font></span>)</span>
 ;<br/>

<a NAME="E2:17_2_2"/><b>then </b>
<font color="Maroon">c<sub>10</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 <font color="Maroon">c<sub>1</sub></font> : (  <a href="yellow_0.html#NK3" target="_self">sup</a> <font color="Maroon">c<sub>6</sub></font> <a href="orders_2.html#NR2" target="_self">&gt;=</a> <font color="Olive">b<sub>1</sub></font> &amp; <font color="Olive">b<sub>1</sub></font> is <a href="waybel_3.html#V1">compact</a> ) </span>}</span> 
 
<b>by </b><i><a class="ref" href="waybel_8.html#D2">WAYBEL_8:def 2</a></i>;<br/>
<b>then consider </b><font color="Maroon">c<sub>11</sub></font> being   <a href="struct_0.html#NM1">Element</a> of <font color="Maroon">c<sub>1</sub></font><b> such that </b><br/><a NAME="E4:17_2_2"/><i><font color="Green">E18</font></i>: 
<font color="Maroon">c<sub>11</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>10</sub></font>
 <b>and </b><br/><a NAME="E5:17_2_2"/><i><font color="Green">E19</font></i>: 
<font color="Maroon">c<sub>11</sub></font> <a href="orders_2.html#R3">&lt;=</a>  <a href="yellow_0.html#NK3" target="_self">sup</a> <font color="Maroon">c<sub>6</sub></font>
 <b>and </b><br/><a NAME="E6:17_2_2"/><i><font color="Green">E20</font></i>: 
<font color="Maroon">c<sub>11</sub></font> is <a href="waybel_3.html#V1">compact</a>
 ;<br/>
<a NAME="E7:17_2_2"/>
<font color="Maroon">c<sub>11</sub></font> <a href="waybel_3.html#NR2" target="_self">&lt;&lt;</a> <font color="Maroon">c<sub>11</sub></font>
 
<b>by </b><i><a class="txt" href="waybel13.html#E6:17_2_2"><i><font color="Green">E20</font></i></a>, <a class="ref" href="waybel_3.html#D2">WAYBEL_3:def 2</a></i>;<br/>
<b>then consider </b><font color="Maroon">c<sub>12</sub></font> being   <a href="struct_0.html#NM1">Element</a> of <font color="Maroon">c<sub>1</sub></font><b> such that </b><br/><a NAME="E9:17_2_2"/><i><font color="Green">E21</font></i>: 
<font color="Maroon">c<sub>12</sub></font> <a href="hidden.html#R2">in</a> <font color="Maroon">c<sub>6</sub></font>
 <b>and </b><br/><a NAME="E10:17_2_2"/><i><font color="Green">E22</font></i>: 
<font color="Maroon">c<sub>11</sub></font> <a href="orders_2.html#R3">&lt;=</a> <font color="Maroon">c<sub>12</sub></font>
 <b>by </b><i><a class="txt" href="waybel13.html#E5:17_2_2"><i><font color="Green">E19</font></i></a>, <a class="ref" href="waybel_3.html#D1">WAYBEL_3:def 1</a></i>;<br/>
<b>reconsider </b><font color="Maroon">c<sub>13</sub></font> = <font color="Maroon">c<sub>11</sub></font> as   <a href="struct_0.html#NM1">Element</a> of <span class="p1">(<span class="default"><a href="waybel_8.html#K1">CompactSublatt</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <b>by </b><i><a class="txt" href="waybel13.html#E6:17_2_2"><i><font color="Green">E20</font></i></a>, <a class="ref" href="waybel_8.html#D1">WAYBEL_8:def 1</a></i>;<br/>
<b>reconsider </b><font color="Maroon">c<sub>14</sub></font> = <font color="Maroon">c<sub>12</sub></font> as   <a href="struct_0.html#NM1">Element</a> of <span class="p1">(<span class="default"><a href="waybel_8.html#K1">CompactSublatt</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <b>by </b><i><a class="txt" href="waybel13.html#E9:17_2_2"><i><font color="Green">E21</font></i></a></i>;<br/>
<a NAME="E13:17_2_2"/>
<font color="Maroon">c<sub>13</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="waybel13.html#E10:17_2_2"><i><font color="Green">E22</font></i></a>, <a class="ref" href="yellow_0.html#T61">YELLOW_0:61</a></i>;<br/>
<b>hence </b><a NAME="E14:17_2_2"/>
<font color="Maroon">c<sub>10</sub></font> <a href="hidden.html#R2">in</a> <font color="Maroon">c<sub>4</sub></font>
 <b>by </b><i><a class="txt" href="waybel13.html#E4:17_2_2"><i><font color="Green">E18</font></i></a>, <a class="txt" href="waybel13.html#E9:17_2_2"><i><font color="Green">E21</font></i></a>, <a class="ref" href="waybel_0.html#D19">WAYBEL_0:def 19</a></i>;<br/>


</div><b>end;</b></div><b>hence </b><font color="Maroon">c<sub>3</sub></font> = 
 <a href="waybel_8.html#K2">compactbelow</a> <span class="p1">(<span class="default"><a href="yellow_0.html#NK3" target="_self">sup</a> <font color="Maroon">c<sub>6</sub></font></span>)</span>
<b>by </b><i><a class="txt" href="waybel13.html#E7:17_2"><i><font color="Green">E17</font></i></a>, <a class="ref" href="xboole_0.html#D10">XBOOLE_0:def 10</a></i>
<br/>.= 
<font color="Maroon">c<sub>2</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="waybel13.html#E1:17"><i><font color="Green">E15</font></i></a></i>
;<br/><br/></div><b>end;</b></div>
<a NAME="E5:17"/><b>then </b><i><font color="Green">E17</font></i>: 
 <a href="relset_1.html#K5">rng</a> <font color="Maroon">c<sub>2</sub></font> <a href="hidden.html#R1">=</a> the <a href="struct_0.html#U1">carrier</a> of <span class="p1">(<span class="default"><a href="yellow_1.html#K2">InclPoset</a> <span class="p2">(<span class="default"><a href="waybel_0.html#K7">Ids</a> <span class="p3">(<span class="default"><a href="waybel_8.html#K1">CompactSublatt</a> <font color="Maroon">c<sub>1</sub></font></span>)</span></span>)</span></span>)</span>
 
<b>by </b><i><a class="ref" href="funct_2.html#T16">FUNCT_2:16</a></i>;<br/>
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="17_3"><b>now </b></a><div class="add"><b>let </b><font color="Maroon">c<sub>3</sub></font>, <font color="Maroon">c<sub>4</sub></font> be   <a href="struct_0.html#NM1">Element</a> of <font color="Maroon">c<sub>1</sub></font>;<br/><b>thus </b><a NAME="E1:17_3"/>
( <font color="Maroon">c<sub>3</sub></font> <a href="orders_2.html#R3">&lt;=</a> <font color="Maroon">c<sub>4</sub></font> implies <font color="Maroon">c<sub>2</sub></font> <a href="funct_2.html#K3">.</a> <font color="Maroon">c<sub>3</sub></font> <a href="orders_2.html#R3">&lt;=</a> <font color="Maroon">c<sub>2</sub></font> <a href="funct_2.html#K3">.</a> <font color="Maroon">c<sub>4</sub></font> )
 <div><a class="txt" onclick="hs2(this)" href="javascript:()" title="17_3_1"><b>proof </b></a><div class="add">

<b>assume </b><a NAME="E1:17_3_1"/>
<font color="Maroon">c<sub>3</sub></font> <a href="orders_2.html#R3">&lt;=</a> <font color="Maroon">c<sub>4</sub></font>
 ;<br/>

<a NAME="E2:17_3_1"/><b>then </b>
 <a href="waybel_8.html#K2">compactbelow</a> <font color="Maroon">c<sub>3</sub></font> <a href="tarski.html#R1">c=</a>  <a href="waybel_8.html#K2">compactbelow</a> <font color="Maroon">c<sub>4</sub></font>
 
<b>by </b><i><a class="ref" href="waybel13.html#T1" target="_self">Th1</a></i>;<br/>
<a NAME="E3:17_3_1"/><b>then </b>
<font color="Maroon">c<sub>2</sub></font> <a href="funct_2.html#K3">.</a> <font color="Maroon">c<sub>3</sub></font> <a href="tarski.html#R1">c=</a>  <a href="waybel_8.html#K2">compactbelow</a> <font color="Maroon">c<sub>4</sub></font>
 
<b>by </b><i><a class="txt" href="waybel13.html#E1:17"><i><font color="Green">E15</font></i></a></i>;<br/>
<a NAME="E4:17_3_1"/><b>then </b>
<font color="Maroon">c<sub>2</sub></font> <a href="funct_2.html#K3">.</a> <font color="Maroon">c<sub>3</sub></font> <a href="tarski.html#R1">c=</a> <font color="Maroon">c<sub>2</sub></font> <a href="funct_2.html#K3">.</a> <font color="Maroon">c<sub>4</sub></font>
 
<b>by </b><i><a class="txt" href="waybel13.html#E1:17"><i><font color="Green">E15</font></i></a></i>;<br/>
<b>hence </b><a NAME="E5:17_3_1"/>
<font color="Maroon">c<sub>2</sub></font> <a href="funct_2.html#K3">.</a> <font color="Maroon">c<sub>3</sub></font> <a href="orders_2.html#R3">&lt;=</a> <font color="Maroon">c<sub>2</sub></font> <a href="funct_2.html#K3">.</a> <font color="Maroon">c<sub>4</sub></font>
 <b>by </b><i><a class="ref" href="yellow_1.html#T3">YELLOW_1:3</a></i>;<br/>


</div><b>end;</b></div><b>thus </b><a NAME="E2:17_3"/>
( <font color="Maroon">c<sub>2</sub></font> <a href="funct_2.html#K3">.</a> <font color="Maroon">c<sub>3</sub></font> <a href="orders_2.html#R3">&lt;=</a> <font color="Maroon">c<sub>2</sub></font> <a href="funct_2.html#K3">.</a> <font color="Maroon">c<sub>4</sub></font> implies <font color="Maroon">c<sub>3</sub></font> <a href="orders_2.html#R3">&lt;=</a> <font color="Maroon">c<sub>4</sub></font> )
 <div><a class="txt" onclick="hs2(this)" href="javascript:()" title="17_3_2"><b>proof </b></a><div class="add">

<a NAME="E1:17_3_2"/><i><font color="Green">E18</font></i>: 
 <a href="yellow_0.html#R1">ex_sup_of</a>  <a href="waybel_8.html#K2">compactbelow</a> <font color="Maroon">c<sub>3</sub></font>,<font color="Maroon">c<sub>1</sub></font>
 
<b>by </b><i><a class="ref" href="yellow_0.html#T17">YELLOW_0:17</a></i>;<br/>
<a NAME="E2:17_3_2"/><i><font color="Green">E19</font></i>: 
 <a href="yellow_0.html#R1">ex_sup_of</a>  <a href="waybel_8.html#K2">compactbelow</a> <font color="Maroon">c<sub>4</sub></font>,<font color="Maroon">c<sub>1</sub></font>
 
<b>by </b><i><a class="ref" href="yellow_0.html#T17">YELLOW_0:17</a></i>;<br/>
<b>assume </b><a NAME="E3:17_3_2"/>
<font color="Maroon">c<sub>2</sub></font> <a href="funct_2.html#K3">.</a> <font color="Maroon">c<sub>3</sub></font> <a href="orders_2.html#R3">&lt;=</a> <font color="Maroon">c<sub>2</sub></font> <a href="funct_2.html#K3">.</a> <font color="Maroon">c<sub>4</sub></font>
 ;<br/>

<a NAME="E4:17_3_2"/><b>then </b>
<font color="Maroon">c<sub>2</sub></font> <a href="funct_2.html#K3">.</a> <font color="Maroon">c<sub>3</sub></font> <a href="tarski.html#R1">c=</a> <font color="Maroon">c<sub>2</sub></font> <a href="funct_2.html#K3">.</a> <font color="Maroon">c<sub>4</sub></font>
 
<b>by </b><i><a class="ref" href="yellow_1.html#T3">YELLOW_1:3</a></i>;<br/>
<a NAME="E5:17_3_2"/><b>then </b>
<font color="Maroon">c<sub>2</sub></font> <a href="funct_2.html#K3">.</a> <font color="Maroon">c<sub>3</sub></font> <a href="tarski.html#R1">c=</a>  <a href="waybel_8.html#K2">compactbelow</a> <font color="Maroon">c<sub>4</sub></font>
 
<b>by </b><i><a class="txt" href="waybel13.html#E1:17"><i><font color="Green">E15</font></i></a></i>;<br/>
<a NAME="E6:17_3_2"/><b>then </b>
 <a href="waybel_8.html#K2">compactbelow</a> <font color="Maroon">c<sub>3</sub></font> <a href="tarski.html#R1">c=</a>  <a href="waybel_8.html#K2">compactbelow</a> <font color="Maroon">c<sub>4</sub></font>
 
<b>by </b><i><a class="txt" href="waybel13.html#E1:17"><i><font color="Green">E15</font></i></a></i>;<br/>
<a NAME="E7:17_3_2"/><b>then </b>
 <a href="yellow_0.html#NK3" target="_self">sup</a> <span class="p1">(<span class="default"><a href="waybel_8.html#K2">compactbelow</a> <font color="Maroon">c<sub>3</sub></font></span>)</span> <a href="orders_2.html#R3">&lt;=</a>  <a href="yellow_0.html#NK3" target="_self">sup</a> <span class="p1">(<span class="default"><a href="waybel_8.html#K2">compactbelow</a> <font color="Maroon">c<sub>4</sub></font></span>)</span>
 
<b>by </b><i><a class="txt" href="waybel13.html#E1:17_3_2"><i><font color="Green">E18</font></i></a>, <a class="txt" href="waybel13.html#E2:17_3_2"><i><font color="Green">E19</font></i></a>, <a class="ref" href="yellow_0.html#T34">YELLOW_0:34</a></i>;<br/>
<a NAME="E8:17_3_2"/><b>then </b>
 <a href="yellow_0.html#NK3" target="_self">sup</a> <span class="p1">(<span class="default"><a href="waybel_8.html#K2">compactbelow</a> <font color="Maroon">c<sub>3</sub></font></span>)</span> <a href="orders_2.html#R3">&lt;=</a> <font color="Maroon">c<sub>4</sub></font>
 
<b>by </b><i><a class="ref" href="waybel_8.html#D3">WAYBEL_8:def 3</a></i>;<br/>
<b>hence </b><a NAME="E9:17_3_2"/>
<font color="Maroon">c<sub>3</sub></font> <a href="orders_2.html#R3">&lt;=</a> <font color="Maroon">c<sub>4</sub></font>
 <b>by </b><i><a class="ref" href="waybel_8.html#D3">WAYBEL_8:def 3</a></i>;<br/>


</div><b>end;</b></div></div><b>end;</b></div>
<b>hence </b><a NAME="E7:17"/>
<font color="Maroon">c<sub>2</sub></font> is <a href="waybel_0.html#V23">isomorphic</a>
 <b>by </b><i><a class="txt" href="waybel13.html#E3:17"><i><font color="Green">E16</font></i></a>, <a class="txt" href="waybel13.html#E5:17"><i><font color="Green">E17</font></i></a>, <a class="ref" href="waybel_0.html#T66">WAYBEL_0:66</a></i>;<br/>


</div>
