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

<b>let </b><font color="Maroon">L</font> be   <a href="waybel_0.html#NM8">LATTICE</a>;<br/>

<b>set </b><font color="Maroon">cn</font> = the <a href="struct_0.html#U1">carrier</a> of <a href="yellow11.html#K2" target="_self">M_3</a> ;<br/>
<a NAME="E1:15"/><i><font color="Green">E35</font></i>: 
the <a href="struct_0.html#U1">carrier</a> of <a href="yellow11.html#K2" target="_self">M_3</a>  <a href="hidden.html#R1">=</a> <span class="p1"><a href="enumset1.html#K3">{</a><span class="default">0,1,<span class="p2">(<span class="default">2 <a href="subset_1.html#K6">\</a> 1</span>)</span>,<span class="p2">(<span class="default">3 <a href="subset_1.html#K6">\</a> 2</span>)</span>,3</span><a href="enumset1.html#K3">}</a></span>
 
<b>by </b><i><a class="ref" href="yellow_1.html#T1">YELLOW_1:1</a></i>;<br/>
<b>thus </b><a NAME="E2:15"/>
(  ex <font color="Olive">K</font> being <a href="yellow_0.html#V4">full</a> <a href="lattice5.html#NM2">Sublattice</a> of <font color="Maroon">L</font> st  <a href="yellow11.html#K2" target="_self">M_3</a> ,<font color="Olive">K</font> <a href="waybel_1.html#R5">are_isomorphic</a>  implies  ex <font color="Olive">a</font>, <font color="Olive">b</font>, <font color="Olive">c</font>, <font color="Olive">d</font>, <font color="Olive">e</font> being  <a href="struct_0.html#NM1">Element</a> of <font color="Maroon">L</font> st <br/>( <font color="Olive">a</font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> <font color="Olive">b</font> &amp; <font color="Olive">a</font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> <font color="Olive">c</font> &amp; <font color="Olive">a</font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> <font color="Olive">d</font> &amp; <font color="Olive">a</font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> <font color="Olive">e</font> &amp; <font color="Olive">b</font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> <font color="Olive">c</font> &amp; <font color="Olive">b</font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> <font color="Olive">d</font> &amp; <font color="Olive">b</font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> <font color="Olive">e</font> &amp; <font color="Olive">c</font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> <font color="Olive">d</font> &amp; <font color="Olive">c</font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> <font color="Olive">e</font> &amp; <font color="Olive">d</font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> <font color="Olive">e</font> &amp; <font color="Olive">a</font> <a href="lattice3.html#K12">"/\"</a> <font color="Olive">b</font> <a href="hidden.html#R1">=</a> <font color="Olive">a</font> &amp; <font color="Olive">a</font> <a href="lattice3.html#K12">"/\"</a> <font color="Olive">c</font> <a href="hidden.html#R1">=</a> <font color="Olive">a</font> &amp; <font color="Olive">a</font> <a href="lattice3.html#K12">"/\"</a> <font color="Olive">d</font> <a href="hidden.html#R1">=</a> <font color="Olive">a</font> &amp; <font color="Olive">b</font> <a href="lattice3.html#K12">"/\"</a> <font color="Olive">e</font> <a href="hidden.html#R1">=</a> <font color="Olive">b</font> &amp; <font color="Olive">c</font> <a href="lattice3.html#K12">"/\"</a> <font color="Olive">e</font> <a href="hidden.html#R1">=</a> <font color="Olive">c</font> &amp; <font color="Olive">d</font> <a href="lattice3.html#K12">"/\"</a> <font color="Olive">e</font> <a href="hidden.html#R1">=</a> <font color="Olive">d</font> &amp; <font color="Olive">b</font> <a href="lattice3.html#K12">"/\"</a> <font color="Olive">c</font> <a href="hidden.html#R1">=</a> <font color="Olive">a</font> &amp; <font color="Olive">b</font> <a href="lattice3.html#K12">"/\"</a> <font color="Olive">d</font> <a href="hidden.html#R1">=</a> <font color="Olive">a</font> &amp; <font color="Olive">c</font> <a href="lattice3.html#K12">"/\"</a> <font color="Olive">d</font> <a href="hidden.html#R1">=</a> <font color="Olive">a</font> &amp; <font color="Olive">b</font> <a href="lattice3.html#K13">"\/"</a> <font color="Olive">c</font> <a href="hidden.html#R1">=</a> <font color="Olive">e</font> &amp; <font color="Olive">b</font> <a href="lattice3.html#K13">"\/"</a> <font color="Olive">d</font> <a href="hidden.html#R1">=</a> <font color="Olive">e</font> &amp; <font color="Olive">c</font> <a href="lattice3.html#K13">"\/"</a> <font color="Olive">d</font> <a href="hidden.html#R1">=</a> <font color="Olive">e</font> ) )
 <div><a class="txt" onclick="hs2(this)" href="javascript:()" title="15_1"><b>proof </b></a><div class="add">

<b>given </b><font color="Maroon">K</font> being  <a href="yellow_0.html#V4">full</a> <a href="lattice5.html#NM2">Sublattice</a> of <font color="Maroon">L</font><b> such that </b><a NAME="E1:15_1"/><i><font color="Green">E36</font></i>: 
 <a href="yellow11.html#K2" target="_self">M_3</a> ,<font color="Maroon">K</font> <a href="waybel_1.html#R5">are_isomorphic</a> 
 ;<br/>

<b>consider </b><font color="Maroon">f</font> being   <a href="struct_0.html#NM6">Function</a> of <a href="yellow11.html#K2" target="_self">M_3</a> ,<font color="Maroon">K</font><b> such that </b><br/><a NAME="E3:15_1"/><i><font color="Green">E37</font></i>: 
<font color="Maroon">f</font> is <a href="waybel_0.html#V23">isomorphic</a>
 <b>by </b><i>, <a class="ref" href="waybel_1.html#D8">WAYBEL_1:def 8</a></i>;<br/>
<a NAME="E4:15_1"/><i><font color="Green">E41</font></i>: 
not <font color="Maroon">K</font> is <a href="struct_0.html#V3">empty</a>
 
<b>by </b><i>, <a class="ref" href="waybel_0.html#D38">WAYBEL_0:def 38</a></i>;<br/>
<b>reconsider </b><font color="Maroon">K</font> = <font color="Maroon">K</font> as  non <a href="struct_0.html#V3">empty</a>  <a href="yellow_0.html#M1">SubRelStr</a> of <font color="Maroon">L</font> <b>by </b><i>, <a class="ref" href="waybel_0.html#D38">WAYBEL_0:def 38</a></i>;<br/>
<a NAME="E6:15_1"/><i><font color="Green">E42</font></i>: 
( <font color="Maroon">f</font> is <a href="funct_1.html#V2">one-to-one</a> &amp; <font color="Maroon">f</font> is <a href="orders_3.html#V5">monotone</a> )
 
<b>by </b><i>, , <a class="ref" href="waybel_0.html#D38">WAYBEL_0:def 38</a></i>;<br/>
<b>reconsider </b><font color="Maroon">z</font> = 0 as   <a href="struct_0.html#NM1">Element</a> of <a href="yellow11.html#K2" target="_self">M_3</a>  <b>by </b><i>, <a class="ref" href="enumset1.html#D3">ENUMSET1:def 3</a></i>;<br/>
<b>reconsider </b><font color="Maroon">j</font> = 1 as   <a href="struct_0.html#NM1">Element</a> of <a href="yellow11.html#K2" target="_self">M_3</a>  <b>by </b><i>, <a class="ref" href="enumset1.html#D3">ENUMSET1:def 3</a></i>;<br/>
<b>reconsider </b><font color="Maroon">dj</font> = 2 <a href="subset_1.html#K6">\</a> 1 as   <a href="struct_0.html#NM1">Element</a> of <a href="yellow11.html#K2" target="_self">M_3</a>  <b>by </b><i>, <a class="ref" href="enumset1.html#D3">ENUMSET1:def 3</a></i>;<br/>
<b>reconsider </b><font color="Maroon">td</font> = 3 <a href="subset_1.html#K6">\</a> 2 as   <a href="struct_0.html#NM1">Element</a> of <a href="yellow11.html#K2" target="_self">M_3</a>  <b>by </b><i>, <a class="ref" href="enumset1.html#D3">ENUMSET1:def 3</a></i>;<br/>
<b>reconsider </b><font color="Maroon">t</font> = 3 as   <a href="struct_0.html#NM1">Element</a> of <a href="yellow11.html#K2" target="_self">M_3</a>  <b>by </b><i>, <a class="ref" href="enumset1.html#D3">ENUMSET1:def 3</a></i>;<br/>
<b>reconsider </b><font color="Maroon">cl</font> = the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">L</font> as  non <a href="xboole_0.html#V1">empty</a>  <a href="hidden.html#M1">set</a>  ;<br/>
<b>reconsider </b><font color="Maroon">ck</font> = the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">K</font> as  non <a href="xboole_0.html#V1">empty</a>  <a href="hidden.html#M1">set</a>  ;<br/>
<a NAME="E14:15_1"/><i><font color="Green">E43</font></i>: 
<font color="Maroon">ck</font> <a href="hidden.html#R1">=</a>  <a href="relset_1.html#K5">rng</a> <font color="Maroon">f</font>
 
<b>by </b><i>, <a class="ref" href="waybel_0.html#T66">WAYBEL_0:66</a></i>;<br/>
<b>reconsider </b><font color="Maroon">g</font> = <font color="Maroon">f</font> as   <a href="funct_2.html#NM1">Function</a> of the <a href="struct_0.html#U1">carrier</a> of <a href="yellow11.html#K2" target="_self">M_3</a> ,<font color="Maroon">ck</font> ;<br/>
<b>reconsider </b><font color="Maroon">a</font> = <font color="Maroon">g</font> <a href="funct_2.html#K3">.</a> <font color="Maroon">z</font>, <font color="Maroon">b</font> = <font color="Maroon">g</font> <a href="funct_2.html#K3">.</a> <font color="Maroon">j</font>, <font color="Maroon">c</font> = <font color="Maroon">g</font> <a href="funct_2.html#K3">.</a> <font color="Maroon">dj</font>, <font color="Maroon">d</font> = <font color="Maroon">g</font> <a href="funct_2.html#K3">.</a> <font color="Maroon">td</font>, <font color="Maroon">e</font> = <font color="Maroon">g</font> <a href="funct_2.html#K3">.</a> <font color="Maroon">t</font> as   <a href="struct_0.html#NM1">Element</a> of <font color="Maroon">K</font> ;<br/>
<b>reconsider </b><font color="Maroon">ck</font> = <font color="Maroon">ck</font> as  non <a href="xboole_0.html#V1">empty</a> <a href="subset_1.html#NM2">Subset</a> of <font color="Maroon">cl</font> <b>by </b><i><a class="ref" href="yellow_0.html#D13">YELLOW_0:def 13</a></i>;<br/>
<a NAME="E18:15_1"/>
( <font color="Maroon">a</font> <a href="hidden.html#R2">in</a> <font color="Maroon">ck</font> &amp; <font color="Maroon">b</font> <a href="hidden.html#R2">in</a> <font color="Maroon">ck</font> &amp; <font color="Maroon">c</font> <a href="hidden.html#R2">in</a> <font color="Maroon">ck</font> &amp; <font color="Maroon">d</font> <a href="hidden.html#R2">in</a> <font color="Maroon">ck</font> &amp; <font color="Maroon">e</font> <a href="hidden.html#R2">in</a> <font color="Maroon">ck</font> )
 
;<br/>
<b>then reconsider </b><font color="Maroon">A</font> = <font color="Maroon">a</font>, <font color="Maroon">B</font> = <font color="Maroon">b</font>, <font color="Maroon">C</font> = <font color="Maroon">c</font>, <font color="Maroon">D</font> = <font color="Maroon">d</font>, <font color="Maroon">E</font> = <font color="Maroon">e</font> as   <a href="struct_0.html#NM1">Element</a> of <font color="Maroon">L</font> ;<br/>
<b>take </b>
<font color="Maroon">A</font>
;<br/>

<b>take </b>
<font color="Maroon">B</font>
;<br/>

<b>take </b>
<font color="Maroon">C</font>
;<br/>

<b>take </b>
<font color="Maroon">D</font>
;<br/>

<b>take </b>
<font color="Maroon">E</font>
;<br/>

<b>thus </b><a NAME="E20:15_1"/>
<font color="Maroon">A</font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> <font color="Maroon">B</font>
 <b>by </b><i>, <a class="ref" href="waybel_1.html#D1">WAYBEL_1:def 1</a></i>;<br/>

<b>thus </b><a NAME="E21:15_1"/>
<font color="Maroon">A</font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> <font color="Maroon">C</font>
 <b>by </b><i>, , <a class="ref" href="waybel_1.html#D1">WAYBEL_1:def 1</a></i>;<br/>

<b>thus </b><a NAME="E22:15_1"/>
<font color="Maroon">A</font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> <font color="Maroon">D</font>
 <b>by </b><i>, , <a class="ref" href="waybel_1.html#D1">WAYBEL_1:def 1</a></i>;<br/>

<b>thus </b><a NAME="E23:15_1"/>
<font color="Maroon">A</font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> <font color="Maroon">E</font>
 <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="15_1_1"><b>now </b></a><div class="add"><b>assume </b><a NAME="E1:15_1_1"/>
<font color="Maroon">f</font> <a href="funct_2.html#K3">.</a> <font color="Maroon">j</font> <a href="hidden.html#R1">=</a> <font color="Maroon">f</font> <a href="funct_2.html#K3">.</a> <font color="Maroon">dj</font>
 ;<br/><a NAME="E2:15_1_1"/><b>then </b>
<font color="Maroon">j</font> <a href="hidden.html#R1">=</a> <font color="Maroon">dj</font>
 <b>by </b><i>, , <a class="ref" href="waybel_1.html#D1">WAYBEL_1:def 1</a></i>;<br/><a NAME="E3:15_1_1"/><b>then </b>
1 <a href="hidden.html#R2">in</a> 1
 <b>by </b><i>, <a class="ref" href="tarski.html#D1">TARSKI:def 1</a></i>;<br/><b>hence </b><a NAME="E4:15_1_1"/>
contradiction
 ;<br/></div><b>end;</b></div>
<b>hence </b><a NAME="E25:15_1"/>
<font color="Maroon">B</font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> <font color="Maroon">C</font>
 ;<br/>

<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="15_1_2"><b>now </b></a><div class="add"><b>assume </b><a NAME="E1:15_1_2"/>
<font color="Maroon">f</font> <a href="funct_2.html#K3">.</a> <font color="Maroon">j</font> <a href="hidden.html#R1">=</a> <font color="Maroon">f</font> <a href="funct_2.html#K3">.</a> <font color="Maroon">td</font>
 ;<br/><a NAME="E2:15_1_2"/><b>then </b><i><font color="Green">E44</font></i>: 
<font color="Maroon">j</font> <a href="hidden.html#R1">=</a> <font color="Maroon">td</font>
 <b>by </b><i>, , <a class="ref" href="waybel_1.html#D1">WAYBEL_1:def 1</a></i>;<br/><a NAME="E3:15_1_2"/>
( 0 <a href="hidden.html#R2">in</a> <font color="Maroon">j</font> &amp; 0 <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> 2 )
 <b>by </b><i><a class="ref" href="card_5.html#T1">CARD_5:1</a>, <a class="ref" href="tarski.html#D1">TARSKI:def 1</a></i>;<br/><b>hence </b><a NAME="E4:15_1_2"/>
contradiction
 <b>by </b><i>, , <a class="ref" href="tarski.html#D1">TARSKI:def 1</a></i>;<br/></div><b>end;</b></div>
<b>hence </b><a NAME="E27:15_1"/>
<font color="Maroon">B</font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> <font color="Maroon">D</font>
 ;<br/>

<b>thus </b><a NAME="E28:15_1"/>
<font color="Maroon">B</font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> <font color="Maroon">E</font>
 <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="15_1_3"><b>now </b></a><div class="add"><b>assume </b><a NAME="E1:15_1_3"/>
<font color="Maroon">f</font> <a href="funct_2.html#K3">.</a> <font color="Maroon">dj</font> <a href="hidden.html#R1">=</a> <font color="Maroon">f</font> <a href="funct_2.html#K3">.</a> <font color="Maroon">td</font>
 ;<br/><a NAME="E2:15_1_3"/><b>then </b><i><font color="Green">E45</font></i>: 
<font color="Maroon">dj</font> <a href="hidden.html#R1">=</a> <font color="Maroon">td</font>
 <b>by </b><i>, , <a class="ref" href="waybel_1.html#D1">WAYBEL_1:def 1</a></i>;<br/><a NAME="E3:15_1_3"/>
( 1 <a href="hidden.html#R2">in</a> <font color="Maroon">dj</font> &amp; 1 <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> 2 )
 <b>by </b><i>, <a class="ref" href="tarski.html#D1">TARSKI:def 1</a></i>;<br/><b>hence </b><a NAME="E4:15_1_3"/>
contradiction
 <b>by </b><i>, , <a class="ref" href="tarski.html#D1">TARSKI:def 1</a></i>;<br/></div><b>end;</b></div>
<b>hence </b><a NAME="E30:15_1"/>
<font color="Maroon">C</font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> <font color="Maroon">D</font>
 ;<br/>

<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="15_1_4"><b>now </b></a><div class="add"><b>assume </b><a NAME="E1:15_1_4"/>
<font color="Maroon">f</font> <a href="funct_2.html#K3">.</a> <font color="Maroon">dj</font> <a href="hidden.html#R1">=</a> <font color="Maroon">f</font> <a href="funct_2.html#K3">.</a> <font color="Maroon">t</font>
 ;<br/><a NAME="E2:15_1_4"/><b>then </b><i><font color="Green">E49</font></i>: 
<font color="Maroon">dj</font> <a href="hidden.html#R1">=</a> <font color="Maroon">t</font>
 <b>by </b><i>, , <a class="ref" href="waybel_1.html#D1">WAYBEL_1:def 1</a></i>;<br/><a NAME="E3:15_1_4"/>
( 0 <a href="hidden.html#R2">in</a> <font color="Maroon">t</font> &amp; 0 <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> 1 )
 <b>by </b><i>, <a class="ref" href="enumset1.html#D1">ENUMSET1:def 1</a></i>;<br/><b>hence </b><a NAME="E4:15_1_4"/>
contradiction
 <b>by </b><i>, , <a class="ref" href="tarski.html#D1">TARSKI:def 1</a></i>;<br/></div><b>end;</b></div>
<b>hence </b><a NAME="E32:15_1"/>
<font color="Maroon">C</font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> <font color="Maroon">E</font>
 ;<br/>

<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="15_1_5"><b>now </b></a><div class="add"><b>assume </b><a NAME="E1:15_1_5"/>
<font color="Maroon">f</font> <a href="funct_2.html#K3">.</a> <font color="Maroon">td</font> <a href="hidden.html#R1">=</a> <font color="Maroon">f</font> <a href="funct_2.html#K3">.</a> <font color="Maroon">t</font>
 ;<br/><a NAME="E2:15_1_5"/><b>then </b><i><font color="Green">E50</font></i>: 
<font color="Maroon">td</font> <a href="hidden.html#R1">=</a> <font color="Maroon">t</font>
 <b>by </b><i>, , <a class="ref" href="waybel_1.html#D1">WAYBEL_1:def 1</a></i>;<br/><a NAME="E3:15_1_5"/>
( 0 <a href="hidden.html#R2">in</a> <font color="Maroon">t</font> &amp; 0 <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> 2 )
 <b>by </b><i>, <a class="ref" href="enumset1.html#D1">ENUMSET1:def 1</a></i>;<br/><b>hence </b><a NAME="E4:15_1_5"/>
contradiction
 <b>by </b><i>, , <a class="ref" href="tarski.html#D1">TARSKI:def 1</a></i>;<br/></div><b>end;</b></div>
<b>hence </b><a NAME="E34:15_1"/>
<font color="Maroon">D</font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> <font color="Maroon">E</font>
 ;<br/>

<a NAME="E35:15_1"/>
<font color="Maroon">z</font> <a href="tarski.html#R1">c=</a> <font color="Maroon">j</font>
 
<b>by </b><i><a class="ref" href="xboole_1.html#T2">XBOOLE_1:2</a></i>;<br/>
<a NAME="E36:15_1"/><b>then </b>
<font color="Maroon">z</font> <a href="orders_2.html#R3">&lt;=</a> <font color="Maroon">j</font>
 
<b>by </b><i><a class="ref" href="yellow_1.html#T3">YELLOW_1:3</a></i>;<br/>
<a NAME="E37:15_1"/><b>then </b>
<font color="Maroon">a</font> <a href="orders_2.html#R1">&lt;=</a> <font color="Maroon">b</font>
 
<b>by </b><i>, <a class="ref" href="waybel_0.html#T66">WAYBEL_0:66</a></i>;<br/>
<a NAME="E38:15_1"/><b>then </b>
<font color="Maroon">A</font> <a href="orders_2.html#R3">&lt;=</a> <font color="Maroon">B</font>
 
<b>by </b><i><a class="ref" href="yellow_0.html#T60">YELLOW_0:60</a></i>;<br/>
<b>hence </b><a NAME="E39:15_1"/>
<font color="Maroon">A</font> <a href="lattice3.html#K12">"/\"</a> <font color="Maroon">B</font> <a href="hidden.html#R1">=</a> <font color="Maroon">A</font>
 <b>by </b><i><a class="ref" href="yellow_0.html#T25">YELLOW_0:25</a></i>;<br/>

<a NAME="E40:15_1"/>
<font color="Maroon">z</font> <a href="tarski.html#R1">c=</a> <font color="Maroon">dj</font>
 
<b>by </b><i><a class="ref" href="xboole_1.html#T2">XBOOLE_1:2</a></i>;<br/>
<a NAME="E41:15_1"/><b>then </b>
<font color="Maroon">z</font> <a href="orders_2.html#R3">&lt;=</a> <font color="Maroon">dj</font>
 
<b>by </b><i><a class="ref" href="yellow_1.html#T3">YELLOW_1:3</a></i>;<br/>
<a NAME="E42:15_1"/><b>then </b>
<font color="Maroon">a</font> <a href="orders_2.html#R1">&lt;=</a> <font color="Maroon">c</font>
 
<b>by </b><i>, <a class="ref" href="waybel_0.html#T66">WAYBEL_0:66</a></i>;<br/>
<a NAME="E43:15_1"/><b>then </b>
<font color="Maroon">A</font> <a href="orders_2.html#R3">&lt;=</a> <font color="Maroon">C</font>
 
<b>by </b><i><a class="ref" href="yellow_0.html#T60">YELLOW_0:60</a></i>;<br/>
<b>hence </b><a NAME="E44:15_1"/>
<font color="Maroon">A</font> <a href="lattice3.html#K12">"/\"</a> <font color="Maroon">C</font> <a href="hidden.html#R1">=</a> <font color="Maroon">A</font>
 <b>by </b><i><a class="ref" href="yellow_0.html#T25">YELLOW_0:25</a></i>;<br/>

<a NAME="E45:15_1"/>
<font color="Maroon">z</font> <a href="tarski.html#R1">c=</a> <font color="Maroon">td</font>
 
<b>by </b><i><a class="ref" href="xboole_1.html#T2">XBOOLE_1:2</a></i>;<br/>
<a NAME="E46:15_1"/><b>then </b>
<font color="Maroon">z</font> <a href="orders_2.html#R3">&lt;=</a> <font color="Maroon">td</font>
 
<b>by </b><i><a class="ref" href="yellow_1.html#T3">YELLOW_1:3</a></i>;<br/>
<a NAME="E47:15_1"/><b>then </b>
<font color="Maroon">a</font> <a href="orders_2.html#R1">&lt;=</a> <font color="Maroon">d</font>
 
<b>by </b><i>, <a class="ref" href="waybel_0.html#T66">WAYBEL_0:66</a></i>;<br/>
<a NAME="E48:15_1"/><b>then </b>
<font color="Maroon">A</font> <a href="orders_2.html#R3">&lt;=</a> <font color="Maroon">D</font>
 
<b>by </b><i><a class="ref" href="yellow_0.html#T60">YELLOW_0:60</a></i>;<br/>
<b>hence </b><a NAME="E49:15_1"/>
<font color="Maroon">A</font> <a href="lattice3.html#K12">"/\"</a> <font color="Maroon">D</font> <a href="hidden.html#R1">=</a> <font color="Maroon">A</font>
 <b>by </b><i><a class="ref" href="yellow_0.html#T25">YELLOW_0:25</a></i>;<br/>

<a NAME="E50:15_1"/>
<font color="Maroon">j</font> <a href="tarski.html#R1">c=</a> <font color="Maroon">t</font>
 
<b>by </b><i><a class="ref" href="card_1.html#T56">CARD_1:56</a></i>;<br/>
<a NAME="E51:15_1"/><b>then </b>
<font color="Maroon">j</font> <a href="orders_2.html#R3">&lt;=</a> <font color="Maroon">t</font>
 
<b>by </b><i><a class="ref" href="yellow_1.html#T3">YELLOW_1:3</a></i>;<br/>
<a NAME="E52:15_1"/><b>then </b>
<font color="Maroon">b</font> <a href="orders_2.html#R1">&lt;=</a> <font color="Maroon">e</font>
 
<b>by </b><i>, <a class="ref" href="waybel_0.html#T66">WAYBEL_0:66</a></i>;<br/>
<a NAME="E53:15_1"/><b>then </b>
<font color="Maroon">B</font> <a href="orders_2.html#R3">&lt;=</a> <font color="Maroon">E</font>
 
<b>by </b><i><a class="ref" href="yellow_0.html#T60">YELLOW_0:60</a></i>;<br/>
<b>hence </b><a NAME="E54:15_1"/>
<font color="Maroon">B</font> <a href="lattice3.html#K12">"/\"</a> <font color="Maroon">E</font> <a href="hidden.html#R1">=</a> <font color="Maroon">B</font>
 <b>by </b><i><a class="ref" href="yellow_0.html#T25">YELLOW_0:25</a></i>;<br/>

<a NAME="E55:15_1"/>
<font color="Maroon">dj</font> <a href="tarski.html#R1">c=</a> <font color="Maroon">t</font>
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="15_1_6"><b>proof </b></a><div class="add">

<b>let </b><font color="Maroon">x</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="E1:15_1_6"/>
<font color="Maroon">x</font> <a href="hidden.html#R2">in</a> <font color="Maroon">dj</font>
 ;<br/>

<a NAME="E2:15_1_6"/><b>then </b>
<font color="Maroon">x</font> <a href="hidden.html#R1">=</a> 1
 
<b>by </b><i>, <a class="ref" href="tarski.html#D1">TARSKI:def 1</a></i>;<br/>
<b>hence </b><a NAME="E3:15_1_6"/>
<font color="Maroon">x</font> <a href="hidden.html#R2">in</a> <font color="Maroon">t</font>
 <b>by </b><i>, <a class="ref" href="enumset1.html#D1">ENUMSET1:def 1</a></i>;<br/>


</div><b>end;</b></div>
<a NAME="E56:15_1"/><b>then </b>
<font color="Maroon">dj</font> <a href="orders_2.html#R3">&lt;=</a> <font color="Maroon">t</font>
 
<b>by </b><i><a class="ref" href="yellow_1.html#T3">YELLOW_1:3</a></i>;<br/>
<a NAME="E57:15_1"/><b>then </b>
<font color="Maroon">c</font> <a href="orders_2.html#R1">&lt;=</a> <font color="Maroon">e</font>
 
<b>by </b><i>, <a class="ref" href="waybel_0.html#T66">WAYBEL_0:66</a></i>;<br/>
<a NAME="E58:15_1"/><b>then </b>
<font color="Maroon">C</font> <a href="orders_2.html#R3">&lt;=</a> <font color="Maroon">E</font>
 
<b>by </b><i><a class="ref" href="yellow_0.html#T60">YELLOW_0:60</a></i>;<br/>
<b>hence </b><a NAME="E59:15_1"/>
<font color="Maroon">C</font> <a href="lattice3.html#K12">"/\"</a> <font color="Maroon">E</font> <a href="hidden.html#R1">=</a> <font color="Maroon">C</font>
 <b>by </b><i><a class="ref" href="yellow_0.html#T25">YELLOW_0:25</a></i>;<br/>

<a NAME="E60:15_1"/>
<font color="Maroon">td</font> <a href="orders_2.html#R3">&lt;=</a> <font color="Maroon">t</font>
 
<b>by </b><i><a class="ref" href="yellow_1.html#T3">YELLOW_1:3</a></i>;<br/>
<a NAME="E61:15_1"/><b>then </b>
<font color="Maroon">d</font> <a href="orders_2.html#R1">&lt;=</a> <font color="Maroon">e</font>
 
<b>by </b><i>, <a class="ref" href="waybel_0.html#T66">WAYBEL_0:66</a></i>;<br/>
<a NAME="E62:15_1"/><b>then </b>
<font color="Maroon">D</font> <a href="orders_2.html#R3">&lt;=</a> <font color="Maroon">E</font>
 
<b>by </b><i><a class="ref" href="yellow_0.html#T60">YELLOW_0:60</a></i>;<br/>
<b>hence </b><a NAME="E63:15_1"/>
<font color="Maroon">D</font> <a href="lattice3.html#K12">"/\"</a> <font color="Maroon">E</font> <a href="hidden.html#R1">=</a> <font color="Maroon">D</font>
 <b>by </b><i><a class="ref" href="yellow_0.html#T25">YELLOW_0:25</a></i>;<br/>

<b>thus </b><a NAME="E64:15_1"/>
<font color="Maroon">B</font> <a href="lattice3.html#K12">"/\"</a> <font color="Maroon">C</font> <a href="hidden.html#R1">=</a> <font color="Maroon">A</font>
 <div><a class="txt" onclick="hs2(this)" href="javascript:()" title="15_1_7"><b>proof </b></a><div class="add">

<a NAME="E1:15_1_7"/>
( <font color="Maroon">B</font> <a href="hidden.html#R2">in</a> the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">K</font> &amp; <font color="Maroon">C</font> <a href="hidden.html#R2">in</a> the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">K</font> &amp;  <a href="yellow_0.html#R2">ex_inf_of</a> <span class="p1"><a href="domain_1.html#K7">{</a><span class="default"><font color="Maroon">B</font>,<font color="Maroon">C</font></span><a href="domain_1.html#K7">}</a></span>,<font color="Maroon">L</font> )
 
<b>by </b><i><a class="ref" href="yellow_0.html#T21">YELLOW_0:21</a></i>;<br/>
<a NAME="E2:15_1_7"/><b>then </b>
 <a href="yellow_0.html#NK4" target="_self">inf</a> <span class="p1"><a href="domain_1.html#K7">{</a><span class="default"><font color="Maroon">B</font>,<font color="Maroon">C</font></span><a href="domain_1.html#K7">}</a></span> <a href="hidden.html#R2">in</a> the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">K</font>
 
<b>by </b><i><a class="ref" href="yellow_0.html#D16">YELLOW_0:def 16</a></i>;<br/>
<a NAME="E3:15_1_7"/><b>then </b>
<font color="Maroon">B</font> <a href="lattice3.html#K12">"/\"</a> <font color="Maroon">C</font> <a href="hidden.html#R2">in</a>  <a href="relset_1.html#K5">rng</a> <font color="Maroon">f</font>
 
<b>by </b><i>, <a class="ref" href="yellow_0.html#T40">YELLOW_0:40</a></i>;<br/>
<b>then consider </b><font color="Maroon">x</font> being    <a href="hidden.html#M1">set</a> <b> such that </b><br/><a NAME="E5:15_1_7"/><i><font color="Green">E51</font></i>: 
( <font color="Maroon">x</font> <a href="hidden.html#R2">in</a>  <a href="relset_1.html#K4">dom</a> <font color="Maroon">f</font> &amp; <font color="Maroon">B</font> <a href="lattice3.html#K12">"/\"</a> <font color="Maroon">C</font> <a href="hidden.html#R1">=</a> <font color="Maroon">f</font> <a href="funct_1.html#K1">.</a> <font color="Maroon">x</font> )
 <b>by </b><i><a class="ref" href="funct_1.html#D5">FUNCT_1:def 5</a></i>;<br/>
<b>reconsider </b><font color="Maroon">x</font> = <font color="Maroon">x</font> as   <a href="struct_0.html#NM1">Element</a> of <a href="yellow11.html#K2" target="_self">M_3</a>  <b>by </b><i/>;<br/>
<a NAME="E7:15_1_7"/><i><font color="Green">E52</font></i>: 
( <font color="Maroon">x</font> <a href="hidden.html#R1">=</a> <font color="Maroon">z</font> or <font color="Maroon">x</font> <a href="hidden.html#R1">=</a> <font color="Maroon">j</font> or <font color="Maroon">x</font> <a href="hidden.html#R1">=</a> <font color="Maroon">dj</font> or <font color="Maroon">x</font> <a href="hidden.html#R1">=</a> <font color="Maroon">td</font> or <font color="Maroon">x</font> <a href="hidden.html#R1">=</a> <font color="Maroon">t</font> )
 
<b>by </b><i>, <a class="ref" href="enumset1.html#D3">ENUMSET1:def 3</a></i>;<br/>
<div><i><font color="Green">E53</font></i>: <a class="txt" onclick="hs2(this)" href="javascript:()" title="15_1_7_1"><b>now </b></a><div class="add"><b>assume </b><a NAME="E1:15_1_7_1"/>
<font color="Maroon">B</font> <a href="lattice3.html#K12">"/\"</a> <font color="Maroon">C</font> <a href="hidden.html#R1">=</a> <font color="Maroon">B</font>
 ;<br/><a NAME="E2:15_1_7_1"/><b>then </b>
<font color="Maroon">B</font> <a href="orders_2.html#R3">&lt;=</a> <font color="Maroon">C</font>
 <b>by </b><i><a class="ref" href="yellow_0.html#T25">YELLOW_0:25</a></i>;<br/><a NAME="E3:15_1_7_1"/><b>then </b>
<font color="Maroon">b</font> <a href="orders_2.html#R1">&lt;=</a> <font color="Maroon">c</font>
 <b>by </b><i><a class="ref" href="yellow_0.html#T61">YELLOW_0:61</a></i>;<br/><a NAME="E4:15_1_7_1"/><b>then </b>
<font color="Maroon">j</font> <a href="orders_2.html#R3">&lt;=</a> <font color="Maroon">dj</font>
 <b>by </b><i>, <a class="ref" href="waybel_0.html#T66">WAYBEL_0:66</a></i>;<br/><a NAME="E5:15_1_7_1"/><b>then </b><i><font color="Green">E54</font></i>: 
<font color="Maroon">j</font> <a href="tarski.html#R1">c=</a> <font color="Maroon">dj</font>
 <b>by </b><i><a class="ref" href="yellow_1.html#T3">YELLOW_1:3</a></i>;<br/><a NAME="E6:15_1_7_1"/>
0 <a href="hidden.html#R2">in</a> <font color="Maroon">j</font>
 <b>by </b><i><a class="ref" href="card_5.html#T1">CARD_5:1</a>, <a class="ref" href="tarski.html#D1">TARSKI:def 1</a></i>;<br/><b>hence </b><a NAME="E7:15_1_7_1"/>
contradiction
 <b>by </b><i>, , <a class="ref" href="tarski.html#D1">TARSKI:def 1</a></i>;<br/></div><b>end;</b></div>
<div><i><font color="Green">E55</font></i>: <a class="txt" onclick="hs2(this)" href="javascript:()" title="15_1_7_2"><b>now </b></a><div class="add"><b>assume </b><a NAME="E1:15_1_7_2"/>
<font color="Maroon">B</font> <a href="lattice3.html#K12">"/\"</a> <font color="Maroon">C</font> <a href="hidden.html#R1">=</a> <font color="Maroon">C</font>
 ;<br/><a NAME="E2:15_1_7_2"/><b>then </b>
<font color="Maroon">C</font> <a href="orders_2.html#R3">&lt;=</a> <font color="Maroon">B</font>
 <b>by </b><i><a class="ref" href="yellow_0.html#T25">YELLOW_0:25</a></i>;<br/><a NAME="E3:15_1_7_2"/><b>then </b>
<font color="Maroon">c</font> <a href="orders_2.html#R1">&lt;=</a> <font color="Maroon">b</font>
 <b>by </b><i><a class="ref" href="yellow_0.html#T61">YELLOW_0:61</a></i>;<br/><a NAME="E4:15_1_7_2"/><b>then </b>
<font color="Maroon">dj</font> <a href="orders_2.html#R3">&lt;=</a> <font color="Maroon">j</font>
 <b>by </b><i>, <a class="ref" href="waybel_0.html#T66">WAYBEL_0:66</a></i>;<br/><a NAME="E5:15_1_7_2"/><b>then </b><i><font color="Green">E56</font></i>: 
<font color="Maroon">dj</font> <a href="tarski.html#R1">c=</a> <font color="Maroon">j</font>
 <b>by </b><i><a class="ref" href="yellow_1.html#T3">YELLOW_1:3</a></i>;<br/><a NAME="E6:15_1_7_2"/>
( 1 <a href="hidden.html#R2">in</a> <font color="Maroon">dj</font> &amp; 0 <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> 1 )
 <b>by </b><i>, <a class="ref" href="tarski.html#D1">TARSKI:def 1</a></i>;<br/><b>hence </b><a NAME="E7:15_1_7_2"/>
contradiction
 <b>by </b><i><a class="ref" href="yellow11.html#T1" target="_self">Th1</a>, <a class="ref" href="card_5.html#T1">CARD_5:1</a>, <a class="ref" href="tarski.html#D1">TARSKI:def 1</a></i>;<br/></div><b>end;</b></div>
<div><i><font color="Green">E57</font></i>: <a class="txt" onclick="hs2(this)" href="javascript:()" title="15_1_7_3"><b>now </b></a><div class="add"><b>assume </b><a NAME="E1:15_1_7_3"/>
<font color="Maroon">B</font> <a href="lattice3.html#K12">"/\"</a> <font color="Maroon">C</font> <a href="hidden.html#R1">=</a> <font color="Maroon">D</font>
 ;<br/><a NAME="E2:15_1_7_3"/><b>then </b>
<font color="Maroon">D</font> <a href="orders_2.html#R3">&lt;=</a> <font color="Maroon">C</font>
 <b>by </b><i><a class="ref" href="yellow_0.html#T23">YELLOW_0:23</a></i>;<br/><a NAME="E3:15_1_7_3"/><b>then </b>
<font color="Maroon">d</font> <a href="orders_2.html#R1">&lt;=</a> <font color="Maroon">c</font>
 <b>by </b><i><a class="ref" href="yellow_0.html#T61">YELLOW_0:61</a></i>;<br/><a NAME="E4:15_1_7_3"/><b>then </b>
<font color="Maroon">td</font> <a href="orders_2.html#R3">&lt;=</a> <font color="Maroon">dj</font>
 <b>by </b><i>, <a class="ref" href="waybel_0.html#T66">WAYBEL_0:66</a></i>;<br/><a NAME="E5:15_1_7_3"/><b>then </b><i><font color="Green">E58</font></i>: 
<font color="Maroon">td</font> <a href="tarski.html#R1">c=</a> <font color="Maroon">dj</font>
 <b>by </b><i><a class="ref" href="yellow_1.html#T3">YELLOW_1:3</a></i>;<br/><a NAME="E6:15_1_7_3"/>
2 <a href="hidden.html#R2">in</a> <font color="Maroon">td</font>
 <b>by </b><i>, <a class="ref" href="tarski.html#D1">TARSKI:def 1</a></i>;<br/><b>hence </b><a NAME="E7:15_1_7_3"/>
contradiction
 <b>by </b><i><a class="ref" href="yellow11.html#T2" target="_self">Th2</a>, , <a class="ref" href="tarski.html#D1">TARSKI:def 1</a></i>;<br/></div><b>end;</b></div>
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="15_1_7_4"><b>now </b></a><div class="add"><b>assume </b><a NAME="E1:15_1_7_4"/>
<font color="Maroon">B</font> <a href="lattice3.html#K12">"/\"</a> <font color="Maroon">C</font> <a href="hidden.html#R1">=</a> <font color="Maroon">E</font>
 ;<br/><a NAME="E2:15_1_7_4"/><b>then </b>
<font color="Maroon">E</font> <a href="orders_2.html#R3">&lt;=</a> <font color="Maroon">C</font>
 <b>by </b><i><a class="ref" href="yellow_0.html#T23">YELLOW_0:23</a></i>;<br/><a NAME="E3:15_1_7_4"/><b>then </b>
<font color="Maroon">e</font> <a href="orders_2.html#R1">&lt;=</a> <font color="Maroon">c</font>
 <b>by </b><i><a class="ref" href="yellow_0.html#T61">YELLOW_0:61</a></i>;<br/><a NAME="E4:15_1_7_4"/><b>then </b>
<font color="Maroon">t</font> <a href="orders_2.html#R3">&lt;=</a> <font color="Maroon">dj</font>
 <b>by </b><i>, <a class="ref" href="waybel_0.html#T66">WAYBEL_0:66</a></i>;<br/><a NAME="E5:15_1_7_4"/><b>then </b><i><font color="Green">E59</font></i>: 
<font color="Maroon">t</font> <a href="tarski.html#R1">c=</a> <font color="Maroon">dj</font>
 <b>by </b><i><a class="ref" href="yellow_1.html#T3">YELLOW_1:3</a></i>;<br/><a NAME="E6:15_1_7_4"/>
2 <a href="hidden.html#R2">in</a> <font color="Maroon">t</font>
 <b>by </b><i>, <a class="ref" href="enumset1.html#D1">ENUMSET1:def 1</a></i>;<br/><b>hence </b><a NAME="E7:15_1_7_4"/>
contradiction
 <b>by </b><i><a class="ref" href="yellow11.html#T2" target="_self">Th2</a>, , <a class="ref" href="tarski.html#D1">TARSKI:def 1</a></i>;<br/></div><b>end;</b></div>
<b>hence </b><a NAME="E12:15_1_7"/>
<font color="Maroon">B</font> <a href="lattice3.html#K12">"/\"</a> <font color="Maroon">C</font> <a href="hidden.html#R1">=</a> <font color="Maroon">A</font>
 <b>by </b><i>, , , , <a class="ref" href="yellow11.html#T1" target="_self">Th1</a></i>;<br/>


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

<b>thus </b><a NAME="E65:15_1"/>
<font color="Maroon">B</font> <a href="lattice3.html#K12">"/\"</a> <font color="Maroon">D</font> <a href="hidden.html#R1">=</a> <font color="Maroon">A</font>
 <div><a class="txt" onclick="hs2(this)" href="javascript:()" title="15_1_8"><b>proof </b></a><div class="add">

<a NAME="E1:15_1_8"/>
( <font color="Maroon">B</font> <a href="hidden.html#R2">in</a> the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">K</font> &amp; <font color="Maroon">D</font> <a href="hidden.html#R2">in</a> the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">K</font> &amp;  <a href="yellow_0.html#R2">ex_inf_of</a> <span class="p1"><a href="domain_1.html#K7">{</a><span class="default"><font color="Maroon">B</font>,<font color="Maroon">D</font></span><a href="domain_1.html#K7">}</a></span>,<font color="Maroon">L</font> )
 
<b>by </b><i><a class="ref" href="yellow_0.html#T21">YELLOW_0:21</a></i>;<br/>
<a NAME="E2:15_1_8"/><b>then </b>
 <a href="yellow_0.html#NK4" target="_self">inf</a> <span class="p1"><a href="domain_1.html#K7">{</a><span class="default"><font color="Maroon">B</font>,<font color="Maroon">D</font></span><a href="domain_1.html#K7">}</a></span> <a href="hidden.html#R2">in</a> the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">K</font>
 
<b>by </b><i><a class="ref" href="yellow_0.html#D16">YELLOW_0:def 16</a></i>;<br/>
<a NAME="E3:15_1_8"/><b>then </b>
<font color="Maroon">B</font> <a href="lattice3.html#K12">"/\"</a> <font color="Maroon">D</font> <a href="hidden.html#R2">in</a>  <a href="relset_1.html#K5">rng</a> <font color="Maroon">f</font>
 
<b>by </b><i>, <a class="ref" href="yellow_0.html#T40">YELLOW_0:40</a></i>;<br/>
<b>then consider </b><font color="Maroon">x</font> being    <a href="hidden.html#M1">set</a> <b> such that </b><br/><a NAME="E5:15_1_8"/><i><font color="Green">E60</font></i>: 
( <font color="Maroon">x</font> <a href="hidden.html#R2">in</a>  <a href="relset_1.html#K4">dom</a> <font color="Maroon">f</font> &amp; <font color="Maroon">B</font> <a href="lattice3.html#K12">"/\"</a> <font color="Maroon">D</font> <a href="hidden.html#R1">=</a> <font color="Maroon">f</font> <a href="funct_1.html#K1">.</a> <font color="Maroon">x</font> )
 <b>by </b><i><a class="ref" href="funct_1.html#D5">FUNCT_1:def 5</a></i>;<br/>
<b>reconsider </b><font color="Maroon">x</font> = <font color="Maroon">x</font> as   <a href="struct_0.html#NM1">Element</a> of <a href="yellow11.html#K2" target="_self">M_3</a>  <b>by </b><i/>;<br/>
<a NAME="E7:15_1_8"/><i><font color="Green">E61</font></i>: 
( <font color="Maroon">x</font> <a href="hidden.html#R1">=</a> <font color="Maroon">z</font> or <font color="Maroon">x</font> <a href="hidden.html#R1">=</a> <font color="Maroon">j</font> or <font color="Maroon">x</font> <a href="hidden.html#R1">=</a> <font color="Maroon">dj</font> or <font color="Maroon">x</font> <a href="hidden.html#R1">=</a> <font color="Maroon">td</font> or <font color="Maroon">x</font> <a href="hidden.html#R1">=</a> <font color="Maroon">t</font> )
 
<b>by </b><i>, <a class="ref" href="enumset1.html#D3">ENUMSET1:def 3</a></i>;<br/>
<div><i><font color="Green">E62</font></i>: <a class="txt" onclick="hs2(this)" href="javascript:()" title="15_1_8_1"><b>now </b></a><div class="add"><b>assume </b><a NAME="E1:15_1_8_1"/>
<font color="Maroon">B</font> <a href="lattice3.html#K12">"/\"</a> <font color="Maroon">D</font> <a href="hidden.html#R1">=</a> <font color="Maroon">B</font>
 ;<br/><a NAME="E2:15_1_8_1"/><b>then </b>
<font color="Maroon">B</font> <a href="orders_2.html#R3">&lt;=</a> <font color="Maroon">D</font>
 <b>by </b><i><a class="ref" href="yellow_0.html#T25">YELLOW_0:25</a></i>;<br/><a NAME="E3:15_1_8_1"/><b>then </b>
<font color="Maroon">b</font> <a href="orders_2.html#R1">&lt;=</a> <font color="Maroon">d</font>
 <b>by </b><i><a class="ref" href="yellow_0.html#T61">YELLOW_0:61</a></i>;<br/><a NAME="E4:15_1_8_1"/><b>then </b>
<font color="Maroon">j</font> <a href="orders_2.html#R3">&lt;=</a> <font color="Maroon">td</font>
 <b>by </b><i>, <a class="ref" href="waybel_0.html#T66">WAYBEL_0:66</a></i>;<br/><a NAME="E5:15_1_8_1"/><b>then </b><i><font color="Green">E63</font></i>: 
<font color="Maroon">j</font> <a href="tarski.html#R1">c=</a> <font color="Maroon">td</font>
 <b>by </b><i><a class="ref" href="yellow_1.html#T3">YELLOW_1:3</a></i>;<br/><a NAME="E6:15_1_8_1"/>
0 <a href="hidden.html#R2">in</a> <font color="Maroon">j</font>
 <b>by </b><i><a class="ref" href="card_5.html#T1">CARD_5:1</a>, <a class="ref" href="tarski.html#D1">TARSKI:def 1</a></i>;<br/><b>hence </b><a NAME="E7:15_1_8_1"/>
contradiction
 <b>by </b><i>, , <a class="ref" href="tarski.html#D1">TARSKI:def 1</a></i>;<br/></div><b>end;</b></div>
<div><i><font color="Green">E64</font></i>: <a class="txt" onclick="hs2(this)" href="javascript:()" title="15_1_8_2"><b>now </b></a><div class="add"><b>assume </b><a NAME="E1:15_1_8_2"/>
<font color="Maroon">B</font> <a href="lattice3.html#K12">"/\"</a> <font color="Maroon">D</font> <a href="hidden.html#R1">=</a> <font color="Maroon">C</font>
 ;<br/><a NAME="E2:15_1_8_2"/><b>then </b>
<font color="Maroon">C</font> <a href="orders_2.html#R3">&lt;=</a> <font color="Maroon">B</font>
 <b>by </b><i><a class="ref" href="yellow_0.html#T23">YELLOW_0:23</a></i>;<br/><a NAME="E3:15_1_8_2"/><b>then </b>
<font color="Maroon">c</font> <a href="orders_2.html#R1">&lt;=</a> <font color="Maroon">b</font>
 <b>by </b><i><a class="ref" href="yellow_0.html#T61">YELLOW_0:61</a></i>;<br/><a NAME="E4:15_1_8_2"/><b>then </b>
<font color="Maroon">dj</font> <a href="orders_2.html#R3">&lt;=</a> <font color="Maroon">j</font>
 <b>by </b><i>, <a class="ref" href="waybel_0.html#T66">WAYBEL_0:66</a></i>;<br/><a NAME="E5:15_1_8_2"/><b>then </b><i><font color="Green">E65</font></i>: 
<font color="Maroon">dj</font> <a href="tarski.html#R1">c=</a> <font color="Maroon">j</font>
 <b>by </b><i><a class="ref" href="yellow_1.html#T3">YELLOW_1:3</a></i>;<br/><a NAME="E6:15_1_8_2"/>
( 1 <a href="hidden.html#R2">in</a> <font color="Maroon">dj</font> &amp; 0 <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> 1 )
 <b>by </b><i>, <a class="ref" href="tarski.html#D1">TARSKI:def 1</a></i>;<br/><b>hence </b><a NAME="E7:15_1_8_2"/>
contradiction
 <b>by </b><i><a class="ref" href="yellow11.html#T1" target="_self">Th1</a>, <a class="ref" href="card_5.html#T1">CARD_5:1</a>, <a class="ref" href="tarski.html#D1">TARSKI:def 1</a></i>;<br/></div><b>end;</b></div>
<div><i><font color="Green">E66</font></i>: <a class="txt" onclick="hs2(this)" href="javascript:()" title="15_1_8_3"><b>now </b></a><div class="add"><b>assume </b><a NAME="E1:15_1_8_3"/>
<font color="Maroon">B</font> <a href="lattice3.html#K12">"/\"</a> <font color="Maroon">D</font> <a href="hidden.html#R1">=</a> <font color="Maroon">D</font>
 ;<br/><a NAME="E2:15_1_8_3"/><b>then </b>
<font color="Maroon">D</font> <a href="orders_2.html#R3">&lt;=</a> <font color="Maroon">B</font>
 <b>by </b><i><a class="ref" href="yellow_0.html#T23">YELLOW_0:23</a></i>;<br/><a NAME="E3:15_1_8_3"/><b>then </b>
<font color="Maroon">d</font> <a href="orders_2.html#R1">&lt;=</a> <font color="Maroon">b</font>
 <b>by </b><i><a class="ref" href="yellow_0.html#T61">YELLOW_0:61</a></i>;<br/><a NAME="E4:15_1_8_3"/><b>then </b>
<font color="Maroon">td</font> <a href="orders_2.html#R3">&lt;=</a> <font color="Maroon">j</font>
 <b>by </b><i>, <a class="ref" href="waybel_0.html#T66">WAYBEL_0:66</a></i>;<br/><a NAME="E5:15_1_8_3"/><b>then </b><i><font color="Green">E67</font></i>: 
<font color="Maroon">td</font> <a href="tarski.html#R1">c=</a> <font color="Maroon">j</font>
 <b>by </b><i><a class="ref" href="yellow_1.html#T3">YELLOW_1:3</a></i>;<br/><a NAME="E6:15_1_8_3"/>
2 <a href="hidden.html#R2">in</a> <font color="Maroon">td</font>
 <b>by </b><i>, <a class="ref" href="tarski.html#D1">TARSKI:def 1</a></i>;<br/><b>hence </b><a NAME="E7:15_1_8_3"/>
contradiction
 <b>by </b><i><a class="ref" href="yellow11.html#T2" target="_self">Th2</a>, <a class="ref" href="card_5.html#T1">CARD_5:1</a>, <a class="ref" href="tarski.html#D1">TARSKI:def 1</a></i>;<br/></div><b>end;</b></div>
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="15_1_8_4"><b>now </b></a><div class="add"><b>assume </b><a NAME="E1:15_1_8_4"/>
<font color="Maroon">B</font> <a href="lattice3.html#K12">"/\"</a> <font color="Maroon">D</font> <a href="hidden.html#R1">=</a> <font color="Maroon">E</font>
 ;<br/><a NAME="E2:15_1_8_4"/><b>then </b>
<font color="Maroon">E</font> <a href="orders_2.html#R3">&lt;=</a> <font color="Maroon">B</font>
 <b>by </b><i><a class="ref" href="yellow_0.html#T23">YELLOW_0:23</a></i>;<br/><a NAME="E3:15_1_8_4"/><b>then </b>
<font color="Maroon">e</font> <a href="orders_2.html#R1">&lt;=</a> <font color="Maroon">b</font>
 <b>by </b><i><a class="ref" href="yellow_0.html#T61">YELLOW_0:61</a></i>;<br/><a NAME="E4:15_1_8_4"/><b>then </b>
<font color="Maroon">t</font> <a href="orders_2.html#R3">&lt;=</a> <font color="Maroon">j</font>
 <b>by </b><i>, <a class="ref" href="waybel_0.html#T66">WAYBEL_0:66</a></i>;<br/><a NAME="E5:15_1_8_4"/><b>then </b><i><font color="Green">E68</font></i>: 
<font color="Maroon">t</font> <a href="tarski.html#R1">c=</a> <font color="Maroon">j</font>
 <b>by </b><i><a class="ref" href="yellow_1.html#T3">YELLOW_1:3</a></i>;<br/><a NAME="E6:15_1_8_4"/>
2 <a href="hidden.html#R2">in</a> <font color="Maroon">t</font>
 <b>by </b><i>, <a class="ref" href="enumset1.html#D1">ENUMSET1:def 1</a></i>;<br/><b>hence </b><a NAME="E7:15_1_8_4"/>
contradiction
 <b>by </b><i><a class="ref" href="yellow11.html#T2" target="_self">Th2</a>, <a class="ref" href="card_5.html#T1">CARD_5:1</a>, <a class="ref" href="tarski.html#D1">TARSKI:def 1</a></i>;<br/></div><b>end;</b></div>
<b>hence </b><a NAME="E12:15_1_8"/>
<font color="Maroon">B</font> <a href="lattice3.html#K12">"/\"</a> <font color="Maroon">D</font> <a href="hidden.html#R1">=</a> <font color="Maroon">A</font>
 <b>by </b><i>, , , , <a class="ref" href="yellow11.html#T1" target="_self">Th1</a></i>;<br/>


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

<b>thus </b><a NAME="E66:15_1"/>
<font color="Maroon">C</font> <a href="lattice3.html#K12">"/\"</a> <font color="Maroon">D</font> <a href="hidden.html#R1">=</a> <font color="Maroon">A</font>
 <div><a class="txt" onclick="hs2(this)" href="javascript:()" title="15_1_9"><b>proof </b></a><div class="add">

<a NAME="E1:15_1_9"/>
( <font color="Maroon">C</font> <a href="hidden.html#R2">in</a> the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">K</font> &amp; <font color="Maroon">D</font> <a href="hidden.html#R2">in</a> the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">K</font> &amp;  <a href="yellow_0.html#R2">ex_inf_of</a> <span class="p1"><a href="domain_1.html#K7">{</a><span class="default"><font color="Maroon">C</font>,<font color="Maroon">D</font></span><a href="domain_1.html#K7">}</a></span>,<font color="Maroon">L</font> )
 
<b>by </b><i><a class="ref" href="yellow_0.html#T21">YELLOW_0:21</a></i>;<br/>
<a NAME="E2:15_1_9"/><b>then </b>
 <a href="yellow_0.html#NK4" target="_self">inf</a> <span class="p1"><a href="domain_1.html#K7">{</a><span class="default"><font color="Maroon">C</font>,<font color="Maroon">D</font></span><a href="domain_1.html#K7">}</a></span> <a href="hidden.html#R2">in</a> the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">K</font>
 
<b>by </b><i><a class="ref" href="yellow_0.html#D16">YELLOW_0:def 16</a></i>;<br/>
<a NAME="E3:15_1_9"/><b>then </b>
<font color="Maroon">C</font> <a href="lattice3.html#K12">"/\"</a> <font color="Maroon">D</font> <a href="hidden.html#R2">in</a>  <a href="relset_1.html#K5">rng</a> <font color="Maroon">f</font>
 
<b>by </b><i>, <a class="ref" href="yellow_0.html#T40">YELLOW_0:40</a></i>;<br/>
<b>then consider </b><font color="Maroon">x</font> being    <a href="hidden.html#M1">set</a> <b> such that </b><br/><a NAME="E5:15_1_9"/><i><font color="Green">E70</font></i>: 
( <font color="Maroon">x</font> <a href="hidden.html#R2">in</a>  <a href="relset_1.html#K4">dom</a> <font color="Maroon">f</font> &amp; <font color="Maroon">C</font> <a href="lattice3.html#K12">"/\"</a> <font color="Maroon">D</font> <a href="hidden.html#R1">=</a> <font color="Maroon">f</font> <a href="funct_1.html#K1">.</a> <font color="Maroon">x</font> )
 <b>by </b><i><a class="ref" href="funct_1.html#D5">FUNCT_1:def 5</a></i>;<br/>
<b>reconsider </b><font color="Maroon">x</font> = <font color="Maroon">x</font> as   <a href="struct_0.html#NM1">Element</a> of <a href="yellow11.html#K2" target="_self">M_3</a>  <b>by </b><i/>;<br/>
<a NAME="E7:15_1_9"/><i><font color="Green">E71</font></i>: 
( <font color="Maroon">x</font> <a href="hidden.html#R1">=</a> <font color="Maroon">z</font> or <font color="Maroon">x</font> <a href="hidden.html#R1">=</a> <font color="Maroon">j</font> or <font color="Maroon">x</font> <a href="hidden.html#R1">=</a> <font color="Maroon">dj</font> or <font color="Maroon">x</font> <a href="hidden.html#R1">=</a> <font color="Maroon">td</font> or <font color="Maroon">x</font> <a href="hidden.html#R1">=</a> <font color="Maroon">t</font> )
 
<b>by </b><i>, <a class="ref" href="enumset1.html#D3">ENUMSET1:def 3</a></i>;<br/>
<div><i><font color="Green">E72</font></i>: <a class="txt" onclick="hs2(this)" href="javascript:()" title="15_1_9_1"><b>now </b></a><div class="add"><b>assume </b><a NAME="E1:15_1_9_1"/>
<font color="Maroon">C</font> <a href="lattice3.html#K12">"/\"</a> <font color="Maroon">D</font> <a href="hidden.html#R1">=</a> <font color="Maroon">B</font>
 ;<br/><a NAME="E2:15_1_9_1"/><b>then </b>
<font color="Maroon">B</font> <a href="orders_2.html#R3">&lt;=</a> <font color="Maroon">C</font>
 <b>by </b><i><a class="ref" href="yellow_0.html#T23">YELLOW_0:23</a></i>;<br/><a NAME="E3:15_1_9_1"/><b>then </b>
<font color="Maroon">b</font> <a href="orders_2.html#R1">&lt;=</a> <font color="Maroon">c</font>
 <b>by </b><i><a class="ref" href="yellow_0.html#T61">YELLOW_0:61</a></i>;<br/><a NAME="E4:15_1_9_1"/><b>then </b>
<font color="Maroon">j</font> <a href="orders_2.html#R3">&lt;=</a> <font color="Maroon">dj</font>
 <b>by </b><i>, <a class="ref" href="waybel_0.html#T66">WAYBEL_0:66</a></i>;<br/><a NAME="E5:15_1_9_1"/><b>then </b><i><font color="Green">E73</font></i>: 
<font color="Maroon">j</font> <a href="tarski.html#R1">c=</a> <font color="Maroon">dj</font>
 <b>by </b><i><a class="ref" href="yellow_1.html#T3">YELLOW_1:3</a></i>;<br/><a NAME="E6:15_1_9_1"/>
0 <a href="hidden.html#R2">in</a> <font color="Maroon">j</font>
 <b>by </b><i><a class="ref" href="card_5.html#T1">CARD_5:1</a>, <a class="ref" href="tarski.html#D1">TARSKI:def 1</a></i>;<br/><b>hence </b><a NAME="E7:15_1_9_1"/>
contradiction
 <b>by </b><i>, , <a class="ref" href="tarski.html#D1">TARSKI:def 1</a></i>;<br/></div><b>end;</b></div>
<div><i><font color="Green">E74</font></i>: <a class="txt" onclick="hs2(this)" href="javascript:()" title="15_1_9_2"><b>now </b></a><div class="add"><b>assume </b><a NAME="E1:15_1_9_2"/>
<font color="Maroon">C</font> <a href="lattice3.html#K12">"/\"</a> <font color="Maroon">D</font> <a href="hidden.html#R1">=</a> <font color="Maroon">C</font>
 ;<br/><a NAME="E2:15_1_9_2"/><b>then </b>
<font color="Maroon">C</font> <a href="orders_2.html#R3">&lt;=</a> <font color="Maroon">D</font>
 <b>by </b><i><a class="ref" href="yellow_0.html#T25">YELLOW_0:25</a></i>;<br/><a NAME="E3:15_1_9_2"/><b>then </b>
<font color="Maroon">c</font> <a href="orders_2.html#R1">&lt;=</a> <font color="Maroon">d</font>
 <b>by </b><i><a class="ref" href="yellow_0.html#T61">YELLOW_0:61</a></i>;<br/><a NAME="E4:15_1_9_2"/><b>then </b>
<font color="Maroon">dj</font> <a href="orders_2.html#R3">&lt;=</a> <font color="Maroon">td</font>
 <b>by </b><i>, <a class="ref" href="waybel_0.html#T66">WAYBEL_0:66</a></i>;<br/><a NAME="E5:15_1_9_2"/><b>then </b><i><font color="Green">E75</font></i>: 
<font color="Maroon">dj</font> <a href="tarski.html#R1">c=</a> <font color="Maroon">td</font>
 <b>by </b><i><a class="ref" href="yellow_1.html#T3">YELLOW_1:3</a></i>;<br/><a NAME="E6:15_1_9_2"/>
( 1 <a href="hidden.html#R2">in</a> <font color="Maroon">dj</font> &amp; 1 <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> 2 )
 <b>by </b><i>, <a class="ref" href="tarski.html#D1">TARSKI:def 1</a></i>;<br/><b>hence </b><a NAME="E7:15_1_9_2"/>
contradiction
 <b>by </b><i><a class="ref" href="yellow11.html#T1" target="_self">Th1</a>, , <a class="ref" href="tarski.html#D1">TARSKI:def 1</a></i>;<br/></div><b>end;</b></div>
<div><i><font color="Green">E76</font></i>: <a class="txt" onclick="hs2(this)" href="javascript:()" title="15_1_9_3"><b>now </b></a><div class="add"><b>assume </b><a NAME="E1:15_1_9_3"/>
<font color="Maroon">C</font> <a href="lattice3.html#K12">"/\"</a> <font color="Maroon">D</font> <a href="hidden.html#R1">=</a> <font color="Maroon">D</font>
 ;<br/><a NAME="E2:15_1_9_3"/><b>then </b>
<font color="Maroon">D</font> <a href="orders_2.html#R3">&lt;=</a> <font color="Maroon">C</font>
 <b>by </b><i><a class="ref" href="yellow_0.html#T23">YELLOW_0:23</a></i>;<br/><a NAME="E3:15_1_9_3"/><b>then </b>
<font color="Maroon">d</font> <a href="orders_2.html#R1">&lt;=</a> <font color="Maroon">c</font>
 <b>by </b><i><a class="ref" href="yellow_0.html#T61">YELLOW_0:61</a></i>;<br/><a NAME="E4:15_1_9_3"/><b>then </b>
<font color="Maroon">td</font> <a href="orders_2.html#R3">&lt;=</a> <font color="Maroon">dj</font>
 <b>by </b><i>, <a class="ref" href="waybel_0.html#T66">WAYBEL_0:66</a></i>;<br/><a NAME="E5:15_1_9_3"/><b>then </b><i><font color="Green">E77</font></i>: 
<font color="Maroon">td</font> <a href="tarski.html#R1">c=</a> <font color="Maroon">dj</font>
 <b>by </b><i><a class="ref" href="yellow_1.html#T3">YELLOW_1:3</a></i>;<br/><a NAME="E6:15_1_9_3"/>
2 <a href="hidden.html#R2">in</a> <font color="Maroon">td</font>
 <b>by </b><i>, <a class="ref" href="tarski.html#D1">TARSKI:def 1</a></i>;<br/><b>hence </b><a NAME="E7:15_1_9_3"/>
contradiction
 <b>by </b><i><a class="ref" href="yellow11.html#T2" target="_self">Th2</a>, , <a class="ref" href="tarski.html#D1">TARSKI:def 1</a></i>;<br/></div><b>end;</b></div>
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="15_1_9_4"><b>now </b></a><div class="add"><b>assume </b><a NAME="E1:15_1_9_4"/>
<font color="Maroon">C</font> <a href="lattice3.html#K12">"/\"</a> <font color="Maroon">D</font> <a href="hidden.html#R1">=</a> <font color="Maroon">E</font>
 ;<br/><a NAME="E2:15_1_9_4"/><b>then </b>
<font color="Maroon">E</font> <a href="orders_2.html#R3">&lt;=</a> <font color="Maroon">C</font>
 <b>by </b><i><a class="ref" href="yellow_0.html#T23">YELLOW_0:23</a></i>;<br/><a NAME="E3:15_1_9_4"/><b>then </b>
<font color="Maroon">e</font> <a href="orders_2.html#R1">&lt;=</a> <font color="Maroon">c</font>
 <b>by </b><i><a class="ref" href="yellow_0.html#T61">YELLOW_0:61</a></i>;<br/><a NAME="E4:15_1_9_4"/><b>then </b>
<font color="Maroon">t</font> <a href="orders_2.html#R3">&lt;=</a> <font color="Maroon">dj</font>
 <b>by </b><i>, <a class="ref" href="waybel_0.html#T66">WAYBEL_0:66</a></i>;<br/><a NAME="E5:15_1_9_4"/><b>then </b><i><font color="Green">E78</font></i>: 
<font color="Maroon">t</font> <a href="tarski.html#R1">c=</a> <font color="Maroon">dj</font>
 <b>by </b><i><a class="ref" href="yellow_1.html#T3">YELLOW_1:3</a></i>;<br/><a NAME="E6:15_1_9_4"/>
2 <a href="hidden.html#R2">in</a> <font color="Maroon">t</font>
 <b>by </b><i>, <a class="ref" href="enumset1.html#D1">ENUMSET1:def 1</a></i>;<br/><b>hence </b><a NAME="E7:15_1_9_4"/>
contradiction
 <b>by </b><i><a class="ref" href="yellow11.html#T2" target="_self">Th2</a>, , <a class="ref" href="tarski.html#D1">TARSKI:def 1</a></i>;<br/></div><b>end;</b></div>
<b>hence </b><a NAME="E12:15_1_9"/>
<font color="Maroon">C</font> <a href="lattice3.html#K12">"/\"</a> <font color="Maroon">D</font> <a href="hidden.html#R1">=</a> <font color="Maroon">A</font>
 <b>by </b><i>, , , , <a class="ref" href="yellow11.html#T1" target="_self">Th1</a></i>;<br/>


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

<b>thus </b><a NAME="E67:15_1"/>
<font color="Maroon">B</font> <a href="lattice3.html#K13">"\/"</a> <font color="Maroon">C</font> <a href="hidden.html#R1">=</a> <font color="Maroon">E</font>
 <div><a class="txt" onclick="hs2(this)" href="javascript:()" title="15_1_10"><b>proof </b></a><div class="add">

<a NAME="E1:15_1_10"/>
( <font color="Maroon">B</font> <a href="hidden.html#R2">in</a> the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">K</font> &amp; <font color="Maroon">B</font> <a href="hidden.html#R2">in</a> the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">K</font> &amp;  <a href="yellow_0.html#R1">ex_sup_of</a> <span class="p1"><a href="domain_1.html#K7">{</a><span class="default"><font color="Maroon">B</font>,<font color="Maroon">C</font></span><a href="domain_1.html#K7">}</a></span>,<font color="Maroon">L</font> )
 
<b>by </b><i><a class="ref" href="yellow_0.html#T20">YELLOW_0:20</a></i>;<br/>
<a NAME="E2:15_1_10"/><b>then </b>
 <a href="yellow_0.html#NK3" target="_self">sup</a> <span class="p1"><a href="domain_1.html#K7">{</a><span class="default"><font color="Maroon">B</font>,<font color="Maroon">C</font></span><a href="domain_1.html#K7">}</a></span> <a href="hidden.html#R2">in</a> the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">K</font>
 
<b>by </b><i><a class="ref" href="yellow_0.html#D17">YELLOW_0:def 17</a></i>;<br/>
<a NAME="E3:15_1_10"/><b>then </b>
<font color="Maroon">B</font> <a href="lattice3.html#K13">"\/"</a> <font color="Maroon">C</font> <a href="hidden.html#R2">in</a>  <a href="relset_1.html#K5">rng</a> <font color="Maroon">f</font>
 
<b>by </b><i>, <a class="ref" href="yellow_0.html#T41">YELLOW_0:41</a></i>;<br/>
<b>then consider </b><font color="Maroon">x</font> being    <a href="hidden.html#M1">set</a> <b> such that </b><br/><a NAME="E5:15_1_10"/><i><font color="Green">E79</font></i>: 
( <font color="Maroon">x</font> <a href="hidden.html#R2">in</a>  <a href="relset_1.html#K4">dom</a> <font color="Maroon">f</font> &amp; <font color="Maroon">B</font> <a href="lattice3.html#K13">"\/"</a> <font color="Maroon">C</font> <a href="hidden.html#R1">=</a> <font color="Maroon">f</font> <a href="funct_1.html#K1">.</a> <font color="Maroon">x</font> )
 <b>by </b><i><a class="ref" href="funct_1.html#D5">FUNCT_1:def 5</a></i>;<br/>
<b>reconsider </b><font color="Maroon">x</font> = <font color="Maroon">x</font> as   <a href="struct_0.html#NM1">Element</a> of <a href="yellow11.html#K2" target="_self">M_3</a>  <b>by </b><i/>;<br/>
<a NAME="E7:15_1_10"/><i><font color="Green">E80</font></i>: 
( <font color="Maroon">x</font> <a href="hidden.html#R1">=</a> <font color="Maroon">z</font> or <font color="Maroon">x</font> <a href="hidden.html#R1">=</a> <font color="Maroon">j</font> or <font color="Maroon">x</font> <a href="hidden.html#R1">=</a> <font color="Maroon">dj</font> or <font color="Maroon">x</font> <a href="hidden.html#R1">=</a> <font color="Maroon">td</font> or <font color="Maroon">x</font> <a href="hidden.html#R1">=</a> <font color="Maroon">t</font> )
 
<b>by </b><i>, <a class="ref" href="enumset1.html#D3">ENUMSET1:def 3</a></i>;<br/>
<div><i><font color="Green">E81</font></i>: <a class="txt" onclick="hs2(this)" href="javascript:()" title="15_1_10_1"><b>now </b></a><div class="add"><b>assume </b><a NAME="E1:15_1_10_1"/>
<font color="Maroon">B</font> <a href="lattice3.html#K13">"\/"</a> <font color="Maroon">C</font> <a href="hidden.html#R1">=</a> <font color="Maroon">B</font>
 ;<br/><a NAME="E2:15_1_10_1"/><b>then </b>
<font color="Maroon">B</font> <a href="orders_2.html#NR2" target="_self">&gt;=</a> <font color="Maroon">C</font>
 <b>by </b><i><a class="ref" href="yellow_0.html#T24">YELLOW_0:24</a></i>;<br/><a NAME="E3:15_1_10_1"/><b>then </b>
<font color="Maroon">b</font> <a href="orders_2.html#NR2" target="_self">&gt;=</a> <font color="Maroon">c</font>
 <b>by </b><i><a class="ref" href="yellow_0.html#T61">YELLOW_0:61</a></i>;<br/><a NAME="E4:15_1_10_1"/><b>then </b>
<font color="Maroon">j</font> <a href="orders_2.html#NR2" target="_self">&gt;=</a> <font color="Maroon">dj</font>
 <b>by </b><i>, <a class="ref" href="waybel_0.html#T66">WAYBEL_0:66</a></i>;<br/><a NAME="E5:15_1_10_1"/><b>then </b><i><font color="Green">E82</font></i>: 
<font color="Maroon">dj</font> <a href="tarski.html#R1">c=</a> <font color="Maroon">j</font>
 <b>by </b><i><a class="ref" href="yellow_1.html#T3">YELLOW_1:3</a></i>;<br/><a NAME="E6:15_1_10_1"/>
( 1 <a href="hidden.html#R2">in</a> <font color="Maroon">dj</font> &amp; 0 <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> 1 )
 <b>by </b><i>, <a class="ref" href="tarski.html#D1">TARSKI:def 1</a></i>;<br/><b>hence </b><a NAME="E7:15_1_10_1"/>
contradiction
 <b>by </b><i>, <a class="ref" href="card_5.html#T1">CARD_5:1</a>, <a class="ref" href="tarski.html#D1">TARSKI:def 1</a></i>;<br/></div><b>end;</b></div>
<div><i><font color="Green">E83</font></i>: <a class="txt" onclick="hs2(this)" href="javascript:()" title="15_1_10_2"><b>now </b></a><div class="add"><b>assume </b><a NAME="E1:15_1_10_2"/>
<font color="Maroon">B</font> <a href="lattice3.html#K13">"\/"</a> <font color="Maroon">C</font> <a href="hidden.html#R1">=</a> <font color="Maroon">C</font>
 ;<br/><a NAME="E2:15_1_10_2"/><b>then </b>
<font color="Maroon">C</font> <a href="orders_2.html#NR2" target="_self">&gt;=</a> <font color="Maroon">B</font>
 <b>by </b><i><a class="ref" href="yellow_0.html#T24">YELLOW_0:24</a></i>;<br/><a NAME="E3:15_1_10_2"/><b>then </b>
<font color="Maroon">c</font> <a href="orders_2.html#NR2" target="_self">&gt;=</a> <font color="Maroon">b</font>
 <b>by </b><i><a class="ref" href="yellow_0.html#T61">YELLOW_0:61</a></i>;<br/><a NAME="E4:15_1_10_2"/><b>then </b>
<font color="Maroon">dj</font> <a href="orders_2.html#NR2" target="_self">&gt;=</a> <font color="Maroon">j</font>
 <b>by </b><i>, <a class="ref" href="waybel_0.html#T66">WAYBEL_0:66</a></i>;<br/><a NAME="E5:15_1_10_2"/><b>then </b><i><font color="Green">E84</font></i>: 
<font color="Maroon">j</font> <a href="tarski.html#R1">c=</a> <font color="Maroon">dj</font>
 <b>by </b><i><a class="ref" href="yellow_1.html#T3">YELLOW_1:3</a></i>;<br/><a NAME="E6:15_1_10_2"/>
0 <a href="hidden.html#R2">in</a> <font color="Maroon">j</font>
 <b>by </b><i><a class="ref" href="card_5.html#T1">CARD_5:1</a>, <a class="ref" href="tarski.html#D1">TARSKI:def 1</a></i>;<br/><b>hence </b><a NAME="E7:15_1_10_2"/>
contradiction
 <b>by </b><i><a class="ref" href="yellow11.html#T1" target="_self">Th1</a>, , <a class="ref" href="tarski.html#D1">TARSKI:def 1</a></i>;<br/></div><b>end;</b></div>
<div><i><font color="Green">E85</font></i>: <a class="txt" onclick="hs2(this)" href="javascript:()" title="15_1_10_3"><b>now </b></a><div class="add"><b>assume </b><a NAME="E1:15_1_10_3"/>
<font color="Maroon">B</font> <a href="lattice3.html#K13">"\/"</a> <font color="Maroon">C</font> <a href="hidden.html#R1">=</a> <font color="Maroon">D</font>
 ;<br/><a NAME="E2:15_1_10_3"/><b>then </b>
<font color="Maroon">D</font> <a href="orders_2.html#NR2" target="_self">&gt;=</a> <font color="Maroon">C</font>
 <b>by </b><i><a class="ref" href="yellow_0.html#T22">YELLOW_0:22</a></i>;<br/><a NAME="E3:15_1_10_3"/><b>then </b>
<font color="Maroon">d</font> <a href="orders_2.html#NR2" target="_self">&gt;=</a> <font color="Maroon">c</font>
 <b>by </b><i><a class="ref" href="yellow_0.html#T61">YELLOW_0:61</a></i>;<br/><a NAME="E4:15_1_10_3"/><b>then </b>
<font color="Maroon">td</font> <a href="orders_2.html#NR2" target="_self">&gt;=</a> <font color="Maroon">dj</font>
 <b>by </b><i>, <a class="ref" href="waybel_0.html#T66">WAYBEL_0:66</a></i>;<br/><a NAME="E5:15_1_10_3"/><b>then </b><i><font color="Green">E86</font></i>: 
<font color="Maroon">dj</font> <a href="tarski.html#R1">c=</a> <font color="Maroon">td</font>
 <b>by </b><i><a class="ref" href="yellow_1.html#T3">YELLOW_1:3</a></i>;<br/><a NAME="E6:15_1_10_3"/>
( 1 <a href="hidden.html#R2">in</a> <font color="Maroon">dj</font> &amp; 2 <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> 1 )
 <b>by </b><i>, <a class="ref" href="tarski.html#D1">TARSKI:def 1</a></i>;<br/><b>hence </b><a NAME="E7:15_1_10_3"/>
contradiction
 <b>by </b><i><a class="ref" href="yellow11.html#T2" target="_self">Th2</a>, , <a class="ref" href="tarski.html#D1">TARSKI:def 1</a></i>;<br/></div><b>end;</b></div>
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="15_1_10_4"><b>now </b></a><div class="add"><b>assume </b><a NAME="E1:15_1_10_4"/>
<font color="Maroon">B</font> <a href="lattice3.html#K13">"\/"</a> <font color="Maroon">C</font> <a href="hidden.html#R1">=</a> <font color="Maroon">A</font>
 ;<br/><a NAME="E2:15_1_10_4"/><b>then </b>
<font color="Maroon">A</font> <a href="orders_2.html#NR2" target="_self">&gt;=</a> <font color="Maroon">C</font>
 <b>by </b><i><a class="ref" href="yellow_0.html#T22">YELLOW_0:22</a></i>;<br/><a NAME="E3:15_1_10_4"/><b>then </b>
<font color="Maroon">a</font> <a href="orders_2.html#NR2" target="_self">&gt;=</a> <font color="Maroon">c</font>
 <b>by </b><i><a class="ref" href="yellow_0.html#T61">YELLOW_0:61</a></i>;<br/><a NAME="E4:15_1_10_4"/><b>then </b>
<font color="Maroon">z</font> <a href="orders_2.html#NR2" target="_self">&gt;=</a> <font color="Maroon">dj</font>
 <b>by </b><i>, <a class="ref" href="waybel_0.html#T66">WAYBEL_0:66</a></i>;<br/><a NAME="E5:15_1_10_4"/><b>then </b>
<font color="Maroon">dj</font> <a href="tarski.html#R1">c=</a> <font color="Maroon">z</font>
 <b>by </b><i><a class="ref" href="yellow_1.html#T3">YELLOW_1:3</a></i>;<br/><b>hence </b><a NAME="E6:15_1_10_4"/>
contradiction
 <b>by </b><i>, <a class="ref" href="xboole_1.html#T3">XBOOLE_1:3</a></i>;<br/></div><b>end;</b></div>
<b>hence </b><a NAME="E12:15_1_10"/>
<font color="Maroon">B</font> <a href="lattice3.html#K13">"\/"</a> <font color="Maroon">C</font> <a href="hidden.html#R1">=</a> <font color="Maroon">E</font>
 <b>by </b><i>, , , , <a class="ref" href="yellow11.html#T1" target="_self">Th1</a></i>;<br/>


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

<b>thus </b><a NAME="E68:15_1"/>
<font color="Maroon">B</font> <a href="lattice3.html#K13">"\/"</a> <font color="Maroon">D</font> <a href="hidden.html#R1">=</a> <font color="Maroon">E</font>
 <div><a class="txt" onclick="hs2(this)" href="javascript:()" title="15_1_11"><b>proof </b></a><div class="add">

<a NAME="E1:15_1_11"/>
( <font color="Maroon">B</font> <a href="hidden.html#R2">in</a> the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">K</font> &amp; <font color="Maroon">D</font> <a href="hidden.html#R2">in</a> the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">K</font> &amp;  <a href="yellow_0.html#R1">ex_sup_of</a> <span class="p1"><a href="domain_1.html#K7">{</a><span class="default"><font color="Maroon">B</font>,<font color="Maroon">D</font></span><a href="domain_1.html#K7">}</a></span>,<font color="Maroon">L</font> )
 
<b>by </b><i><a class="ref" href="yellow_0.html#T20">YELLOW_0:20</a></i>;<br/>
<a NAME="E2:15_1_11"/><b>then </b>
 <a href="yellow_0.html#NK3" target="_self">sup</a> <span class="p1"><a href="domain_1.html#K7">{</a><span class="default"><font color="Maroon">B</font>,<font color="Maroon">D</font></span><a href="domain_1.html#K7">}</a></span> <a href="hidden.html#R2">in</a> the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">K</font>
 
<b>by </b><i><a class="ref" href="yellow_0.html#D17">YELLOW_0:def 17</a></i>;<br/>
<a NAME="E3:15_1_11"/><b>then </b>
<font color="Maroon">B</font> <a href="lattice3.html#K13">"\/"</a> <font color="Maroon">D</font> <a href="hidden.html#R2">in</a>  <a href="relset_1.html#K5">rng</a> <font color="Maroon">f</font>
 
<b>by </b><i>, <a class="ref" href="yellow_0.html#T41">YELLOW_0:41</a></i>;<br/>
<b>then consider </b><font color="Maroon">x</font> being    <a href="hidden.html#M1">set</a> <b> such that </b><br/><a NAME="E5:15_1_11"/><i><font color="Green">E87</font></i>: 
( <font color="Maroon">x</font> <a href="hidden.html#R2">in</a>  <a href="relset_1.html#K4">dom</a> <font color="Maroon">f</font> &amp; <font color="Maroon">B</font> <a href="lattice3.html#K13">"\/"</a> <font color="Maroon">D</font> <a href="hidden.html#R1">=</a> <font color="Maroon">f</font> <a href="funct_1.html#K1">.</a> <font color="Maroon">x</font> )
 <b>by </b><i><a class="ref" href="funct_1.html#D5">FUNCT_1:def 5</a></i>;<br/>
<b>reconsider </b><font color="Maroon">x</font> = <font color="Maroon">x</font> as   <a href="struct_0.html#NM1">Element</a> of <a href="yellow11.html#K2" target="_self">M_3</a>  <b>by </b><i/>;<br/>
<a NAME="E7:15_1_11"/><i><font color="Green">E88</font></i>: 
( <font color="Maroon">x</font> <a href="hidden.html#R1">=</a> <font color="Maroon">z</font> or <font color="Maroon">x</font> <a href="hidden.html#R1">=</a> <font color="Maroon">j</font> or <font color="Maroon">x</font> <a href="hidden.html#R1">=</a> <font color="Maroon">dj</font> or <font color="Maroon">x</font> <a href="hidden.html#R1">=</a> <font color="Maroon">td</font> or <font color="Maroon">x</font> <a href="hidden.html#R1">=</a> <font color="Maroon">t</font> )
 
<b>by </b><i>, <a class="ref" href="enumset1.html#D3">ENUMSET1:def 3</a></i>;<br/>
<div><i><font color="Green">E89</font></i>: <a class="txt" onclick="hs2(this)" href="javascript:()" title="15_1_11_1"><b>now </b></a><div class="add"><b>assume </b><a NAME="E1:15_1_11_1"/>
<font color="Maroon">B</font> <a href="lattice3.html#K13">"\/"</a> <font color="Maroon">D</font> <a href="hidden.html#R1">=</a> <font color="Maroon">B</font>
 ;<br/><a NAME="E2:15_1_11_1"/><b>then </b>
<font color="Maroon">B</font> <a href="orders_2.html#NR2" target="_self">&gt;=</a> <font color="Maroon">D</font>
 <b>by </b><i><a class="ref" href="yellow_0.html#T22">YELLOW_0:22</a></i>;<br/><a NAME="E3:15_1_11_1"/><b>then </b>
<font color="Maroon">b</font> <a href="orders_2.html#NR2" target="_self">&gt;=</a> <font color="Maroon">d</font>
 <b>by </b><i><a class="ref" href="yellow_0.html#T61">YELLOW_0:61</a></i>;<br/><a NAME="E4:15_1_11_1"/><b>then </b>
<font color="Maroon">j</font> <a href="orders_2.html#NR2" target="_self">&gt;=</a> <font color="Maroon">td</font>
 <b>by </b><i>, <a class="ref" href="waybel_0.html#T66">WAYBEL_0:66</a></i>;<br/><a NAME="E5:15_1_11_1"/><b>then </b><i><font color="Green">E90</font></i>: 
<font color="Maroon">td</font> <a href="tarski.html#R1">c=</a> <font color="Maroon">j</font>
 <b>by </b><i><a class="ref" href="yellow_1.html#T3">YELLOW_1:3</a></i>;<br/><a NAME="E6:15_1_11_1"/>
( 2 <a href="hidden.html#R2">in</a> <font color="Maroon">td</font> &amp; 2 <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> 0 )
 <b>by </b><i>, <a class="ref" href="tarski.html#D1">TARSKI:def 1</a></i>;<br/><b>hence </b><a NAME="E7:15_1_11_1"/>
contradiction
 <b>by </b><i>, <a class="ref" href="card_5.html#T1">CARD_5:1</a>, <a class="ref" href="tarski.html#D1">TARSKI:def 1</a></i>;<br/></div><b>end;</b></div>
<div><i><font color="Green">E91</font></i>: <a class="txt" onclick="hs2(this)" href="javascript:()" title="15_1_11_2"><b>now </b></a><div class="add"><b>assume </b><a NAME="E1:15_1_11_2"/>
<font color="Maroon">B</font> <a href="lattice3.html#K13">"\/"</a> <font color="Maroon">D</font> <a href="hidden.html#R1">=</a> <font color="Maroon">C</font>
 ;<br/><a NAME="E2:15_1_11_2"/><b>then </b>
<font color="Maroon">C</font> <a href="orders_2.html#NR2" target="_self">&gt;=</a> <font color="Maroon">D</font>
 <b>by </b><i><a class="ref" href="yellow_0.html#T22">YELLOW_0:22</a></i>;<br/><a NAME="E3:15_1_11_2"/><b>then </b>
<font color="Maroon">c</font> <a href="orders_2.html#NR2" target="_self">&gt;=</a> <font color="Maroon">d</font>
 <b>by </b><i><a class="ref" href="yellow_0.html#T61">YELLOW_0:61</a></i>;<br/><a NAME="E4:15_1_11_2"/><b>then </b>
<font color="Maroon">dj</font> <a href="orders_2.html#NR2" target="_self">&gt;=</a> <font color="Maroon">td</font>
 <b>by </b><i>, <a class="ref" href="waybel_0.html#T66">WAYBEL_0:66</a></i>;<br/><a NAME="E5:15_1_11_2"/><b>then </b><i><font color="Green">E92</font></i>: 
<font color="Maroon">td</font> <a href="tarski.html#R1">c=</a> <font color="Maroon">dj</font>
 <b>by </b><i><a class="ref" href="yellow_1.html#T3">YELLOW_1:3</a></i>;<br/><a NAME="E6:15_1_11_2"/>
( 2 <a href="hidden.html#R2">in</a> <font color="Maroon">td</font> &amp; 2 <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> 1 )
 <b>by </b><i>, <a class="ref" href="tarski.html#D1">TARSKI:def 1</a></i>;<br/><b>hence </b><a NAME="E7:15_1_11_2"/>
contradiction
 <b>by </b><i><a class="ref" href="yellow11.html#T1" target="_self">Th1</a>, , <a class="ref" href="tarski.html#D1">TARSKI:def 1</a></i>;<br/></div><b>end;</b></div>
<div><i><font color="Green">E93</font></i>: <a class="txt" onclick="hs2(this)" href="javascript:()" title="15_1_11_3"><b>now </b></a><div class="add"><b>assume </b><a NAME="E1:15_1_11_3"/>
<font color="Maroon">B</font> <a href="lattice3.html#K13">"\/"</a> <font color="Maroon">D</font> <a href="hidden.html#R1">=</a> <font color="Maroon">D</font>
 ;<br/><a NAME="E2:15_1_11_3"/><b>then </b>
<font color="Maroon">D</font> <a href="orders_2.html#NR2" target="_self">&gt;=</a> <font color="Maroon">B</font>
 <b>by </b><i><a class="ref" href="yellow_0.html#T22">YELLOW_0:22</a></i>;<br/><a NAME="E3:15_1_11_3"/><b>then </b>
<font color="Maroon">d</font> <a href="orders_2.html#NR2" target="_self">&gt;=</a> <font color="Maroon">b</font>
 <b>by </b><i><a class="ref" href="yellow_0.html#T61">YELLOW_0:61</a></i>;<br/><a NAME="E4:15_1_11_3"/><b>then </b>
<font color="Maroon">td</font> <a href="orders_2.html#NR2" target="_self">&gt;=</a> <font color="Maroon">j</font>
 <b>by </b><i>, <a class="ref" href="waybel_0.html#T66">WAYBEL_0:66</a></i>;<br/><a NAME="E5:15_1_11_3"/><b>then </b><i><font color="Green">E94</font></i>: 
<font color="Maroon">j</font> <a href="tarski.html#R1">c=</a> <font color="Maroon">td</font>
 <b>by </b><i><a class="ref" href="yellow_1.html#T3">YELLOW_1:3</a></i>;<br/><a NAME="E6:15_1_11_3"/>
( 0 <a href="hidden.html#R2">in</a> <font color="Maroon">j</font> &amp; 0 <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> 2 )
 <b>by </b><i><a class="ref" href="card_5.html#T1">CARD_5:1</a>, <a class="ref" href="tarski.html#D1">TARSKI:def 1</a></i>;<br/><b>hence </b><a NAME="E7:15_1_11_3"/>
contradiction
 <b>by </b><i><a class="ref" href="yellow11.html#T2" target="_self">Th2</a>, , <a class="ref" href="tarski.html#D1">TARSKI:def 1</a></i>;<br/></div><b>end;</b></div>
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="15_1_11_4"><b>now </b></a><div class="add"><b>assume </b><a NAME="E1:15_1_11_4"/>
<font color="Maroon">B</font> <a href="lattice3.html#K13">"\/"</a> <font color="Maroon">D</font> <a href="hidden.html#R1">=</a> <font color="Maroon">A</font>
 ;<br/><a NAME="E2:15_1_11_4"/><b>then </b>
<font color="Maroon">A</font> <a href="orders_2.html#NR2" target="_self">&gt;=</a> <font color="Maroon">B</font>
 <b>by </b><i><a class="ref" href="yellow_0.html#T22">YELLOW_0:22</a></i>;<br/><a NAME="E3:15_1_11_4"/><b>then </b>
<font color="Maroon">a</font> <a href="orders_2.html#NR2" target="_self">&gt;=</a> <font color="Maroon">b</font>
 <b>by </b><i><a class="ref" href="yellow_0.html#T61">YELLOW_0:61</a></i>;<br/><a NAME="E4:15_1_11_4"/><b>then </b>
<font color="Maroon">z</font> <a href="orders_2.html#NR2" target="_self">&gt;=</a> <font color="Maroon">j</font>
 <b>by </b><i>, <a class="ref" href="waybel_0.html#T66">WAYBEL_0:66</a></i>;<br/><a NAME="E5:15_1_11_4"/><b>then </b>
<font color="Maroon">j</font> <a href="tarski.html#R1">c=</a> <font color="Maroon">z</font>
 <b>by </b><i><a class="ref" href="yellow_1.html#T3">YELLOW_1:3</a></i>;<br/><b>hence </b><a NAME="E6:15_1_11_4"/>
contradiction
 <b>by </b><i><a class="ref" href="xboole_1.html#T3">XBOOLE_1:3</a></i>;<br/></div><b>end;</b></div>
<b>hence </b><a NAME="E12:15_1_11"/>
<font color="Maroon">B</font> <a href="lattice3.html#K13">"\/"</a> <font color="Maroon">D</font> <a href="hidden.html#R1">=</a> <font color="Maroon">E</font>
 <b>by </b><i>, , , , <a class="ref" href="yellow11.html#T1" target="_self">Th1</a></i>;<br/>


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

<b>thus </b><a NAME="E69:15_1"/>
<font color="Maroon">C</font> <a href="lattice3.html#K13">"\/"</a> <font color="Maroon">D</font> <a href="hidden.html#R1">=</a> <font color="Maroon">E</font>
 <div><a class="txt" onclick="hs2(this)" href="javascript:()" title="15_1_12"><b>proof </b></a><div class="add">

<a NAME="E1:15_1_12"/>
( <font color="Maroon">C</font> <a href="hidden.html#R2">in</a> the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">K</font> &amp; <font color="Maroon">D</font> <a href="hidden.html#R2">in</a> the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">K</font> &amp;  <a href="yellow_0.html#R1">ex_sup_of</a> <span class="p1"><a href="domain_1.html#K7">{</a><span class="default"><font color="Maroon">C</font>,<font color="Maroon">D</font></span><a href="domain_1.html#K7">}</a></span>,<font color="Maroon">L</font> )
 
<b>by </b><i><a class="ref" href="yellow_0.html#T20">YELLOW_0:20</a></i>;<br/>
<a NAME="E2:15_1_12"/><b>then </b>
 <a href="yellow_0.html#NK3" target="_self">sup</a> <span class="p1"><a href="domain_1.html#K7">{</a><span class="default"><font color="Maroon">C</font>,<font color="Maroon">D</font></span><a href="domain_1.html#K7">}</a></span> <a href="hidden.html#R2">in</a> the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">K</font>
 
<b>by </b><i><a class="ref" href="yellow_0.html#D17">YELLOW_0:def 17</a></i>;<br/>
<a NAME="E3:15_1_12"/><b>then </b>
<font color="Maroon">C</font> <a href="lattice3.html#K13">"\/"</a> <font color="Maroon">D</font> <a href="hidden.html#R2">in</a>  <a href="relset_1.html#K5">rng</a> <font color="Maroon">f</font>
 
<b>by </b><i>, <a class="ref" href="yellow_0.html#T41">YELLOW_0:41</a></i>;<br/>
<b>then consider </b><font color="Maroon">x</font> being    <a href="hidden.html#M1">set</a> <b> such that </b><br/><a NAME="E5:15_1_12"/><i><font color="Green">E95</font></i>: 
( <font color="Maroon">x</font> <a href="hidden.html#R2">in</a>  <a href="relset_1.html#K4">dom</a> <font color="Maroon">f</font> &amp; <font color="Maroon">C</font> <a href="lattice3.html#K13">"\/"</a> <font color="Maroon">D</font> <a href="hidden.html#R1">=</a> <font color="Maroon">f</font> <a href="funct_1.html#K1">.</a> <font color="Maroon">x</font> )
 <b>by </b><i><a class="ref" href="funct_1.html#D5">FUNCT_1:def 5</a></i>;<br/>
<b>reconsider </b><font color="Maroon">x</font> = <font color="Maroon">x</font> as   <a href="struct_0.html#NM1">Element</a> of <a href="yellow11.html#K2" target="_self">M_3</a>  <b>by </b><i/>;<br/>
<a NAME="E7:15_1_12"/><i><font color="Green">E96</font></i>: 
( <font color="Maroon">x</font> <a href="hidden.html#R1">=</a> <font color="Maroon">z</font> or <font color="Maroon">x</font> <a href="hidden.html#R1">=</a> <font color="Maroon">j</font> or <font color="Maroon">x</font> <a href="hidden.html#R1">=</a> <font color="Maroon">dj</font> or <font color="Maroon">x</font> <a href="hidden.html#R1">=</a> <font color="Maroon">td</font> or <font color="Maroon">x</font> <a href="hidden.html#R1">=</a> <font color="Maroon">t</font> )
 
<b>by </b><i>, <a class="ref" href="enumset1.html#D3">ENUMSET1:def 3</a></i>;<br/>
<div><i><font color="Green">E97</font></i>: <a class="txt" onclick="hs2(this)" href="javascript:()" title="15_1_12_1"><b>now </b></a><div class="add"><b>assume </b><a NAME="E1:15_1_12_1"/>
<font color="Maroon">C</font> <a href="lattice3.html#K13">"\/"</a> <font color="Maroon">D</font> <a href="hidden.html#R1">=</a> <font color="Maroon">B</font>
 ;<br/><a NAME="E2:15_1_12_1"/><b>then </b>
<font color="Maroon">B</font> <a href="orders_2.html#NR2" target="_self">&gt;=</a> <font color="Maroon">C</font>
 <b>by </b><i><a class="ref" href="yellow_0.html#T22">YELLOW_0:22</a></i>;<br/><a NAME="E3:15_1_12_1"/><b>then </b>
<font color="Maroon">b</font> <a href="orders_2.html#NR2" target="_self">&gt;=</a> <font color="Maroon">c</font>
 <b>by </b><i><a class="ref" href="yellow_0.html#T61">YELLOW_0:61</a></i>;<br/><a NAME="E4:15_1_12_1"/><b>then </b>
<font color="Maroon">j</font> <a href="orders_2.html#NR2" target="_self">&gt;=</a> <font color="Maroon">dj</font>
 <b>by </b><i>, <a class="ref" href="waybel_0.html#T66">WAYBEL_0:66</a></i>;<br/><a NAME="E5:15_1_12_1"/><b>then </b><i><font color="Green">E98</font></i>: 
<font color="Maroon">dj</font> <a href="tarski.html#R1">c=</a> <font color="Maroon">j</font>
 <b>by </b><i><a class="ref" href="yellow_1.html#T3">YELLOW_1:3</a></i>;<br/><a NAME="E6:15_1_12_1"/>
1 <a href="hidden.html#R2">in</a> <font color="Maroon">dj</font>
 <b>by </b><i>, <a class="ref" href="tarski.html#D1">TARSKI:def 1</a></i>;<br/><a NAME="E7:15_1_12_1"/><b>then </b>
1 <a href="hidden.html#R2">in</a> 1
 <b>by </b><i/>;<br/><b>hence </b><a NAME="E8:15_1_12_1"/>
contradiction
 ;<br/></div><b>end;</b></div>
<div><i><font color="Green">E99</font></i>: <a class="txt" onclick="hs2(this)" href="javascript:()" title="15_1_12_2"><b>now </b></a><div class="add"><b>assume </b><a NAME="E1:15_1_12_2"/>
<font color="Maroon">C</font> <a href="lattice3.html#K13">"\/"</a> <font color="Maroon">D</font> <a href="hidden.html#R1">=</a> <font color="Maroon">C</font>
 ;<br/><a NAME="E2:15_1_12_2"/><b>then </b>
<font color="Maroon">C</font> <a href="orders_2.html#NR2" target="_self">&gt;=</a> <font color="Maroon">D</font>
 <b>by </b><i><a class="ref" href="yellow_0.html#T24">YELLOW_0:24</a></i>;<br/><a NAME="E3:15_1_12_2"/><b>then </b>
<font color="Maroon">c</font> <a href="orders_2.html#NR2" target="_self">&gt;=</a> <font color="Maroon">d</font>
 <b>by </b><i><a class="ref" href="yellow_0.html#T61">YELLOW_0:61</a></i>;<br/><a NAME="E4:15_1_12_2"/><b>then </b>
<font color="Maroon">dj</font> <a href="orders_2.html#NR2" target="_self">&gt;=</a> <font color="Maroon">td</font>
 <b>by </b><i>, <a class="ref" href="waybel_0.html#T66">WAYBEL_0:66</a></i>;<br/><a NAME="E5:15_1_12_2"/><b>then </b><i><font color="Green">E100</font></i>: 
<font color="Maroon">td</font> <a href="tarski.html#R1">c=</a> <font color="Maroon">dj</font>
 <b>by </b><i><a class="ref" href="yellow_1.html#T3">YELLOW_1:3</a></i>;<br/><a NAME="E6:15_1_12_2"/>
( 2 <a href="hidden.html#R2">in</a> <font color="Maroon">td</font> &amp; 2 <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> 1 )
 <b>by </b><i>, <a class="ref" href="tarski.html#D1">TARSKI:def 1</a></i>;<br/><b>hence </b><a NAME="E7:15_1_12_2"/>
contradiction
 <b>by </b><i><a class="ref" href="yellow11.html#T1" target="_self">Th1</a>, , <a class="ref" href="tarski.html#D1">TARSKI:def 1</a></i>;<br/></div><b>end;</b></div>
<div><i><font color="Green">E101</font></i>: <a class="txt" onclick="hs2(this)" href="javascript:()" title="15_1_12_3"><b>now </b></a><div class="add"><b>assume </b><a NAME="E1:15_1_12_3"/>
<font color="Maroon">C</font> <a href="lattice3.html#K13">"\/"</a> <font color="Maroon">D</font> <a href="hidden.html#R1">=</a> <font color="Maroon">D</font>
 ;<br/><a NAME="E2:15_1_12_3"/><b>then </b>
<font color="Maroon">D</font> <a href="orders_2.html#NR2" target="_self">&gt;=</a> <font color="Maroon">C</font>
 <b>by </b><i><a class="ref" href="yellow_0.html#T22">YELLOW_0:22</a></i>;<br/><a NAME="E3:15_1_12_3"/><b>then </b>
<font color="Maroon">d</font> <a href="orders_2.html#NR2" target="_self">&gt;=</a> <font color="Maroon">c</font>
 <b>by </b><i><a class="ref" href="yellow_0.html#T61">YELLOW_0:61</a></i>;<br/><a NAME="E4:15_1_12_3"/><b>then </b>
<font color="Maroon">td</font> <a href="orders_2.html#NR2" target="_self">&gt;=</a> <font color="Maroon">dj</font>
 <b>by </b><i>, <a class="ref" href="waybel_0.html#T66">WAYBEL_0:66</a></i>;<br/><a NAME="E5:15_1_12_3"/><b>then </b><i><font color="Green">E102</font></i>: 
<font color="Maroon">dj</font> <a href="tarski.html#R1">c=</a> <font color="Maroon">td</font>
 <b>by </b><i><a class="ref" href="yellow_1.html#T3">YELLOW_1:3</a></i>;<br/><a NAME="E6:15_1_12_3"/>
( 1 <a href="hidden.html#R2">in</a> <font color="Maroon">dj</font> &amp; 1 <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> 2 )
 <b>by </b><i>, <a class="ref" href="tarski.html#D1">TARSKI:def 1</a></i>;<br/><b>hence </b><a NAME="E7:15_1_12_3"/>
contradiction
 <b>by </b><i><a class="ref" href="yellow11.html#T2" target="_self">Th2</a>, , <a class="ref" href="tarski.html#D1">TARSKI:def 1</a></i>;<br/></div><b>end;</b></div>
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="15_1_12_4"><b>now </b></a><div class="add"><b>assume </b><a NAME="E1:15_1_12_4"/>
<font color="Maroon">C</font> <a href="lattice3.html#K13">"\/"</a> <font color="Maroon">D</font> <a href="hidden.html#R1">=</a> <font color="Maroon">A</font>
 ;<br/><a NAME="E2:15_1_12_4"/><b>then </b>
<font color="Maroon">A</font> <a href="orders_2.html#NR2" target="_self">&gt;=</a> <font color="Maroon">C</font>
 <b>by </b><i><a class="ref" href="yellow_0.html#T22">YELLOW_0:22</a></i>;<br/><a NAME="E3:15_1_12_4"/><b>then </b>
<font color="Maroon">a</font> <a href="orders_2.html#NR2" target="_self">&gt;=</a> <font color="Maroon">c</font>
 <b>by </b><i><a class="ref" href="yellow_0.html#T61">YELLOW_0:61</a></i>;<br/><a NAME="E4:15_1_12_4"/><b>then </b>
<font color="Maroon">z</font> <a href="orders_2.html#NR2" target="_self">&gt;=</a> <font color="Maroon">dj</font>
 <b>by </b><i>, <a class="ref" href="waybel_0.html#T66">WAYBEL_0:66</a></i>;<br/><a NAME="E5:15_1_12_4"/><b>then </b>
<font color="Maroon">dj</font> <a href="tarski.html#R1">c=</a> <font color="Maroon">z</font>
 <b>by </b><i><a class="ref" href="yellow_1.html#T3">YELLOW_1:3</a></i>;<br/><b>hence </b><a NAME="E6:15_1_12_4"/>
contradiction
 <b>by </b><i>, <a class="ref" href="xboole_1.html#T3">XBOOLE_1:3</a></i>;<br/></div><b>end;</b></div>
<b>hence </b><a NAME="E12:15_1_12"/>
<font color="Maroon">C</font> <a href="lattice3.html#K13">"\/"</a> <font color="Maroon">D</font> <a href="hidden.html#R1">=</a> <font color="Maroon">E</font>
 <b>by </b><i>, , , , <a class="ref" href="yellow11.html#T1" target="_self">Th1</a></i>;<br/>


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


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

<b>thus </b><a NAME="E3:15"/>
(  ex <font color="Olive">a</font>, <font color="Olive">b</font>, <font color="Olive">c</font>, <font color="Olive">d</font>, <font color="Olive">e</font> being  <a href="struct_0.html#NM1">Element</a> of <font color="Maroon">L</font> st <br/>( <font color="Olive">a</font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> <font color="Olive">b</font> &amp; <font color="Olive">a</font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> <font color="Olive">c</font> &amp; <font color="Olive">a</font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> <font color="Olive">d</font> &amp; <font color="Olive">a</font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> <font color="Olive">e</font> &amp; <font color="Olive">b</font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> <font color="Olive">c</font> &amp; <font color="Olive">b</font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> <font color="Olive">d</font> &amp; <font color="Olive">b</font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> <font color="Olive">e</font> &amp; <font color="Olive">c</font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> <font color="Olive">d</font> &amp; <font color="Olive">c</font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> <font color="Olive">e</font> &amp; <font color="Olive">d</font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> <font color="Olive">e</font> &amp; <font color="Olive">a</font> <a href="lattice3.html#K12">"/\"</a> <font color="Olive">b</font> <a href="hidden.html#R1">=</a> <font color="Olive">a</font> &amp; <font color="Olive">a</font> <a href="lattice3.html#K12">"/\"</a> <font color="Olive">c</font> <a href="hidden.html#R1">=</a> <font color="Olive">a</font> &amp; <font color="Olive">a</font> <a href="lattice3.html#K12">"/\"</a> <font color="Olive">d</font> <a href="hidden.html#R1">=</a> <font color="Olive">a</font> &amp; <font color="Olive">b</font> <a href="lattice3.html#K12">"/\"</a> <font color="Olive">e</font> <a href="hidden.html#R1">=</a> <font color="Olive">b</font> &amp; <font color="Olive">c</font> <a href="lattice3.html#K12">"/\"</a> <font color="Olive">e</font> <a href="hidden.html#R1">=</a> <font color="Olive">c</font> &amp; <font color="Olive">d</font> <a href="lattice3.html#K12">"/\"</a> <font color="Olive">e</font> <a href="hidden.html#R1">=</a> <font color="Olive">d</font> &amp; <font color="Olive">b</font> <a href="lattice3.html#K12">"/\"</a> <font color="Olive">c</font> <a href="hidden.html#R1">=</a> <font color="Olive">a</font> &amp; <font color="Olive">b</font> <a href="lattice3.html#K12">"/\"</a> <font color="Olive">d</font> <a href="hidden.html#R1">=</a> <font color="Olive">a</font> &amp; <font color="Olive">c</font> <a href="lattice3.html#K12">"/\"</a> <font color="Olive">d</font> <a href="hidden.html#R1">=</a> <font color="Olive">a</font> &amp; <font color="Olive">b</font> <a href="lattice3.html#K13">"\/"</a> <font color="Olive">c</font> <a href="hidden.html#R1">=</a> <font color="Olive">e</font> &amp; <font color="Olive">b</font> <a href="lattice3.html#K13">"\/"</a> <font color="Olive">d</font> <a href="hidden.html#R1">=</a> <font color="Olive">e</font> &amp; <font color="Olive">c</font> <a href="lattice3.html#K13">"\/"</a> <font color="Olive">d</font> <a href="hidden.html#R1">=</a> <font color="Olive">e</font> ) implies  ex <font color="Olive">K</font> being <a href="yellow_0.html#V4">full</a> <a href="lattice5.html#NM2">Sublattice</a> of <font color="Maroon">L</font> st  <a href="yellow11.html#K2" target="_self">M_3</a> ,<font color="Olive">K</font> <a href="waybel_1.html#R5">are_isomorphic</a>  )
 <div><a class="txt" onclick="hs2(this)" href="javascript:()" title="15_2"><b>proof </b></a><div class="add">

<b>given </b><font color="Maroon">a</font> being   <a href="struct_0.html#NM1">Element</a> of <font color="Maroon">L</font>, <font color="Maroon">b</font> being   <a href="struct_0.html#NM1">Element</a> of <font color="Maroon">L</font>, <font color="Maroon">c</font> being   <a href="struct_0.html#NM1">Element</a> of <font color="Maroon">L</font>, <font color="Maroon">d</font> being   <a href="struct_0.html#NM1">Element</a> of <font color="Maroon">L</font>, <font color="Maroon">e</font> being   <a href="struct_0.html#NM1">Element</a> of <font color="Maroon">L</font><b> such that </b><a NAME="E1:15_2"/><i><font color="Green">E103</font></i>: 
( <font color="Maroon">a</font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> <font color="Maroon">b</font> &amp; <font color="Maroon">a</font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> <font color="Maroon">c</font> &amp; <font color="Maroon">a</font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> <font color="Maroon">d</font> &amp; <font color="Maroon">a</font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> <font color="Maroon">e</font> &amp; <font color="Maroon">b</font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> <font color="Maroon">c</font> &amp; <font color="Maroon">b</font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> <font color="Maroon">d</font> &amp; <font color="Maroon">b</font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> <font color="Maroon">e</font> &amp; <font color="Maroon">c</font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> <font color="Maroon">d</font> &amp; <font color="Maroon">c</font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> <font color="Maroon">e</font> &amp; <font color="Maroon">d</font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> <font color="Maroon">e</font> &amp; <font color="Maroon">a</font> <a href="lattice3.html#K12">"/\"</a> <font color="Maroon">b</font> <a href="hidden.html#R1">=</a> <font color="Maroon">a</font> &amp; <font color="Maroon">a</font> <a href="lattice3.html#K12">"/\"</a> <font color="Maroon">c</font> <a href="hidden.html#R1">=</a> <font color="Maroon">a</font> &amp; <font color="Maroon">a</font> <a href="lattice3.html#K12">"/\"</a> <font color="Maroon">d</font> <a href="hidden.html#R1">=</a> <font color="Maroon">a</font> &amp; <font color="Maroon">b</font> <a href="lattice3.html#K12">"/\"</a> <font color="Maroon">e</font> <a href="hidden.html#R1">=</a> <font color="Maroon">b</font> &amp; <font color="Maroon">c</font> <a href="lattice3.html#K12">"/\"</a> <font color="Maroon">e</font> <a href="hidden.html#R1">=</a> <font color="Maroon">c</font> &amp; <font color="Maroon">d</font> <a href="lattice3.html#K12">"/\"</a> <font color="Maroon">e</font> <a href="hidden.html#R1">=</a> <font color="Maroon">d</font> &amp; <font color="Maroon">b</font> <a href="lattice3.html#K12">"/\"</a> <font color="Maroon">c</font> <a href="hidden.html#R1">=</a> <font color="Maroon">a</font> &amp; <font color="Maroon">b</font> <a href="lattice3.html#K12">"/\"</a> <font color="Maroon">d</font> <a href="hidden.html#R1">=</a> <font color="Maroon">a</font> &amp; <font color="Maroon">c</font> <a href="lattice3.html#K12">"/\"</a> <font color="Maroon">d</font> <a href="hidden.html#R1">=</a> <font color="Maroon">a</font> &amp; <font color="Maroon">b</font> <a href="lattice3.html#K13">"\/"</a> <font color="Maroon">c</font> <a href="hidden.html#R1">=</a> <font color="Maroon">e</font> &amp; <font color="Maroon">b</font> <a href="lattice3.html#K13">"\/"</a> <font color="Maroon">d</font> <a href="hidden.html#R1">=</a> <font color="Maroon">e</font> &amp; <font color="Maroon">c</font> <a href="lattice3.html#K13">"\/"</a> <font color="Maroon">d</font> <a href="hidden.html#R1">=</a> <font color="Maroon">e</font> )
 ;<br/>

<b>set </b><font color="Maroon">ck</font> = <span class="p1"><a href="domain_1.html#K10">{</a><span class="default"><font color="Maroon">a</font>,<font color="Maroon">b</font>,<font color="Maroon">c</font>,<font color="Maroon">d</font>,<font color="Maroon">e</font></span><a href="domain_1.html#K10">}</a></span>;<br/>
<b>reconsider </b><font color="Maroon">ck</font> = <span class="p1"><a href="domain_1.html#K10">{</a><span class="default"><font color="Maroon">a</font>,<font color="Maroon">b</font>,<font color="Maroon">c</font>,<font color="Maroon">d</font>,<font color="Maroon">e</font></span><a href="domain_1.html#K10">}</a></span> as   <a href="struct_0.html#NM2">Subset</a> of <font color="Maroon">L</font> ;<br/>
<b>set </b><font color="Maroon">K</font> =  <a href="yellow_0.html#K5">subrelstr</a> <font color="Maroon">ck</font>;<br/>
<a NAME="E3:15_2"/><i><font color="Green">E104</font></i>: 
the <a href="struct_0.html#U1">carrier</a> of <span class="p1">(<span class="default"><a href="yellow_0.html#K5">subrelstr</a> <font color="Maroon">ck</font></span>)</span> <a href="hidden.html#R1">=</a> <font color="Maroon">ck</font>
 
<b>by </b><i><a class="ref" href="yellow_0.html#D15">YELLOW_0:def 15</a></i>;<br/>
<a NAME="E4:15_2"/><i><font color="Green">E105</font></i>: 
 <a href="yellow_0.html#K5">subrelstr</a> <font color="Maroon">ck</font> is <a href="yellow_0.html#V5">meet-inheriting</a>
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="15_2_1"><b>proof </b></a><div class="add">

<b>let </b><font color="Maroon">x</font> be   <a href="struct_0.html#NM1">Element</a> of <font color="Maroon">L</font>, <font color="Maroon">y</font> be   <a href="struct_0.html#NM1">Element</a> of <font color="Maroon">L</font>; <i><font color="Red">:: according to </font></i><a class="ref" href="yellow_0.html#D16">YELLOW_0:def 16</a><br/>

<b>assume </b><a NAME="E1:15_2_1"/><i><font color="Green">E106</font></i>: 
( <font color="Maroon">x</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_0.html#K5">subrelstr</a> <font color="Maroon">ck</font></span>)</span> &amp; <font color="Maroon">y</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_0.html#K5">subrelstr</a> <font color="Maroon">ck</font></span>)</span> &amp;  <a href="yellow_0.html#R2">ex_inf_of</a> <span class="p1"><a href="domain_1.html#K7">{</a><span class="default"><font color="Maroon">x</font>,<font color="Maroon">y</font></span><a href="domain_1.html#K7">}</a></span>,<font color="Maroon">L</font> )
 ;<br/>

<div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="15_2_1_1"><b>per </b></a><a class="txt" onclick="hs(this)" href="javascript:()"><b>cases </b></a><span class="hide"><a NAME="E1:15_2_1_1"/>
( ( <font color="Maroon">x</font> <a href="hidden.html#R1">=</a> <font color="Maroon">a</font> &amp; <font color="Maroon">y</font> <a href="hidden.html#R1">=</a> <font color="Maroon">a</font> ) or ( <font color="Maroon">x</font> <a href="hidden.html#R1">=</a> <font color="Maroon">a</font> &amp; <font color="Maroon">y</font> <a href="hidden.html#R1">=</a> <font color="Maroon">b</font> ) or ( <font color="Maroon">x</font> <a href="hidden.html#R1">=</a> <font color="Maroon">a</font> &amp; <font color="Maroon">y</font> <a href="hidden.html#R1">=</a> <font color="Maroon">c</font> ) or ( <font color="Maroon">x</font> <a href="hidden.html#R1">=</a> <font color="Maroon">a</font> &amp; <font color="Maroon">y</font> <a href="hidden.html#R1">=</a> <font color="Maroon">d</font> ) or ( <font color="Maroon">x</font> <a href="hidden.html#R1">=</a> <font color="Maroon">a</font> &amp; <font color="Maroon">y</font> <a href="hidden.html#R1">=</a> <font color="Maroon">e</font> ) or ( <font color="Maroon">x</font> <a href="hidden.html#R1">=</a> <font color="Maroon">b</font> &amp; <font color="Maroon">y</font> <a href="hidden.html#R1">=</a> <font color="Maroon">a</font> ) or ( <font color="Maroon">x</font> <a href="hidden.html#R1">=</a> <font color="Maroon">b</font> &amp; <font color="Maroon">y</font> <a href="hidden.html#R1">=</a> <font color="Maroon">b</font> ) or ( <font color="Maroon">x</font> <a href="hidden.html#R1">=</a> <font color="Maroon">b</font> &amp; <font color="Maroon">y</font> <a href="hidden.html#R1">=</a> <font color="Maroon">c</font> ) or ( <font color="Maroon">x</font> <a href="hidden.html#R1">=</a> <font color="Maroon">b</font> &amp; <font color="Maroon">y</font> <a href="hidden.html#R1">=</a> <font color="Maroon">d</font> ) or ( <font color="Maroon">x</font> <a href="hidden.html#R1">=</a> <font color="Maroon">b</font> &amp; <font color="Maroon">y</font> <a href="hidden.html#R1">=</a> <font color="Maroon">e</font> ) or ( <font color="Maroon">x</font> <a href="hidden.html#R1">=</a> <font color="Maroon">c</font> &amp; <font color="Maroon">y</font> <a href="hidden.html#R1">=</a> <font color="Maroon">a</font> ) or ( <font color="Maroon">x</font> <a href="hidden.html#R1">=</a> <font color="Maroon">c</font> &amp; <font color="Maroon">y</font> <a href="hidden.html#R1">=</a> <font color="Maroon">b</font> ) or ( <font color="Maroon">x</font> <a href="hidden.html#R1">=</a> <font color="Maroon">c</font> &amp; <font color="Maroon">y</font> <a href="hidden.html#R1">=</a> <font color="Maroon">c</font> ) or ( <font color="Maroon">x</font> <a href="hidden.html#R1">=</a> <font color="Maroon">c</font> &amp; <font color="Maroon">y</font> <a href="hidden.html#R1">=</a> <font color="Maroon">d</font> ) or ( <font color="Maroon">x</font> <a href="hidden.html#R1">=</a> <font color="Maroon">c</font> &amp; <font color="Maroon">y</font> <a href="hidden.html#R1">=</a> <font color="Maroon">e</font> ) or ( <font color="Maroon">x</font> <a href="hidden.html#R1">=</a> <font color="Maroon">d</font> &amp; <font color="Maroon">y</font> <a href="hidden.html#R1">=</a> <font color="Maroon">a</font> ) or ( <font color="Maroon">x</font> <a href="hidden.html#R1">=</a> <font color="Maroon">d</font> &amp; <font color="Maroon">y</font> <a href="hidden.html#R1">=</a> <font color="Maroon">b</font> ) or ( <font color="Maroon">x</font> <a href="hidden.html#R1">=</a> <font color="Maroon">d</font> &amp; <font color="Maroon">y</font> <a href="hidden.html#R1">=</a> <font color="Maroon">c</font> ) or ( <font color="Maroon">x</font> <a href="hidden.html#R1">=</a> <font color="Maroon">d</font> &amp; <font color="Maroon">y</font> <a href="hidden.html#R1">=</a> <font color="Maroon">d</font> ) or ( <font color="Maroon">x</font> <a href="hidden.html#R1">=</a> <font color="Maroon">d</font> &amp; <font color="Maroon">y</font> <a href="hidden.html#R1">=</a> <font color="Maroon">e</font> ) or ( <font color="Maroon">x</font> <a href="hidden.html#R1">=</a> <font color="Maroon">e</font> &amp; <font color="Maroon">y</font> <a href="hidden.html#R1">=</a> <font color="Maroon">a</font> ) or ( <font color="Maroon">x</font> <a href="hidden.html#R1">=</a> <font color="Maroon">e</font> &amp; <font color="Maroon">y</font> <a href="hidden.html#R1">=</a> <font color="Maroon">b</font> ) or ( <font color="Maroon">x</font> <a href="hidden.html#R1">=</a> <font color="Maroon">e</font> &amp; <font color="Maroon">y</font> <a href="hidden.html#R1">=</a> <font color="Maroon">c</font> ) or ( <font color="Maroon">x</font> <a href="hidden.html#R1">=</a> <font color="Maroon">e</font> &amp; <font color="Maroon">y</font> <a href="hidden.html#R1">=</a> <font color="Maroon">d</font> ) or ( <font color="Maroon">x</font> <a href="hidden.html#R1">=</a> <font color="Maroon">e</font> &amp; <font color="Maroon">y</font> <a href="hidden.html#R1">=</a> <font color="Maroon">e</font> ) )
 </span><b>by </b><i>, , <a class="ref" href="enumset1.html#D3">ENUMSET1:def 3</a></i>;<br/><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="15_2_1_1_1"><b>suppose </b></a><a NAME="E1:15_2_1_1_1"/>
( <font color="Maroon">x</font> <a href="hidden.html#R1">=</a> <font color="Maroon">a</font> &amp; <font color="Maroon">y</font> <a href="hidden.html#R1">=</a> <font color="Maroon">a</font> )
 ;<br/><div class="add"><a NAME="E2:15_2_1_1_1"/><b>then </b>
 <a href="yellow_0.html#NK4" target="_self">inf</a> <span class="p1"><a href="domain_1.html#K7">{</a><span class="default"><font color="Maroon">x</font>,<font color="Maroon">y</font></span><a href="domain_1.html#K7">}</a></span> <a href="hidden.html#R1">=</a> <font color="Maroon">a</font> <a href="lattice3.html#K12">"/\"</a> <font color="Maroon">a</font>
 <b>by </b><i><a class="ref" href="yellow_0.html#T40">YELLOW_0:40</a></i>;<br/><a NAME="E3:15_2_1_1_1"/><b>then </b>
 <a href="yellow_0.html#NK4" target="_self">inf</a> <span class="p1"><a href="domain_1.html#K7">{</a><span class="default"><font color="Maroon">x</font>,<font color="Maroon">y</font></span><a href="domain_1.html#K7">}</a></span> <a href="hidden.html#R1">=</a> <font color="Maroon">a</font>
 <b>by </b><i><a class="ref" href="yellow_5.html#T2">YELLOW_5:2</a></i>;<br/><b>hence </b><a NAME="E4:15_2_1_1_1"/>
 <a href="yellow_0.html#K2">"/\"</a> <span class="p1"><a href="domain_1.html#K7">{</a><span class="default"><font color="Maroon">x</font>,<font color="Maroon">y</font></span><a href="domain_1.html#K7">}</a></span>,<font color="Maroon">L</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_0.html#K5">subrelstr</a> <font color="Maroon">ck</font></span>)</span>
 <b>by </b><i>, <a class="ref" href="enumset1.html#D3">ENUMSET1:def 3</a></i>;<br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="15_2_1_1_2"><b>suppose </b></a><a NAME="E1:15_2_1_1_2"/>
( <font color="Maroon">x</font> <a href="hidden.html#R1">=</a> <font color="Maroon">a</font> &amp; <font color="Maroon">y</font> <a href="hidden.html#R1">=</a> <font color="Maroon">b</font> )
 ;<br/><div class="add"><a NAME="E2:15_2_1_1_2"/><b>then </b>
 <a href="yellow_0.html#NK4" target="_self">inf</a> <span class="p1"><a href="domain_1.html#K7">{</a><span class="default"><font color="Maroon">x</font>,<font color="Maroon">y</font></span><a href="domain_1.html#K7">}</a></span> <a href="hidden.html#R1">=</a> <font color="Maroon">a</font> <a href="lattice3.html#K12">"/\"</a> <font color="Maroon">b</font>
 <b>by </b><i><a class="ref" href="yellow_0.html#T40">YELLOW_0:40</a></i>;<br/><b>hence </b><a NAME="E3:15_2_1_1_2"/>
 <a href="yellow_0.html#K2">"/\"</a> <span class="p1"><a href="domain_1.html#K7">{</a><span class="default"><font color="Maroon">x</font>,<font color="Maroon">y</font></span><a href="domain_1.html#K7">}</a></span>,<font color="Maroon">L</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_0.html#K5">subrelstr</a> <font color="Maroon">ck</font></span>)</span>
 <b>by </b><i>, , <a class="ref" href="enumset1.html#D3">ENUMSET1:def 3</a></i>;<br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="15_2_1_1_3"><b>suppose </b></a><a NAME="E1:15_2_1_1_3"/>
( <font color="Maroon">x</font> <a href="hidden.html#R1">=</a> <font color="Maroon">a</font> &amp; <font color="Maroon">y</font> <a href="hidden.html#R1">=</a> <font color="Maroon">c</font> )
 ;<br/><div class="add"><a NAME="E2:15_2_1_1_3"/><b>then </b>
 <a href="yellow_0.html#NK4" target="_self">inf</a> <span class="p1"><a href="domain_1.html#K7">{</a><span class="default"><font color="Maroon">x</font>,<font color="Maroon">y</font></span><a href="domain_1.html#K7">}</a></span> <a href="hidden.html#R1">=</a> <font color="Maroon">a</font> <a href="lattice3.html#K12">"/\"</a> <font color="Maroon">c</font>
 <b>by </b><i><a class="ref" href="yellow_0.html#T40">YELLOW_0:40</a></i>;<br/><b>hence </b><a NAME="E3:15_2_1_1_3"/>
 <a href="yellow_0.html#K2">"/\"</a> <span class="p1"><a href="domain_1.html#K7">{</a><span class="default"><font color="Maroon">x</font>,<font color="Maroon">y</font></span><a href="domain_1.html#K7">}</a></span>,<font color="Maroon">L</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_0.html#K5">subrelstr</a> <font color="Maroon">ck</font></span>)</span>
 <b>by </b><i>, , <a class="ref" href="enumset1.html#D3">ENUMSET1:def 3</a></i>;<br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="15_2_1_1_4"><b>suppose </b></a><a NAME="E1:15_2_1_1_4"/>
( <font color="Maroon">x</font> <a href="hidden.html#R1">=</a> <font color="Maroon">a</font> &amp; <font color="Maroon">y</font> <a href="hidden.html#R1">=</a> <font color="Maroon">d</font> )
 ;<br/><div class="add"><a NAME="E2:15_2_1_1_4"/><b>then </b>
 <a href="yellow_0.html#NK4" target="_self">inf</a> <span class="p1"><a href="domain_1.html#K7">{</a><span class="default"><font color="Maroon">x</font>,<font color="Maroon">y</font></span><a href="domain_1.html#K7">}</a></span> <a href="hidden.html#R1">=</a> <font color="Maroon">a</font> <a href="lattice3.html#K12">"/\"</a> <font color="Maroon">d</font>
 <b>by </b><i><a class="ref" href="yellow_0.html#T40">YELLOW_0:40</a></i>;<br/><b>hence </b><a NAME="E3:15_2_1_1_4"/>
 <a href="yellow_0.html#K2">"/\"</a> <span class="p1"><a href="domain_1.html#K7">{</a><span class="default"><font color="Maroon">x</font>,<font color="Maroon">y</font></span><a href="domain_1.html#K7">}</a></span>,<font color="Maroon">L</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_0.html#K5">subrelstr</a> <font color="Maroon">ck</font></span>)</span>
 <b>by </b><i>, , <a class="ref" href="enumset1.html#D3">ENUMSET1:def 3</a></i>;<br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="15_2_1_1_5"><b>suppose </b></a><a NAME="E1:15_2_1_1_5"/><i><font color="Green">E107</font></i>: 
( <font color="Maroon">x</font> <a href="hidden.html#R1">=</a> <font color="Maroon">a</font> &amp; <font color="Maroon">y</font> <a href="hidden.html#R1">=</a> <font color="Maroon">e</font> )
 ;<br/><div class="add"><a NAME="E2:15_2_1_1_5"/>
( <font color="Maroon">a</font> <a href="orders_2.html#R3">&lt;=</a> <font color="Maroon">c</font> &amp; <font color="Maroon">c</font> <a href="orders_2.html#R3">&lt;=</a> <font color="Maroon">e</font> )
 <b>by </b><i>, <a class="ref" href="yellow_0.html#T25">YELLOW_0:25</a></i>;<br/><a NAME="E3:15_2_1_1_5"/><b>then </b>
<font color="Maroon">a</font> <a href="orders_2.html#R3">&lt;=</a> <font color="Maroon">e</font>
 <b>by </b><i><a class="ref" href="orders_2.html#T26">ORDERS_2:26</a></i>;<br/><a NAME="E4:15_2_1_1_5"/><b>then </b>
<font color="Maroon">a</font> <a href="lattice3.html#K12">"/\"</a> <font color="Maroon">e</font> <a href="hidden.html#R1">=</a> <font color="Maroon">a</font>
 <b>by </b><i><a class="ref" href="yellow_0.html#T25">YELLOW_0:25</a></i>;<br/><a NAME="E5:15_2_1_1_5"/><b>then </b>
 <a href="yellow_0.html#NK4" target="_self">inf</a> <span class="p1"><a href="domain_1.html#K7">{</a><span class="default"><font color="Maroon">x</font>,<font color="Maroon">y</font></span><a href="domain_1.html#K7">}</a></span> <a href="hidden.html#R1">=</a> <font color="Maroon">a</font>
 <b>by </b><i>, <a class="ref" href="yellow_0.html#T40">YELLOW_0:40</a></i>;<br/><b>hence </b><a NAME="E6:15_2_1_1_5"/>
 <a href="yellow_0.html#K2">"/\"</a> <span class="p1"><a href="domain_1.html#K7">{</a><span class="default"><font color="Maroon">x</font>,<font color="Maroon">y</font></span><a href="domain_1.html#K7">}</a></span>,<font color="Maroon">L</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_0.html#K5">subrelstr</a> <font color="Maroon">ck</font></span>)</span>
 <b>by </b><i>, <a class="ref" href="enumset1.html#D3">ENUMSET1:def 3</a></i>;<br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="15_2_1_1_6"><b>suppose </b></a><a NAME="E1:15_2_1_1_6"/>
( <font color="Maroon">x</font> <a href="hidden.html#R1">=</a> <font color="Maroon">b</font> &amp; <font color="Maroon">y</font> <a href="hidden.html#R1">=</a> <font color="Maroon">a</font> )
 ;<br/><div class="add"><a NAME="E2:15_2_1_1_6"/><b>then </b>
 <a href="yellow_0.html#NK4" target="_self">inf</a> <span class="p1"><a href="domain_1.html#K7">{</a><span class="default"><font color="Maroon">x</font>,<font color="Maroon">y</font></span><a href="domain_1.html#K7">}</a></span> <a href="hidden.html#R1">=</a> <font color="Maroon">a</font> <a href="lattice3.html#K12">"/\"</a> <font color="Maroon">b</font>
 <b>by </b><i><a class="ref" href="yellow_0.html#T40">YELLOW_0:40</a></i>;<br/><b>hence </b><a NAME="E3:15_2_1_1_6"/>
 <a href="yellow_0.html#K2">"/\"</a> <span class="p1"><a href="domain_1.html#K7">{</a><span class="default"><font color="Maroon">x</font>,<font color="Maroon">y</font></span><a href="domain_1.html#K7">}</a></span>,<font color="Maroon">L</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_0.html#K5">subrelstr</a> <font color="Maroon">ck</font></span>)</span>
 <b>by </b><i>, , <a class="ref" href="enumset1.html#D3">ENUMSET1:def 3</a></i>;<br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="15_2_1_1_7"><b>suppose </b></a><a NAME="E1:15_2_1_1_7"/>
( <font color="Maroon">x</font> <a href="hidden.html#R1">=</a> <font color="Maroon">b</font> &amp; <font color="Maroon">y</font> <a href="hidden.html#R1">=</a> <font color="Maroon">b</font> )
 ;<br/><div class="add"><a NAME="E2:15_2_1_1_7"/><b>then </b>
 <a href="yellow_0.html#NK4" target="_self">inf</a> <span class="p1"><a href="domain_1.html#K7">{</a><span class="default"><font color="Maroon">x</font>,<font color="Maroon">y</font></span><a href="domain_1.html#K7">}</a></span> <a href="hidden.html#R1">=</a> <font color="Maroon">b</font> <a href="lattice3.html#K12">"/\"</a> <font color="Maroon">b</font>
 <b>by </b><i><a class="ref" href="yellow_0.html#T40">YELLOW_0:40</a></i>;<br/><a NAME="E3:15_2_1_1_7"/><b>then </b>
 <a href="yellow_0.html#NK4" target="_self">inf</a> <span class="p1"><a href="domain_1.html#K7">{</a><span class="default"><font color="Maroon">x</font>,<font color="Maroon">y</font></span><a href="domain_1.html#K7">}</a></span> <a href="hidden.html#R1">=</a> <font color="Maroon">b</font>
 <b>by </b><i><a class="ref" href="yellow_5.html#T2">YELLOW_5:2</a></i>;<br/><b>hence </b><a NAME="E4:15_2_1_1_7"/>
 <a href="yellow_0.html#K2">"/\"</a> <span class="p1"><a href="domain_1.html#K7">{</a><span class="default"><font color="Maroon">x</font>,<font color="Maroon">y</font></span><a href="domain_1.html#K7">}</a></span>,<font color="Maroon">L</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_0.html#K5">subrelstr</a> <font color="Maroon">ck</font></span>)</span>
 <b>by </b><i>, <a class="ref" href="enumset1.html#D3">ENUMSET1:def 3</a></i>;<br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="15_2_1_1_8"><b>suppose </b></a><a NAME="E1:15_2_1_1_8"/>
( <font color="Maroon">x</font> <a href="hidden.html#R1">=</a> <font color="Maroon">b</font> &amp; <font color="Maroon">y</font> <a href="hidden.html#R1">=</a> <font color="Maroon">c</font> )
 ;<br/><div class="add"><a NAME="E2:15_2_1_1_8"/><b>then </b>
 <a href="yellow_0.html#NK4" target="_self">inf</a> <span class="p1"><a href="domain_1.html#K7">{</a><span class="default"><font color="Maroon">x</font>,<font color="Maroon">y</font></span><a href="domain_1.html#K7">}</a></span> <a href="hidden.html#R1">=</a> <font color="Maroon">b</font> <a href="lattice3.html#K12">"/\"</a> <font color="Maroon">c</font>
 <b>by </b><i><a class="ref" href="yellow_0.html#T40">YELLOW_0:40</a></i>;<br/><b>hence </b><a NAME="E3:15_2_1_1_8"/>
 <a href="yellow_0.html#K2">"/\"</a> <span class="p1"><a href="domain_1.html#K7">{</a><span class="default"><font color="Maroon">x</font>,<font color="Maroon">y</font></span><a href="domain_1.html#K7">}</a></span>,<font color="Maroon">L</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_0.html#K5">subrelstr</a> <font color="Maroon">ck</font></span>)</span>
 <b>by </b><i>, , <a class="ref" href="enumset1.html#D3">ENUMSET1:def 3</a></i>;<br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="15_2_1_1_9"><b>suppose </b></a><a NAME="E1:15_2_1_1_9"/>
( <font color="Maroon">x</font> <a href="hidden.html#R1">=</a> <font color="Maroon">b</font> &amp; <font color="Maroon">y</font> <a href="hidden.html#R1">=</a> <font color="Maroon">d</font> )
 ;<br/><div class="add"><a NAME="E2:15_2_1_1_9"/><b>then </b>
 <a href="yellow_0.html#NK4" target="_self">inf</a> <span class="p1"><a href="domain_1.html#K7">{</a><span class="default"><font color="Maroon">x</font>,<font color="Maroon">y</font></span><a href="domain_1.html#K7">}</a></span> <a href="hidden.html#R1">=</a> <font color="Maroon">b</font> <a href="lattice3.html#K12">"/\"</a> <font color="Maroon">d</font>
 <b>by </b><i><a class="ref" href="yellow_0.html#T40">YELLOW_0:40</a></i>;<br/><b>hence </b><a NAME="E3:15_2_1_1_9"/>
 <a href="yellow_0.html#K2">"/\"</a> <span class="p1"><a href="domain_1.html#K7">{</a><span class="default"><font color="Maroon">x</font>,<font color="Maroon">y</font></span><a href="domain_1.html#K7">}</a></span>,<font color="Maroon">L</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_0.html#K5">subrelstr</a> <font color="Maroon">ck</font></span>)</span>
 <b>by </b><i>, , <a class="ref" href="enumset1.html#D3">ENUMSET1:def 3</a></i>;<br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="15_2_1_1_10"><b>suppose </b></a><a NAME="E1:15_2_1_1_10"/>
( <font color="Maroon">x</font> <a href="hidden.html#R1">=</a> <font color="Maroon">b</font> &amp; <font color="Maroon">y</font> <a href="hidden.html#R1">=</a> <font color="Maroon">e</font> )
 ;<br/><div class="add"><a NAME="E2:15_2_1_1_10"/><b>then </b>
 <a href="yellow_0.html#NK4" target="_self">inf</a> <span class="p1"><a href="domain_1.html#K7">{</a><span class="default"><font color="Maroon">x</font>,<font color="Maroon">y</font></span><a href="domain_1.html#K7">}</a></span> <a href="hidden.html#R1">=</a> <font color="Maroon">b</font> <a href="lattice3.html#K12">"/\"</a> <font color="Maroon">e</font>
 <b>by </b><i><a class="ref" href="yellow_0.html#T40">YELLOW_0:40</a></i>;<br/><b>hence </b><a NAME="E3:15_2_1_1_10"/>
 <a href="yellow_0.html#K2">"/\"</a> <span class="p1"><a href="domain_1.html#K7">{</a><span class="default"><font color="Maroon">x</font>,<font color="Maroon">y</font></span><a href="domain_1.html#K7">}</a></span>,<font color="Maroon">L</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_0.html#K5">subrelstr</a> <font color="Maroon">ck</font></span>)</span>
 <b>by </b><i>, , <a class="ref" href="enumset1.html#D3">ENUMSET1:def 3</a></i>;<br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="15_2_1_1_11"><b>suppose </b></a><a NAME="E1:15_2_1_1_11"/>
( <font color="Maroon">x</font> <a href="hidden.html#R1">=</a> <font color="Maroon">c</font> &amp; <font color="Maroon">y</font> <a href="hidden.html#R1">=</a> <font color="Maroon">a</font> )
 ;<br/><div class="add"><a NAME="E2:15_2_1_1_11"/><b>then </b>
 <a href="yellow_0.html#NK4" target="_self">inf</a> <span class="p1"><a href="domain_1.html#K7">{</a><span class="default"><font color="Maroon">x</font>,<font color="Maroon">y</font></span><a href="domain_1.html#K7">}</a></span> <a href="hidden.html#R1">=</a> <font color="Maroon">a</font> <a href="lattice3.html#K12">"/\"</a> <font color="Maroon">c</font>
 <b>by </b><i><a class="ref" href="yellow_0.html#T40">YELLOW_0:40</a></i>;<br/><b>hence </b><a NAME="E3:15_2_1_1_11"/>
 <a href="yellow_0.html#K2">"/\"</a> <span class="p1"><a href="domain_1.html#K7">{</a><span class="default"><font color="Maroon">x</font>,<font color="Maroon">y</font></span><a href="domain_1.html#K7">}</a></span>,<font color="Maroon">L</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_0.html#K5">subrelstr</a> <font color="Maroon">ck</font></span>)</span>
 <b>by </b><i>, , <a class="ref" href="enumset1.html#D3">ENUMSET1:def 3</a></i>;<br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="15_2_1_1_12"><b>suppose </b></a><a NAME="E1:15_2_1_1_12"/>
( <font color="Maroon">x</font> <a href="hidden.html#R1">=</a> <font color="Maroon">c</font> &amp; <font color="Maroon">y</font> <a href="hidden.html#R1">=</a> <font color="Maroon">b</font> )
 ;<br/><div class="add"><a NAME="E2:15_2_1_1_12"/><b>then </b>
 <a href="yellow_0.html#NK4" target="_self">inf</a> <span class="p1"><a href="domain_1.html#K7">{</a><span class="default"><font color="Maroon">x</font>,<font color="Maroon">y</font></span><a href="domain_1.html#K7">}</a></span> <a href="hidden.html#R1">=</a> <font color="Maroon">b</font> <a href="lattice3.html#K12">"/\"</a> <font color="Maroon">c</font>
 <b>by </b><i><a class="ref" href="yellow_0.html#T40">YELLOW_0:40</a></i>;<br/><b>hence </b><a NAME="E3:15_2_1_1_12"/>
 <a href="yellow_0.html#K2">"/\"</a> <span class="p1"><a href="domain_1.html#K7">{</a><span class="default"><font color="Maroon">x</font>,<font color="Maroon">y</font></span><a href="domain_1.html#K7">}</a></span>,<font color="Maroon">L</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_0.html#K5">subrelstr</a> <font color="Maroon">ck</font></span>)</span>
 <b>by </b><i>, , <a class="ref" href="enumset1.html#D3">ENUMSET1:def 3</a></i>;<br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="15_2_1_1_13"><b>suppose </b></a><a NAME="E1:15_2_1_1_13"/>
( <font color="Maroon">x</font> <a href="hidden.html#R1">=</a> <font color="Maroon">c</font> &amp; <font color="Maroon">y</font> <a href="hidden.html#R1">=</a> <font color="Maroon">c</font> )
 ;<br/><div class="add"><a NAME="E2:15_2_1_1_13"/><b>then </b>
 <a href="yellow_0.html#NK4" target="_self">inf</a> <span class="p1"><a href="domain_1.html#K7">{</a><span class="default"><font color="Maroon">x</font>,<font color="Maroon">y</font></span><a href="domain_1.html#K7">}</a></span> <a href="hidden.html#R1">=</a> <font color="Maroon">c</font> <a href="lattice3.html#K12">"/\"</a> <font color="Maroon">c</font>
 <b>by </b><i><a class="ref" href="yellow_0.html#T40">YELLOW_0:40</a></i>;<br/><a NAME="E3:15_2_1_1_13"/><b>then </b>
 <a href="yellow_0.html#NK4" target="_self">inf</a> <span class="p1"><a href="domain_1.html#K7">{</a><span class="default"><font color="Maroon">x</font>,<font color="Maroon">y</font></span><a href="domain_1.html#K7">}</a></span> <a href="hidden.html#R1">=</a> <font color="Maroon">c</font>
 <b>by </b><i><a class="ref" href="yellow_5.html#T2">YELLOW_5:2</a></i>;<br/><b>hence </b><a NAME="E4:15_2_1_1_13"/>
 <a href="yellow_0.html#K2">"/\"</a> <span class="p1"><a href="domain_1.html#K7">{</a><span class="default"><font color="Maroon">x</font>,<font color="Maroon">y</font></span><a href="domain_1.html#K7">}</a></span>,<font color="Maroon">L</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_0.html#K5">subrelstr</a> <font color="Maroon">ck</font></span>)</span>
 <b>by </b><i>, <a class="ref" href="enumset1.html#D3">ENUMSET1:def 3</a></i>;<br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="15_2_1_1_14"><b>suppose </b></a><a NAME="E1:15_2_1_1_14"/>
( <font color="Maroon">x</font> <a href="hidden.html#R1">=</a> <font color="Maroon">c</font> &amp; <font color="Maroon">y</font> <a href="hidden.html#R1">=</a> <font color="Maroon">d</font> )
 ;<br/><div class="add"><a NAME="E2:15_2_1_1_14"/><b>then </b>
 <a href="yellow_0.html#NK4" target="_self">inf</a> <span class="p1"><a href="domain_1.html#K7">{</a><span class="default"><font color="Maroon">x</font>,<font color="Maroon">y</font></span><a href="domain_1.html#K7">}</a></span> <a href="hidden.html#R1">=</a> <font color="Maroon">c</font> <a href="lattice3.html#K12">"/\"</a> <font color="Maroon">d</font>
 <b>by </b><i><a class="ref" href="yellow_0.html#T40">YELLOW_0:40</a></i>;<br/><b>hence </b><a NAME="E3:15_2_1_1_14"/>
 <a href="yellow_0.html#K2">"/\"</a> <span class="p1"><a href="domain_1.html#K7">{</a><span class="default"><font color="Maroon">x</font>,<font color="Maroon">y</font></span><a href="domain_1.html#K7">}</a></span>,<font color="Maroon">L</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_0.html#K5">subrelstr</a> <font color="Maroon">ck</font></span>)</span>
 <b>by </b><i>, , <a class="ref" href="enumset1.html#D3">ENUMSET1:def 3</a></i>;<br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="15_2_1_1_15"><b>suppose </b></a><a NAME="E1:15_2_1_1_15"/>
( <font color="Maroon">x</font> <a href="hidden.html#R1">=</a> <font color="Maroon">c</font> &amp; <font color="Maroon">y</font> <a href="hidden.html#R1">=</a> <font color="Maroon">e</font> )
 ;<br/><div class="add"><a NAME="E2:15_2_1_1_15"/><b>then </b>
 <a href="yellow_0.html#NK4" target="_self">inf</a> <span class="p1"><a href="domain_1.html#K7">{</a><span class="default"><font color="Maroon">x</font>,<font color="Maroon">y</font></span><a href="domain_1.html#K7">}</a></span> <a href="hidden.html#R1">=</a> <font color="Maroon">c</font> <a href="lattice3.html#K12">"/\"</a> <font color="Maroon">e</font>
 <b>by </b><i><a class="ref" href="yellow_0.html#T40">YELLOW_0:40</a></i>;<br/><b>hence </b><a NAME="E3:15_2_1_1_15"/>
 <a href="yellow_0.html#K2">"/\"</a> <span class="p1"><a href="domain_1.html#K7">{</a><span class="default"><font color="Maroon">x</font>,<font color="Maroon">y</font></span><a href="domain_1.html#K7">}</a></span>,<font color="Maroon">L</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_0.html#K5">subrelstr</a> <font color="Maroon">ck</font></span>)</span>
 <b>by </b><i>, , <a class="ref" href="enumset1.html#D3">ENUMSET1:def 3</a></i>;<br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="15_2_1_1_16"><b>suppose </b></a><a NAME="E1:15_2_1_1_16"/>
( <font color="Maroon">x</font> <a href="hidden.html#R1">=</a> <font color="Maroon">d</font> &amp; <font color="Maroon">y</font> <a href="hidden.html#R1">=</a> <font color="Maroon">a</font> )
 ;<br/><div class="add"><a NAME="E2:15_2_1_1_16"/><b>then </b>
 <a href="yellow_0.html#NK4" target="_self">inf</a> <span class="p1"><a href="domain_1.html#K7">{</a><span class="default"><font color="Maroon">x</font>,<font color="Maroon">y</font></span><a href="domain_1.html#K7">}</a></span> <a href="hidden.html#R1">=</a> <font color="Maroon">a</font> <a href="lattice3.html#K12">"/\"</a> <font color="Maroon">d</font>
 <b>by </b><i><a class="ref" href="yellow_0.html#T40">YELLOW_0:40</a></i>;<br/><b>hence </b><a NAME="E3:15_2_1_1_16"/>
 <a href="yellow_0.html#K2">"/\"</a> <span class="p1"><a href="domain_1.html#K7">{</a><span class="default"><font color="Maroon">x</font>,<font color="Maroon">y</font></span><a href="domain_1.html#K7">}</a></span>,<font color="Maroon">L</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_0.html#K5">subrelstr</a> <font color="Maroon">ck</font></span>)</span>
 <b>by </b><i>, , <a class="ref" href="enumset1.html#D3">ENUMSET1:def 3</a></i>;<br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="15_2_1_1_17"><b>suppose </b></a><a NAME="E1:15_2_1_1_17"/>
( <font color="Maroon">x</font> <a href="hidden.html#R1">=</a> <font color="Maroon">d</font> &amp; <font color="Maroon">y</font> <a href="hidden.html#R1">=</a> <font color="Maroon">b</font> )
 ;<br/><div class="add"><a NAME="E2:15_2_1_1_17"/><b>then </b>
 <a href="yellow_0.html#NK4" target="_self">inf</a> <span class="p1"><a href="domain_1.html#K7">{</a><span class="default"><font color="Maroon">x</font>,<font color="Maroon">y</font></span><a href="domain_1.html#K7">}</a></span> <a href="hidden.html#R1">=</a> <font color="Maroon">b</font> <a href="lattice3.html#K12">"/\"</a> <font color="Maroon">d</font>
 <b>by </b><i><a class="ref" href="yellow_0.html#T40">YELLOW_0:40</a></i>;<br/><b>hence </b><a NAME="E3:15_2_1_1_17"/>
 <a href="yellow_0.html#K2">"/\"</a> <span class="p1"><a href="domain_1.html#K7">{</a><span class="default"><font color="Maroon">x</font>,<font color="Maroon">y</font></span><a href="domain_1.html#K7">}</a></span>,<font color="Maroon">L</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_0.html#K5">subrelstr</a> <font color="Maroon">ck</font></span>)</span>
 <b>by </b><i>, , <a class="ref" href="enumset1.html#D3">ENUMSET1:def 3</a></i>;<br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="15_2_1_1_18"><b>suppose </b></a><a NAME="E1:15_2_1_1_18"/>
( <font color="Maroon">x</font> <a href="hidden.html#R1">=</a> <font color="Maroon">d</font> &amp; <font color="Maroon">y</font> <a href="hidden.html#R1">=</a> <font color="Maroon">c</font> )
 ;<br/><div class="add"><a NAME="E2:15_2_1_1_18"/><b>then </b>
 <a href="yellow_0.html#NK4" target="_self">inf</a> <span class="p1"><a href="domain_1.html#K7">{</a><span class="default"><font color="Maroon">x</font>,<font color="Maroon">y</font></span><a href="domain_1.html#K7">}</a></span> <a href="hidden.html#R1">=</a> <font color="Maroon">c</font> <a href="lattice3.html#K12">"/\"</a> <font color="Maroon">d</font>
 <b>by </b><i><a class="ref" href="yellow_0.html#T40">YELLOW_0:40</a></i>;<br/><b>hence </b><a NAME="E3:15_2_1_1_18"/>
 <a href="yellow_0.html#K2">"/\"</a> <span class="p1"><a href="domain_1.html#K7">{</a><span class="default"><font color="Maroon">x</font>,<font color="Maroon">y</font></span><a href="domain_1.html#K7">}</a></span>,<font color="Maroon">L</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_0.html#K5">subrelstr</a> <font color="Maroon">ck</font></span>)</span>
 <b>by </b><i>, , <a class="ref" href="enumset1.html#D3">ENUMSET1:def 3</a></i>;<br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="15_2_1_1_19"><b>suppose </b></a><a NAME="E1:15_2_1_1_19"/>
( <font color="Maroon">x</font> <a href="hidden.html#R1">=</a> <font color="Maroon">d</font> &amp; <font color="Maroon">y</font> <a href="hidden.html#R1">=</a> <font color="Maroon">d</font> )
 ;<br/><div class="add"><a NAME="E2:15_2_1_1_19"/><b>then </b>
 <a href="yellow_0.html#NK4" target="_self">inf</a> <span class="p1"><a href="domain_1.html#K7">{</a><span class="default"><font color="Maroon">x</font>,<font color="Maroon">y</font></span><a href="domain_1.html#K7">}</a></span> <a href="hidden.html#R1">=</a> <font color="Maroon">d</font> <a href="lattice3.html#K12">"/\"</a> <font color="Maroon">d</font>
 <b>by </b><i><a class="ref" href="yellow_0.html#T40">YELLOW_0:40</a></i>;<br/><a NAME="E3:15_2_1_1_19"/><b>then </b>
 <a href="yellow_0.html#NK4" target="_self">inf</a> <span class="p1"><a href="domain_1.html#K7">{</a><span class="default"><font color="Maroon">x</font>,<font color="Maroon">y</font></span><a href="domain_1.html#K7">}</a></span> <a href="hidden.html#R1">=</a> <font color="Maroon">d</font>
 <b>by </b><i><a class="ref" href="yellow_5.html#T2">YELLOW_5:2</a></i>;<br/><b>hence </b><a NAME="E4:15_2_1_1_19"/>
 <a href="yellow_0.html#K2">"/\"</a> <span class="p1"><a href="domain_1.html#K7">{</a><span class="default"><font color="Maroon">x</font>,<font color="Maroon">y</font></span><a href="domain_1.html#K7">}</a></span>,<font color="Maroon">L</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_0.html#K5">subrelstr</a> <font color="Maroon">ck</font></span>)</span>
 <b>by </b><i>, <a class="ref" href="enumset1.html#D3">ENUMSET1:def 3</a></i>;<br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="15_2_1_1_20"><b>suppose </b></a><a NAME="E1:15_2_1_1_20"/>
( <font color="Maroon">x</font> <a href="hidden.html#R1">=</a> <font color="Maroon">d</font> &amp; <font color="Maroon">y</font> <a href="hidden.html#R1">=</a> <font color="Maroon">e</font> )
 ;<br/><div class="add"><a NAME="E2:15_2_1_1_20"/><b>then </b>
 <a href="yellow_0.html#NK4" target="_self">inf</a> <span class="p1"><a href="domain_1.html#K7">{</a><span class="default"><font color="Maroon">x</font>,<font color="Maroon">y</font></span><a href="domain_1.html#K7">}</a></span> <a href="hidden.html#R1">=</a> <font color="Maroon">d</font> <a href="lattice3.html#K12">"/\"</a> <font color="Maroon">e</font>
 <b>by </b><i><a class="ref" href="yellow_0.html#T40">YELLOW_0:40</a></i>;<br/><b>hence </b><a NAME="E3:15_2_1_1_20"/>
 <a href="yellow_0.html#K2">"/\"</a> <span class="p1"><a href="domain_1.html#K7">{</a><span class="default"><font color="Maroon">x</font>,<font color="Maroon">y</font></span><a href="domain_1.html#K7">}</a></span>,<font color="Maroon">L</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_0.html#K5">subrelstr</a> <font color="Maroon">ck</font></span>)</span>
 <b>by </b><i>, , <a class="ref" href="enumset1.html#D3">ENUMSET1:def 3</a></i>;<br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="15_2_1_1_21"><b>suppose </b></a><a NAME="E1:15_2_1_1_21"/><i><font color="Green">E108</font></i>: 
( <font color="Maroon">x</font> <a href="hidden.html#R1">=</a> <font color="Maroon">e</font> &amp; <font color="Maroon">y</font> <a href="hidden.html#R1">=</a> <font color="Maroon">a</font> )
 ;<br/><div class="add"><a NAME="E2:15_2_1_1_21"/>
( <font color="Maroon">a</font> <a href="orders_2.html#R3">&lt;=</a> <font color="Maroon">c</font> &amp; <font color="Maroon">c</font> <a href="orders_2.html#R3">&lt;=</a> <font color="Maroon">e</font> )
 <b>by </b><i>, <a class="ref" href="yellow_0.html#T25">YELLOW_0:25</a></i>;<br/><a NAME="E3:15_2_1_1_21"/><b>then </b>
<font color="Maroon">a</font> <a href="orders_2.html#R3">&lt;=</a> <font color="Maroon">e</font>
 <b>by </b><i><a class="ref" href="orders_2.html#T26">ORDERS_2:26</a></i>;<br/><a NAME="E4:15_2_1_1_21"/><b>then </b>
<font color="Maroon">a</font> <a href="lattice3.html#K12">"/\"</a> <font color="Maroon">e</font> <a href="hidden.html#R1">=</a> <font color="Maroon">a</font>
 <b>by </b><i><a class="ref" href="yellow_0.html#T25">YELLOW_0:25</a></i>;<br/><a NAME="E5:15_2_1_1_21"/><b>then </b>
 <a href="yellow_0.html#NK4" target="_self">inf</a> <span class="p1"><a href="domain_1.html#K7">{</a><span class="default"><font color="Maroon">x</font>,<font color="Maroon">y</font></span><a href="domain_1.html#K7">}</a></span> <a href="hidden.html#R1">=</a> <font color="Maroon">a</font>
 <b>by </b><i>, <a class="ref" href="yellow_0.html#T40">YELLOW_0:40</a></i>;<br/><b>hence </b><a NAME="E6:15_2_1_1_21"/>
 <a href="yellow_0.html#K2">"/\"</a> <span class="p1"><a href="domain_1.html#K7">{</a><span class="default"><font color="Maroon">x</font>,<font color="Maroon">y</font></span><a href="domain_1.html#K7">}</a></span>,<font color="Maroon">L</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_0.html#K5">subrelstr</a> <font color="Maroon">ck</font></span>)</span>
 <b>by </b><i>, <a class="ref" href="enumset1.html#D3">ENUMSET1:def 3</a></i>;<br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="15_2_1_1_22"><b>suppose </b></a><a NAME="E1:15_2_1_1_22"/>
( <font color="Maroon">x</font> <a href="hidden.html#R1">=</a> <font color="Maroon">e</font> &amp; <font color="Maroon">y</font> <a href="hidden.html#R1">=</a> <font color="Maroon">b</font> )
 ;<br/><div class="add"><a NAME="E2:15_2_1_1_22"/><b>then </b>
 <a href="yellow_0.html#NK4" target="_self">inf</a> <span class="p1"><a href="domain_1.html#K7">{</a><span class="default"><font color="Maroon">x</font>,<font color="Maroon">y</font></span><a href="domain_1.html#K7">}</a></span> <a href="hidden.html#R1">=</a> <font color="Maroon">b</font> <a href="lattice3.html#K12">"/\"</a> <font color="Maroon">e</font>
 <b>by </b><i><a class="ref" href="yellow_0.html#T40">YELLOW_0:40</a></i>;<br/><b>hence </b><a NAME="E3:15_2_1_1_22"/>
 <a href="yellow_0.html#K2">"/\"</a> <span class="p1"><a href="domain_1.html#K7">{</a><span class="default"><font color="Maroon">x</font>,<font color="Maroon">y</font></span><a href="domain_1.html#K7">}</a></span>,<font color="Maroon">L</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_0.html#K5">subrelstr</a> <font color="Maroon">ck</font></span>)</span>
 <b>by </b><i>, , <a class="ref" href="enumset1.html#D3">ENUMSET1:def 3</a></i>;<br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="15_2_1_1_23"><b>suppose </b></a><a NAME="E1:15_2_1_1_23"/>
( <font color="Maroon">x</font> <a href="hidden.html#R1">=</a> <font color="Maroon">e</font> &amp; <font color="Maroon">y</font> <a href="hidden.html#R1">=</a> <font color="Maroon">c</font> )
 ;<br/><div class="add"><a NAME="E2:15_2_1_1_23"/><b>then </b>
 <a href="yellow_0.html#NK4" target="_self">inf</a> <span class="p1"><a href="domain_1.html#K7">{</a><span class="default"><font color="Maroon">x</font>,<font color="Maroon">y</font></span><a href="domain_1.html#K7">}</a></span> <a href="hidden.html#R1">=</a> <font color="Maroon">c</font> <a href="lattice3.html#K12">"/\"</a> <font color="Maroon">e</font>
 <b>by </b><i><a class="ref" href="yellow_0.html#T40">YELLOW_0:40</a></i>;<br/><b>hence </b><a NAME="E3:15_2_1_1_23"/>
 <a href="yellow_0.html#K2">"/\"</a> <span class="p1"><a href="domain_1.html#K7">{</a><span class="default"><font color="Maroon">x</font>,<font color="Maroon">y</font></span><a href="domain_1.html#K7">}</a></span>,<font color="Maroon">L</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_0.html#K5">subrelstr</a> <font color="Maroon">ck</font></span>)</span>
 <b>by </b><i>, , <a class="ref" href="enumset1.html#D3">ENUMSET1:def 3</a></i>;<br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="15_2_1_1_24"><b>suppose </b></a><a NAME="E1:15_2_1_1_24"/>
( <font color="Maroon">x</font> <a href="hidden.html#R1">=</a> <font color="Maroon">e</font> &amp; <font color="Maroon">y</font> <a href="hidden.html#R1">=</a> <font color="Maroon">d</font> )
 ;<br/><div class="add"><a NAME="E2:15_2_1_1_24"/><b>then </b>
 <a href="yellow_0.html#NK4" target="_self">inf</a> <span class="p1"><a href="domain_1.html#K7">{</a><span class="default"><font color="Maroon">x</font>,<font color="Maroon">y</font></span><a href="domain_1.html#K7">}</a></span> <a href="hidden.html#R1">=</a> <font color="Maroon">d</font> <a href="lattice3.html#K12">"/\"</a> <font color="Maroon">e</font>
 <b>by </b><i><a class="ref" href="yellow_0.html#T40">YELLOW_0:40</a></i>;<br/><b>hence </b><a NAME="E3:15_2_1_1_24"/>
 <a href="yellow_0.html#K2">"/\"</a> <span class="p1"><a href="domain_1.html#K7">{</a><span class="default"><font color="Maroon">x</font>,<font color="Maroon">y</font></span><a href="domain_1.html#K7">}</a></span>,<font color="Maroon">L</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_0.html#K5">subrelstr</a> <font color="Maroon">ck</font></span>)</span>
 <b>by </b><i>, , <a class="ref" href="enumset1.html#D3">ENUMSET1:def 3</a></i>;<br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="15_2_1_1_25"><b>suppose </b></a><a NAME="E1:15_2_1_1_25"/>
( <font color="Maroon">x</font> <a href="hidden.html#R1">=</a> <font color="Maroon">e</font> &amp; <font color="Maroon">y</font> <a href="hidden.html#R1">=</a> <font color="Maroon">e</font> )
 ;<br/><div class="add"><a NAME="E2:15_2_1_1_25"/><b>then </b>
 <a href="yellow_0.html#NK4" target="_self">inf</a> <span class="p1"><a href="domain_1.html#K7">{</a><span class="default"><font color="Maroon">x</font>,<font color="Maroon">y</font></span><a href="domain_1.html#K7">}</a></span> <a href="hidden.html#R1">=</a> <font color="Maroon">e</font> <a href="lattice3.html#K12">"/\"</a> <font color="Maroon">e</font>
 <b>by </b><i><a class="ref" href="yellow_0.html#T40">YELLOW_0:40</a></i>;<br/><a NAME="E3:15_2_1_1_25"/><b>then </b>
 <a href="yellow_0.html#NK4" target="_self">inf</a> <span class="p1"><a href="domain_1.html#K7">{</a><span class="default"><font color="Maroon">x</font>,<font color="Maroon">y</font></span><a href="domain_1.html#K7">}</a></span> <a href="hidden.html#R1">=</a> <font color="Maroon">e</font>
 <b>by </b><i><a class="ref" href="yellow_5.html#T2">YELLOW_5:2</a></i>;<br/><b>hence </b><a NAME="E4:15_2_1_1_25"/>
 <a href="yellow_0.html#K2">"/\"</a> <span class="p1"><a href="domain_1.html#K7">{</a><span class="default"><font color="Maroon">x</font>,<font color="Maroon">y</font></span><a href="domain_1.html#K7">}</a></span>,<font color="Maroon">L</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_0.html#K5">subrelstr</a> <font color="Maroon">ck</font></span>)</span>
 <b>by </b><i>, <a class="ref" href="enumset1.html#D3">ENUMSET1:def 3</a></i>;<br/></div><b>end;</b></div></div><b>end;</b></div>

</div><b>end;</b></div>
<a NAME="E5:15_2"/>
 <a href="yellow_0.html#K5">subrelstr</a> <font color="Maroon">ck</font> is <a href="yellow_0.html#V6">join-inheriting</a>
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="15_2_2"><b>proof </b></a><div class="add">

<b>let </b><font color="Maroon">x</font> be   <a href="struct_0.html#NM1">Element</a> of <font color="Maroon">L</font>, <font color="Maroon">y</font> be   <a href="struct_0.html#NM1">Element</a> of <font color="Maroon">L</font>; <i><font color="Red">:: according to </font></i><a class="ref" href="yellow_0.html#D17">YELLOW_0:def 17</a><br/>

<b>assume </b><a NAME="E1:15_2_2"/><i><font color="Green">E109</font></i>: 
( <font color="Maroon">x</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_0.html#K5">subrelstr</a> <font color="Maroon">ck</font></span>)</span> &amp; <font color="Maroon">y</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_0.html#K5">subrelstr</a> <font color="Maroon">ck</font></span>)</span> &amp;  <a href="yellow_0.html#R1">ex_sup_of</a> <span class="p1"><a href="domain_1.html#K7">{</a><span class="default"><font color="Maroon">x</font>,<font color="Maroon">y</font></span><a href="domain_1.html#K7">}</a></span>,<font color="Maroon">L</font> )
 ;<br/>

<div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="15_2_2_1"><b>per </b></a><a class="txt" onclick="hs(this)" href="javascript:()"><b>cases </b></a><span class="hide"><a NAME="E1:15_2_2_1"/>
( ( <font color="Maroon">x</font> <a href="hidden.html#R1">=</a> <font color="Maroon">a</font> &amp; <font color="Maroon">y</font> <a href="hidden.html#R1">=</a> <font color="Maroon">a</font> ) or ( <font color="Maroon">x</font> <a href="hidden.html#R1">=</a> <font color="Maroon">a</font> &amp; <font color="Maroon">y</font> <a href="hidden.html#R1">=</a> <font color="Maroon">b</font> ) or ( <font color="Maroon">x</font> <a href="hidden.html#R1">=</a> <font color="Maroon">a</font> &amp; <font color="Maroon">y</font> <a href="hidden.html#R1">=</a> <font color="Maroon">c</font> ) or ( <font color="Maroon">x</font> <a href="hidden.html#R1">=</a> <font color="Maroon">a</font> &amp; <font color="Maroon">y</font> <a href="hidden.html#R1">=</a> <font color="Maroon">d</font> ) or ( <font color="Maroon">x</font> <a href="hidden.html#R1">=</a> <font color="Maroon">a</font> &amp; <font color="Maroon">y</font> <a href="hidden.html#R1">=</a> <font color="Maroon">e</font> ) or ( <font color="Maroon">x</font> <a href="hidden.html#R1">=</a> <font color="Maroon">b</font> &amp; <font color="Maroon">y</font> <a href="hidden.html#R1">=</a> <font color="Maroon">a</font> ) or ( <font color="Maroon">x</font> <a href="hidden.html#R1">=</a> <font color="Maroon">b</font> &amp; <font color="Maroon">y</font> <a href="hidden.html#R1">=</a> <font color="Maroon">b</font> ) or ( <font color="Maroon">x</font> <a href="hidden.html#R1">=</a> <font color="Maroon">b</font> &amp; <font color="Maroon">y</font> <a href="hidden.html#R1">=</a> <font color="Maroon">c</font> ) or ( <font color="Maroon">x</font> <a href="hidden.html#R1">=</a> <font color="Maroon">b</font> &amp; <font color="Maroon">y</font> <a href="hidden.html#R1">=</a> <font color="Maroon">d</font> ) or ( <font color="Maroon">x</font> <a href="hidden.html#R1">=</a> <font color="Maroon">b</font> &amp; <font color="Maroon">y</font> <a href="hidden.html#R1">=</a> <font color="Maroon">e</font> ) or ( <font color="Maroon">x</font> <a href="hidden.html#R1">=</a> <font color="Maroon">c</font> &amp; <font color="Maroon">y</font> <a href="hidden.html#R1">=</a> <font color="Maroon">a</font> ) or ( <font color="Maroon">x</font> <a href="hidden.html#R1">=</a> <font color="Maroon">c</font> &amp; <font color="Maroon">y</font> <a href="hidden.html#R1">=</a> <font color="Maroon">b</font> ) or ( <font color="Maroon">x</font> <a href="hidden.html#R1">=</a> <font color="Maroon">c</font> &amp; <font color="Maroon">y</font> <a href="hidden.html#R1">=</a> <font color="Maroon">c</font> ) or ( <font color="Maroon">x</font> <a href="hidden.html#R1">=</a> <font color="Maroon">c</font> &amp; <font color="Maroon">y</font> <a href="hidden.html#R1">=</a> <font color="Maroon">d</font> ) or ( <font color="Maroon">x</font> <a href="hidden.html#R1">=</a> <font color="Maroon">c</font> &amp; <font color="Maroon">y</font> <a href="hidden.html#R1">=</a> <font color="Maroon">e</font> ) or ( <font color="Maroon">x</font> <a href="hidden.html#R1">=</a> <font color="Maroon">d</font> &amp; <font color="Maroon">y</font> <a href="hidden.html#R1">=</a> <font color="Maroon">a</font> ) or ( <font color="Maroon">x</font> <a href="hidden.html#R1">=</a> <font color="Maroon">d</font> &amp; <font color="Maroon">y</font> <a href="hidden.html#R1">=</a> <font color="Maroon">b</font> ) or ( <font color="Maroon">x</font> <a href="hidden.html#R1">=</a> <font color="Maroon">d</font> &amp; <font color="Maroon">y</font> <a href="hidden.html#R1">=</a> <font color="Maroon">c</font> ) or ( <font color="Maroon">x</font> <a href="hidden.html#R1">=</a> <font color="Maroon">d</font> &amp; <font color="Maroon">y</font> <a href="hidden.html#R1">=</a> <font color="Maroon">d</font> ) or ( <font color="Maroon">x</font> <a href="hidden.html#R1">=</a> <font color="Maroon">d</font> &amp; <font color="Maroon">y</font> <a href="hidden.html#R1">=</a> <font color="Maroon">e</font> ) or ( <font color="Maroon">x</font> <a href="hidden.html#R1">=</a> <font color="Maroon">e</font> &amp; <font color="Maroon">y</font> <a href="hidden.html#R1">=</a> <font color="Maroon">a</font> ) or ( <font color="Maroon">x</font> <a href="hidden.html#R1">=</a> <font color="Maroon">e</font> &amp; <font color="Maroon">y</font> <a href="hidden.html#R1">=</a> <font color="Maroon">b</font> ) or ( <font color="Maroon">x</font> <a href="hidden.html#R1">=</a> <font color="Maroon">e</font> &amp; <font color="Maroon">y</font> <a href="hidden.html#R1">=</a> <font color="Maroon">c</font> ) or ( <font color="Maroon">x</font> <a href="hidden.html#R1">=</a> <font color="Maroon">e</font> &amp; <font color="Maroon">y</font> <a href="hidden.html#R1">=</a> <font color="Maroon">d</font> ) or ( <font color="Maroon">x</font> <a href="hidden.html#R1">=</a> <font color="Maroon">e</font> &amp; <font color="Maroon">y</font> <a href="hidden.html#R1">=</a> <font color="Maroon">e</font> ) )
 </span><b>by </b><i>, , <a class="ref" href="enumset1.html#D3">ENUMSET1:def 3</a></i>;<br/><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="15_2_2_1_1"><b>suppose </b></a><a NAME="E1:15_2_2_1_1"/>
( <font color="Maroon">x</font> <a href="hidden.html#R1">=</a> <font color="Maroon">a</font> &amp; <font color="Maroon">y</font> <a href="hidden.html#R1">=</a> <font color="Maroon">a</font> )
 ;<br/><div class="add"><a NAME="E2:15_2_2_1_1"/><b>then </b>
 <a href="yellow_0.html#NK3" target="_self">sup</a> <span class="p1"><a href="domain_1.html#K7">{</a><span class="default"><font color="Maroon">x</font>,<font color="Maroon">y</font></span><a href="domain_1.html#K7">}</a></span> <a href="hidden.html#R1">=</a> <font color="Maroon">a</font> <a href="lattice3.html#K13">"\/"</a> <font color="Maroon">a</font>
 <b>by </b><i><a class="ref" href="yellow_0.html#T41">YELLOW_0:41</a></i>;<br/><a NAME="E3:15_2_2_1_1"/><b>then </b>
 <a href="yellow_0.html#NK3" target="_self">sup</a> <span class="p1"><a href="domain_1.html#K7">{</a><span class="default"><font color="Maroon">x</font>,<font color="Maroon">y</font></span><a href="domain_1.html#K7">}</a></span> <a href="hidden.html#R1">=</a> <font color="Maroon">a</font>
 <b>by </b><i><a class="ref" href="yellow_5.html#T1">YELLOW_5:1</a></i>;<br/><b>hence </b><a NAME="E4:15_2_2_1_1"/>
 <a href="yellow_0.html#K1">"\/"</a> <span class="p1"><a href="domain_1.html#K7">{</a><span class="default"><font color="Maroon">x</font>,<font color="Maroon">y</font></span><a href="domain_1.html#K7">}</a></span>,<font color="Maroon">L</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_0.html#K5">subrelstr</a> <font color="Maroon">ck</font></span>)</span>
 <b>by </b><i>, <a class="ref" href="enumset1.html#D3">ENUMSET1:def 3</a></i>;<br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="15_2_2_1_2"><b>suppose </b></a><a NAME="E1:15_2_2_1_2"/>
( <font color="Maroon">x</font> <a href="hidden.html#R1">=</a> <font color="Maroon">a</font> &amp; <font color="Maroon">y</font> <a href="hidden.html#R1">=</a> <font color="Maroon">b</font> )
 ;<br/><div class="add"><a NAME="E2:15_2_2_1_2"/><b>then </b>
<font color="Maroon">x</font> <a href="lattice3.html#K13">"\/"</a> <font color="Maroon">y</font> <a href="hidden.html#R1">=</a> <font color="Maroon">b</font>
 <b>by </b><i>, </i>;<br/><a NAME="E3:15_2_2_1_2"/><b>then </b>
 <a href="yellow_0.html#NK3" target="_self">sup</a> <span class="p1"><a href="domain_1.html#K7">{</a><span class="default"><font color="Maroon">x</font>,<font color="Maroon">y</font></span><a href="domain_1.html#K7">}</a></span> <a href="hidden.html#R1">=</a> <font color="Maroon">b</font>
 <b>by </b><i><a class="ref" href="yellow_0.html#T41">YELLOW_0:41</a></i>;<br/><b>hence </b><a NAME="E4:15_2_2_1_2"/>
 <a href="yellow_0.html#K1">"\/"</a> <span class="p1"><a href="domain_1.html#K7">{</a><span class="default"><font color="Maroon">x</font>,<font color="Maroon">y</font></span><a href="domain_1.html#K7">}</a></span>,<font color="Maroon">L</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_0.html#K5">subrelstr</a> <font color="Maroon">ck</font></span>)</span>
 <b>by </b><i>, <a class="ref" href="enumset1.html#D3">ENUMSET1:def 3</a></i>;<br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="15_2_2_1_3"><b>suppose </b></a><a NAME="E1:15_2_2_1_3"/>
( <font color="Maroon">x</font> <a href="hidden.html#R1">=</a> <font color="Maroon">a</font> &amp; <font color="Maroon">y</font> <a href="hidden.html#R1">=</a> <font color="Maroon">c</font> )
 ;<br/><div class="add"><a NAME="E2:15_2_2_1_3"/><b>then </b>
<font color="Maroon">x</font> <a href="lattice3.html#K13">"\/"</a> <font color="Maroon">y</font> <a href="hidden.html#R1">=</a> <font color="Maroon">c</font>
 <b>by </b><i>, </i>;<br/><a NAME="E3:15_2_2_1_3"/><b>then </b>
 <a href="yellow_0.html#NK3" target="_self">sup</a> <span class="p1"><a href="domain_1.html#K7">{</a><span class="default"><font color="Maroon">x</font>,<font color="Maroon">y</font></span><a href="domain_1.html#K7">}</a></span> <a href="hidden.html#R1">=</a> <font color="Maroon">c</font>
 <b>by </b><i><a class="ref" href="yellow_0.html#T41">YELLOW_0:41</a></i>;<br/><b>hence </b><a NAME="E4:15_2_2_1_3"/>
 <a href="yellow_0.html#K1">"\/"</a> <span class="p1"><a href="domain_1.html#K7">{</a><span class="default"><font color="Maroon">x</font>,<font color="Maroon">y</font></span><a href="domain_1.html#K7">}</a></span>,<font color="Maroon">L</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_0.html#K5">subrelstr</a> <font color="Maroon">ck</font></span>)</span>
 <b>by </b><i>, <a class="ref" href="enumset1.html#D3">ENUMSET1:def 3</a></i>;<br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="15_2_2_1_4"><b>suppose </b></a><a NAME="E1:15_2_2_1_4"/>
( <font color="Maroon">x</font> <a href="hidden.html#R1">=</a> <font color="Maroon">a</font> &amp; <font color="Maroon">y</font> <a href="hidden.html#R1">=</a> <font color="Maroon">d</font> )
 ;<br/><div class="add"><a NAME="E2:15_2_2_1_4"/><b>then </b>
<font color="Maroon">x</font> <a href="lattice3.html#K13">"\/"</a> <font color="Maroon">y</font> <a href="hidden.html#R1">=</a> <font color="Maroon">d</font>
 <b>by </b><i>, </i>;<br/><a NAME="E3:15_2_2_1_4"/><b>then </b>
 <a href="yellow_0.html#NK3" target="_self">sup</a> <span class="p1"><a href="domain_1.html#K7">{</a><span class="default"><font color="Maroon">x</font>,<font color="Maroon">y</font></span><a href="domain_1.html#K7">}</a></span> <a href="hidden.html#R1">=</a> <font color="Maroon">d</font>
 <b>by </b><i><a class="ref" href="yellow_0.html#T41">YELLOW_0:41</a></i>;<br/><b>hence </b><a NAME="E4:15_2_2_1_4"/>
 <a href="yellow_0.html#K1">"\/"</a> <span class="p1"><a href="domain_1.html#K7">{</a><span class="default"><font color="Maroon">x</font>,<font color="Maroon">y</font></span><a href="domain_1.html#K7">}</a></span>,<font color="Maroon">L</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_0.html#K5">subrelstr</a> <font color="Maroon">ck</font></span>)</span>
 <b>by </b><i>, <a class="ref" href="enumset1.html#D3">ENUMSET1:def 3</a></i>;<br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="15_2_2_1_5"><b>suppose </b></a><a NAME="E1:15_2_2_1_5"/><i><font color="Green">E110</font></i>: 
( <font color="Maroon">x</font> <a href="hidden.html#R1">=</a> <font color="Maroon">a</font> &amp; <font color="Maroon">y</font> <a href="hidden.html#R1">=</a> <font color="Maroon">e</font> )
 ;<br/><div class="add"><a NAME="E2:15_2_2_1_5"/>
( <font color="Maroon">a</font> <a href="orders_2.html#R3">&lt;=</a> <font color="Maroon">c</font> &amp; <font color="Maroon">c</font> <a href="orders_2.html#R3">&lt;=</a> <font color="Maroon">e</font> )
 <b>by </b><i>, <a class="ref" href="yellow_0.html#T25">YELLOW_0:25</a></i>;<br/><a NAME="E3:15_2_2_1_5"/><b>then </b>
<font color="Maroon">a</font> <a href="orders_2.html#R3">&lt;=</a> <font color="Maroon">e</font>
 <b>by </b><i><a class="ref" href="orders_2.html#T26">ORDERS_2:26</a></i>;<br/><a NAME="E4:15_2_2_1_5"/><b>then </b>
<font color="Maroon">a</font> <a href="lattice3.html#K12">"/\"</a> <font color="Maroon">e</font> <a href="hidden.html#R1">=</a> <font color="Maroon">a</font>
 <b>by </b><i><a class="ref" href="yellow_0.html#T25">YELLOW_0:25</a></i>;<br/><a NAME="E5:15_2_2_1_5"/><b>then </b>
<font color="Maroon">a</font> <a href="lattice3.html#K13">"\/"</a> <font color="Maroon">e</font> <a href="hidden.html#R1">=</a> <font color="Maroon">e</font>
 <b>by </b><i/>;<br/><a NAME="E6:15_2_2_1_5"/><b>then </b>
 <a href="yellow_0.html#NK3" target="_self">sup</a> <span class="p1"><a href="domain_1.html#K7">{</a><span class="default"><font color="Maroon">x</font>,<font color="Maroon">y</font></span><a href="domain_1.html#K7">}</a></span> <a href="hidden.html#R1">=</a> <font color="Maroon">e</font>
 <b>by </b><i>, <a class="ref" href="yellow_0.html#T41">YELLOW_0:41</a></i>;<br/><b>hence </b><a NAME="E7:15_2_2_1_5"/>
 <a href="yellow_0.html#K1">"\/"</a> <span class="p1"><a href="domain_1.html#K7">{</a><span class="default"><font color="Maroon">x</font>,<font color="Maroon">y</font></span><a href="domain_1.html#K7">}</a></span>,<font color="Maroon">L</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_0.html#K5">subrelstr</a> <font color="Maroon">ck</font></span>)</span>
 <b>by </b><i>, <a class="ref" href="enumset1.html#D3">ENUMSET1:def 3</a></i>;<br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="15_2_2_1_6"><b>suppose </b></a><a NAME="E1:15_2_2_1_6"/><i><font color="Green">E111</font></i>: 
( <font color="Maroon">x</font> <a href="hidden.html#R1">=</a> <font color="Maroon">b</font> &amp; <font color="Maroon">y</font> <a href="hidden.html#R1">=</a> <font color="Maroon">a</font> )
 ;<br/><div class="add"><a NAME="E2:15_2_2_1_6"/>
<font color="Maroon">a</font> <a href="lattice3.html#K13">"\/"</a> <font color="Maroon">b</font> <a href="hidden.html#R1">=</a> <font color="Maroon">b</font>
 <b>by </b><i>, </i>;<br/><a NAME="E3:15_2_2_1_6"/><b>then </b>
 <a href="yellow_0.html#NK3" target="_self">sup</a> <span class="p1"><a href="domain_1.html#K7">{</a><span class="default"><font color="Maroon">x</font>,<font color="Maroon">y</font></span><a href="domain_1.html#K7">}</a></span> <a href="hidden.html#R1">=</a> <font color="Maroon">b</font>
 <b>by </b><i>, <a class="ref" href="yellow_0.html#T41">YELLOW_0:41</a></i>;<br/><b>hence </b><a NAME="E4:15_2_2_1_6"/>
 <a href="yellow_0.html#K1">"\/"</a> <span class="p1"><a href="domain_1.html#K7">{</a><span class="default"><font color="Maroon">x</font>,<font color="Maroon">y</font></span><a href="domain_1.html#K7">}</a></span>,<font color="Maroon">L</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_0.html#K5">subrelstr</a> <font color="Maroon">ck</font></span>)</span>
 <b>by </b><i>, <a class="ref" href="enumset1.html#D3">ENUMSET1:def 3</a></i>;<br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="15_2_2_1_7"><b>suppose </b></a><a NAME="E1:15_2_2_1_7"/>
( <font color="Maroon">x</font> <a href="hidden.html#R1">=</a> <font color="Maroon">b</font> &amp; <font color="Maroon">y</font> <a href="hidden.html#R1">=</a> <font color="Maroon">b</font> )
 ;<br/><div class="add"><a NAME="E2:15_2_2_1_7"/><b>then </b>
 <a href="yellow_0.html#NK3" target="_self">sup</a> <span class="p1"><a href="domain_1.html#K7">{</a><span class="default"><font color="Maroon">x</font>,<font color="Maroon">y</font></span><a href="domain_1.html#K7">}</a></span> <a href="hidden.html#R1">=</a> <font color="Maroon">b</font> <a href="lattice3.html#K13">"\/"</a> <font color="Maroon">b</font>
 <b>by </b><i><a class="ref" href="yellow_0.html#T41">YELLOW_0:41</a></i>;<br/><a NAME="E3:15_2_2_1_7"/><b>then </b>
 <a href="yellow_0.html#NK3" target="_self">sup</a> <span class="p1"><a href="domain_1.html#K7">{</a><span class="default"><font color="Maroon">x</font>,<font color="Maroon">y</font></span><a href="domain_1.html#K7">}</a></span> <a href="hidden.html#R1">=</a> <font color="Maroon">b</font>
 <b>by </b><i><a class="ref" href="yellow_5.html#T1">YELLOW_5:1</a></i>;<br/><b>hence </b><a NAME="E4:15_2_2_1_7"/>
 <a href="yellow_0.html#K1">"\/"</a> <span class="p1"><a href="domain_1.html#K7">{</a><span class="default"><font color="Maroon">x</font>,<font color="Maroon">y</font></span><a href="domain_1.html#K7">}</a></span>,<font color="Maroon">L</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_0.html#K5">subrelstr</a> <font color="Maroon">ck</font></span>)</span>
 <b>by </b><i>, <a class="ref" href="enumset1.html#D3">ENUMSET1:def 3</a></i>;<br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="15_2_2_1_8"><b>suppose </b></a><a NAME="E1:15_2_2_1_8"/>
( <font color="Maroon">x</font> <a href="hidden.html#R1">=</a> <font color="Maroon">b</font> &amp; <font color="Maroon">y</font> <a href="hidden.html#R1">=</a> <font color="Maroon">c</font> )
 ;<br/><div class="add"><a NAME="E2:15_2_2_1_8"/><b>then </b>
 <a href="yellow_0.html#NK3" target="_self">sup</a> <span class="p1"><a href="domain_1.html#K7">{</a><span class="default"><font color="Maroon">x</font>,<font color="Maroon">y</font></span><a href="domain_1.html#K7">}</a></span> <a href="hidden.html#R1">=</a> <font color="Maroon">b</font> <a href="lattice3.html#K13">"\/"</a> <font color="Maroon">c</font>
 <b>by </b><i><a class="ref" href="yellow_0.html#T41">YELLOW_0:41</a></i>;<br/><b>hence </b><a NAME="E3:15_2_2_1_8"/>
 <a href="yellow_0.html#K1">"\/"</a> <span class="p1"><a href="domain_1.html#K7">{</a><span class="default"><font color="Maroon">x</font>,<font color="Maroon">y</font></span><a href="domain_1.html#K7">}</a></span>,<font color="Maroon">L</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_0.html#K5">subrelstr</a> <font color="Maroon">ck</font></span>)</span>
 <b>by </b><i>, , <a class="ref" href="enumset1.html#D3">ENUMSET1:def 3</a></i>;<br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="15_2_2_1_9"><b>suppose </b></a><a NAME="E1:15_2_2_1_9"/>
( <font color="Maroon">x</font> <a href="hidden.html#R1">=</a> <font color="Maroon">b</font> &amp; <font color="Maroon">y</font> <a href="hidden.html#R1">=</a> <font color="Maroon">d</font> )
 ;<br/><div class="add"><a NAME="E2:15_2_2_1_9"/><b>then </b>
 <a href="yellow_0.html#NK3" target="_self">sup</a> <span class="p1"><a href="domain_1.html#K7">{</a><span class="default"><font color="Maroon">x</font>,<font color="Maroon">y</font></span><a href="domain_1.html#K7">}</a></span> <a href="hidden.html#R1">=</a> <font color="Maroon">b</font> <a href="lattice3.html#K13">"\/"</a> <font color="Maroon">d</font>
 <b>by </b><i><a class="ref" href="yellow_0.html#T41">YELLOW_0:41</a></i>;<br/><b>hence </b><a NAME="E3:15_2_2_1_9"/>
 <a href="yellow_0.html#K1">"\/"</a> <span class="p1"><a href="domain_1.html#K7">{</a><span class="default"><font color="Maroon">x</font>,<font color="Maroon">y</font></span><a href="domain_1.html#K7">}</a></span>,<font color="Maroon">L</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_0.html#K5">subrelstr</a> <font color="Maroon">ck</font></span>)</span>
 <b>by </b><i>, , <a class="ref" href="enumset1.html#D3">ENUMSET1:def 3</a></i>;<br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="15_2_2_1_10"><b>suppose </b></a><a NAME="E1:15_2_2_1_10"/><i><font color="Green">E112</font></i>: 
( <font color="Maroon">x</font> <a href="hidden.html#R1">=</a> <font color="Maroon">b</font> &amp; <font color="Maroon">y</font> <a href="hidden.html#R1">=</a> <font color="Maroon">e</font> )
 ;<br/><div class="add"><a NAME="E2:15_2_2_1_10"/>
<font color="Maroon">b</font> <a href="lattice3.html#K13">"\/"</a> <font color="Maroon">e</font> <a href="hidden.html#R1">=</a> <font color="Maroon">e</font>
 <b>by </b><i>, </i>;<br/><a NAME="E3:15_2_2_1_10"/><b>then </b>
 <a href="yellow_0.html#NK3" target="_self">sup</a> <span class="p1"><a href="domain_1.html#K7">{</a><span class="default"><font color="Maroon">x</font>,<font color="Maroon">y</font></span><a href="domain_1.html#K7">}</a></span> <a href="hidden.html#R1">=</a> <font color="Maroon">e</font>
 <b>by </b><i>, <a class="ref" href="yellow_0.html#T41">YELLOW_0:41</a></i>;<br/><b>hence </b><a NAME="E4:15_2_2_1_10"/>
 <a href="yellow_0.html#K1">"\/"</a> <span class="p1"><a href="domain_1.html#K7">{</a><span class="default"><font color="Maroon">x</font>,<font color="Maroon">y</font></span><a href="domain_1.html#K7">}</a></span>,<font color="Maroon">L</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_0.html#K5">subrelstr</a> <font color="Maroon">ck</font></span>)</span>
 <b>by </b><i>, <a class="ref" href="enumset1.html#D3">ENUMSET1:def 3</a></i>;<br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="15_2_2_1_11"><b>suppose </b></a><a NAME="E1:15_2_2_1_11"/><i><font color="Green">E113</font></i>: 
( <font color="Maroon">x</font> <a href="hidden.html#R1">=</a> <font color="Maroon">c</font> &amp; <font color="Maroon">y</font> <a href="hidden.html#R1">=</a> <font color="Maroon">a</font> )
 ;<br/><div class="add"><a NAME="E2:15_2_2_1_11"/>
<font color="Maroon">c</font> <a href="lattice3.html#K13">"\/"</a> <font color="Maroon">a</font> <a href="hidden.html#R1">=</a> <font color="Maroon">c</font>
 <b>by </b><i>, </i>;<br/><a NAME="E3:15_2_2_1_11"/><b>then </b>
 <a href="yellow_0.html#NK3" target="_self">sup</a> <span class="p1"><a href="domain_1.html#K7">{</a><span class="default"><font color="Maroon">x</font>,<font color="Maroon">y</font></span><a href="domain_1.html#K7">}</a></span> <a href="hidden.html#R1">=</a> <font color="Maroon">c</font>
 <b>by </b><i>, <a class="ref" href="yellow_0.html#T41">YELLOW_0:41</a></i>;<br/><b>hence </b><a NAME="E4:15_2_2_1_11"/>
 <a href="yellow_0.html#K1">"\/"</a> <span class="p1"><a href="domain_1.html#K7">{</a><span class="default"><font color="Maroon">x</font>,<font color="Maroon">y</font></span><a href="domain_1.html#K7">}</a></span>,<font color="Maroon">L</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_0.html#K5">subrelstr</a> <font color="Maroon">ck</font></span>)</span>
 <b>by </b><i>, <a class="ref" href="enumset1.html#D3">ENUMSET1:def 3</a></i>;<br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="15_2_2_1_12"><b>suppose </b></a><a NAME="E1:15_2_2_1_12"/>
( <font color="Maroon">x</font> <a href="hidden.html#R1">=</a> <font color="Maroon">c</font> &amp; <font color="Maroon">y</font> <a href="hidden.html#R1">=</a> <font color="Maroon">b</font> )
 ;<br/><div class="add"><a NAME="E2:15_2_2_1_12"/><b>then </b>
 <a href="yellow_0.html#NK3" target="_self">sup</a> <span class="p1"><a href="domain_1.html#K7">{</a><span class="default"><font color="Maroon">x</font>,<font color="Maroon">y</font></span><a href="domain_1.html#K7">}</a></span> <a href="hidden.html#R1">=</a> <font color="Maroon">b</font> <a href="lattice3.html#K13">"\/"</a> <font color="Maroon">c</font>
 <b>by </b><i><a class="ref" href="yellow_0.html#T41">YELLOW_0:41</a></i>;<br/><b>hence </b><a NAME="E3:15_2_2_1_12"/>
 <a href="yellow_0.html#K1">"\/"</a> <span class="p1"><a href="domain_1.html#K7">{</a><span class="default"><font color="Maroon">x</font>,<font color="Maroon">y</font></span><a href="domain_1.html#K7">}</a></span>,<font color="Maroon">L</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_0.html#K5">subrelstr</a> <font color="Maroon">ck</font></span>)</span>
 <b>by </b><i>, , <a class="ref" href="enumset1.html#D3">ENUMSET1:def 3</a></i>;<br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="15_2_2_1_13"><b>suppose </b></a><a NAME="E1:15_2_2_1_13"/>
( <font color="Maroon">x</font> <a href="hidden.html#R1">=</a> <font color="Maroon">c</font> &amp; <font color="Maroon">y</font> <a href="hidden.html#R1">=</a> <font color="Maroon">c</font> )
 ;<br/><div class="add"><a NAME="E2:15_2_2_1_13"/><b>then </b>
 <a href="yellow_0.html#NK3" target="_self">sup</a> <span class="p1"><a href="domain_1.html#K7">{</a><span class="default"><font color="Maroon">x</font>,<font color="Maroon">y</font></span><a href="domain_1.html#K7">}</a></span> <a href="hidden.html#R1">=</a> <font color="Maroon">c</font> <a href="lattice3.html#K13">"\/"</a> <font color="Maroon">c</font>
 <b>by </b><i><a class="ref" href="yellow_0.html#T41">YELLOW_0:41</a></i>;<br/><a NAME="E3:15_2_2_1_13"/><b>then </b>
 <a href="yellow_0.html#NK3" target="_self">sup</a> <span class="p1"><a href="domain_1.html#K7">{</a><span class="default"><font color="Maroon">x</font>,<font color="Maroon">y</font></span><a href="domain_1.html#K7">}</a></span> <a href="hidden.html#R1">=</a> <font color="Maroon">c</font>
 <b>by </b><i><a class="ref" href="yellow_5.html#T1">YELLOW_5:1</a></i>;<br/><b>hence </b><a NAME="E4:15_2_2_1_13"/>
 <a href="yellow_0.html#K1">"\/"</a> <span class="p1"><a href="domain_1.html#K7">{</a><span class="default"><font color="Maroon">x</font>,<font color="Maroon">y</font></span><a href="domain_1.html#K7">}</a></span>,<font color="Maroon">L</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_0.html#K5">subrelstr</a> <font color="Maroon">ck</font></span>)</span>
 <b>by </b><i>, <a class="ref" href="enumset1.html#D3">ENUMSET1:def 3</a></i>;<br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="15_2_2_1_14"><b>suppose </b></a><a NAME="E1:15_2_2_1_14"/>
( <font color="Maroon">x</font> <a href="hidden.html#R1">=</a> <font color="Maroon">c</font> &amp; <font color="Maroon">y</font> <a href="hidden.html#R1">=</a> <font color="Maroon">d</font> )
 ;<br/><div class="add"><a NAME="E2:15_2_2_1_14"/><b>then </b>
 <a href="yellow_0.html#NK3" target="_self">sup</a> <span class="p1"><a href="domain_1.html#K7">{</a><span class="default"><font color="Maroon">x</font>,<font color="Maroon">y</font></span><a href="domain_1.html#K7">}</a></span> <a href="hidden.html#R1">=</a> <font color="Maroon">c</font> <a href="lattice3.html#K13">"\/"</a> <font color="Maroon">d</font>
 <b>by </b><i><a class="ref" href="yellow_0.html#T41">YELLOW_0:41</a></i>;<br/><b>hence </b><a NAME="E3:15_2_2_1_14"/>
 <a href="yellow_0.html#K1">"\/"</a> <span class="p1"><a href="domain_1.html#K7">{</a><span class="default"><font color="Maroon">x</font>,<font color="Maroon">y</font></span><a href="domain_1.html#K7">}</a></span>,<font color="Maroon">L</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_0.html#K5">subrelstr</a> <font color="Maroon">ck</font></span>)</span>
 <b>by </b><i>, , <a class="ref" href="enumset1.html#D3">ENUMSET1:def 3</a></i>;<br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="15_2_2_1_15"><b>suppose </b></a><a NAME="E1:15_2_2_1_15"/><i><font color="Green">E114</font></i>: 
( <font color="Maroon">x</font> <a href="hidden.html#R1">=</a> <font color="Maroon">c</font> &amp; <font color="Maroon">y</font> <a href="hidden.html#R1">=</a> <font color="Maroon">e</font> )
 ;<br/><div class="add"><a NAME="E2:15_2_2_1_15"/>
<font color="Maroon">c</font> <a href="lattice3.html#K13">"\/"</a> <font color="Maroon">e</font> <a href="hidden.html#R1">=</a> <font color="Maroon">e</font>
 <b>by </b><i>, </i>;<br/><a NAME="E3:15_2_2_1_15"/><b>then </b>
 <a href="yellow_0.html#NK3" target="_self">sup</a> <span class="p1"><a href="domain_1.html#K7">{</a><span class="default"><font color="Maroon">x</font>,<font color="Maroon">y</font></span><a href="domain_1.html#K7">}</a></span> <a href="hidden.html#R1">=</a> <font color="Maroon">e</font>
 <b>by </b><i>, <a class="ref" href="yellow_0.html#T41">YELLOW_0:41</a></i>;<br/><b>hence </b><a NAME="E4:15_2_2_1_15"/>
 <a href="yellow_0.html#K1">"\/"</a> <span class="p1"><a href="domain_1.html#K7">{</a><span class="default"><font color="Maroon">x</font>,<font color="Maroon">y</font></span><a href="domain_1.html#K7">}</a></span>,<font color="Maroon">L</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_0.html#K5">subrelstr</a> <font color="Maroon">ck</font></span>)</span>
 <b>by </b><i>, <a class="ref" href="enumset1.html#D3">ENUMSET1:def 3</a></i>;<br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="15_2_2_1_16"><b>suppose </b></a><a NAME="E1:15_2_2_1_16"/>
( <font color="Maroon">x</font> <a href="hidden.html#R1">=</a> <font color="Maroon">d</font> &amp; <font color="Maroon">y</font> <a href="hidden.html#R1">=</a> <font color="Maroon">a</font> )
 ;<br/><div class="add"><a NAME="E2:15_2_2_1_16"/><b>then </b>
<font color="Maroon">x</font> <a href="lattice3.html#K13">"\/"</a> <font color="Maroon">y</font> <a href="hidden.html#R1">=</a> <font color="Maroon">d</font>
 <b>by </b><i>, </i>;<br/><a NAME="E3:15_2_2_1_16"/><b>then </b>
 <a href="yellow_0.html#NK3" target="_self">sup</a> <span class="p1"><a href="domain_1.html#K7">{</a><span class="default"><font color="Maroon">x</font>,<font color="Maroon">y</font></span><a href="domain_1.html#K7">}</a></span> <a href="hidden.html#R1">=</a> <font color="Maroon">d</font>
 <b>by </b><i><a class="ref" href="yellow_0.html#T41">YELLOW_0:41</a></i>;<br/><b>hence </b><a NAME="E4:15_2_2_1_16"/>
 <a href="yellow_0.html#K1">"\/"</a> <span class="p1"><a href="domain_1.html#K7">{</a><span class="default"><font color="Maroon">x</font>,<font color="Maroon">y</font></span><a href="domain_1.html#K7">}</a></span>,<font color="Maroon">L</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_0.html#K5">subrelstr</a> <font color="Maroon">ck</font></span>)</span>
 <b>by </b><i>, <a class="ref" href="enumset1.html#D3">ENUMSET1:def 3</a></i>;<br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="15_2_2_1_17"><b>suppose </b></a><a NAME="E1:15_2_2_1_17"/>
( <font color="Maroon">x</font> <a href="hidden.html#R1">=</a> <font color="Maroon">d</font> &amp; <font color="Maroon">y</font> <a href="hidden.html#R1">=</a> <font color="Maroon">b</font> )
 ;<br/><div class="add"><a NAME="E2:15_2_2_1_17"/><b>then </b>
 <a href="yellow_0.html#NK3" target="_self">sup</a> <span class="p1"><a href="domain_1.html#K7">{</a><span class="default"><font color="Maroon">x</font>,<font color="Maroon">y</font></span><a href="domain_1.html#K7">}</a></span> <a href="hidden.html#R1">=</a> <font color="Maroon">b</font> <a href="lattice3.html#K13">"\/"</a> <font color="Maroon">d</font>
 <b>by </b><i><a class="ref" href="yellow_0.html#T41">YELLOW_0:41</a></i>;<br/><b>hence </b><a NAME="E3:15_2_2_1_17"/>
 <a href="yellow_0.html#K1">"\/"</a> <span class="p1"><a href="domain_1.html#K7">{</a><span class="default"><font color="Maroon">x</font>,<font color="Maroon">y</font></span><a href="domain_1.html#K7">}</a></span>,<font color="Maroon">L</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_0.html#K5">subrelstr</a> <font color="Maroon">ck</font></span>)</span>
 <b>by </b><i>, , <a class="ref" href="enumset1.html#D3">ENUMSET1:def 3</a></i>;<br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="15_2_2_1_18"><b>suppose </b></a><a NAME="E1:15_2_2_1_18"/>
( <font color="Maroon">x</font> <a href="hidden.html#R1">=</a> <font color="Maroon">d</font> &amp; <font color="Maroon">y</font> <a href="hidden.html#R1">=</a> <font color="Maroon">c</font> )
 ;<br/><div class="add"><a NAME="E2:15_2_2_1_18"/><b>then </b>
 <a href="yellow_0.html#NK3" target="_self">sup</a> <span class="p1"><a href="domain_1.html#K7">{</a><span class="default"><font color="Maroon">x</font>,<font color="Maroon">y</font></span><a href="domain_1.html#K7">}</a></span> <a href="hidden.html#R1">=</a> <font color="Maroon">c</font> <a href="lattice3.html#K13">"\/"</a> <font color="Maroon">d</font>
 <b>by </b><i><a class="ref" href="yellow_0.html#T41">YELLOW_0:41</a></i>;<br/><b>hence </b><a NAME="E3:15_2_2_1_18"/>
 <a href="yellow_0.html#K1">"\/"</a> <span class="p1"><a href="domain_1.html#K7">{</a><span class="default"><font color="Maroon">x</font>,<font color="Maroon">y</font></span><a href="domain_1.html#K7">}</a></span>,<font color="Maroon">L</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_0.html#K5">subrelstr</a> <font color="Maroon">ck</font></span>)</span>
 <b>by </b><i>, , <a class="ref" href="enumset1.html#D3">ENUMSET1:def 3</a></i>;<br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="15_2_2_1_19"><b>suppose </b></a><a NAME="E1:15_2_2_1_19"/>
( <font color="Maroon">x</font> <a href="hidden.html#R1">=</a> <font color="Maroon">d</font> &amp; <font color="Maroon">y</font> <a href="hidden.html#R1">=</a> <font color="Maroon">d</font> )
 ;<br/><div class="add"><a NAME="E2:15_2_2_1_19"/><b>then </b>
 <a href="yellow_0.html#NK3" target="_self">sup</a> <span class="p1"><a href="domain_1.html#K7">{</a><span class="default"><font color="Maroon">x</font>,<font color="Maroon">y</font></span><a href="domain_1.html#K7">}</a></span> <a href="hidden.html#R1">=</a> <font color="Maroon">d</font> <a href="lattice3.html#K13">"\/"</a> <font color="Maroon">d</font>
 <b>by </b><i><a class="ref" href="yellow_0.html#T41">YELLOW_0:41</a></i>;<br/><a NAME="E3:15_2_2_1_19"/><b>then </b>
 <a href="yellow_0.html#NK3" target="_self">sup</a> <span class="p1"><a href="domain_1.html#K7">{</a><span class="default"><font color="Maroon">x</font>,<font color="Maroon">y</font></span><a href="domain_1.html#K7">}</a></span> <a href="hidden.html#R1">=</a> <font color="Maroon">d</font>
 <b>by </b><i><a class="ref" href="yellow_5.html#T1">YELLOW_5:1</a></i>;<br/><b>hence </b><a NAME="E4:15_2_2_1_19"/>
 <a href="yellow_0.html#K1">"\/"</a> <span class="p1"><a href="domain_1.html#K7">{</a><span class="default"><font color="Maroon">x</font>,<font color="Maroon">y</font></span><a href="domain_1.html#K7">}</a></span>,<font color="Maroon">L</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_0.html#K5">subrelstr</a> <font color="Maroon">ck</font></span>)</span>
 <b>by </b><i>, <a class="ref" href="enumset1.html#D3">ENUMSET1:def 3</a></i>;<br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="15_2_2_1_20"><b>suppose </b></a><a NAME="E1:15_2_2_1_20"/><i><font color="Green">E115</font></i>: 
( <font color="Maroon">x</font> <a href="hidden.html#R1">=</a> <font color="Maroon">d</font> &amp; <font color="Maroon">y</font> <a href="hidden.html#R1">=</a> <font color="Maroon">e</font> )
 ;<br/><div class="add"><a NAME="E2:15_2_2_1_20"/>
<font color="Maroon">d</font> <a href="lattice3.html#K13">"\/"</a> <font color="Maroon">e</font> <a href="hidden.html#R1">=</a> <font color="Maroon">e</font>
 <b>by </b><i>, </i>;<br/><a NAME="E3:15_2_2_1_20"/><b>then </b>
 <a href="yellow_0.html#NK3" target="_self">sup</a> <span class="p1"><a href="domain_1.html#K7">{</a><span class="default"><font color="Maroon">x</font>,<font color="Maroon">y</font></span><a href="domain_1.html#K7">}</a></span> <a href="hidden.html#R1">=</a> <font color="Maroon">e</font>
 <b>by </b><i>, <a class="ref" href="yellow_0.html#T41">YELLOW_0:41</a></i>;<br/><b>hence </b><a NAME="E4:15_2_2_1_20"/>
 <a href="yellow_0.html#K1">"\/"</a> <span class="p1"><a href="domain_1.html#K7">{</a><span class="default"><font color="Maroon">x</font>,<font color="Maroon">y</font></span><a href="domain_1.html#K7">}</a></span>,<font color="Maroon">L</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_0.html#K5">subrelstr</a> <font color="Maroon">ck</font></span>)</span>
 <b>by </b><i>, <a class="ref" href="enumset1.html#D3">ENUMSET1:def 3</a></i>;<br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="15_2_2_1_21"><b>suppose </b></a><a NAME="E1:15_2_2_1_21"/><i><font color="Green">E134</font></i>: 
( <font color="Maroon">x</font> <a href="hidden.html#R1">=</a> <font color="Maroon">e</font> &amp; <font color="Maroon">y</font> <a href="hidden.html#R1">=</a> <font color="Maroon">a</font> )
 ;<br/><div class="add"><a NAME="E2:15_2_2_1_21"/>
( <font color="Maroon">a</font> <a href="orders_2.html#R3">&lt;=</a> <font color="Maroon">c</font> &amp; <font color="Maroon">c</font> <a href="orders_2.html#R3">&lt;=</a> <font color="Maroon">e</font> )
 <b>by </b><i>, <a class="ref" href="yellow_0.html#T25">YELLOW_0:25</a></i>;<br/><a NAME="E3:15_2_2_1_21"/><b>then </b>
<font color="Maroon">a</font> <a href="orders_2.html#R3">&lt;=</a> <font color="Maroon">e</font>
 <b>by </b><i><a class="ref" href="orders_2.html#T26">ORDERS_2:26</a></i>;<br/><a NAME="E4:15_2_2_1_21"/><b>then </b>
<font color="Maroon">a</font> <a href="lattice3.html#K12">"/\"</a> <font color="Maroon">e</font> <a href="hidden.html#R1">=</a> <font color="Maroon">a</font>
 <b>by </b><i><a class="ref" href="yellow_0.html#T25">YELLOW_0:25</a></i>;<br/><a NAME="E5:15_2_2_1_21"/><b>then </b>
<font color="Maroon">a</font> <a href="lattice3.html#K13">"\/"</a> <font color="Maroon">e</font> <a href="hidden.html#R1">=</a> <font color="Maroon">e</font>
 <b>by </b><i/>;<br/><a NAME="E6:15_2_2_1_21"/><b>then </b>
 <a href="yellow_0.html#NK3" target="_self">sup</a> <span class="p1"><a href="domain_1.html#K7">{</a><span class="default"><font color="Maroon">x</font>,<font color="Maroon">y</font></span><a href="domain_1.html#K7">}</a></span> <a href="hidden.html#R1">=</a> <font color="Maroon">e</font>
 <b>by </b><i>, <a class="ref" href="yellow_0.html#T41">YELLOW_0:41</a></i>;<br/><b>hence </b><a NAME="E7:15_2_2_1_21"/>
 <a href="yellow_0.html#K1">"\/"</a> <span class="p1"><a href="domain_1.html#K7">{</a><span class="default"><font color="Maroon">x</font>,<font color="Maroon">y</font></span><a href="domain_1.html#K7">}</a></span>,<font color="Maroon">L</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_0.html#K5">subrelstr</a> <font color="Maroon">ck</font></span>)</span>
 <b>by </b><i>, <a class="ref" href="enumset1.html#D3">ENUMSET1:def 3</a></i>;<br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="15_2_2_1_22"><b>suppose </b></a><a NAME="E1:15_2_2_1_22"/><i><font color="Green">E135</font></i>: 
( <font color="Maroon">x</font> <a href="hidden.html#R1">=</a> <font color="Maroon">e</font> &amp; <font color="Maroon">y</font> <a href="hidden.html#R1">=</a> <font color="Maroon">b</font> )
 ;<br/><div class="add"><a NAME="E2:15_2_2_1_22"/>
<font color="Maroon">b</font> <a href="lattice3.html#K13">"\/"</a> <font color="Maroon">e</font> <a href="hidden.html#R1">=</a> <font color="Maroon">e</font>
 <b>by </b><i>, </i>;<br/><a NAME="E3:15_2_2_1_22"/><b>then </b>
 <a href="yellow_0.html#NK3" target="_self">sup</a> <span class="p1"><a href="domain_1.html#K7">{</a><span class="default"><font color="Maroon">x</font>,<font color="Maroon">y</font></span><a href="domain_1.html#K7">}</a></span> <a href="hidden.html#R1">=</a> <font color="Maroon">e</font>
 <b>by </b><i>, <a class="ref" href="yellow_0.html#T41">YELLOW_0:41</a></i>;<br/><b>hence </b><a NAME="E4:15_2_2_1_22"/>
 <a href="yellow_0.html#K1">"\/"</a> <span class="p1"><a href="domain_1.html#K7">{</a><span class="default"><font color="Maroon">x</font>,<font color="Maroon">y</font></span><a href="domain_1.html#K7">}</a></span>,<font color="Maroon">L</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_0.html#K5">subrelstr</a> <font color="Maroon">ck</font></span>)</span>
 <b>by </b><i>, <a class="ref" href="enumset1.html#D3">ENUMSET1:def 3</a></i>;<br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="15_2_2_1_23"><b>suppose </b></a><a NAME="E1:15_2_2_1_23"/><i><font color="Green">E136</font></i>: 
( <font color="Maroon">x</font> <a href="hidden.html#R1">=</a> <font color="Maroon">e</font> &amp; <font color="Maroon">y</font> <a href="hidden.html#R1">=</a> <font color="Maroon">c</font> )
 ;<br/><div class="add"><a NAME="E2:15_2_2_1_23"/>
<font color="Maroon">c</font> <a href="lattice3.html#K13">"\/"</a> <font color="Maroon">e</font> <a href="hidden.html#R1">=</a> <font color="Maroon">e</font>
 <b>by </b><i>, </i>;<br/><a NAME="E3:15_2_2_1_23"/><b>then </b>
 <a href="yellow_0.html#NK3" target="_self">sup</a> <span class="p1"><a href="domain_1.html#K7">{</a><span class="default"><font color="Maroon">x</font>,<font color="Maroon">y</font></span><a href="domain_1.html#K7">}</a></span> <a href="hidden.html#R1">=</a> <font color="Maroon">e</font>
 <b>by </b><i>, <a class="ref" href="yellow_0.html#T41">YELLOW_0:41</a></i>;<br/><b>hence </b><a NAME="E4:15_2_2_1_23"/>
 <a href="yellow_0.html#K1">"\/"</a> <span class="p1"><a href="domain_1.html#K7">{</a><span class="default"><font color="Maroon">x</font>,<font color="Maroon">y</font></span><a href="domain_1.html#K7">}</a></span>,<font color="Maroon">L</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_0.html#K5">subrelstr</a> <font color="Maroon">ck</font></span>)</span>
 <b>by </b><i>, <a class="ref" href="enumset1.html#D3">ENUMSET1:def 3</a></i>;<br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="15_2_2_1_24"><b>suppose </b></a><a NAME="E1:15_2_2_1_24"/><i><font color="Green">E137</font></i>: 
( <font color="Maroon">x</font> <a href="hidden.html#R1">=</a> <font color="Maroon">e</font> &amp; <font color="Maroon">y</font> <a href="hidden.html#R1">=</a> <font color="Maroon">d</font> )
 ;<br/><div class="add"><a NAME="E2:15_2_2_1_24"/>
<font color="Maroon">d</font> <a href="lattice3.html#K13">"\/"</a> <font color="Maroon">e</font> <a href="hidden.html#R1">=</a> <font color="Maroon">e</font>
 <b>by </b><i>, </i>;<br/><a NAME="E3:15_2_2_1_24"/><b>then </b>
 <a href="yellow_0.html#NK3" target="_self">sup</a> <span class="p1"><a href="domain_1.html#K7">{</a><span class="default"><font color="Maroon">x</font>,<font color="Maroon">y</font></span><a href="domain_1.html#K7">}</a></span> <a href="hidden.html#R1">=</a> <font color="Maroon">e</font>
 <b>by </b><i>, <a class="ref" href="yellow_0.html#T41">YELLOW_0:41</a></i>;<br/><b>hence </b><a NAME="E4:15_2_2_1_24"/>
 <a href="yellow_0.html#K1">"\/"</a> <span class="p1"><a href="domain_1.html#K7">{</a><span class="default"><font color="Maroon">x</font>,<font color="Maroon">y</font></span><a href="domain_1.html#K7">}</a></span>,<font color="Maroon">L</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_0.html#K5">subrelstr</a> <font color="Maroon">ck</font></span>)</span>
 <b>by </b><i>, <a class="ref" href="enumset1.html#D3">ENUMSET1:def 3</a></i>;<br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="15_2_2_1_25"><b>suppose </b></a><a NAME="E1:15_2_2_1_25"/>
( <font color="Maroon">x</font> <a href="hidden.html#R1">=</a> <font color="Maroon">e</font> &amp; <font color="Maroon">y</font> <a href="hidden.html#R1">=</a> <font color="Maroon">e</font> )
 ;<br/><div class="add"><a NAME="E2:15_2_2_1_25"/><b>then </b>
 <a href="yellow_0.html#NK3" target="_self">sup</a> <span class="p1"><a href="domain_1.html#K7">{</a><span class="default"><font color="Maroon">x</font>,<font color="Maroon">y</font></span><a href="domain_1.html#K7">}</a></span> <a href="hidden.html#R1">=</a> <font color="Maroon">e</font> <a href="lattice3.html#K13">"\/"</a> <font color="Maroon">e</font>
 <b>by </b><i><a class="ref" href="yellow_0.html#T41">YELLOW_0:41</a></i>;<br/><a NAME="E3:15_2_2_1_25"/><b>then </b>
 <a href="yellow_0.html#NK3" target="_self">sup</a> <span class="p1"><a href="domain_1.html#K7">{</a><span class="default"><font color="Maroon">x</font>,<font color="Maroon">y</font></span><a href="domain_1.html#K7">}</a></span> <a href="hidden.html#R1">=</a> <font color="Maroon">e</font>
 <b>by </b><i><a class="ref" href="yellow_5.html#T1">YELLOW_5:1</a></i>;<br/><b>hence </b><a NAME="E4:15_2_2_1_25"/>
 <a href="yellow_0.html#K1">"\/"</a> <span class="p1"><a href="domain_1.html#K7">{</a><span class="default"><font color="Maroon">x</font>,<font color="Maroon">y</font></span><a href="domain_1.html#K7">}</a></span>,<font color="Maroon">L</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_0.html#K5">subrelstr</a> <font color="Maroon">ck</font></span>)</span>
 <b>by </b><i>, <a class="ref" href="enumset1.html#D3">ENUMSET1:def 3</a></i>;<br/></div><b>end;</b></div></div><b>end;</b></div>

</div><b>end;</b></div>
<b>then reconsider </b><font color="Maroon">K</font> =  <a href="yellow_0.html#K5">subrelstr</a> <font color="Maroon">ck</font> as  non <a href="struct_0.html#V3">empty</a> <a href="yellow_0.html#V4">full</a> <a href="lattice5.html#NM2">Sublattice</a> of <font color="Maroon">L</font> <b>by </b><i>, , <a class="ref" href="struct_0.html#D1">STRUCT_0:def 1</a></i>;<br/>
<b>take </b>
<font color="Maroon">K</font>
;<br/>

<b>thus </b><a NAME="E7:15_2"/>
 <a href="yellow11.html#K2" target="_self">M_3</a> ,<font color="Maroon">K</font> <a href="waybel_1.html#R5">are_isomorphic</a> 
 <div><a class="txt" onclick="hs2(this)" href="javascript:()" title="15_2_3"><b>proof </b></a><div class="add">

<b>reconsider </b><font color="Maroon">z</font> = 0 as   <a href="struct_0.html#NM1">Element</a> of <a href="yellow11.html#K2" target="_self">M_3</a>  <b>by </b><i>, <a class="ref" href="enumset1.html#D3">ENUMSET1:def 3</a></i>;<br/>
<b>reconsider </b><font color="Maroon">j</font> = 1 as   <a href="struct_0.html#NM1">Element</a> of <a href="yellow11.html#K2" target="_self">M_3</a>  <b>by </b><i>, <a class="ref" href="enumset1.html#D3">ENUMSET1:def 3</a></i>;<br/>
<b>reconsider </b><font color="Maroon">dj</font> = 2 <a href="subset_1.html#K6">\</a> 1 as   <a href="struct_0.html#NM1">Element</a> of <a href="yellow11.html#K2" target="_self">M_3</a>  <b>by </b><i>, <a class="ref" href="enumset1.html#D3">ENUMSET1:def 3</a></i>;<br/>
<b>reconsider </b><font color="Maroon">td</font> = 3 <a href="subset_1.html#K6">\</a> 2 as   <a href="struct_0.html#NM1">Element</a> of <a href="yellow11.html#K2" target="_self">M_3</a>  <b>by </b><i>, <a class="ref" href="enumset1.html#D3">ENUMSET1:def 3</a></i>;<br/>
<b>reconsider </b><font color="Maroon">t</font> = 3 as   <a href="struct_0.html#NM1">Element</a> of <a href="yellow11.html#K2" target="_self">M_3</a>  <b>by </b><i>, <a class="ref" href="enumset1.html#D3">ENUMSET1:def 3</a></i>;<br/>
<div><i><font color="Green">E138</font></i>: <a class="txt" onclick="hs2(this)" href="javascript:()" title="15_2_3_1"><b>now </b></a><div class="add"><b>assume </b><a NAME="E1:15_2_3_1"/><i><font color="Green">E139</font></i>: 
<font color="Maroon">j</font> <a href="hidden.html#R1">=</a> <font color="Maroon">dj</font>
 ;<br/><a NAME="E2:15_2_3_1"/>
1 <a href="hidden.html#R2">in</a> <font color="Maroon">dj</font>
 <b>by </b><i>, <a class="ref" href="tarski.html#D1">TARSKI:def 1</a></i>;<br/><b>hence </b><a NAME="E3:15_2_3_1"/>
contradiction
 <b>by </b><i/>;<br/></div><b>end;</b></div>
<div><i><font color="Green">E141</font></i>: <a class="txt" onclick="hs2(this)" href="javascript:()" title="15_2_3_2"><b>now </b></a><div class="add"><b>assume </b><a NAME="E1:15_2_3_2"/><i><font color="Green">E142</font></i>: 
<font color="Maroon">j</font> <a href="hidden.html#R1">=</a> <font color="Maroon">td</font>
 ;<br/><a NAME="E2:15_2_3_2"/>
( 2 <a href="hidden.html#R2">in</a> <font color="Maroon">td</font> &amp; 0 <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> 2 )
 <b>by </b><i>, <a class="ref" href="tarski.html#D1">TARSKI:def 1</a></i>;<br/><b>hence </b><a NAME="E3:15_2_3_2"/>
contradiction
 <b>by </b><i>, <a class="ref" href="card_5.html#T1">CARD_5:1</a>, <a class="ref" href="tarski.html#D1">TARSKI:def 1</a></i>;<br/></div><b>end;</b></div>
<div><i><font color="Green">E143</font></i>: <a class="txt" onclick="hs2(this)" href="javascript:()" title="15_2_3_3"><b>now </b></a><div class="add"><b>assume </b><a NAME="E1:15_2_3_3"/><i><font color="Green">E144</font></i>: 
<font color="Maroon">dj</font> <a href="hidden.html#R1">=</a> <font color="Maroon">td</font>
 ;<br/><a NAME="E2:15_2_3_3"/>
( 2 <a href="hidden.html#R2">in</a> <font color="Maroon">td</font> &amp; 1 <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> 2 )
 <b>by </b><i>, <a class="ref" href="tarski.html#D1">TARSKI:def 1</a></i>;<br/><b>hence </b><a NAME="E3:15_2_3_3"/>
contradiction
 <b>by </b><i>, , <a class="ref" href="tarski.html#D1">TARSKI:def 1</a></i>;<br/></div><b>end;</b></div>
<div><i><font color="Green">E145</font></i>: <a class="txt" onclick="hs2(this)" href="javascript:()" title="15_2_3_4"><b>now </b></a><div class="add"><b>assume </b><a NAME="E1:15_2_3_4"/><i><font color="Green">E146</font></i>: 
<font color="Maroon">dj</font> <a href="hidden.html#R1">=</a> <font color="Maroon">t</font>
 ;<br/><a NAME="E2:15_2_3_4"/>
( 2 <a href="hidden.html#R2">in</a> <font color="Maroon">t</font> &amp; 1 <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> 2 )
 <b>by </b><i>, <a class="ref" href="enumset1.html#D1">ENUMSET1:def 1</a></i>;<br/><b>hence </b><a NAME="E3:15_2_3_4"/>
contradiction
 <b>by </b><i>, , <a class="ref" href="tarski.html#D1">TARSKI:def 1</a></i>;<br/></div><b>end;</b></div>
<div><i><font color="Green">E147</font></i>: <a class="txt" onclick="hs2(this)" href="javascript:()" title="15_2_3_5"><b>now </b></a><div class="add"><b>assume </b><a NAME="E1:15_2_3_5"/><i><font color="Green">E148</font></i>: 
<font color="Maroon">td</font> <a href="hidden.html#R1">=</a> <font color="Maroon">t</font>
 ;<br/><a NAME="E2:15_2_3_5"/>
( 0 <a href="hidden.html#R2">in</a> <font color="Maroon">t</font> &amp; 0 <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> 2 )
 <b>by </b><i>, <a class="ref" href="enumset1.html#D1">ENUMSET1:def 1</a></i>;<br/><b>hence </b><a NAME="E3:15_2_3_5"/>
contradiction
 <b>by </b><i>, , <a class="ref" href="tarski.html#D1">TARSKI:def 1</a></i>;<br/></div><b>end;</b></div>
<b>defpred </b><font color="Maroon">S<sub>1</sub></font>[   <a href="hidden.html#M1">set</a> ,   <a href="hidden.html#M1">set</a> ] <b>means </b>for <font color="Olive">X</font> being  <a href="struct_0.html#NM1">Element</a> of <a href="yellow11.html#K2" target="_self">M_3</a>   st <font color="Olive">X</font> <a href="hidden.html#R1">=</a> <font color="Maroon">a<sub>1</sub></font> holds <br/>( ( <font color="Olive">X</font> <a href="hidden.html#R1">=</a> <font color="Maroon">z</font> implies <font color="Maroon">a<sub>2</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">a</font> ) &amp; ( <font color="Olive">X</font> <a href="hidden.html#R1">=</a> <font color="Maroon">j</font> implies <font color="Maroon">a<sub>2</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">b</font> ) &amp; ( <font color="Olive">X</font> <a href="hidden.html#R1">=</a> <font color="Maroon">dj</font> implies <font color="Maroon">a<sub>2</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c</font> ) &amp; ( <font color="Olive">X</font> <a href="hidden.html#R1">=</a> <font color="Maroon">td</font> implies <font color="Maroon">a<sub>2</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">d</font> ) &amp; ( <font color="Olive">X</font> <a href="hidden.html#R1">=</a> <font color="Maroon">t</font> implies <font color="Maroon">a<sub>2</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">e</font> ) );<br/>
<a NAME="E11:15_2_3"/><i><font color="Green">E149</font></i>: 
for <font color="Olive">x</font> being   <a href="hidden.html#M1">set</a>   st <font color="Olive">x</font> <a href="hidden.html#R2">in</a> the <a href="struct_0.html#U1">carrier</a> of <a href="yellow11.html#K2" target="_self">M_3</a>  holds <br/> ex <font color="Olive">y</font> being   <a href="hidden.html#M1">set</a>  st <br/>( <font color="Olive">y</font> <a href="hidden.html#R2">in</a> <font color="Maroon">ck</font> &amp; <font color="Maroon">S<sub>1</sub></font>[<font color="Olive">x</font>,<font color="Olive">y</font>] )
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="15_2_3_6"><b>proof </b></a><div class="add">

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

<b>assume </b><a NAME="E1:15_2_3_6"/><i><font color="Green">E150</font></i>: 
<font color="Maroon">x</font> <a href="hidden.html#R2">in</a> the <a href="struct_0.html#U1">carrier</a> of <a href="yellow11.html#K2" target="_self">M_3</a> 
 ;<br/>

<div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="15_2_3_6_1"><b>per </b></a><a class="txt" onclick="hs(this)" href="javascript:()"><b>cases </b></a><span class="hide"><a NAME="E1:15_2_3_6_1"/>
( <font color="Maroon">x</font> <a href="hidden.html#R1">=</a> 0 or <font color="Maroon">x</font> <a href="hidden.html#R1">=</a> 1 or <font color="Maroon">x</font> <a href="hidden.html#R1">=</a> 2 <a href="subset_1.html#K6">\</a> 1 or <font color="Maroon">x</font> <a href="hidden.html#R1">=</a> 3 <a href="subset_1.html#K6">\</a> 2 or <font color="Maroon">x</font> <a href="hidden.html#R1">=</a> 3 )
 </span><b>by </b><i>, <a class="ref" href="yellow11.html#T1" target="_self">Th1</a>, <a class="ref" href="enumset1.html#D3">ENUMSET1:def 3</a></i>;<br/><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="15_2_3_6_1_1"><b>suppose </b></a><a NAME="E1:15_2_3_6_1_1"/><i><font color="Green">E151</font></i>: 
<font color="Maroon">x</font> <a href="hidden.html#R1">=</a> 0
 ;<br/><div class="add"><b>take </b><font color="Maroon">y</font> = <font color="Maroon">a</font>;<br/><b>thus </b><a NAME="E2:15_2_3_6_1_1"/>
<font color="Maroon">y</font> <a href="hidden.html#R2">in</a> <font color="Maroon">ck</font>
 <b>by </b><i><a class="ref" href="enumset1.html#D3">ENUMSET1:def 3</a></i>;<br/><b>let </b><font color="Maroon">X</font> be   <a href="struct_0.html#NM1">Element</a> of <a href="yellow11.html#K2" target="_self">M_3</a> ;<br/><b>thus </b><a NAME="E3:15_2_3_6_1_1"/>
( <font color="Maroon">X</font> <a href="hidden.html#R1">=</a> <font color="Maroon">x</font> implies ( ( <font color="Maroon">X</font> <a href="hidden.html#R1">=</a> <font color="Maroon">z</font> implies <font color="Maroon">y</font> <a href="hidden.html#R1">=</a> <font color="Maroon">a</font> ) &amp; ( <font color="Maroon">X</font> <a href="hidden.html#R1">=</a> <font color="Maroon">j</font> implies <font color="Maroon">y</font> <a href="hidden.html#R1">=</a> <font color="Maroon">b</font> ) &amp; ( <font color="Maroon">X</font> <a href="hidden.html#R1">=</a> <font color="Maroon">dj</font> implies <font color="Maroon">y</font> <a href="hidden.html#R1">=</a> <font color="Maroon">c</font> ) &amp; ( <font color="Maroon">X</font> <a href="hidden.html#R1">=</a> <font color="Maroon">td</font> implies <font color="Maroon">y</font> <a href="hidden.html#R1">=</a> <font color="Maroon">d</font> ) &amp; ( <font color="Maroon">X</font> <a href="hidden.html#R1">=</a> <font color="Maroon">t</font> implies <font color="Maroon">y</font> <a href="hidden.html#R1">=</a> <font color="Maroon">e</font> ) ) )
 <b>by </b><i><a class="ref" href="yellow11.html#T2" target="_self">Th2</a>, , </i>;<br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="15_2_3_6_1_2"><b>suppose </b></a><a NAME="E1:15_2_3_6_1_2"/><i><font color="Green">E152</font></i>: 
<font color="Maroon">x</font> <a href="hidden.html#R1">=</a> 1
 ;<br/><div class="add"><b>take </b><font color="Maroon">y</font> = <font color="Maroon">b</font>;<br/><b>thus </b><a NAME="E2:15_2_3_6_1_2"/>
<font color="Maroon">y</font> <a href="hidden.html#R2">in</a> <font color="Maroon">ck</font>
 <b>by </b><i><a class="ref" href="enumset1.html#D3">ENUMSET1:def 3</a></i>;<br/><b>let </b><font color="Maroon">X</font> be   <a href="struct_0.html#NM1">Element</a> of <a href="yellow11.html#K2" target="_self">M_3</a> ;<br/><b>thus </b><a NAME="E3:15_2_3_6_1_2"/>
( <font color="Maroon">X</font> <a href="hidden.html#R1">=</a> <font color="Maroon">x</font> implies ( ( <font color="Maroon">X</font> <a href="hidden.html#R1">=</a> <font color="Maroon">z</font> implies <font color="Maroon">y</font> <a href="hidden.html#R1">=</a> <font color="Maroon">a</font> ) &amp; ( <font color="Maroon">X</font> <a href="hidden.html#R1">=</a> <font color="Maroon">j</font> implies <font color="Maroon">y</font> <a href="hidden.html#R1">=</a> <font color="Maroon">b</font> ) &amp; ( <font color="Maroon">X</font> <a href="hidden.html#R1">=</a> <font color="Maroon">dj</font> implies <font color="Maroon">y</font> <a href="hidden.html#R1">=</a> <font color="Maroon">c</font> ) &amp; ( <font color="Maroon">X</font> <a href="hidden.html#R1">=</a> <font color="Maroon">td</font> implies <font color="Maroon">y</font> <a href="hidden.html#R1">=</a> <font color="Maroon">d</font> ) &amp; ( <font color="Maroon">X</font> <a href="hidden.html#R1">=</a> <font color="Maroon">t</font> implies <font color="Maroon">y</font> <a href="hidden.html#R1">=</a> <font color="Maroon">e</font> ) ) )
 <b>by </b><i>, , <a class="ref" href="yellow11.html#T2" target="_self">Th2</a></i>;<br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="15_2_3_6_1_3"><b>suppose </b></a><a NAME="E1:15_2_3_6_1_3"/><i><font color="Green">E153</font></i>: 
<font color="Maroon">x</font> <a href="hidden.html#R1">=</a> 2 <a href="subset_1.html#K6">\</a> 1
 ;<br/><div class="add"><b>take </b><font color="Maroon">y</font> = <font color="Maroon">c</font>;<br/><b>thus </b><a NAME="E2:15_2_3_6_1_3"/>
<font color="Maroon">y</font> <a href="hidden.html#R2">in</a> <font color="Maroon">ck</font>
 <b>by </b><i><a class="ref" href="enumset1.html#D3">ENUMSET1:def 3</a></i>;<br/><b>let </b><font color="Maroon">X</font> be   <a href="struct_0.html#NM1">Element</a> of <a href="yellow11.html#K2" target="_self">M_3</a> ;<br/><b>thus </b><a NAME="E3:15_2_3_6_1_3"/>
( <font color="Maroon">X</font> <a href="hidden.html#R1">=</a> <font color="Maroon">x</font> implies ( ( <font color="Maroon">X</font> <a href="hidden.html#R1">=</a> <font color="Maroon">z</font> implies <font color="Maroon">y</font> <a href="hidden.html#R1">=</a> <font color="Maroon">a</font> ) &amp; ( <font color="Maroon">X</font> <a href="hidden.html#R1">=</a> <font color="Maroon">j</font> implies <font color="Maroon">y</font> <a href="hidden.html#R1">=</a> <font color="Maroon">b</font> ) &amp; ( <font color="Maroon">X</font> <a href="hidden.html#R1">=</a> <font color="Maroon">dj</font> implies <font color="Maroon">y</font> <a href="hidden.html#R1">=</a> <font color="Maroon">c</font> ) &amp; ( <font color="Maroon">X</font> <a href="hidden.html#R1">=</a> <font color="Maroon">td</font> implies <font color="Maroon">y</font> <a href="hidden.html#R1">=</a> <font color="Maroon">d</font> ) &amp; ( <font color="Maroon">X</font> <a href="hidden.html#R1">=</a> <font color="Maroon">t</font> implies <font color="Maroon">y</font> <a href="hidden.html#R1">=</a> <font color="Maroon">e</font> ) ) )
 <b>by </b><i>, , , <a class="ref" href="yellow11.html#T2" target="_self">Th2</a>, </i>;<br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="15_2_3_6_1_4"><b>suppose </b></a><a NAME="E1:15_2_3_6_1_4"/><i><font color="Green">E154</font></i>: 
<font color="Maroon">x</font> <a href="hidden.html#R1">=</a> 3 <a href="subset_1.html#K6">\</a> 2
 ;<br/><div class="add"><b>take </b><font color="Maroon">y</font> = <font color="Maroon">d</font>;<br/><b>thus </b><a NAME="E2:15_2_3_6_1_4"/>
<font color="Maroon">y</font> <a href="hidden.html#R2">in</a> <font color="Maroon">ck</font>
 <b>by </b><i><a class="ref" href="enumset1.html#D3">ENUMSET1:def 3</a></i>;<br/><b>let </b><font color="Maroon">X</font> be   <a href="struct_0.html#NM1">Element</a> of <a href="yellow11.html#K2" target="_self">M_3</a> ;<br/><b>thus </b><a NAME="E3:15_2_3_6_1_4"/>
( <font color="Maroon">X</font> <a href="hidden.html#R1">=</a> <font color="Maroon">x</font> implies ( ( <font color="Maroon">X</font> <a href="hidden.html#R1">=</a> <font color="Maroon">z</font> implies <font color="Maroon">y</font> <a href="hidden.html#R1">=</a> <font color="Maroon">a</font> ) &amp; ( <font color="Maroon">X</font> <a href="hidden.html#R1">=</a> <font color="Maroon">j</font> implies <font color="Maroon">y</font> <a href="hidden.html#R1">=</a> <font color="Maroon">b</font> ) &amp; ( <font color="Maroon">X</font> <a href="hidden.html#R1">=</a> <font color="Maroon">dj</font> implies <font color="Maroon">y</font> <a href="hidden.html#R1">=</a> <font color="Maroon">c</font> ) &amp; ( <font color="Maroon">X</font> <a href="hidden.html#R1">=</a> <font color="Maroon">td</font> implies <font color="Maroon">y</font> <a href="hidden.html#R1">=</a> <font color="Maroon">d</font> ) &amp; ( <font color="Maroon">X</font> <a href="hidden.html#R1">=</a> <font color="Maroon">t</font> implies <font color="Maroon">y</font> <a href="hidden.html#R1">=</a> <font color="Maroon">e</font> ) ) )
 <b>by </b><i>, , , <a class="ref" href="yellow11.html#T2" target="_self">Th2</a>, </i>;<br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="15_2_3_6_1_5"><b>suppose </b></a><a NAME="E1:15_2_3_6_1_5"/><i><font color="Green">E155</font></i>: 
<font color="Maroon">x</font> <a href="hidden.html#R1">=</a> 3
 ;<br/><div class="add"><b>take </b><font color="Maroon">y</font> = <font color="Maroon">e</font>;<br/><b>thus </b><a NAME="E2:15_2_3_6_1_5"/>
<font color="Maroon">y</font> <a href="hidden.html#R2">in</a> <font color="Maroon">ck</font>
 <b>by </b><i><a class="ref" href="enumset1.html#D3">ENUMSET1:def 3</a></i>;<br/><b>let </b><font color="Maroon">X</font> be   <a href="struct_0.html#NM1">Element</a> of <a href="yellow11.html#K2" target="_self">M_3</a> ;<br/><b>thus </b><a NAME="E3:15_2_3_6_1_5"/>
( <font color="Maroon">X</font> <a href="hidden.html#R1">=</a> <font color="Maroon">x</font> implies ( ( <font color="Maroon">X</font> <a href="hidden.html#R1">=</a> <font color="Maroon">z</font> implies <font color="Maroon">y</font> <a href="hidden.html#R1">=</a> <font color="Maroon">a</font> ) &amp; ( <font color="Maroon">X</font> <a href="hidden.html#R1">=</a> <font color="Maroon">j</font> implies <font color="Maroon">y</font> <a href="hidden.html#R1">=</a> <font color="Maroon">b</font> ) &amp; ( <font color="Maroon">X</font> <a href="hidden.html#R1">=</a> <font color="Maroon">dj</font> implies <font color="Maroon">y</font> <a href="hidden.html#R1">=</a> <font color="Maroon">c</font> ) &amp; ( <font color="Maroon">X</font> <a href="hidden.html#R1">=</a> <font color="Maroon">td</font> implies <font color="Maroon">y</font> <a href="hidden.html#R1">=</a> <font color="Maroon">d</font> ) &amp; ( <font color="Maroon">X</font> <a href="hidden.html#R1">=</a> <font color="Maroon">t</font> implies <font color="Maroon">y</font> <a href="hidden.html#R1">=</a> <font color="Maroon">e</font> ) ) )
 <b>by </b><i>, , <a class="ref" href="yellow11.html#T2" target="_self">Th2</a></i>;<br/></div><b>end;</b></div></div><b>end;</b></div>

</div><b>end;</b></div>
<b>consider </b><font color="Maroon">f</font> being   <a href="funct_2.html#NM1">Function</a> of the <a href="struct_0.html#U1">carrier</a> of <a href="yellow11.html#K2" target="_self">M_3</a> ,<font color="Maroon">ck</font><b> such that </b><br/><a NAME="E13:15_2_3"/><i><font color="Green">E156</font></i>: 
for <font color="Olive">x</font> being   <a href="hidden.html#M1">set</a>   st <font color="Olive">x</font> <a href="hidden.html#R2">in</a> the <a href="struct_0.html#U1">carrier</a> of <a href="yellow11.html#K2" target="_self">M_3</a>  holds <br/><font color="Maroon">S<sub>1</sub></font>[<font color="Olive">x</font>,<font color="Maroon">f</font> <a href="funct_1.html#K1">.</a> <font color="Olive">x</font>]
 <b>from </b><i><a class="ref" href="funct_2.html#S1">FUNCT_2:sch 1</a>();<br/></i>
<b>reconsider </b><font color="Maroon">f</font> = <font color="Maroon">f</font> as   <a href="struct_0.html#NM6">Function</a> of <a href="yellow11.html#K2" target="_self">M_3</a> ,<font color="Maroon">K</font> <b>by </b><i/>;<br/>
<b>take </b>
<font color="Maroon">f</font>
; <i><font color="Red">:: according to </font></i><a class="ref" href="waybel_1.html#D8">WAYBEL_1:def 8</a><br/>

<a NAME="E15:15_2_3"/><i><font color="Green">E157</font></i>: 
<font color="Maroon">f</font> is <a href="funct_1.html#V2">one-to-one</a>
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="15_2_3_7"><b>proof </b></a><div class="add">

<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="15_2_3_7_1"><b>now </b></a><div class="add"><b>let </b><font color="Maroon">x</font> be   <a href="struct_0.html#NM1">Element</a> of <a href="yellow11.html#K2" target="_self">M_3</a> , <font color="Maroon">y</font> be   <a href="struct_0.html#NM1">Element</a> of <a href="yellow11.html#K2" target="_self">M_3</a> ;<br/><b>assume </b><a NAME="E1:15_2_3_7_1"/><i><font color="Green">E158</font></i>: 
<font color="Maroon">f</font> <a href="funct_2.html#K3">.</a> <font color="Maroon">x</font> <a href="hidden.html#R1">=</a> <font color="Maroon">f</font> <a href="funct_2.html#K3">.</a> <font color="Maroon">y</font>
 ;<br/><b>thus </b><a NAME="E2:15_2_3_7_1"/>
<font color="Maroon">x</font> <a href="hidden.html#R1">=</a> <font color="Maroon">y</font>
 <div><a class="txt" onclick="hs2(this)" href="javascript:()" title="15_2_3_7_1_1"><b>proof </b></a><div class="add">

<div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="15_2_3_7_1_1_1"><b>per </b></a><a class="txt" onclick="hs(this)" href="javascript:()"><b>cases </b></a><span class="hide"><a NAME="E1:15_2_3_7_1_1_1"/>
( ( <font color="Maroon">x</font> <a href="hidden.html#R1">=</a> <font color="Maroon">z</font> &amp; <font color="Maroon">y</font> <a href="hidden.html#R1">=</a> <font color="Maroon">z</font> ) or ( <font color="Maroon">x</font> <a href="hidden.html#R1">=</a> <font color="Maroon">j</font> &amp; <font color="Maroon">y</font> <a href="hidden.html#R1">=</a> <font color="Maroon">j</font> ) or ( <font color="Maroon">x</font> <a href="hidden.html#R1">=</a> <font color="Maroon">dj</font> &amp; <font color="Maroon">y</font> <a href="hidden.html#R1">=</a> <font color="Maroon">dj</font> ) or ( <font color="Maroon">x</font> <a href="hidden.html#R1">=</a> <font color="Maroon">td</font> &amp; <font color="Maroon">y</font> <a href="hidden.html#R1">=</a> <font color="Maroon">td</font> ) or ( <font color="Maroon">x</font> <a href="hidden.html#R1">=</a> <font color="Maroon">t</font> &amp; <font color="Maroon">y</font> <a href="hidden.html#R1">=</a> <font color="Maroon">t</font> ) or ( <font color="Maroon">x</font> <a href="hidden.html#R1">=</a> <font color="Maroon">z</font> &amp; <font color="Maroon">y</font> <a href="hidden.html#R1">=</a> <font color="Maroon">j</font> ) or ( <font color="Maroon">x</font> <a href="hidden.html#R1">=</a> <font color="Maroon">z</font> &amp; <font color="Maroon">y</font> <a href="hidden.html#R1">=</a> <font color="Maroon">dj</font> ) or ( <font color="Maroon">x</font> <a href="hidden.html#R1">=</a> <font color="Maroon">z</font> &amp; <font color="Maroon">y</font> <a href="hidden.html#R1">=</a> <font color="Maroon">td</font> ) or ( <font color="Maroon">x</font> <a href="hidden.html#R1">=</a> <font color="Maroon">z</font> &amp; <font color="Maroon">y</font> <a href="hidden.html#R1">=</a> <font color="Maroon">t</font> ) or ( <font color="Maroon">x</font> <a href="hidden.html#R1">=</a> <font color="Maroon">j</font> &amp; <font color="Maroon">y</font> <a href="hidden.html#R1">=</a> <font color="Maroon">z</font> ) or ( <font color="Maroon">x</font> <a href="hidden.html#R1">=</a> <font color="Maroon">j</font> &amp; <font color="Maroon">y</font> <a href="hidden.html#R1">=</a> <font color="Maroon">dj</font> ) or ( <font color="Maroon">x</font> <a href="hidden.html#R1">=</a> <font color="Maroon">j</font> &amp; <font color="Maroon">y</font> <a href="hidden.html#R1">=</a> <font color="Maroon">td</font> ) or ( <font color="Maroon">x</font> <a href="hidden.html#R1">=</a> <font color="Maroon">j</font> &amp; <font color="Maroon">y</font> <a href="hidden.html#R1">=</a> <font color="Maroon">t</font> ) or ( <font color="Maroon">x</font> <a href="hidden.html#R1">=</a> <font color="Maroon">dj</font> &amp; <font color="Maroon">y</font> <a href="hidden.html#R1">=</a> <font color="Maroon">z</font> ) or ( <font color="Maroon">x</font> <a href="hidden.html#R1">=</a> <font color="Maroon">dj</font> &amp; <font color="Maroon">y</font> <a href="hidden.html#R1">=</a> <font color="Maroon">j</font> ) or ( <font color="Maroon">x</font> <a href="hidden.html#R1">=</a> <font color="Maroon">dj</font> &amp; <font color="Maroon">y</font> <a href="hidden.html#R1">=</a> <font color="Maroon">td</font> ) or ( <font color="Maroon">x</font> <a href="hidden.html#R1">=</a> <font color="Maroon">dj</font> &amp; <font color="Maroon">y</font> <a href="hidden.html#R1">=</a> <font color="Maroon">t</font> ) or ( <font color="Maroon">x</font> <a href="hidden.html#R1">=</a> <font color="Maroon">td</font> &amp; <font color="Maroon">y</font> <a href="hidden.html#R1">=</a> <font color="Maroon">z</font> ) or ( <font color="Maroon">x</font> <a href="hidden.html#R1">=</a> <font color="Maroon">td</font> &amp; <font color="Maroon">y</font> <a href="hidden.html#R1">=</a> <font color="Maroon">j</font> ) or ( <font color="Maroon">x</font> <a href="hidden.html#R1">=</a> <font color="Maroon">td</font> &amp; <font color="Maroon">y</font> <a href="hidden.html#R1">=</a> <font color="Maroon">dj</font> ) or ( <font color="Maroon">x</font> <a href="hidden.html#R1">=</a> <font color="Maroon">td</font> &amp; <font color="Maroon">y</font> <a href="hidden.html#R1">=</a> <font color="Maroon">t</font> ) or ( <font color="Maroon">x</font> <a href="hidden.html#R1">=</a> <font color="Maroon">t</font> &amp; <font color="Maroon">y</font> <a href="hidden.html#R1">=</a> <font color="Maroon">z</font> ) or ( <font color="Maroon">x</font> <a href="hidden.html#R1">=</a> <font color="Maroon">t</font> &amp; <font color="Maroon">y</font> <a href="hidden.html#R1">=</a> <font color="Maroon">j</font> ) or ( <font color="Maroon">x</font> <a href="hidden.html#R1">=</a> <font color="Maroon">t</font> &amp; <font color="Maroon">y</font> <a href="hidden.html#R1">=</a> <font color="Maroon">dj</font> ) or ( <font color="Maroon">x</font> <a href="hidden.html#R1">=</a> <font color="Maroon">t</font> &amp; <font color="Maroon">y</font> <a href="hidden.html#R1">=</a> <font color="Maroon">td</font> ) )
 </span><b>by </b><i>, <a class="ref" href="enumset1.html#D3">ENUMSET1:def 3</a></i>;<br/><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="15_2_3_7_1_1_1_1"><b>suppose </b></a><a NAME="E1:15_2_3_7_1_1_1_1"/>
( <font color="Maroon">x</font> <a href="hidden.html#R1">=</a> <font color="Maroon">z</font> &amp; <font color="Maroon">y</font> <a href="hidden.html#R1">=</a> <font color="Maroon">z</font> )
 ;<br/><div class="add"><b>hence </b><a NAME="E2:15_2_3_7_1_1_1_1"/>
<font color="Maroon">x</font> <a href="hidden.html#R1">=</a> <font color="Maroon">y</font>
 ;<br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="15_2_3_7_1_1_1_2"><b>suppose </b></a><a NAME="E1:15_2_3_7_1_1_1_2"/>
( <font color="Maroon">x</font> <a href="hidden.html#R1">=</a> <font color="Maroon">j</font> &amp; <font color="Maroon">y</font> <a href="hidden.html#R1">=</a> <font color="Maroon">j</font> )
 ;<br/><div class="add"><b>hence </b><a NAME="E2:15_2_3_7_1_1_1_2"/>
<font color="Maroon">x</font> <a href="hidden.html#R1">=</a> <font color="Maroon">y</font>
 ;<br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="15_2_3_7_1_1_1_3"><b>suppose </b></a><a NAME="E1:15_2_3_7_1_1_1_3"/>
( <font color="Maroon">x</font> <a href="hidden.html#R1">=</a> <font color="Maroon">dj</font> &amp; <font color="Maroon">y</font> <a href="hidden.html#R1">=</a> <font color="Maroon">dj</font> )
 ;<br/><div class="add"><b>hence </b><a NAME="E2:15_2_3_7_1_1_1_3"/>
<font color="Maroon">x</font> <a href="hidden.html#R1">=</a> <font color="Maroon">y</font>
 ;<br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="15_2_3_7_1_1_1_4"><b>suppose </b></a><a NAME="E1:15_2_3_7_1_1_1_4"/>
( <font color="Maroon">x</font> <a href="hidden.html#R1">=</a> <font color="Maroon">td</font> &amp; <font color="Maroon">y</font> <a href="hidden.html#R1">=</a> <font color="Maroon">td</font> )
 ;<br/><div class="add"><b>hence </b><a NAME="E2:15_2_3_7_1_1_1_4"/>
<font color="Maroon">x</font> <a href="hidden.html#R1">=</a> <font color="Maroon">y</font>
 ;<br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="15_2_3_7_1_1_1_5"><b>suppose </b></a><a NAME="E1:15_2_3_7_1_1_1_5"/>
( <font color="Maroon">x</font> <a href="hidden.html#R1">=</a> <font color="Maroon">t</font> &amp; <font color="Maroon">y</font> <a href="hidden.html#R1">=</a> <font color="Maroon">t</font> )
 ;<br/><div class="add"><b>hence </b><a NAME="E2:15_2_3_7_1_1_1_5"/>
<font color="Maroon">x</font> <a href="hidden.html#R1">=</a> <font color="Maroon">y</font>
 ;<br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="15_2_3_7_1_1_1_6"><b>suppose </b></a><a NAME="E1:15_2_3_7_1_1_1_6"/>
( <font color="Maroon">x</font> <a href="hidden.html#R1">=</a> <font color="Maroon">z</font> &amp; <font color="Maroon">y</font> <a href="hidden.html#R1">=</a> <font color="Maroon">j</font> )
 ;<br/><div class="add"><a NAME="E2:15_2_3_7_1_1_1_6"/><b>then </b>
( <font color="Maroon">f</font> <a href="funct_2.html#K3">.</a> <font color="Maroon">x</font> <a href="hidden.html#R1">=</a> <font color="Maroon">a</font> &amp; <font color="Maroon">f</font> <a href="funct_2.html#K3">.</a> <font color="Maroon">y</font> <a href="hidden.html#R1">=</a> <font color="Maroon">b</font> )
 <b>by </b><i><a class="ref" href="yellow11.html#T1" target="_self">Th1</a></i>;<br/><b>hence </b><a NAME="E3:15_2_3_7_1_1_1_6"/>
<font color="Maroon">x</font> <a href="hidden.html#R1">=</a> <font color="Maroon">y</font>
 <b>by </b><i>, <a class="ref" href="yellow11.html#T3" target="_self">Th3</a></i>;<br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="15_2_3_7_1_1_1_7"><b>suppose </b></a><a NAME="E1:15_2_3_7_1_1_1_7"/>
( <font color="Maroon">x</font> <a href="hidden.html#R1">=</a> <font color="Maroon">z</font> &amp; <font color="Maroon">y</font> <a href="hidden.html#R1">=</a> <font color="Maroon">dj</font> )
 ;<br/><div class="add"><a NAME="E2:15_2_3_7_1_1_1_7"/><b>then </b>
( <font color="Maroon">f</font> <a href="funct_2.html#K3">.</a> <font color="Maroon">x</font> <a href="hidden.html#R1">=</a> <font color="Maroon">a</font> &amp; <font color="Maroon">f</font> <a href="funct_2.html#K3">.</a> <font color="Maroon">y</font> <a href="hidden.html#R1">=</a> <font color="Maroon">c</font> )
 <b>by </b><i><a class="ref" href="yellow11.html#T1" target="_self">Th1</a></i>;<br/><b>hence </b><a NAME="E3:15_2_3_7_1_1_1_7"/>
<font color="Maroon">x</font> <a href="hidden.html#R1">=</a> <font color="Maroon">y</font>
 <b>by </b><i>, <a class="ref" href="yellow11.html#T3" target="_self">Th3</a></i>;<br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="15_2_3_7_1_1_1_8"><b>suppose </b></a><a NAME="E1:15_2_3_7_1_1_1_8"/>
( <font color="Maroon">x</font> <a href="hidden.html#R1">=</a> <font color="Maroon">z</font> &amp; <font color="Maroon">y</font> <a href="hidden.html#R1">=</a> <font color="Maroon">td</font> )
 ;<br/><div class="add"><a NAME="E2:15_2_3_7_1_1_1_8"/><b>then </b>
( <font color="Maroon">f</font> <a href="funct_2.html#K3">.</a> <font color="Maroon">x</font> <a href="hidden.html#R1">=</a> <font color="Maroon">a</font> &amp; <font color="Maroon">f</font> <a href="funct_2.html#K3">.</a> <font color="Maroon">y</font> <a href="hidden.html#R1">=</a> <font color="Maroon">d</font> )
 <b>by </b><i><a class="ref" href="yellow11.html#T1" target="_self">Th1</a></i>;<br/><b>hence </b><a NAME="E3:15_2_3_7_1_1_1_8"/>
<font color="Maroon">x</font> <a href="hidden.html#R1">=</a> <font color="Maroon">y</font>
 <b>by </b><i>, <a class="ref" href="yellow11.html#T3" target="_self">Th3</a></i>;<br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="15_2_3_7_1_1_1_9"><b>suppose </b></a><a NAME="E1:15_2_3_7_1_1_1_9"/>
( <font color="Maroon">x</font> <a href="hidden.html#R1">=</a> <font color="Maroon">z</font> &amp; <font color="Maroon">y</font> <a href="hidden.html#R1">=</a> <font color="Maroon">t</font> )
 ;<br/><div class="add"><a NAME="E2:15_2_3_7_1_1_1_9"/><b>then </b>
( <font color="Maroon">f</font> <a href="funct_2.html#K3">.</a> <font color="Maroon">x</font> <a href="hidden.html#R1">=</a> <font color="Maroon">a</font> &amp; <font color="Maroon">f</font> <a href="funct_2.html#K3">.</a> <font color="Maroon">y</font> <a href="hidden.html#R1">=</a> <font color="Maroon">e</font> )
 <b>by </b><i><a class="ref" href="yellow11.html#T1" target="_self">Th1</a></i>;<br/><b>hence </b><a NAME="E3:15_2_3_7_1_1_1_9"/>
<font color="Maroon">x</font> <a href="hidden.html#R1">=</a> <font color="Maroon">y</font>
 <b>by </b><i>, <a class="ref" href="yellow11.html#T3" target="_self">Th3</a></i>;<br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="15_2_3_7_1_1_1_10"><b>suppose </b></a><a NAME="E1:15_2_3_7_1_1_1_10"/>
( <font color="Maroon">x</font> <a href="hidden.html#R1">=</a> <font color="Maroon">j</font> &amp; <font color="Maroon">y</font> <a href="hidden.html#R1">=</a> <font color="Maroon">z</font> )
 ;<br/><div class="add"><a NAME="E2:15_2_3_7_1_1_1_10"/><b>then </b>
( <font color="Maroon">f</font> <a href="funct_2.html#K3">.</a> <font color="Maroon">x</font> <a href="hidden.html#R1">=</a> <font color="Maroon">b</font> &amp; <font color="Maroon">f</font> <a href="funct_2.html#K3">.</a> <font color="Maroon">y</font> <a href="hidden.html#R1">=</a> <font color="Maroon">a</font> )
 <b>by </b><i><a class="ref" href="yellow11.html#T1" target="_self">Th1</a></i>;<br/><b>hence </b><a NAME="E3:15_2_3_7_1_1_1_10"/>
<font color="Maroon">x</font> <a href="hidden.html#R1">=</a> <font color="Maroon">y</font>
 <b>by </b><i>, <a class="ref" href="yellow11.html#T3" target="_self">Th3</a></i>;<br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="15_2_3_7_1_1_1_11"><b>suppose </b></a><a NAME="E1:15_2_3_7_1_1_1_11"/>
( <font color="Maroon">x</font> <a href="hidden.html#R1">=</a> <font color="Maroon">j</font> &amp; <font color="Maroon">y</font> <a href="hidden.html#R1">=</a> <font color="Maroon">dj</font> )
 ;<br/><div class="add"><a NAME="E2:15_2_3_7_1_1_1_11"/><b>then </b>
( <font color="Maroon">f</font> <a href="funct_2.html#K3">.</a> <font color="Maroon">x</font> <a href="hidden.html#R1">=</a> <font color="Maroon">b</font> &amp; <font color="Maroon">f</font> <a href="funct_2.html#K3">.</a> <font color="Maroon">y</font> <a href="hidden.html#R1">=</a> <font color="Maroon">c</font> )
 <b>by </b><i><a class="ref" href="yellow11.html#T1" target="_self">Th1</a></i>;<br/><b>hence </b><a NAME="E3:15_2_3_7_1_1_1_11"/>
<font color="Maroon">x</font> <a href="hidden.html#R1">=</a> <font color="Maroon">y</font>
 <b>by </b><i>, <a class="ref" href="yellow11.html#T3" target="_self">Th3</a></i>;<br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="15_2_3_7_1_1_1_12"><b>suppose </b></a><a NAME="E1:15_2_3_7_1_1_1_12"/>
( <font color="Maroon">x</font> <a href="hidden.html#R1">=</a> <font color="Maroon">j</font> &amp; <font color="Maroon">y</font> <a href="hidden.html#R1">=</a> <font color="Maroon">td</font> )
 ;<br/><div class="add"><a NAME="E2:15_2_3_7_1_1_1_12"/><b>then </b>
( <font color="Maroon">f</font> <a href="funct_2.html#K3">.</a> <font color="Maroon">x</font> <a href="hidden.html#R1">=</a> <font color="Maroon">b</font> &amp; <font color="Maroon">f</font> <a href="funct_2.html#K3">.</a> <font color="Maroon">y</font> <a href="hidden.html#R1">=</a> <font color="Maroon">d</font> )
 <b>by </b><i><a class="ref" href="yellow11.html#T1" target="_self">Th1</a></i>;<br/><b>hence </b><a NAME="E3:15_2_3_7_1_1_1_12"/>
<font color="Maroon">x</font> <a href="hidden.html#R1">=</a> <font color="Maroon">y</font>
 <b>by </b><i>, <a class="ref" href="yellow11.html#T3" target="_self">Th3</a></i>;<br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="15_2_3_7_1_1_1_13"><b>suppose </b></a><a NAME="E1:15_2_3_7_1_1_1_13"/>
( <font color="Maroon">x</font> <a href="hidden.html#R1">=</a> <font color="Maroon">j</font> &amp; <font color="Maroon">y</font> <a href="hidden.html#R1">=</a> <font color="Maroon">t</font> )
 ;<br/><div class="add"><a NAME="E2:15_2_3_7_1_1_1_13"/><b>then </b>
( <font color="Maroon">f</font> <a href="funct_2.html#K3">.</a> <font color="Maroon">x</font> <a href="hidden.html#R1">=</a> <font color="Maroon">b</font> &amp; <font color="Maroon">f</font> <a href="funct_2.html#K3">.</a> <font color="Maroon">y</font> <a href="hidden.html#R1">=</a> <font color="Maroon">e</font> )
 <b>by </b><i><a class="ref" href="yellow11.html#T1" target="_self">Th1</a></i>;<br/><b>hence </b><a NAME="E3:15_2_3_7_1_1_1_13"/>
<font color="Maroon">x</font> <a href="hidden.html#R1">=</a> <font color="Maroon">y</font>
 <b>by </b><i>, <a class="ref" href="yellow11.html#T3" target="_self">Th3</a></i>;<br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="15_2_3_7_1_1_1_14"><b>suppose </b></a><a NAME="E1:15_2_3_7_1_1_1_14"/>
( <font color="Maroon">x</font> <a href="hidden.html#R1">=</a> <font color="Maroon">dj</font> &amp; <font color="Maroon">y</font> <a href="hidden.html#R1">=</a> <font color="Maroon">z</font> )
 ;<br/><div class="add"><a NAME="E2:15_2_3_7_1_1_1_14"/><b>then </b>
( <font color="Maroon">f</font> <a href="funct_2.html#K3">.</a> <font color="Maroon">x</font> <a href="hidden.html#R1">=</a> <font color="Maroon">c</font> &amp; <font color="Maroon">f</font> <a href="funct_2.html#K3">.</a> <font color="Maroon">y</font> <a href="hidden.html#R1">=</a> <font color="Maroon">a</font> )
 <b>by </b><i><a class="ref" href="yellow11.html#T1" target="_self">Th1</a></i>;<br/><b>hence </b><a NAME="E3:15_2_3_7_1_1_1_14"/>
<font color="Maroon">x</font> <a href="hidden.html#R1">=</a> <font color="Maroon">y</font>
 <b>by </b><i>, <a class="ref" href="yellow11.html#T3" target="_self">Th3</a></i>;<br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="15_2_3_7_1_1_1_15"><b>suppose </b></a><a NAME="E1:15_2_3_7_1_1_1_15"/>
( <font color="Maroon">x</font> <a href="hidden.html#R1">=</a> <font color="Maroon">dj</font> &amp; <font color="Maroon">y</font> <a href="hidden.html#R1">=</a> <font color="Maroon">j</font> )
 ;<br/><div class="add"><a NAME="E2:15_2_3_7_1_1_1_15"/><b>then </b>
( <font color="Maroon">f</font> <a href="funct_2.html#K3">.</a> <font color="Maroon">x</font> <a href="hidden.html#R1">=</a> <font color="Maroon">c</font> &amp; <font color="Maroon">f</font> <a href="funct_2.html#K3">.</a> <font color="Maroon">y</font> <a href="hidden.html#R1">=</a> <font color="Maroon">b</font> )
 <b>by </b><i><a class="ref" href="yellow11.html#T1" target="_self">Th1</a></i>;<br/><b>hence </b><a NAME="E3:15_2_3_7_1_1_1_15"/>
<font color="Maroon">x</font> <a href="hidden.html#R1">=</a> <font color="Maroon">y</font>
 <b>by </b><i>, <a class="ref" href="yellow11.html#T3" target="_self">Th3</a></i>;<br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="15_2_3_7_1_1_1_16"><b>suppose </b></a><a NAME="E1:15_2_3_7_1_1_1_16"/>
( <font color="Maroon">x</font> <a href="hidden.html#R1">=</a> <font color="Maroon">dj</font> &amp; <font color="Maroon">y</font> <a href="hidden.html#R1">=</a> <font color="Maroon">td</font> )
 ;<br/><div class="add"><a NAME="E2:15_2_3_7_1_1_1_16"/><b>then </b>
( <font color="Maroon">f</font> <a href="funct_2.html#K3">.</a> <font color="Maroon">x</font> <a href="hidden.html#R1">=</a> <font color="Maroon">c</font> &amp; <font color="Maroon">f</font> <a href="funct_2.html#K3">.</a> <font color="Maroon">y</font> <a href="hidden.html#R1">=</a> <font color="Maroon">d</font> )
 <b>by </b><i><a class="ref" href="yellow11.html#T1" target="_self">Th1</a></i>;<br/><b>hence </b><a NAME="E3:15_2_3_7_1_1_1_16"/>
<font color="Maroon">x</font> <a href="hidden.html#R1">=</a> <font color="Maroon">y</font>
 <b>by </b><i>, <a class="ref" href="yellow11.html#T3" target="_self">Th3</a></i>;<br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="15_2_3_7_1_1_1_17"><b>suppose </b></a><a NAME="E1:15_2_3_7_1_1_1_17"/>
( <font color="Maroon">x</font> <a href="hidden.html#R1">=</a> <font color="Maroon">dj</font> &amp; <font color="Maroon">y</font> <a href="hidden.html#R1">=</a> <font color="Maroon">t</font> )
 ;<br/><div class="add"><a NAME="E2:15_2_3_7_1_1_1_17"/><b>then </b>
( <font color="Maroon">f</font> <a href="funct_2.html#K3">.</a> <font color="Maroon">x</font> <a href="hidden.html#R1">=</a> <font color="Maroon">c</font> &amp; <font color="Maroon">f</font> <a href="funct_2.html#K3">.</a> <font color="Maroon">y</font> <a href="hidden.html#R1">=</a> <font color="Maroon">e</font> )
 <b>by </b><i><a class="ref" href="yellow11.html#T1" target="_self">Th1</a></i>;<br/><b>hence </b><a NAME="E3:15_2_3_7_1_1_1_17"/>
<font color="Maroon">x</font> <a href="hidden.html#R1">=</a> <font color="Maroon">y</font>
 <b>by </b><i>, <a class="ref" href="yellow11.html#T3" target="_self">Th3</a></i>;<br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="15_2_3_7_1_1_1_18"><b>suppose </b></a><a NAME="E1:15_2_3_7_1_1_1_18"/>
( <font color="Maroon">x</font> <a href="hidden.html#R1">=</a> <font color="Maroon">td</font> &amp; <font color="Maroon">y</font> <a href="hidden.html#R1">=</a> <font color="Maroon">z</font> )
 ;<br/><div class="add"><a NAME="E2:15_2_3_7_1_1_1_18"/><b>then </b>
( <font color="Maroon">f</font> <a href="funct_2.html#K3">.</a> <font color="Maroon">x</font> <a href="hidden.html#R1">=</a> <font color="Maroon">d</font> &amp; <font color="Maroon">f</font> <a href="funct_2.html#K3">.</a> <font color="Maroon">y</font> <a href="hidden.html#R1">=</a> <font color="Maroon">a</font> )
 <b>by </b><i><a class="ref" href="yellow11.html#T1" target="_self">Th1</a></i>;<br/><b>hence </b><a NAME="E3:15_2_3_7_1_1_1_18"/>
<font color="Maroon">x</font> <a href="hidden.html#R1">=</a> <font color="Maroon">y</font>
 <b>by </b><i>, <a class="ref" href="yellow11.html#T3" target="_self">Th3</a></i>;<br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="15_2_3_7_1_1_1_19"><b>suppose </b></a><a NAME="E1:15_2_3_7_1_1_1_19"/>
( <font color="Maroon">x</font> <a href="hidden.html#R1">=</a> <font color="Maroon">td</font> &amp; <font color="Maroon">y</font> <a href="hidden.html#R1">=</a> <font color="Maroon">j</font> )
 ;<br/><div class="add"><a NAME="E2:15_2_3_7_1_1_1_19"/><b>then </b>
( <font color="Maroon">f</font> <a href="funct_2.html#K3">.</a> <font color="Maroon">x</font> <a href="hidden.html#R1">=</a> <font color="Maroon">d</font> &amp; <font color="Maroon">f</font> <a href="funct_2.html#K3">.</a> <font color="Maroon">y</font> <a href="hidden.html#R1">=</a> <font color="Maroon">b</font> )
 <b>by </b><i><a class="ref" href="yellow11.html#T1" target="_self">Th1</a></i>;<br/><b>hence </b><a NAME="E3:15_2_3_7_1_1_1_19"/>
<font color="Maroon">x</font> <a href="hidden.html#R1">=</a> <font color="Maroon">y</font>
 <b>by </b><i>, <a class="ref" href="yellow11.html#T3" target="_self">Th3</a></i>;<br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="15_2_3_7_1_1_1_20"><b>suppose </b></a><a NAME="E1:15_2_3_7_1_1_1_20"/>
( <font color="Maroon">x</font> <a href="hidden.html#R1">=</a> <font color="Maroon">td</font> &amp; <font color="Maroon">y</font> <a href="hidden.html#R1">=</a> <font color="Maroon">dj</font> )
 ;<br/><div class="add"><a NAME="E2:15_2_3_7_1_1_1_20"/><b>then </b>
( <font color="Maroon">f</font> <a href="funct_2.html#K3">.</a> <font color="Maroon">x</font> <a href="hidden.html#R1">=</a> <font color="Maroon">d</font> &amp; <font color="Maroon">f</font> <a href="funct_2.html#K3">.</a> <font color="Maroon">y</font> <a href="hidden.html#R1">=</a> <font color="Maroon">c</font> )
 <b>by </b><i><a class="ref" href="yellow11.html#T1" target="_self">Th1</a></i>;<br/><b>hence </b><a NAME="E3:15_2_3_7_1_1_1_20"/>
<font color="Maroon">x</font> <a href="hidden.html#R1">=</a> <font color="Maroon">y</font>
 <b>by </b><i>, <a class="ref" href="yellow11.html#T3" target="_self">Th3</a></i>;<br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="15_2_3_7_1_1_1_21"><b>suppose </b></a><a NAME="E1:15_2_3_7_1_1_1_21"/>
( <font color="Maroon">x</font> <a href="hidden.html#R1">=</a> <font color="Maroon">td</font> &amp; <font color="Maroon">y</font> <a href="hidden.html#R1">=</a> <font color="Maroon">t</font> )
 ;<br/><div class="add"><a NAME="E2:15_2_3_7_1_1_1_21"/><b>then </b>
( <font color="Maroon">f</font> <a href="funct_2.html#K3">.</a> <font color="Maroon">x</font> <a href="hidden.html#R1">=</a> <font color="Maroon">d</font> &amp; <font color="Maroon">f</font> <a href="funct_2.html#K3">.</a> <font color="Maroon">y</font> <a href="hidden.html#R1">=</a> <font color="Maroon">e</font> )
 <b>by </b><i><a class="ref" href="yellow11.html#T1" target="_self">Th1</a></i>;<br/><b>hence </b><a NAME="E3:15_2_3_7_1_1_1_21"/>
<font color="Maroon">x</font> <a href="hidden.html#R1">=</a> <font color="Maroon">y</font>
 <b>by </b><i>, <a class="ref" href="yellow11.html#T3" target="_self">Th3</a></i>;<br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="15_2_3_7_1_1_1_22"><b>suppose </b></a><a NAME="E1:15_2_3_7_1_1_1_22"/>
( <font color="Maroon">x</font> <a href="hidden.html#R1">=</a> <font color="Maroon">t</font> &amp; <font color="Maroon">y</font> <a href="hidden.html#R1">=</a> <font color="Maroon">z</font> )
 ;<br/><div class="add"><a NAME="E2:15_2_3_7_1_1_1_22"/><b>then </b>
( <font color="Maroon">f</font> <a href="funct_2.html#K3">.</a> <font color="Maroon">x</font> <a href="hidden.html#R1">=</a> <font color="Maroon">e</font> &amp; <font color="Maroon">f</font> <a href="funct_2.html#K3">.</a> <font color="Maroon">y</font> <a href="hidden.html#R1">=</a> <font color="Maroon">a</font> )
 <b>by </b><i><a class="ref" href="yellow11.html#T1" target="_self">Th1</a></i>;<br/><b>hence </b><a NAME="E3:15_2_3_7_1_1_1_22"/>
<font color="Maroon">x</font> <a href="hidden.html#R1">=</a> <font color="Maroon">y</font>
 <b>by </b><i>, <a class="ref" href="yellow11.html#T3" target="_self">Th3</a></i>;<br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="15_2_3_7_1_1_1_23"><b>suppose </b></a><a NAME="E1:15_2_3_7_1_1_1_23"/>
( <font color="Maroon">x</font> <a href="hidden.html#R1">=</a> <font color="Maroon">t</font> &amp; <font color="Maroon">y</font> <a href="hidden.html#R1">=</a> <font color="Maroon">j</font> )
 ;<br/><div class="add"><a NAME="E2:15_2_3_7_1_1_1_23"/><b>then </b>
( <font color="Maroon">f</font> <a href="funct_2.html#K3">.</a> <font color="Maroon">x</font> <a href="hidden.html#R1">=</a> <font color="Maroon">e</font> &amp; <font color="Maroon">f</font> <a href="funct_2.html#K3">.</a> <font color="Maroon">y</font> <a href="hidden.html#R1">=</a> <font color="Maroon">b</font> )
 <b>by </b><i><a class="ref" href="yellow11.html#T1" target="_self">Th1</a></i>;<br/><b>hence </b><a NAME="E3:15_2_3_7_1_1_1_23"/>
<font color="Maroon">x</font> <a href="hidden.html#R1">=</a> <font color="Maroon">y</font>
 <b>by </b><i>, <a class="ref" href="yellow11.html#T3" target="_self">Th3</a></i>;<br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="15_2_3_7_1_1_1_24"><b>suppose </b></a><a NAME="E1:15_2_3_7_1_1_1_24"/>
( <font color="Maroon">x</font> <a href="hidden.html#R1">=</a> <font color="Maroon">t</font> &amp; <font color="Maroon">y</font> <a href="hidden.html#R1">=</a> <font color="Maroon">dj</font> )
 ;<br/><div class="add"><a NAME="E2:15_2_3_7_1_1_1_24"/><b>then </b>
( <font color="Maroon">f</font> <a href="funct_2.html#K3">.</a> <font color="Maroon">x</font> <a href="hidden.html#R1">=</a> <font color="Maroon">e</font> &amp; <font color="Maroon">f</font> <a href="funct_2.html#K3">.</a> <font color="Maroon">y</font> <a href="hidden.html#R1">=</a> <font color="Maroon">c</font> )
 <b>by </b><i><a class="ref" href="yellow11.html#T1" target="_self">Th1</a></i>;<br/><b>hence </b><a NAME="E3:15_2_3_7_1_1_1_24"/>
<font color="Maroon">x</font> <a href="hidden.html#R1">=</a> <font color="Maroon">y</font>
 <b>by </b><i>, <a class="ref" href="yellow11.html#T3" target="_self">Th3</a></i>;<br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="15_2_3_7_1_1_1_25"><b>suppose </b></a><a NAME="E1:15_2_3_7_1_1_1_25"/>
( <font color="Maroon">x</font> <a href="hidden.html#R1">=</a> <font color="Maroon">t</font> &amp; <font color="Maroon">y</font> <a href="hidden.html#R1">=</a> <font color="Maroon">td</font> )
 ;<br/><div class="add"><a NAME="E2:15_2_3_7_1_1_1_25"/><b>then </b>
( <font color="Maroon">f</font> <a href="funct_2.html#K3">.</a> <font color="Maroon">x</font> <a href="hidden.html#R1">=</a> <font color="Maroon">e</font> &amp; <font color="Maroon">f</font> <a href="funct_2.html#K3">.</a> <font color="Maroon">y</font> <a href="hidden.html#R1">=</a> <font color="Maroon">d</font> )
 <b>by </b><i><a class="ref" href="yellow11.html#T1" target="_self">Th1</a></i>;<br/><b>hence </b><a NAME="E3:15_2_3_7_1_1_1_25"/>
<font color="Maroon">x</font> <a href="hidden.html#R1">=</a> <font color="Maroon">y</font>
 <b>by </b><i>, <a class="ref" href="yellow11.html#T3" target="_self">Th3</a></i>;<br/></div><b>end;</b></div></div><b>end;</b></div>

</div><b>end;</b></div></div><b>end;</b></div>
<b>hence </b><a NAME="E2:15_2_3_7"/>
<font color="Maroon">f</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><b>end;</b></div>
<a NAME="E16:15_2_3"/><i><font color="Green">E159</font></i>: 
 <a href="relset_1.html#K4">dom</a> <font color="Maroon">f</font> <a href="hidden.html#R1">=</a> the <a href="struct_0.html#U1">carrier</a> of <a href="yellow11.html#K2" target="_self">M_3</a> 
 
<b>by </b><i><a class="ref" href="funct_2.html#D1">FUNCT_2:def 1</a></i>;<br/>
<a NAME="E17:15_2_3"/><i><font color="Green">E160</font></i>: 
 <a href="relset_1.html#K5">rng</a> <font color="Maroon">f</font> <a href="hidden.html#R1">=</a> <font color="Maroon">ck</font>
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="15_2_3_8"><b>proof </b></a><div class="add">

<b>thus </b><a NAME="E1:15_2_3_8"/>
 <a href="relset_1.html#K5">rng</a> <font color="Maroon">f</font> <a href="tarski.html#R1">c=</a> <font color="Maroon">ck</font>
  <i><font color="Red">:: according to </font></i><a class="ref" href="xboole_0.html#D10">XBOOLE_0:def 10</a><div><a class="txt" onclick="hs2(this)" href="javascript:()" title="15_2_3_8_1"><b>proof </b></a><div class="add">

<b>let </b><font color="Maroon">y</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="E1:15_2_3_8_1"/>
<font color="Maroon">y</font> <a href="hidden.html#R2">in</a>  <a href="relset_1.html#K5">rng</a> <font color="Maroon">f</font>
 ;<br/>

<b>then consider </b><font color="Maroon">x</font> being    <a href="hidden.html#M1">set</a> <b> such that </b><br/><a NAME="E3:15_2_3_8_1"/><i><font color="Green">E161</font></i>: 
( <font color="Maroon">x</font> <a href="hidden.html#R2">in</a>  <a href="relset_1.html#K4">dom</a> <font color="Maroon">f</font> &amp; <font color="Maroon">y</font> <a href="hidden.html#R1">=</a> <font color="Maroon">f</font> <a href="funct_1.html#K1">.</a> <font color="Maroon">x</font> )
 <b>by </b><i><a class="ref" href="funct_1.html#D5">FUNCT_1:def 5</a></i>;<br/>
<b>reconsider </b><font color="Maroon">x</font> = <font color="Maroon">x</font> as   <a href="struct_0.html#NM1">Element</a> of <a href="yellow11.html#K2" target="_self">M_3</a>  <b>by </b><i><a class="txt" href="yellow11.html#E5"><i><font color="Green">Lemma26</font></i></a></i>;<br/>
<a NAME="E5:15_2_3_8_1"/>
( <font color="Maroon">x</font> <a href="hidden.html#R1">=</a> <font color="Maroon">z</font> or <font color="Maroon">x</font> <a href="hidden.html#R1">=</a> <font color="Maroon">j</font> or <font color="Maroon">x</font> <a href="hidden.html#R1">=</a> <font color="Maroon">dj</font> or <font color="Maroon">x</font> <a href="hidden.html#R1">=</a> <font color="Maroon">td</font> or <font color="Maroon">x</font> <a href="hidden.html#R1">=</a> <font color="Maroon">t</font> )
 
<b>by </b><i>, <a class="ref" href="enumset1.html#D3">ENUMSET1:def 3</a></i>;<br/>
<a NAME="E6:15_2_3_8_1"/><b>then </b>
( <font color="Maroon">y</font> <a href="hidden.html#R1">=</a> <font color="Maroon">a</font> or <font color="Maroon">y</font> <a href="hidden.html#R1">=</a> <font color="Maroon">d</font> or <font color="Maroon">y</font> <a href="hidden.html#R1">=</a> <font color="Maroon">c</font> or <font color="Maroon">y</font> <a href="hidden.html#R1">=</a> <font color="Maroon">b</font> or <font color="Maroon">y</font> <a href="hidden.html#R1">=</a> <font color="Maroon">e</font> )
 
<b>by </b><i><a class="ref" href="yellow11.html#T1" target="_self">Th1</a>, <a class="txt" href="yellow11.html#E5"><i><font color="Green">Lemma26</font></i></a></i>;<br/>
<b>hence </b><a NAME="E7:15_2_3_8_1"/>
<font color="Maroon">y</font> <a href="hidden.html#R2">in</a> <font color="Maroon">ck</font>
 <b>by </b><i><a class="ref" href="enumset1.html#D3">ENUMSET1:def 3</a></i>;<br/>


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

<b>thus </b><a NAME="E2:15_2_3_8"/>
<font color="Maroon">ck</font> <a href="tarski.html#R1">c=</a>  <a href="relset_1.html#K5">rng</a> <font color="Maroon">f</font>
 <div><a class="txt" onclick="hs2(this)" href="javascript:()" title="15_2_3_8_2"><b>proof </b></a><div class="add">

<b>let </b><font color="Maroon">y</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="E1:15_2_3_8_2"/><i><font color="Green">E162</font></i>: 
<font color="Maroon">y</font> <a href="hidden.html#R2">in</a> <font color="Maroon">ck</font>
 ;<br/>

<div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="15_2_3_8_2_1"><b>per </b></a><a class="txt" onclick="hs(this)" href="javascript:()"><b>cases </b></a><span class="hide"><a NAME="E1:15_2_3_8_2_1"/>
( <font color="Maroon">y</font> <a href="hidden.html#R1">=</a> <font color="Maroon">a</font> or <font color="Maroon">y</font> <a href="hidden.html#R1">=</a> <font color="Maroon">b</font> or <font color="Maroon">y</font> <a href="hidden.html#R1">=</a> <font color="Maroon">c</font> or <font color="Maroon">y</font> <a href="hidden.html#R1">=</a> <font color="Maroon">d</font> or <font color="Maroon">y</font> <a href="hidden.html#R1">=</a> <font color="Maroon">e</font> )
 </span><b>by </b><i><a class="txt" href="yellow11.html#E5"><i><font color="Green">Lemma26</font></i></a>, <a class="ref" href="enumset1.html#D3">ENUMSET1:def 3</a></i>;<br/><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="15_2_3_8_2_1_1"><b>suppose </b></a><a NAME="E1:15_2_3_8_2_1_1"/><i><font color="Green">E163</font></i>: 
<font color="Maroon">y</font> <a href="hidden.html#R1">=</a> <font color="Maroon">a</font>
 ;<br/><div class="add"><a NAME="E2:15_2_3_8_2_1_1"/>
( <font color="Maroon">z</font> <a href="hidden.html#R2">in</a>  <a href="relset_1.html#K4">dom</a> <font color="Maroon">f</font> &amp; <font color="Maroon">a</font> <a href="hidden.html#R1">=</a> <font color="Maroon">f</font> <a href="funct_2.html#K3">.</a> <font color="Maroon">z</font> )
 <b>by </b><i><a class="ref" href="yellow11.html#T1" target="_self">Th1</a>, <a class="ref" href="yellow11.html#T3" target="_self">Th3</a></i>;<br/><b>hence </b><a NAME="E3:15_2_3_8_2_1_1"/>
<font color="Maroon">y</font> <a href="hidden.html#R2">in</a>  <a href="relset_1.html#K5">rng</a> <font color="Maroon">f</font>
 <b>by </b><i><a class="ref" href="yellow11.html#T5" target="_self">Th5</a>, <a class="ref" href="funct_1.html#D5">FUNCT_1:def 5</a></i>;<br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="15_2_3_8_2_1_2"><b>suppose </b></a><a NAME="E1:15_2_3_8_2_1_2"/><i><font color="Green">E164</font></i>: 
<font color="Maroon">y</font> <a href="hidden.html#R1">=</a> <font color="Maroon">b</font>
 ;<br/><div class="add"><a NAME="E2:15_2_3_8_2_1_2"/>
( <font color="Maroon">j</font> <a href="hidden.html#R2">in</a>  <a href="relset_1.html#K4">dom</a> <font color="Maroon">f</font> &amp; <font color="Maroon">b</font> <a href="hidden.html#R1">=</a> <font color="Maroon">f</font> <a href="funct_2.html#K3">.</a> <font color="Maroon">j</font> )
 <b>by </b><i><a class="ref" href="yellow11.html#T1" target="_self">Th1</a>, <a class="ref" href="yellow11.html#T3" target="_self">Th3</a></i>;<br/><b>hence </b><a NAME="E3:15_2_3_8_2_1_2"/>
<font color="Maroon">y</font> <a href="hidden.html#R2">in</a>  <a href="relset_1.html#K5">rng</a> <font color="Maroon">f</font>
 <b>by </b><i><a class="ref" href="yellow11.html#T5" target="_self">Th5</a>, <a class="ref" href="funct_1.html#D5">FUNCT_1:def 5</a></i>;<br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="15_2_3_8_2_1_3"><b>suppose </b></a><a NAME="E1:15_2_3_8_2_1_3"/><i><font color="Green">E165</font></i>: 
<font color="Maroon">y</font> <a href="hidden.html#R1">=</a> <font color="Maroon">c</font>
 ;<br/><div class="add"><a NAME="E2:15_2_3_8_2_1_3"/>
( <font color="Maroon">dj</font> <a href="hidden.html#R2">in</a>  <a href="relset_1.html#K4">dom</a> <font color="Maroon">f</font> &amp; <font color="Maroon">c</font> <a href="hidden.html#R1">=</a> <font color="Maroon">f</font> <a href="funct_2.html#K3">.</a> <font color="Maroon">dj</font> )
 <b>by </b><i><a class="ref" href="yellow11.html#T1" target="_self">Th1</a>, <a class="ref" href="yellow11.html#T3" target="_self">Th3</a></i>;<br/><b>hence </b><a NAME="E3:15_2_3_8_2_1_3"/>
<font color="Maroon">y</font> <a href="hidden.html#R2">in</a>  <a href="relset_1.html#K5">rng</a> <font color="Maroon">f</font>
 <b>by </b><i><a class="ref" href="yellow11.html#T5" target="_self">Th5</a>, <a class="ref" href="funct_1.html#D5">FUNCT_1:def 5</a></i>;<br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="15_2_3_8_2_1_4"><b>suppose </b></a><a NAME="E1:15_2_3_8_2_1_4"/><i><font color="Green">E166</font></i>: 
<font color="Maroon">y</font> <a href="hidden.html#R1">=</a> <font color="Maroon">d</font>
 ;<br/><div class="add"><a NAME="E2:15_2_3_8_2_1_4"/>
( <font color="Maroon">td</font> <a href="hidden.html#R2">in</a>  <a href="relset_1.html#K4">dom</a> <font color="Maroon">f</font> &amp; <font color="Maroon">d</font> <a href="hidden.html#R1">=</a> <font color="Maroon">f</font> <a href="funct_2.html#K3">.</a> <font color="Maroon">td</font> )
 <b>by </b><i><a class="ref" href="yellow11.html#T1" target="_self">Th1</a>, <a class="ref" href="yellow11.html#T3" target="_self">Th3</a></i>;<br/><b>hence </b><a NAME="E3:15_2_3_8_2_1_4"/>
<font color="Maroon">y</font> <a href="hidden.html#R2">in</a>  <a href="relset_1.html#K5">rng</a> <font color="Maroon">f</font>
 <b>by </b><i><a class="ref" href="yellow11.html#T5" target="_self">Th5</a>, <a class="ref" href="funct_1.html#D5">FUNCT_1:def 5</a></i>;<br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="15_2_3_8_2_1_5"><b>suppose </b></a><a NAME="E1:15_2_3_8_2_1_5"/><i><font color="Green">E167</font></i>: 
<font color="Maroon">y</font> <a href="hidden.html#R1">=</a> <font color="Maroon">e</font>
 ;<br/><div class="add"><a NAME="E2:15_2_3_8_2_1_5"/>
( <font color="Maroon">t</font> <a href="hidden.html#R2">in</a>  <a href="relset_1.html#K4">dom</a> <font color="Maroon">f</font> &amp; <font color="Maroon">e</font> <a href="hidden.html#R1">=</a> <font color="Maroon">f</font> <a href="funct_2.html#K3">.</a> <font color="Maroon">t</font> )
 <b>by </b><i><a class="ref" href="yellow11.html#T1" target="_self">Th1</a>, <a class="ref" href="yellow11.html#T3" target="_self">Th3</a></i>;<br/><b>hence </b><a NAME="E3:15_2_3_8_2_1_5"/>
<font color="Maroon">y</font> <a href="hidden.html#R2">in</a>  <a href="relset_1.html#K5">rng</a> <font color="Maroon">f</font>
 <b>by </b><i><a class="ref" href="yellow11.html#T5" target="_self">Th5</a>, <a class="ref" href="funct_1.html#D5">FUNCT_1:def 5</a></i>;<br/></div><b>end;</b></div></div><b>end;</b></div>

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


</div><b>end;</b></div>
<a NAME="E18:15_2_3"/>
for <font color="Olive">x</font>, <font color="Olive">y</font> being  <a href="struct_0.html#NM1">Element</a> of <a href="yellow11.html#K2" target="_self">M_3</a>  holds <br/> ( <font color="Olive">x</font> <a href="orders_2.html#R3">&lt;=</a> <font color="Olive">y</font> iff <font color="Maroon">f</font> <a href="funct_2.html#K3">.</a> <font color="Olive">x</font> <a href="orders_2.html#R3">&lt;=</a> <font color="Maroon">f</font> <a href="funct_2.html#K3">.</a> <font color="Olive">y</font> )
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="15_2_3_9"><b>proof </b></a><div class="add">

<b>let </b><font color="Maroon">x</font> be   <a href="struct_0.html#NM1">Element</a> of <a href="yellow11.html#K2" target="_self">M_3</a> , <font color="Maroon">y</font> be   <a href="struct_0.html#NM1">Element</a> of <a href="yellow11.html#K2" target="_self">M_3</a> ;<br/>

<b>thus </b><a NAME="E1:15_2_3_9"/>
( <font color="Maroon">x</font> <a href="orders_2.html#R3">&lt;=</a> <font color="Maroon">y</font> implies <font color="Maroon">f</font> <a href="funct_2.html#K3">.</a> <font color="Maroon">x</font> <a href="orders_2.html#R3">&lt;=</a> <font color="Maroon">f</font> <a href="funct_2.html#K3">.</a> <font color="Maroon">y</font> )
 <div><a class="txt" onclick="hs2(this)" href="javascript:()" title="15_2_3_9_1"><b>proof </b></a><div class="add">

<b>assume </b><a NAME="E1:15_2_3_9_1"/><i><font color="Green">E168</font></i>: 
<font color="Maroon">x</font> <a href="orders_2.html#R3">&lt;=</a> <font color="Maroon">y</font>
 ;<br/>

<div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="15_2_3_9_1_1"><b>per </b></a><a class="txt" onclick="hs(this)" href="javascript:()"><b>cases </b></a><span class="hide"><a NAME="E1:15_2_3_9_1_1"/>
( ( <font color="Maroon">x</font> <a href="hidden.html#R1">=</a> <font color="Maroon">z</font> &amp; <font color="Maroon">y</font> <a href="hidden.html#R1">=</a> <font color="Maroon">z</font> ) or ( <font color="Maroon">x</font> <a href="hidden.html#R1">=</a> <font color="Maroon">z</font> &amp; <font color="Maroon">y</font> <a href="hidden.html#R1">=</a> <font color="Maroon">j</font> ) or ( <font color="Maroon">x</font> <a href="hidden.html#R1">=</a> <font color="Maroon">z</font> &amp; <font color="Maroon">y</font> <a href="hidden.html#R1">=</a> <font color="Maroon">dj</font> ) or ( <font color="Maroon">x</font> <a href="hidden.html#R1">=</a> <font color="Maroon">z</font> &amp; <font color="Maroon">y</font> <a href="hidden.html#R1">=</a> <font color="Maroon">td</font> ) or ( <font color="Maroon">x</font> <a href="hidden.html#R1">=</a> <font color="Maroon">z</font> &amp; <font color="Maroon">y</font> <a href="hidden.html#R1">=</a> <font color="Maroon">t</font> ) or ( <font color="Maroon">x</font> <a href="hidden.html#R1">=</a> <font color="Maroon">j</font> &amp; <font color="Maroon">y</font> <a href="hidden.html#R1">=</a> <font color="Maroon">z</font> ) or ( <font color="Maroon">x</font> <a href="hidden.html#R1">=</a> <font color="Maroon">j</font> &amp; <font color="Maroon">y</font> <a href="hidden.html#R1">=</a> <font color="Maroon">j</font> ) or ( <font color="Maroon">x</font> <a href="hidden.html#R1">=</a> <font color="Maroon">j</font> &amp; <font color="Maroon">y</font> <a href="hidden.html#R1">=</a> <font color="Maroon">dj</font> ) or ( <font color="Maroon">x</font> <a href="hidden.html#R1">=</a> <font color="Maroon">j</font> &amp; <font color="Maroon">y</font> <a href="hidden.html#R1">=</a> <font color="Maroon">td</font> ) or ( <font color="Maroon">x</font> <a href="hidden.html#R1">=</a> <font color="Maroon">j</font> &amp; <font color="Maroon">y</font> <a href="hidden.html#R1">=</a> <font color="Maroon">t</font> ) or ( <font color="Maroon">x</font> <a href="hidden.html#R1">=</a> <font color="Maroon">dj</font> &amp; <font color="Maroon">y</font> <a href="hidden.html#R1">=</a> <font color="Maroon">z</font> ) or ( <font color="Maroon">x</font> <a href="hidden.html#R1">=</a> <font color="Maroon">dj</font> &amp; <font color="Maroon">y</font> <a href="hidden.html#R1">=</a> <font color="Maroon">j</font> ) or ( <font color="Maroon">x</font> <a href="hidden.html#R1">=</a> <font color="Maroon">dj</font> &amp; <font color="Maroon">y</font> <a href="hidden.html#R1">=</a> <font color="Maroon">dj</font> ) or ( <font color="Maroon">x</font> <a href="hidden.html#R1">=</a> <font color="Maroon">dj</font> &amp; <font color="Maroon">y</font> <a href="hidden.html#R1">=</a> <font color="Maroon">td</font> ) or ( <font color="Maroon">x</font> <a href="hidden.html#R1">=</a> <font color="Maroon">dj</font> &amp; <font color="Maroon">y</font> <a href="hidden.html#R1">=</a> <font color="Maroon">t</font> ) or ( <font color="Maroon">x</font> <a href="hidden.html#R1">=</a> <font color="Maroon">td</font> &amp; <font color="Maroon">y</font> <a href="hidden.html#R1">=</a> <font color="Maroon">z</font> ) or ( <font color="Maroon">x</font> <a href="hidden.html#R1">=</a> <font color="Maroon">td</font> &amp; <font color="Maroon">y</font> <a href="hidden.html#R1">=</a> <font color="Maroon">j</font> ) or ( <font color="Maroon">x</font> <a href="hidden.html#R1">=</a> <font color="Maroon">td</font> &amp; <font color="Maroon">y</font> <a href="hidden.html#R1">=</a> <font color="Maroon">dj</font> ) or ( <font color="Maroon">x</font> <a href="hidden.html#R1">=</a> <font color="Maroon">td</font> &amp; <font color="Maroon">y</font> <a href="hidden.html#R1">=</a> <font color="Maroon">td</font> ) or ( <font color="Maroon">x</font> <a href="hidden.html#R1">=</a> <font color="Maroon">td</font> &amp; <font color="Maroon">y</font> <a href="hidden.html#R1">=</a> <font color="Maroon">t</font> ) or ( <font color="Maroon">x</font> <a href="hidden.html#R1">=</a> <font color="Maroon">t</font> &amp; <font color="Maroon">y</font> <a href="hidden.html#R1">=</a> <font color="Maroon">z</font> ) or ( <font color="Maroon">x</font> <a href="hidden.html#R1">=</a> <font color="Maroon">t</font> &amp; <font color="Maroon">y</font> <a href="hidden.html#R1">=</a> <font color="Maroon">j</font> ) or ( <font color="Maroon">x</font> <a href="hidden.html#R1">=</a> <font color="Maroon">t</font> &amp; <font color="Maroon">y</font> <a href="hidden.html#R1">=</a> <font color="Maroon">dj</font> ) or ( <font color="Maroon">x</font> <a href="hidden.html#R1">=</a> <font color="Maroon">t</font> &amp; <font color="Maroon">y</font> <a href="hidden.html#R1">=</a> <font color="Maroon">td</font> ) or ( <font color="Maroon">x</font> <a href="hidden.html#R1">=</a> <font color="Maroon">t</font> &amp; <font color="Maroon">y</font> <a href="hidden.html#R1">=</a> <font color="Maroon">t</font> ) )
 </span><b>by </b><i>, <a class="ref" href="enumset1.html#D3">ENUMSET1:def 3</a></i>;<br/><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="15_2_3_9_1_1_1"><b>suppose </b></a><a NAME="E1:15_2_3_9_1_1_1"/>
( <font color="Maroon">x</font> <a href="hidden.html#R1">=</a> <font color="Maroon">z</font> &amp; <font color="Maroon">y</font> <a href="hidden.html#R1">=</a> <font color="Maroon">z</font> )
 ;<br/><div class="add"><b>hence </b><a NAME="E2:15_2_3_9_1_1_1"/>
<font color="Maroon">f</font> <a href="funct_2.html#K3">.</a> <font color="Maroon">x</font> <a href="orders_2.html#R3">&lt;=</a> <font color="Maroon">f</font> <a href="funct_2.html#K3">.</a> <font color="Maroon">y</font>
 ;<br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="15_2_3_9_1_1_2"><b>suppose </b></a><a NAME="E1:15_2_3_9_1_1_2"/>
( <font color="Maroon">x</font> <a href="hidden.html#R1">=</a> <font color="Maroon">z</font> &amp; <font color="Maroon">y</font> <a href="hidden.html#R1">=</a> <font color="Maroon">j</font> )
 ;<br/><div class="add"><a NAME="E2:15_2_3_9_1_1_2"/><b>then </b><i><font color="Green">E169</font></i>: 
( <font color="Maroon">f</font> <a href="funct_2.html#K3">.</a> <font color="Maroon">x</font> <a href="hidden.html#R1">=</a> <font color="Maroon">a</font> &amp; <font color="Maroon">f</font> <a href="funct_2.html#K3">.</a> <font color="Maroon">y</font> <a href="hidden.html#R1">=</a> <font color="Maroon">b</font> )
 <b>by </b><i><a class="ref" href="yellow11.html#T1" target="_self">Th1</a></i>;<br/><b>reconsider </b><font color="Maroon">A</font> = <font color="Maroon">a</font>, <font color="Maroon">B</font> = <font color="Maroon">b</font> as   <a href="struct_0.html#NM1">Element</a> of <font color="Maroon">K</font> <b>by </b><i>, <a class="ref" href="enumset1.html#D3">ENUMSET1:def 3</a></i>;<br/><a NAME="E4:15_2_3_9_1_1_2"/>
( <font color="Maroon">a</font> <a href="orders_2.html#R3">&lt;=</a> <font color="Maroon">b</font> &amp; <font color="Maroon">A</font> <a href="hidden.html#R2">in</a> the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">K</font> &amp; <font color="Maroon">B</font> <a href="hidden.html#R2">in</a> the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">K</font> )
 <b>by </b><i>, <a class="ref" href="yellow_0.html#T25">YELLOW_0:25</a></i>;<br/><b>hence </b><a NAME="E5:15_2_3_9_1_1_2"/>
<font color="Maroon">f</font> <a href="funct_2.html#K3">.</a> <font color="Maroon">x</font> <a href="orders_2.html#R3">&lt;=</a> <font color="Maroon">f</font> <a href="funct_2.html#K3">.</a> <font color="Maroon">y</font>
 <b>by </b><i><a class="ref" href="yellow11.html#T5" target="_self">Th5</a>, <a class="ref" href="yellow_0.html#T61">YELLOW_0:61</a></i>;<br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="15_2_3_9_1_1_3"><b>suppose </b></a><a NAME="E1:15_2_3_9_1_1_3"/>
( <font color="Maroon">x</font> <a href="hidden.html#R1">=</a> <font color="Maroon">z</font> &amp; <font color="Maroon">y</font> <a href="hidden.html#R1">=</a> <font color="Maroon">dj</font> )
 ;<br/><div class="add"><a NAME="E2:15_2_3_9_1_1_3"/><b>then </b><i><font color="Green">E170</font></i>: 
( <font color="Maroon">f</font> <a href="funct_2.html#K3">.</a> <font color="Maroon">x</font> <a href="hidden.html#R1">=</a> <font color="Maroon">a</font> &amp; <font color="Maroon">f</font> <a href="funct_2.html#K3">.</a> <font color="Maroon">y</font> <a href="hidden.html#R1">=</a> <font color="Maroon">c</font> )
 <b>by </b><i><a class="ref" href="yellow11.html#T1" target="_self">Th1</a></i>;<br/><b>reconsider </b><font color="Maroon">A</font> = <font color="Maroon">a</font>, <font color="Maroon">C</font> = <font color="Maroon">c</font> as   <a href="struct_0.html#NM1">Element</a> of <font color="Maroon">K</font> <b>by </b><i>, <a class="ref" href="enumset1.html#D3">ENUMSET1:def 3</a></i>;<br/><a NAME="E4:15_2_3_9_1_1_3"/>
( <font color="Maroon">a</font> <a href="orders_2.html#R3">&lt;=</a> <font color="Maroon">c</font> &amp; <font color="Maroon">A</font> <a href="hidden.html#R2">in</a> the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">K</font> &amp; <font color="Maroon">C</font> <a href="hidden.html#R2">in</a> the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">K</font> )
 <b>by </b><i>, <a class="ref" href="yellow_0.html#T25">YELLOW_0:25</a></i>;<br/><b>hence </b><a NAME="E5:15_2_3_9_1_1_3"/>
<font color="Maroon">f</font> <a href="funct_2.html#K3">.</a> <font color="Maroon">x</font> <a href="orders_2.html#R3">&lt;=</a> <font color="Maroon">f</font> <a href="funct_2.html#K3">.</a> <font color="Maroon">y</font>
 <b>by </b><i><a class="ref" href="yellow11.html#T5" target="_self">Th5</a>, <a class="ref" href="yellow_0.html#T61">YELLOW_0:61</a></i>;<br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="15_2_3_9_1_1_4"><b>suppose </b></a><a NAME="E1:15_2_3_9_1_1_4"/>
( <font color="Maroon">x</font> <a href="hidden.html#R1">=</a> <font color="Maroon">z</font> &amp; <font color="Maroon">y</font> <a href="hidden.html#R1">=</a> <font color="Maroon">td</font> )
 ;<br/><div class="add"><a NAME="E2:15_2_3_9_1_1_4"/><b>then </b><i><font color="Green">E171</font></i>: 
( <font color="Maroon">f</font> <a href="funct_2.html#K3">.</a> <font color="Maroon">x</font> <a href="hidden.html#R1">=</a> <font color="Maroon">a</font> &amp; <font color="Maroon">f</font> <a href="funct_2.html#K3">.</a> <font color="Maroon">y</font> <a href="hidden.html#R1">=</a> <font color="Maroon">d</font> )
 <b>by </b><i><a class="ref" href="yellow11.html#T1" target="_self">Th1</a></i>;<br/><b>reconsider </b><font color="Maroon">A</font> = <font color="Maroon">a</font>, <font color="Maroon">D</font> = <font color="Maroon">d</font> as   <a href="struct_0.html#NM1">Element</a> of <font color="Maroon">K</font> <b>by </b><i>, <a class="ref" href="enumset1.html#D3">ENUMSET1:def 3</a></i>;<br/><a NAME="E4:15_2_3_9_1_1_4"/>
( <font color="Maroon">a</font> <a href="orders_2.html#R3">&lt;=</a> <font color="Maroon">d</font> &amp; <font color="Maroon">A</font> <a href="hidden.html#R2">in</a> the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">K</font> &amp; <font color="Maroon">D</font> <a href="hidden.html#R2">in</a> the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">K</font> )
 <b>by </b><i>, <a class="ref" href="yellow_0.html#T25">YELLOW_0:25</a></i>;<br/><b>hence </b><a NAME="E5:15_2_3_9_1_1_4"/>
<font color="Maroon">f</font> <a href="funct_2.html#K3">.</a> <font color="Maroon">x</font> <a href="orders_2.html#R3">&lt;=</a> <font color="Maroon">f</font> <a href="funct_2.html#K3">.</a> <font color="Maroon">y</font>
 <b>by </b><i><a class="ref" href="yellow11.html#T5" target="_self">Th5</a>, <a class="ref" href="yellow_0.html#T61">YELLOW_0:61</a></i>;<br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="15_2_3_9_1_1_5"><b>suppose </b></a><a NAME="E1:15_2_3_9_1_1_5"/>
( <font color="Maroon">x</font> <a href="hidden.html#R1">=</a> <font color="Maroon">z</font> &amp; <font color="Maroon">y</font> <a href="hidden.html#R1">=</a> <font color="Maroon">t</font> )
 ;<br/><div class="add"><a NAME="E2:15_2_3_9_1_1_5"/><b>then </b><i><font color="Green">E172</font></i>: 
( <font color="Maroon">f</font> <a href="funct_2.html#K3">.</a> <font color="Maroon">x</font> <a href="hidden.html#R1">=</a> <font color="Maroon">a</font> &amp; <font color="Maroon">f</font> <a href="funct_2.html#K3">.</a> <font color="Maroon">y</font> <a href="hidden.html#R1">=</a> <font color="Maroon">e</font> )
 <b>by </b><i><a class="ref" href="yellow11.html#T1" target="_self">Th1</a></i>;<br/><b>reconsider </b><font color="Maroon">A</font> = <font color="Maroon">a</font>, <font color="Maroon">E</font> = <font color="Maroon">e</font> as   <a href="struct_0.html#NM1">Element</a> of <font color="Maroon">K</font> <b>by </b><i>, <a class="ref" href="enumset1.html#D3">ENUMSET1:def 3</a></i>;<br/><a NAME="E4:15_2_3_9_1_1_5"/>
( <font color="Maroon">a</font> <a href="orders_2.html#R3">&lt;=</a> <font color="Maroon">c</font> &amp; <font color="Maroon">c</font> <a href="orders_2.html#R3">&lt;=</a> <font color="Maroon">e</font> )
 <b>by </b><i>, <a class="ref" href="yellow_0.html#T25">YELLOW_0:25</a></i>;<br/><a NAME="E5:15_2_3_9_1_1_5"/><b>then </b>
( <font color="Maroon">a</font> <a href="orders_2.html#R3">&lt;=</a> <font color="Maroon">e</font> &amp; <font color="Maroon">A</font> <a href="hidden.html#R2">in</a> the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">K</font> &amp; <font color="Maroon">E</font> <a href="hidden.html#R2">in</a> the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">K</font> )
 <b>by </b><i><a class="ref" href="orders_2.html#T26">ORDERS_2:26</a></i>;<br/><b>hence </b><a NAME="E6:15_2_3_9_1_1_5"/>
<font color="Maroon">f</font> <a href="funct_2.html#K3">.</a> <font color="Maroon">x</font> <a href="orders_2.html#R3">&lt;=</a> <font color="Maroon">f</font> <a href="funct_2.html#K3">.</a> <font color="Maroon">y</font>
 <b>by </b><i><a class="ref" href="yellow11.html#T5" target="_self">Th5</a>, <a class="ref" href="yellow_0.html#T61">YELLOW_0:61</a></i>;<br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="15_2_3_9_1_1_6"><b>suppose </b></a><a NAME="E1:15_2_3_9_1_1_6"/>
( <font color="Maroon">x</font> <a href="hidden.html#R1">=</a> <font color="Maroon">j</font> &amp; <font color="Maroon">y</font> <a href="hidden.html#R1">=</a> <font color="Maroon">z</font> )
 ;<br/><div class="add"><a NAME="E2:15_2_3_9_1_1_6"/><b>then </b>
<font color="Maroon">j</font> <a href="tarski.html#R1">c=</a> <font color="Maroon">z</font>
 <b>by </b><i><a class="txt" href="yellow11.html#E5"><i><font color="Green">Lemma26</font></i></a>, <a class="ref" href="yellow_1.html#T3">YELLOW_1:3</a></i>;<br/><b>hence </b><a NAME="E3:15_2_3_9_1_1_6"/>
<font color="Maroon">f</font> <a href="funct_2.html#K3">.</a> <font color="Maroon">x</font> <a href="orders_2.html#R3">&lt;=</a> <font color="Maroon">f</font> <a href="funct_2.html#K3">.</a> <font color="Maroon">y</font>
 <b>by </b><i><a class="ref" href="xboole_1.html#T3">XBOOLE_1:3</a></i>;<br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="15_2_3_9_1_1_7"><b>suppose </b></a><a NAME="E1:15_2_3_9_1_1_7"/>
( <font color="Maroon">x</font> <a href="hidden.html#R1">=</a> <font color="Maroon">j</font> &amp; <font color="Maroon">y</font> <a href="hidden.html#R1">=</a> <font color="Maroon">j</font> )
 ;<br/><div class="add"><b>hence </b><a NAME="E2:15_2_3_9_1_1_7"/>
<font color="Maroon">f</font> <a href="funct_2.html#K3">.</a> <font color="Maroon">x</font> <a href="orders_2.html#R3">&lt;=</a> <font color="Maroon">f</font> <a href="funct_2.html#K3">.</a> <font color="Maroon">y</font>
 ;<br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="15_2_3_9_1_1_8"><b>suppose </b></a><a NAME="E1:15_2_3_9_1_1_8"/><i><font color="Green">E173</font></i>: 
( <font color="Maroon">x</font> <a href="hidden.html#R1">=</a> <font color="Maroon">j</font> &amp; <font color="Maroon">y</font> <a href="hidden.html#R1">=</a> <font color="Maroon">dj</font> )
 ;<br/><div class="add"><a NAME="E2:15_2_3_9_1_1_8"/>
( 0 <a href="hidden.html#R2">in</a> <font color="Maroon">j</font> &amp; not 0 <a href="hidden.html#R2">in</a> <font color="Maroon">dj</font> )
 <b>by </b><i>, <a class="ref" href="card_5.html#T1">CARD_5:1</a>, <a class="ref" href="tarski.html#D1">TARSKI:def 1</a></i>;<br/><a NAME="E3:15_2_3_9_1_1_8"/><b>then </b>
not <font color="Maroon">j</font> <a href="tarski.html#R1">c=</a> <font color="Maroon">dj</font>
 ;<br/><b>hence </b><a NAME="E4:15_2_3_9_1_1_8"/>
<font color="Maroon">f</font> <a href="funct_2.html#K3">.</a> <font color="Maroon">x</font> <a href="orders_2.html#R3">&lt;=</a> <font color="Maroon">f</font> <a href="funct_2.html#K3">.</a> <font color="Maroon">y</font>
 <b>by </b><i><a class="txt" href="yellow11.html#E5"><i><font color="Green">Lemma26</font></i></a>, <a class="ref" href="yellow11.html#T5" target="_self">Th5</a>, <a class="ref" href="yellow_1.html#T3">YELLOW_1:3</a></i>;<br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="15_2_3_9_1_1_9"><b>suppose </b></a><a NAME="E1:15_2_3_9_1_1_9"/><i><font color="Green">E174</font></i>: 
( <font color="Maroon">x</font> <a href="hidden.html#R1">=</a> <font color="Maroon">j</font> &amp; <font color="Maroon">y</font> <a href="hidden.html#R1">=</a> <font color="Maroon">td</font> )
 ;<br/><div class="add"><a NAME="E2:15_2_3_9_1_1_9"/>
( 0 <a href="hidden.html#R2">in</a> <font color="Maroon">j</font> &amp; not 0 <a href="hidden.html#R2">in</a> <font color="Maroon">td</font> )
 <b>by </b><i>, <a class="ref" href="card_5.html#T1">CARD_5:1</a>, <a class="ref" href="tarski.html#D1">TARSKI:def 1</a></i>;<br/><a NAME="E3:15_2_3_9_1_1_9"/><b>then </b>
not <font color="Maroon">j</font> <a href="tarski.html#R1">c=</a> <font color="Maroon">td</font>
 ;<br/><b>hence </b><a NAME="E4:15_2_3_9_1_1_9"/>
<font color="Maroon">f</font> <a href="funct_2.html#K3">.</a> <font color="Maroon">x</font> <a href="orders_2.html#R3">&lt;=</a> <font color="Maroon">f</font> <a href="funct_2.html#K3">.</a> <font color="Maroon">y</font>
 <b>by </b><i><a class="txt" href="yellow11.html#E5"><i><font color="Green">Lemma26</font></i></a>, <a class="ref" href="yellow11.html#T5" target="_self">Th5</a>, <a class="ref" href="yellow_1.html#T3">YELLOW_1:3</a></i>;<br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="15_2_3_9_1_1_10"><b>suppose </b></a><a NAME="E1:15_2_3_9_1_1_10"/>
( <font color="Maroon">x</font> <a href="hidden.html#R1">=</a> <font color="Maroon">j</font> &amp; <font color="Maroon">y</font> <a href="hidden.html#R1">=</a> <font color="Maroon">t</font> )
 ;<br/><div class="add"><a NAME="E2:15_2_3_9_1_1_10"/><b>then </b><i><font color="Green">E175</font></i>: 
( <font color="Maroon">f</font> <a href="funct_2.html#K3">.</a> <font color="Maroon">x</font> <a href="hidden.html#R1">=</a> <font color="Maroon">b</font> &amp; <font color="Maroon">f</font> <a href="funct_2.html#K3">.</a> <font color="Maroon">y</font> <a href="hidden.html#R1">=</a> <font color="Maroon">e</font> )
 <b>by </b><i><a class="ref" href="yellow11.html#T1" target="_self">Th1</a></i>;<br/><b>reconsider </b><font color="Maroon">B</font> = <font color="Maroon">b</font>, <font color="Maroon">E</font> = <font color="Maroon">e</font> as   <a href="struct_0.html#NM1">Element</a> of <font color="Maroon">K</font> <b>by </b><i>, <a class="ref" href="enumset1.html#D3">ENUMSET1:def 3</a></i>;<br/><a NAME="E4:15_2_3_9_1_1_10"/>
( <font color="Maroon">b</font> <a href="orders_2.html#R3">&lt;=</a> <font color="Maroon">e</font> &amp; <font color="Maroon">B</font> <a href="hidden.html#R2">in</a> the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">K</font> &amp; <font color="Maroon">E</font> <a href="hidden.html#R2">in</a> the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">K</font> )
 <b>by </b><i>, <a class="ref" href="yellow_0.html#T25">YELLOW_0:25</a></i>;<br/><b>hence </b><a NAME="E5:15_2_3_9_1_1_10"/>
<font color="Maroon">f</font> <a href="funct_2.html#K3">.</a> <font color="Maroon">x</font> <a href="orders_2.html#R3">&lt;=</a> <font color="Maroon">f</font> <a href="funct_2.html#K3">.</a> <font color="Maroon">y</font>
 <b>by </b><i><a class="ref" href="yellow11.html#T5" target="_self">Th5</a>, <a class="ref" href="yellow_0.html#T61">YELLOW_0:61</a></i>;<br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="15_2_3_9_1_1_11"><b>suppose </b></a><a NAME="E1:15_2_3_9_1_1_11"/>
( <font color="Maroon">x</font> <a href="hidden.html#R1">=</a> <font color="Maroon">dj</font> &amp; <font color="Maroon">y</font> <a href="hidden.html#R1">=</a> <font color="Maroon">z</font> )
 ;<br/><div class="add"><a NAME="E2:15_2_3_9_1_1_11"/><b>then </b>
<font color="Maroon">dj</font> <a href="tarski.html#R1">c=</a> <font color="Maroon">z</font>
 <b>by </b><i><a class="txt" href="yellow11.html#E5"><i><font color="Green">Lemma26</font></i></a>, <a class="ref" href="yellow_1.html#T3">YELLOW_1:3</a></i>;<br/><b>hence </b><a NAME="E3:15_2_3_9_1_1_11"/>
<font color="Maroon">f</font> <a href="funct_2.html#K3">.</a> <font color="Maroon">x</font> <a href="orders_2.html#R3">&lt;=</a> <font color="Maroon">f</font> <a href="funct_2.html#K3">.</a> <font color="Maroon">y</font>
 <b>by </b><i>, <a class="ref" href="xboole_1.html#T3">XBOOLE_1:3</a></i>;<br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="15_2_3_9_1_1_12"><b>suppose </b></a><a NAME="E1:15_2_3_9_1_1_12"/><i><font color="Green">E176</font></i>: 
( <font color="Maroon">x</font> <a href="hidden.html#R1">=</a> <font color="Maroon">dj</font> &amp; <font color="Maroon">y</font> <a href="hidden.html#R1">=</a> <font color="Maroon">j</font> )
 ;<br/><div class="add"><a NAME="E2:15_2_3_9_1_1_12"/>
( 1 <a href="hidden.html#R2">in</a> <font color="Maroon">dj</font> &amp; not 1 <a href="hidden.html#R2">in</a> <font color="Maroon">j</font> )
 <b>by </b><i>, <a class="ref" href="tarski.html#D1">TARSKI:def 1</a></i>;<br/><a NAME="E3:15_2_3_9_1_1_12"/><b>then </b>
not <font color="Maroon">dj</font> <a href="tarski.html#R1">c=</a> <font color="Maroon">j</font>
 ;<br/><b>hence </b><a NAME="E4:15_2_3_9_1_1_12"/>
<font color="Maroon">f</font> <a href="funct_2.html#K3">.</a> <font color="Maroon">x</font> <a href="orders_2.html#R3">&lt;=</a> <font color="Maroon">f</font> <a href="funct_2.html#K3">.</a> <font color="Maroon">y</font>
 <b>by </b><i><a class="txt" href="yellow11.html#E5"><i><font color="Green">Lemma26</font></i></a>, <a class="ref" href="yellow11.html#T5" target="_self">Th5</a>, <a class="ref" href="yellow_1.html#T3">YELLOW_1:3</a></i>;<br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="15_2_3_9_1_1_13"><b>suppose </b></a><a NAME="E1:15_2_3_9_1_1_13"/>
( <font color="Maroon">x</font> <a href="hidden.html#R1">=</a> <font color="Maroon">dj</font> &amp; <font color="Maroon">y</font> <a href="hidden.html#R1">=</a> <font color="Maroon">dj</font> )
 ;<br/><div class="add"><b>hence </b><a NAME="E2:15_2_3_9_1_1_13"/>
<font color="Maroon">f</font> <a href="funct_2.html#K3">.</a> <font color="Maroon">x</font> <a href="orders_2.html#R3">&lt;=</a> <font color="Maroon">f</font> <a href="funct_2.html#K3">.</a> <font color="Maroon">y</font>
 ;<br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="15_2_3_9_1_1_14"><b>suppose </b></a><a NAME="E1:15_2_3_9_1_1_14"/><i><font color="Green">E177</font></i>: 
( <font color="Maroon">x</font> <a href="hidden.html#R1">=</a> <font color="Maroon">dj</font> &amp; <font color="Maroon">y</font> <a href="hidden.html#R1">=</a> <font color="Maroon">td</font> )
 ;<br/><div class="add"><a NAME="E2:15_2_3_9_1_1_14"/>
( 1 <a href="hidden.html#R2">in</a> <font color="Maroon">dj</font> &amp; not 1 <a href="hidden.html#R2">in</a> <font color="Maroon">td</font> )
 <b>by </b><i>, , <a class="ref" href="tarski.html#D1">TARSKI:def 1</a></i>;<br/><a NAME="E3:15_2_3_9_1_1_14"/><b>then </b>
not <font color="Maroon">dj</font> <a href="tarski.html#R1">c=</a> <font color="Maroon">td</font>
 ;<br/><b>hence </b><a NAME="E4:15_2_3_9_1_1_14"/>
<font color="Maroon">f</font> <a href="funct_2.html#K3">.</a> <font color="Maroon">x</font> <a href="orders_2.html#R3">&lt;=</a> <font color="Maroon">f</font> <a href="funct_2.html#K3">.</a> <font color="Maroon">y</font>
 <b>by </b><i><a class="txt" href="yellow11.html#E5"><i><font color="Green">Lemma26</font></i></a>, <a class="ref" href="yellow11.html#T5" target="_self">Th5</a>, <a class="ref" href="yellow_1.html#T3">YELLOW_1:3</a></i>;<br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="15_2_3_9_1_1_15"><b>suppose </b></a><a NAME="E1:15_2_3_9_1_1_15"/>
( <font color="Maroon">x</font> <a href="hidden.html#R1">=</a> <font color="Maroon">dj</font> &amp; <font color="Maroon">y</font> <a href="hidden.html#R1">=</a> <font color="Maroon">t</font> )
 ;<br/><div class="add"><a NAME="E2:15_2_3_9_1_1_15"/><b>then </b><i><font color="Green">E178</font></i>: 
( <font color="Maroon">f</font> <a href="funct_2.html#K3">.</a> <font color="Maroon">x</font> <a href="hidden.html#R1">=</a> <font color="Maroon">c</font> &amp; <font color="Maroon">f</font> <a href="funct_2.html#K3">.</a> <font color="Maroon">y</font> <a href="hidden.html#R1">=</a> <font color="Maroon">e</font> )
 <b>by </b><i><a class="ref" href="yellow11.html#T1" target="_self">Th1</a></i>;<br/><b>reconsider </b><font color="Maroon">C</font> = <font color="Maroon">c</font>, <font color="Maroon">E</font> = <font color="Maroon">e</font> as   <a href="struct_0.html#NM1">Element</a> of <font color="Maroon">K</font> <b>by </b><i>, <a class="ref" href="enumset1.html#D3">ENUMSET1:def 3</a></i>;<br/><a NAME="E4:15_2_3_9_1_1_15"/>
( <font color="Maroon">c</font> <a href="orders_2.html#R3">&lt;=</a> <font color="Maroon">e</font> &amp; <font color="Maroon">C</font> <a href="hidden.html#R2">in</a> the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">K</font> &amp; <font color="Maroon">E</font> <a href="hidden.html#R2">in</a> the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">K</font> )
 <b>by </b><i>, <a class="ref" href="yellow_0.html#T25">YELLOW_0:25</a></i>;<br/><b>hence </b><a NAME="E5:15_2_3_9_1_1_15"/>
<font color="Maroon">f</font> <a href="funct_2.html#K3">.</a> <font color="Maroon">x</font> <a href="orders_2.html#R3">&lt;=</a> <font color="Maroon">f</font> <a href="funct_2.html#K3">.</a> <font color="Maroon">y</font>
 <b>by </b><i><a class="ref" href="yellow11.html#T5" target="_self">Th5</a>, <a class="ref" href="yellow_0.html#T61">YELLOW_0:61</a></i>;<br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="15_2_3_9_1_1_16"><b>suppose </b></a><a NAME="E1:15_2_3_9_1_1_16"/>
( <font color="Maroon">x</font> <a href="hidden.html#R1">=</a> <font color="Maroon">td</font> &amp; <font color="Maroon">y</font> <a href="hidden.html#R1">=</a> <font color="Maroon">z</font> )
 ;<br/><div class="add"><a NAME="E2:15_2_3_9_1_1_16"/><b>then </b>
<font color="Maroon">td</font> <a href="tarski.html#R1">c=</a> <font color="Maroon">z</font>
 <b>by </b><i><a class="txt" href="yellow11.html#E5"><i><font color="Green">Lemma26</font></i></a>, <a class="ref" href="yellow_1.html#T3">YELLOW_1:3</a></i>;<br/><b>hence </b><a NAME="E3:15_2_3_9_1_1_16"/>
<font color="Maroon">f</font> <a href="funct_2.html#K3">.</a> <font color="Maroon">x</font> <a href="orders_2.html#R3">&lt;=</a> <font color="Maroon">f</font> <a href="funct_2.html#K3">.</a> <font color="Maroon">y</font>
 <b>by </b><i>, <a class="ref" href="xboole_1.html#T3">XBOOLE_1:3</a></i>;<br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="15_2_3_9_1_1_17"><b>suppose </b></a><a NAME="E1:15_2_3_9_1_1_17"/><i><font color="Green">E179</font></i>: 
( <font color="Maroon">x</font> <a href="hidden.html#R1">=</a> <font color="Maroon">td</font> &amp; <font color="Maroon">y</font> <a href="hidden.html#R1">=</a> <font color="Maroon">j</font> )
 ;<br/><div class="add"><a NAME="E2:15_2_3_9_1_1_17"/>
( 2 <a href="hidden.html#R2">in</a> <font color="Maroon">td</font> &amp; not 2 <a href="hidden.html#R2">in</a> <font color="Maroon">j</font> )
 <b>by </b><i>, <a class="ref" href="card_5.html#T1">CARD_5:1</a>, <a class="ref" href="tarski.html#D1">TARSKI:def 1</a></i>;<br/><a NAME="E3:15_2_3_9_1_1_17"/><b>then </b>
not <font color="Maroon">td</font> <a href="tarski.html#R1">c=</a> <font color="Maroon">j</font>
 ;<br/><b>hence </b><a NAME="E4:15_2_3_9_1_1_17"/>
<font color="Maroon">f</font> <a href="funct_2.html#K3">.</a> <font color="Maroon">x</font> <a href="orders_2.html#R3">&lt;=</a> <font color="Maroon">f</font> <a href="funct_2.html#K3">.</a> <font color="Maroon">y</font>
 <b>by </b><i><a class="txt" href="yellow11.html#E5"><i><font color="Green">Lemma26</font></i></a>, <a class="ref" href="yellow11.html#T5" target="_self">Th5</a>, <a class="ref" href="yellow_1.html#T3">YELLOW_1:3</a></i>;<br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="15_2_3_9_1_1_18"><b>suppose </b></a><a NAME="E1:15_2_3_9_1_1_18"/><i><font color="Green">E180</font></i>: 
( <font color="Maroon">x</font> <a href="hidden.html#R1">=</a> <font color="Maroon">td</font> &amp; <font color="Maroon">y</font> <a href="hidden.html#R1">=</a> <font color="Maroon">dj</font> )
 ;<br/><div class="add"><a NAME="E2:15_2_3_9_1_1_18"/>
( 2 <a href="hidden.html#R2">in</a> <font color="Maroon">td</font> &amp; not 2 <a href="hidden.html#R2">in</a> <font color="Maroon">dj</font> )
 <b>by </b><i>, , <a class="ref" href="tarski.html#D1">TARSKI:def 1</a></i>;<br/><a NAME="E3:15_2_3_9_1_1_18"/><b>then </b>
not <font color="Maroon">td</font> <a href="tarski.html#R1">c=</a> <font color="Maroon">dj</font>
 ;<br/><b>hence </b><a NAME="E4:15_2_3_9_1_1_18"/>
<font color="Maroon">f</font> <a href="funct_2.html#K3">.</a> <font color="Maroon">x</font> <a href="orders_2.html#R3">&lt;=</a> <font color="Maroon">f</font> <a href="funct_2.html#K3">.</a> <font color="Maroon">y</font>
 <b>by </b><i><a class="txt" href="yellow11.html#E5"><i><font color="Green">Lemma26</font></i></a>, <a class="ref" href="yellow11.html#T5" target="_self">Th5</a>, <a class="ref" href="yellow_1.html#T3">YELLOW_1:3</a></i>;<br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="15_2_3_9_1_1_19"><b>suppose </b></a><a NAME="E1:15_2_3_9_1_1_19"/>
( <font color="Maroon">x</font> <a href="hidden.html#R1">=</a> <font color="Maroon">td</font> &amp; <font color="Maroon">y</font> <a href="hidden.html#R1">=</a> <font color="Maroon">td</font> )
 ;<br/><div class="add"><b>hence </b><a NAME="E2:15_2_3_9_1_1_19"/>
<font color="Maroon">f</font> <a href="funct_2.html#K3">.</a> <font color="Maroon">x</font> <a href="orders_2.html#R3">&lt;=</a> <font color="Maroon">f</font> <a href="funct_2.html#K3">.</a> <font color="Maroon">y</font>
 ;<br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="15_2_3_9_1_1_20"><b>suppose </b></a><a NAME="E1:15_2_3_9_1_1_20"/>
( <font color="Maroon">x</font> <a href="hidden.html#R1">=</a> <font color="Maroon">td</font> &amp; <font color="Maroon">y</font> <a href="hidden.html#R1">=</a> <font color="Maroon">t</font> )
 ;<br/><div class="add"><a NAME="E2:15_2_3_9_1_1_20"/><b>then </b><i><font color="Green">E181</font></i>: 
( <font color="Maroon">f</font> <a href="funct_2.html#K3">.</a> <font color="Maroon">x</font> <a href="hidden.html#R1">=</a> <font color="Maroon">d</font> &amp; <font color="Maroon">f</font> <a href="funct_2.html#K3">.</a> <font color="Maroon">y</font> <a href="hidden.html#R1">=</a> <font color="Maroon">e</font> )
 <b>by </b><i><a class="ref" href="yellow11.html#T1" target="_self">Th1</a></i>;<br/><b>reconsider </b><font color="Maroon">D</font> = <font color="Maroon">d</font>, <font color="Maroon">E</font> = <font color="Maroon">e</font> as   <a href="struct_0.html#NM1">Element</a> of <font color="Maroon">K</font> <b>by </b><i>, <a class="ref" href="enumset1.html#D3">ENUMSET1:def 3</a></i>;<br/><a NAME="E4:15_2_3_9_1_1_20"/>
( <font color="Maroon">d</font> <a href="orders_2.html#R3">&lt;=</a> <font color="Maroon">e</font> &amp; <font color="Maroon">D</font> <a href="hidden.html#R2">in</a> the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">K</font> &amp; <font color="Maroon">E</font> <a href="hidden.html#R2">in</a> the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">K</font> )
 <b>by </b><i>, <a class="ref" href="yellow_0.html#T25">YELLOW_0:25</a></i>;<br/><b>hence </b><a NAME="E5:15_2_3_9_1_1_20"/>
<font color="Maroon">f</font> <a href="funct_2.html#K3">.</a> <font color="Maroon">x</font> <a href="orders_2.html#R3">&lt;=</a> <font color="Maroon">f</font> <a href="funct_2.html#K3">.</a> <font color="Maroon">y</font>
 <b>by </b><i><a class="ref" href="yellow11.html#T5" target="_self">Th5</a>, <a class="ref" href="yellow_0.html#T61">YELLOW_0:61</a></i>;<br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="15_2_3_9_1_1_21"><b>suppose </b></a><a NAME="E1:15_2_3_9_1_1_21"/>
( <font color="Maroon">x</font> <a href="hidden.html#R1">=</a> <font color="Maroon">t</font> &amp; <font color="Maroon">y</font> <a href="hidden.html#R1">=</a> <font color="Maroon">z</font> )
 ;<br/><div class="add"><a NAME="E2:15_2_3_9_1_1_21"/><b>then </b>
<font color="Maroon">t</font> <a href="tarski.html#R1">c=</a> <font color="Maroon">z</font>
 <b>by </b><i><a class="txt" href="yellow11.html#E5"><i><font color="Green">Lemma26</font></i></a>, <a class="ref" href="yellow_1.html#T3">YELLOW_1:3</a></i>;<br/><b>hence </b><a NAME="E3:15_2_3_9_1_1_21"/>
<font color="Maroon">f</font> <a href="funct_2.html#K3">.</a> <font color="Maroon">x</font> <a href="orders_2.html#R3">&lt;=</a> <font color="Maroon">f</font> <a href="funct_2.html#K3">.</a> <font color="Maroon">y</font>
 <b>by </b><i><a class="ref" href="xboole_1.html#T3">XBOOLE_1:3</a></i>;<br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="15_2_3_9_1_1_22"><b>suppose </b></a><a NAME="E1:15_2_3_9_1_1_22"/><i><font color="Green">E182</font></i>: 
( <font color="Maroon">x</font> <a href="hidden.html#R1">=</a> <font color="Maroon">t</font> &amp; <font color="Maroon">y</font> <a href="hidden.html#R1">=</a> <font color="Maroon">j</font> )
 ;<br/><div class="add"><a NAME="E2:15_2_3_9_1_1_22"/>
( 1 <a href="hidden.html#R2">in</a> <font color="Maroon">t</font> &amp; not 1 <a href="hidden.html#R2">in</a> <font color="Maroon">j</font> )
 <b>by </b><i>, <a class="ref" href="enumset1.html#D1">ENUMSET1:def 1</a></i>;<br/><a NAME="E3:15_2_3_9_1_1_22"/><b>then </b>
not <font color="Maroon">t</font> <a href="tarski.html#R1">c=</a> <font color="Maroon">j</font>
 ;<br/><b>hence </b><a NAME="E4:15_2_3_9_1_1_22"/>
<font color="Maroon">f</font> <a href="funct_2.html#K3">.</a> <font color="Maroon">x</font> <a href="orders_2.html#R3">&lt;=</a> <font color="Maroon">f</font> <a href="funct_2.html#K3">.</a> <font color="Maroon">y</font>
 <b>by </b><i><a class="txt" href="yellow11.html#E5"><i><font color="Green">Lemma26</font></i></a>, <a class="ref" href="yellow11.html#T5" target="_self">Th5</a>, <a class="ref" href="yellow_1.html#T3">YELLOW_1:3</a></i>;<br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="15_2_3_9_1_1_23"><b>suppose </b></a><a NAME="E1:15_2_3_9_1_1_23"/><i><font color="Green">E183</font></i>: 
( <font color="Maroon">x</font> <a href="hidden.html#R1">=</a> <font color="Maroon">t</font> &amp; <font color="Maroon">y</font> <a href="hidden.html#R1">=</a> <font color="Maroon">dj</font> )
 ;<br/><div class="add"><a NAME="E2:15_2_3_9_1_1_23"/>
( 2 <a href="hidden.html#R2">in</a> <font color="Maroon">t</font> &amp; not 2 <a href="hidden.html#R2">in</a> <font color="Maroon">dj</font> )
 <b>by </b><i>, , <a class="ref" href="enumset1.html#D1">ENUMSET1:def 1</a>, <a class="ref" href="tarski.html#D1">TARSKI:def 1</a></i>;<br/><a NAME="E3:15_2_3_9_1_1_23"/><b>then </b>
not <font color="Maroon">t</font> <a href="tarski.html#R1">c=</a> <font color="Maroon">dj</font>
 ;<br/><b>hence </b><a NAME="E4:15_2_3_9_1_1_23"/>
<font color="Maroon">f</font> <a href="funct_2.html#K3">.</a> <font color="Maroon">x</font> <a href="orders_2.html#R3">&lt;=</a> <font color="Maroon">f</font> <a href="funct_2.html#K3">.</a> <font color="Maroon">y</font>
 <b>by </b><i><a class="txt" href="yellow11.html#E5"><i><font color="Green">Lemma26</font></i></a>, <a class="ref" href="yellow11.html#T5" target="_self">Th5</a>, <a class="ref" href="yellow_1.html#T3">YELLOW_1:3</a></i>;<br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="15_2_3_9_1_1_24"><b>suppose </b></a><a NAME="E1:15_2_3_9_1_1_24"/><i><font color="Green">E184</font></i>: 
( <font color="Maroon">x</font> <a href="hidden.html#R1">=</a> <font color="Maroon">t</font> &amp; <font color="Maroon">y</font> <a href="hidden.html#R1">=</a> <font color="Maroon">td</font> )
 ;<br/><div class="add"><a NAME="E2:15_2_3_9_1_1_24"/>
( 0 <a href="hidden.html#R2">in</a> <font color="Maroon">t</font> &amp; not 0 <a href="hidden.html#R2">in</a> <font color="Maroon">td</font> )
 <b>by </b><i>, , <a class="ref" href="enumset1.html#D1">ENUMSET1:def 1</a>, <a class="ref" href="tarski.html#D1">TARSKI:def 1</a></i>;<br/><a NAME="E3:15_2_3_9_1_1_24"/><b>then </b>
not <font color="Maroon">t</font> <a href="tarski.html#R1">c=</a> <font color="Maroon">td</font>
 ;<br/><b>hence </b><a NAME="E4:15_2_3_9_1_1_24"/>
<font color="Maroon">f</font> <a href="funct_2.html#K3">.</a> <font color="Maroon">x</font> <a href="orders_2.html#R3">&lt;=</a> <font color="Maroon">f</font> <a href="funct_2.html#K3">.</a> <font color="Maroon">y</font>
 <b>by </b><i><a class="txt" href="yellow11.html#E5"><i><font color="Green">Lemma26</font></i></a>, <a class="ref" href="yellow11.html#T5" target="_self">Th5</a>, <a class="ref" href="yellow_1.html#T3">YELLOW_1:3</a></i>;<br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="15_2_3_9_1_1_25"><b>suppose </b></a><a NAME="E1:15_2_3_9_1_1_25"/>
( <font color="Maroon">x</font> <a href="hidden.html#R1">=</a> <font color="Maroon">t</font> &amp; <font color="Maroon">y</font> <a href="hidden.html#R1">=</a> <font color="Maroon">t</font> )
 ;<br/><div class="add"><b>hence </b><a NAME="E2:15_2_3_9_1_1_25"/>
<font color="Maroon">f</font> <a href="funct_2.html#K3">.</a> <font color="Maroon">x</font> <a href="orders_2.html#R3">&lt;=</a> <font color="Maroon">f</font> <a href="funct_2.html#K3">.</a> <font color="Maroon">y</font>
 ;<br/></div><b>end;</b></div></div><b>end;</b></div>

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

<b>thus </b><a NAME="E2:15_2_3_9"/>
( <font color="Maroon">f</font> <a href="funct_2.html#K3">.</a> <font color="Maroon">x</font> <a href="orders_2.html#R3">&lt;=</a> <font color="Maroon">f</font> <a href="funct_2.html#K3">.</a> <font color="Maroon">y</font> implies <font color="Maroon">x</font> <a href="orders_2.html#R3">&lt;=</a> <font color="Maroon">y</font> )
 <div><a class="txt" onclick="hs2(this)" href="javascript:()" title="15_2_3_9_2"><b>proof </b></a><div class="add">

<b>assume </b><a NAME="E1:15_2_3_9_2"/><i><font color="Green">E185</font></i>: 
<font color="Maroon">f</font> <a href="funct_2.html#K3">.</a> <font color="Maroon">x</font> <a href="orders_2.html#R3">&lt;=</a> <font color="Maroon">f</font> <a href="funct_2.html#K3">.</a> <font color="Maroon">y</font>
 ;<br/>

<a NAME="E2:15_2_3_9_2"/><i><font color="Green">E186</font></i>: 
( <font color="Maroon">f</font> <a href="funct_2.html#K3">.</a> <font color="Maroon">x</font> <a href="hidden.html#R2">in</a> <font color="Maroon">ck</font> &amp; <font color="Maroon">f</font> <a href="funct_2.html#K3">.</a> <font color="Maroon">y</font> <a href="hidden.html#R2">in</a> <font color="Maroon">ck</font> )
 
<b>by </b><i><a class="ref" href="yellow11.html#T3" target="_self">Th3</a>, <a class="ref" href="yellow11.html#T4" target="_self">Th4</a>, <a class="ref" href="funct_1.html#D5">FUNCT_1:def 5</a></i>;<br/>
<a NAME="E3:15_2_3_9_2"/><i><font color="Green">E187</font></i>: 
<font color="Maroon">dj</font> <a href="tarski.html#R1">c=</a> <font color="Maroon">t</font>
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="15_2_3_9_2_1"><b>proof </b></a><div class="add">

<b>let </b><font color="Maroon">X</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="E1:15_2_3_9_2_1"/>
<font color="Maroon">X</font> <a href="hidden.html#R2">in</a> <font color="Maroon">dj</font>
 ;<br/>

<a NAME="E2:15_2_3_9_2_1"/><b>then </b>
<font color="Maroon">X</font> <a href="hidden.html#R1">=</a> 1
 
<b>by </b><i>, <a class="ref" href="tarski.html#D1">TARSKI:def 1</a></i>;<br/>
<b>hence </b><a NAME="E3:15_2_3_9_2_1"/>
<font color="Maroon">X</font> <a href="hidden.html#R2">in</a> <font color="Maroon">t</font>
 <b>by </b><i>, <a class="ref" href="enumset1.html#D1">ENUMSET1:def 1</a></i>;<br/>


</div><b>end;</b></div>
<div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="15_2_3_9_2_2"><b>per </b></a><a class="txt" onclick="hs(this)" href="javascript:()"><b>cases </b></a><span class="hide"><a NAME="E1:15_2_3_9_2_2"/>
( ( <font color="Maroon">f</font> <a href="funct_2.html#K3">.</a> <font color="Maroon">x</font> <a href="hidden.html#R1">=</a> <font color="Maroon">a</font> &amp; <font color="Maroon">f</font> <a href="funct_2.html#K3">.</a> <font color="Maroon">y</font> <a href="hidden.html#R1">=</a> <font color="Maroon">a</font> ) or ( <font color="Maroon">f</font> <a href="funct_2.html#K3">.</a> <font color="Maroon">x</font> <a href="hidden.html#R1">=</a> <font color="Maroon">a</font> &amp; <font color="Maroon">f</font> <a href="funct_2.html#K3">.</a> <font color="Maroon">y</font> <a href="hidden.html#R1">=</a> <font color="Maroon">b</font> ) or ( <font color="Maroon">f</font> <a href="funct_2.html#K3">.</a> <font color="Maroon">x</font> <a href="hidden.html#R1">=</a> <font color="Maroon">a</font> &amp; <font color="Maroon">f</font> <a href="funct_2.html#K3">.</a> <font color="Maroon">y</font> <a href="hidden.html#R1">=</a> <font color="Maroon">c</font> ) or ( <font color="Maroon">f</font> <a href="funct_2.html#K3">.</a> <font color="Maroon">x</font> <a href="hidden.html#R1">=</a> <font color="Maroon">a</font> &amp; <font color="Maroon">f</font> <a href="funct_2.html#K3">.</a> <font color="Maroon">y</font> <a href="hidden.html#R1">=</a> <font color="Maroon">d</font> ) or ( <font color="Maroon">f</font> <a href="funct_2.html#K3">.</a> <font color="Maroon">x</font> <a href="hidden.html#R1">=</a> <font color="Maroon">a</font> &amp; <font color="Maroon">f</font> <a href="funct_2.html#K3">.</a> <font color="Maroon">y</font> <a href="hidden.html#R1">=</a> <font color="Maroon">e</font> ) or ( <font color="Maroon">f</font> <a href="funct_2.html#K3">.</a> <font color="Maroon">x</font> <a href="hidden.html#R1">=</a> <font color="Maroon">b</font> &amp; <font color="Maroon">f</font> <a href="funct_2.html#K3">.</a> <font color="Maroon">y</font> <a href="hidden.html#R1">=</a> <font color="Maroon">a</font> ) or ( <font color="Maroon">f</font> <a href="funct_2.html#K3">.</a> <font color="Maroon">x</font> <a href="hidden.html#R1">=</a> <font color="Maroon">b</font> &amp; <font color="Maroon">f</font> <a href="funct_2.html#K3">.</a> <font color="Maroon">y</font> <a href="hidden.html#R1">=</a> <font color="Maroon">b</font> ) or ( <font color="Maroon">f</font> <a href="funct_2.html#K3">.</a> <font color="Maroon">x</font> <a href="hidden.html#R1">=</a> <font color="Maroon">b</font> &amp; <font color="Maroon">f</font> <a href="funct_2.html#K3">.</a> <font color="Maroon">y</font> <a href="hidden.html#R1">=</a> <font color="Maroon">c</font> ) or ( <font color="Maroon">f</font> <a href="funct_2.html#K3">.</a> <font color="Maroon">x</font> <a href="hidden.html#R1">=</a> <font color="Maroon">b</font> &amp; <font color="Maroon">f</font> <a href="funct_2.html#K3">.</a> <font color="Maroon">y</font> <a href="hidden.html#R1">=</a> <font color="Maroon">d</font> ) or ( <font color="Maroon">f</font> <a href="funct_2.html#K3">.</a> <font color="Maroon">x</font> <a href="hidden.html#R1">=</a> <font color="Maroon">b</font> &amp; <font color="Maroon">f</font> <a href="funct_2.html#K3">.</a> <font color="Maroon">y</font> <a href="hidden.html#R1">=</a> <font color="Maroon">e</font> ) or ( <font color="Maroon">f</font> <a href="funct_2.html#K3">.</a> <font color="Maroon">x</font> <a href="hidden.html#R1">=</a> <font color="Maroon">c</font> &amp; <font color="Maroon">f</font> <a href="funct_2.html#K3">.</a> <font color="Maroon">y</font> <a href="hidden.html#R1">=</a> <font color="Maroon">a</font> ) or ( <font color="Maroon">f</font> <a href="funct_2.html#K3">.</a> <font color="Maroon">x</font> <a href="hidden.html#R1">=</a> <font color="Maroon">c</font> &amp; <font color="Maroon">f</font> <a href="funct_2.html#K3">.</a> <font color="Maroon">y</font> <a href="hidden.html#R1">=</a> <font color="Maroon">b</font> ) or ( <font color="Maroon">f</font> <a href="funct_2.html#K3">.</a> <font color="Maroon">x</font> <a href="hidden.html#R1">=</a> <font color="Maroon">c</font> &amp; <font color="Maroon">f</font> <a href="funct_2.html#K3">.</a> <font color="Maroon">y</font> <a href="hidden.html#R1">=</a> <font color="Maroon">c</font> ) or ( <font color="Maroon">f</font> <a href="funct_2.html#K3">.</a> <font color="Maroon">x</font> <a href="hidden.html#R1">=</a> <font color="Maroon">c</font> &amp; <font color="Maroon">f</font> <a href="funct_2.html#K3">.</a> <font color="Maroon">y</font> <a href="hidden.html#R1">=</a> <font color="Maroon">d</font> ) or ( <font color="Maroon">f</font> <a href="funct_2.html#K3">.</a> <font color="Maroon">x</font> <a href="hidden.html#R1">=</a> <font color="Maroon">c</font> &amp; <font color="Maroon">f</font> <a href="funct_2.html#K3">.</a> <font color="Maroon">y</font> <a href="hidden.html#R1">=</a> <font color="Maroon">e</font> ) or ( <font color="Maroon">f</font> <a href="funct_2.html#K3">.</a> <font color="Maroon">x</font> <a href="hidden.html#R1">=</a> <font color="Maroon">d</font> &amp; <font color="Maroon">f</font> <a href="funct_2.html#K3">.</a> <font color="Maroon">y</font> <a href="hidden.html#R1">=</a> <font color="Maroon">a</font> ) or ( <font color="Maroon">f</font> <a href="funct_2.html#K3">.</a> <font color="Maroon">x</font> <a href="hidden.html#R1">=</a> <font color="Maroon">d</font> &amp; <font color="Maroon">f</font> <a href="funct_2.html#K3">.</a> <font color="Maroon">y</font> <a href="hidden.html#R1">=</a> <font color="Maroon">b</font> ) or ( <font color="Maroon">f</font> <a href="funct_2.html#K3">.</a> <font color="Maroon">x</font> <a href="hidden.html#R1">=</a> <font color="Maroon">d</font> &amp; <font color="Maroon">f</font> <a href="funct_2.html#K3">.</a> <font color="Maroon">y</font> <a href="hidden.html#R1">=</a> <font color="Maroon">c</font> ) or ( <font color="Maroon">f</font> <a href="funct_2.html#K3">.</a> <font color="Maroon">x</font> <a href="hidden.html#R1">=</a> <font color="Maroon">d</font> &amp; <font color="Maroon">f</font> <a href="funct_2.html#K3">.</a> <font color="Maroon">y</font> <a href="hidden.html#R1">=</a> <font color="Maroon">d</font> ) or ( <font color="Maroon">f</font> <a href="funct_2.html#K3">.</a> <font color="Maroon">x</font> <a href="hidden.html#R1">=</a> <font color="Maroon">d</font> &amp; <font color="Maroon">f</font> <a href="funct_2.html#K3">.</a> <font color="Maroon">y</font> <a href="hidden.html#R1">=</a> <font color="Maroon">e</font> ) or ( <font color="Maroon">f</font> <a href="funct_2.html#K3">.</a> <font color="Maroon">x</font> <a href="hidden.html#R1">=</a> <font color="Maroon">e</font> &amp; <font color="Maroon">f</font> <a href="funct_2.html#K3">.</a> <font color="Maroon">y</font> <a href="hidden.html#R1">=</a> <font color="Maroon">a</font> ) or ( <font color="Maroon">f</font> <a href="funct_2.html#K3">.</a> <font color="Maroon">x</font> <a href="hidden.html#R1">=</a> <font color="Maroon">e</font> &amp; <font color="Maroon">f</font> <a href="funct_2.html#K3">.</a> <font color="Maroon">y</font> <a href="hidden.html#R1">=</a> <font color="Maroon">b</font> ) or ( <font color="Maroon">f</font> <a href="funct_2.html#K3">.</a> <font color="Maroon">x</font> <a href="hidden.html#R1">=</a> <font color="Maroon">e</font> &amp; <font color="Maroon">f</font> <a href="funct_2.html#K3">.</a> <font color="Maroon">y</font> <a href="hidden.html#R1">=</a> <font color="Maroon">c</font> ) or ( <font color="Maroon">f</font> <a href="funct_2.html#K3">.</a> <font color="Maroon">x</font> <a href="hidden.html#R1">=</a> <font color="Maroon">e</font> &amp; <font color="Maroon">f</font> <a href="funct_2.html#K3">.</a> <font color="Maroon">y</font> <a href="hidden.html#R1">=</a> <font color="Maroon">d</font> ) or ( <font color="Maroon">f</font> <a href="funct_2.html#K3">.</a> <font color="Maroon">x</font> <a href="hidden.html#R1">=</a> <font color="Maroon">e</font> &amp; <font color="Maroon">f</font> <a href="funct_2.html#K3">.</a> <font color="Maroon">y</font> <a href="hidden.html#R1">=</a> <font color="Maroon">e</font> ) )
 </span><b>by </b><i><a class="ref" href="yellow11.html#T5" target="_self">Th5</a>, <a class="ref" href="enumset1.html#D3">ENUMSET1:def 3</a></i>;<br/><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="15_2_3_9_2_2_1"><b>suppose </b></a><a NAME="E1:15_2_3_9_2_2_1"/>
( <font color="Maroon">f</font> <a href="funct_2.html#K3">.</a> <font color="Maroon">x</font> <a href="hidden.html#R1">=</a> <font color="Maroon">a</font> &amp; <font color="Maroon">f</font> <a href="funct_2.html#K3">.</a> <font color="Maroon">y</font> <a href="hidden.html#R1">=</a> <font color="Maroon">a</font> )
 ;<br/><div class="add"><b>hence </b><a NAME="E2:15_2_3_9_2_2_1"/>
<font color="Maroon">x</font> <a href="orders_2.html#R3">&lt;=</a> <font color="Maroon">y</font>
 <b>by </b><i><a class="ref" href="yellow11.html#T2" target="_self">Th2</a>, <a class="ref" href="waybel_1.html#D1">WAYBEL_1:def 1</a></i>;<br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="15_2_3_9_2_2_2"><b>suppose </b></a><a NAME="E1:15_2_3_9_2_2_2"/><i><font color="Green">E188</font></i>: 
( <font color="Maroon">f</font> <a href="funct_2.html#K3">.</a> <font color="Maroon">x</font> <a href="hidden.html#R1">=</a> <font color="Maroon">a</font> &amp; <font color="Maroon">f</font> <a href="funct_2.html#K3">.</a> <font color="Maroon">y</font> <a href="hidden.html#R1">=</a> <font color="Maroon">b</font> )
 ;<br/><div class="add"><a NAME="E2:15_2_3_9_2_2_2"/>
( <font color="Maroon">f</font> <a href="funct_2.html#K3">.</a> <font color="Maroon">z</font> <a href="hidden.html#R1">=</a> <font color="Maroon">a</font> &amp; <font color="Maroon">f</font> <a href="funct_2.html#K3">.</a> <font color="Maroon">j</font> <a href="hidden.html#R1">=</a> <font color="Maroon">b</font> )
 <b>by </b><i><a class="ref" href="yellow11.html#T1" target="_self">Th1</a></i>;<br/><a NAME="E3:15_2_3_9_2_2_2"/><b>then </b>
( <font color="Maroon">z</font> <a href="hidden.html#R1">=</a> <font color="Maroon">x</font> &amp; <font color="Maroon">j</font> <a href="hidden.html#R1">=</a> <font color="Maroon">y</font> )
 <b>by </b><i><a class="ref" href="yellow11.html#T2" target="_self">Th2</a>, , <a class="ref" href="waybel_1.html#D1">WAYBEL_1:def 1</a></i>;<br/><a NAME="E4:15_2_3_9_2_2_2"/><b>then </b>
<font color="Maroon">x</font> <a href="tarski.html#R1">c=</a> <font color="Maroon">y</font>
 <b>by </b><i><a class="ref" href="xboole_1.html#T2">XBOOLE_1:2</a></i>;<br/><b>hence </b><a NAME="E5:15_2_3_9_2_2_2"/>
<font color="Maroon">x</font> <a href="orders_2.html#R3">&lt;=</a> <font color="Maroon">y</font>
 <b>by </b><i><a class="ref" href="yellow_1.html#T3">YELLOW_1:3</a></i>;<br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="15_2_3_9_2_2_3"><b>suppose </b></a><a NAME="E1:15_2_3_9_2_2_3"/><i><font color="Green">E189</font></i>: 
( <font color="Maroon">f</font> <a href="funct_2.html#K3">.</a> <font color="Maroon">x</font> <a href="hidden.html#R1">=</a> <font color="Maroon">a</font> &amp; <font color="Maroon">f</font> <a href="funct_2.html#K3">.</a> <font color="Maroon">y</font> <a href="hidden.html#R1">=</a> <font color="Maroon">c</font> )
 ;<br/><div class="add"><a NAME="E2:15_2_3_9_2_2_3"/>
( <font color="Maroon">f</font> <a href="funct_2.html#K3">.</a> <font color="Maroon">z</font> <a href="hidden.html#R1">=</a> <font color="Maroon">a</font> &amp; <font color="Maroon">f</font> <a href="funct_2.html#K3">.</a> <font color="Maroon">dj</font> <a href="hidden.html#R1">=</a> <font color="Maroon">c</font> )
 <b>by </b><i><a class="ref" href="yellow11.html#T1" target="_self">Th1</a></i>;<br/><a NAME="E3:15_2_3_9_2_2_3"/><b>then </b>
( <font color="Maroon">z</font> <a href="hidden.html#R1">=</a> <font color="Maroon">x</font> &amp; <font color="Maroon">dj</font> <a href="hidden.html#R1">=</a> <font color="Maroon">y</font> )
 <b>by </b><i><a class="ref" href="yellow11.html#T2" target="_self">Th2</a>, , <a class="ref" href="waybel_1.html#D1">WAYBEL_1:def 1</a></i>;<br/><a NAME="E4:15_2_3_9_2_2_3"/><b>then </b>
<font color="Maroon">x</font> <a href="tarski.html#R1">c=</a> <font color="Maroon">y</font>
 <b>by </b><i><a class="ref" href="xboole_1.html#T2">XBOOLE_1:2</a></i>;<br/><b>hence </b><a NAME="E5:15_2_3_9_2_2_3"/>
<font color="Maroon">x</font> <a href="orders_2.html#R3">&lt;=</a> <font color="Maroon">y</font>
 <b>by </b><i><a class="ref" href="yellow_1.html#T3">YELLOW_1:3</a></i>;<br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="15_2_3_9_2_2_4"><b>suppose </b></a><a NAME="E1:15_2_3_9_2_2_4"/><i><font color="Green">E193</font></i>: 
( <font color="Maroon">f</font> <a href="funct_2.html#K3">.</a> <font color="Maroon">x</font> <a href="hidden.html#R1">=</a> <font color="Maroon">a</font> &amp; <font color="Maroon">f</font> <a href="funct_2.html#K3">.</a> <font color="Maroon">y</font> <a href="hidden.html#R1">=</a> <font color="Maroon">d</font> )
 ;<br/><div class="add"><a NAME="E2:15_2_3_9_2_2_4"/>
( <font color="Maroon">f</font> <a href="funct_2.html#K3">.</a> <font color="Maroon">z</font> <a href="hidden.html#R1">=</a> <font color="Maroon">a</font> &amp; <font color="Maroon">f</font> <a href="funct_2.html#K3">.</a> <font color="Maroon">td</font> <a href="hidden.html#R1">=</a> <font color="Maroon">d</font> )
 <b>by </b><i><a class="ref" href="yellow11.html#T1" target="_self">Th1</a></i>;<br/><a NAME="E3:15_2_3_9_2_2_4"/><b>then </b>
( <font color="Maroon">z</font> <a href="hidden.html#R1">=</a> <font color="Maroon">x</font> &amp; <font color="Maroon">td</font> <a href="hidden.html#R1">=</a> <font color="Maroon">y</font> )
 <b>by </b><i><a class="ref" href="yellow11.html#T2" target="_self">Th2</a>, , <a class="ref" href="waybel_1.html#D1">WAYBEL_1:def 1</a></i>;<br/><a NAME="E4:15_2_3_9_2_2_4"/><b>then </b>
<font color="Maroon">x</font> <a href="tarski.html#R1">c=</a> <font color="Maroon">y</font>
 <b>by </b><i><a class="ref" href="xboole_1.html#T2">XBOOLE_1:2</a></i>;<br/><b>hence </b><a NAME="E5:15_2_3_9_2_2_4"/>
<font color="Maroon">x</font> <a href="orders_2.html#R3">&lt;=</a> <font color="Maroon">y</font>
 <b>by </b><i><a class="ref" href="yellow_1.html#T3">YELLOW_1:3</a></i>;<br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="15_2_3_9_2_2_5"><b>suppose </b></a><a NAME="E1:15_2_3_9_2_2_5"/><i><font color="Green">E194</font></i>: 
( <font color="Maroon">f</font> <a href="funct_2.html#K3">.</a> <font color="Maroon">x</font> <a href="hidden.html#R1">=</a> <font color="Maroon">a</font> &amp; <font color="Maroon">f</font> <a href="funct_2.html#K3">.</a> <font color="Maroon">y</font> <a href="hidden.html#R1">=</a> <font color="Maroon">e</font> )
 ;<br/><div class="add"><a NAME="E2:15_2_3_9_2_2_5"/>
( <font color="Maroon">f</font> <a href="funct_2.html#K3">.</a> <font color="Maroon">z</font> <a href="hidden.html#R1">=</a> <font color="Maroon">a</font> &amp; <font color="Maroon">f</font> <a href="funct_2.html#K3">.</a> <font color="Maroon">t</font> <a href="hidden.html#R1">=</a> <font color="Maroon">e</font> )
 <b>by </b><i><a class="ref" href="yellow11.html#T1" target="_self">Th1</a></i>;<br/><a NAME="E3:15_2_3_9_2_2_5"/><b>then </b>
( <font color="Maroon">z</font> <a href="hidden.html#R1">=</a> <font color="Maroon">x</font> &amp; <font color="Maroon">t</font> <a href="hidden.html#R1">=</a> <font color="Maroon">y</font> )
 <b>by </b><i><a class="ref" href="yellow11.html#T2" target="_self">Th2</a>, , <a class="ref" href="waybel_1.html#D1">WAYBEL_1:def 1</a></i>;<br/><a NAME="E4:15_2_3_9_2_2_5"/><b>then </b>
<font color="Maroon">x</font> <a href="tarski.html#R1">c=</a> <font color="Maroon">y</font>
 <b>by </b><i><a class="ref" href="xboole_1.html#T2">XBOOLE_1:2</a></i>;<br/><b>hence </b><a NAME="E5:15_2_3_9_2_2_5"/>
<font color="Maroon">x</font> <a href="orders_2.html#R3">&lt;=</a> <font color="Maroon">y</font>
 <b>by </b><i><a class="ref" href="yellow_1.html#T3">YELLOW_1:3</a></i>;<br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="15_2_3_9_2_2_6"><b>suppose </b></a><a NAME="E1:15_2_3_9_2_2_6"/>
( <font color="Maroon">f</font> <a href="funct_2.html#K3">.</a> <font color="Maroon">x</font> <a href="hidden.html#R1">=</a> <font color="Maroon">b</font> &amp; <font color="Maroon">f</font> <a href="funct_2.html#K3">.</a> <font color="Maroon">y</font> <a href="hidden.html#R1">=</a> <font color="Maroon">a</font> )
 ;<br/><div class="add"><a NAME="E2:15_2_3_9_2_2_6"/><b>then </b>
<font color="Maroon">b</font> <a href="orders_2.html#R3">&lt;=</a> <font color="Maroon">a</font>
 <b>by </b><i><a class="txt" href="yellow11.html#E5"><i><font color="Green">Lemma26</font></i></a>, <a class="ref" href="yellow_0.html#T60">YELLOW_0:60</a></i>;<br/><b>hence </b><a NAME="E3:15_2_3_9_2_2_6"/>
<font color="Maroon">x</font> <a href="orders_2.html#R3">&lt;=</a> <font color="Maroon">y</font>
 <b>by </b><i>, <a class="ref" href="yellow_0.html#T25">YELLOW_0:25</a></i>;<br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="15_2_3_9_2_2_7"><b>suppose </b></a><a NAME="E1:15_2_3_9_2_2_7"/>
( <font color="Maroon">f</font> <a href="funct_2.html#K3">.</a> <font color="Maroon">x</font> <a href="hidden.html#R1">=</a> <font color="Maroon">b</font> &amp; <font color="Maroon">f</font> <a href="funct_2.html#K3">.</a> <font color="Maroon">y</font> <a href="hidden.html#R1">=</a> <font color="Maroon">b</font> )
 ;<br/><div class="add"><b>hence </b><a NAME="E2:15_2_3_9_2_2_7"/>
<font color="Maroon">x</font> <a href="orders_2.html#R3">&lt;=</a> <font color="Maroon">y</font>
 <b>by </b><i><a class="ref" href="yellow11.html#T2" target="_self">Th2</a>, <a class="ref" href="waybel_1.html#D1">WAYBEL_1:def 1</a></i>;<br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="15_2_3_9_2_2_8"><b>suppose </b></a><a NAME="E1:15_2_3_9_2_2_8"/>
( <font color="Maroon">f</font> <a href="funct_2.html#K3">.</a> <font color="Maroon">x</font> <a href="hidden.html#R1">=</a> <font color="Maroon">b</font> &amp; <font color="Maroon">f</font> <a href="funct_2.html#K3">.</a> <font color="Maroon">y</font> <a href="hidden.html#R1">=</a> <font color="Maroon">c</font> )
 ;<br/><div class="add"><a NAME="E2:15_2_3_9_2_2_8"/><b>then </b>
<font color="Maroon">b</font> <a href="orders_2.html#R3">&lt;=</a> <font color="Maroon">c</font>
 <b>by </b><i><a class="txt" href="yellow11.html#E5"><i><font color="Green">Lemma26</font></i></a>, <a class="ref" href="yellow_0.html#T60">YELLOW_0:60</a></i>;<br/><b>hence </b><a NAME="E3:15_2_3_9_2_2_8"/>
<font color="Maroon">x</font> <a href="orders_2.html#R3">&lt;=</a> <font color="Maroon">y</font>
 <b>by </b><i>, <a class="ref" href="yellow_0.html#T25">YELLOW_0:25</a></i>;<br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="15_2_3_9_2_2_9"><b>suppose </b></a><a NAME="E1:15_2_3_9_2_2_9"/>
( <font color="Maroon">f</font> <a href="funct_2.html#K3">.</a> <font color="Maroon">x</font> <a href="hidden.html#R1">=</a> <font color="Maroon">b</font> &amp; <font color="Maroon">f</font> <a href="funct_2.html#K3">.</a> <font color="Maroon">y</font> <a href="hidden.html#R1">=</a> <font color="Maroon">d</font> )
 ;<br/><div class="add"><a NAME="E2:15_2_3_9_2_2_9"/><b>then </b>
<font color="Maroon">b</font> <a href="orders_2.html#R3">&lt;=</a> <font color="Maroon">d</font>
 <b>by </b><i><a class="txt" href="yellow11.html#E5"><i><font color="Green">Lemma26</font></i></a>, <a class="ref" href="yellow_0.html#T60">YELLOW_0:60</a></i>;<br/><b>hence </b><a NAME="E3:15_2_3_9_2_2_9"/>
<font color="Maroon">x</font> <a href="orders_2.html#R3">&lt;=</a> <font color="Maroon">y</font>
 <b>by </b><i>, <a class="ref" href="yellow_0.html#T25">YELLOW_0:25</a></i>;<br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="15_2_3_9_2_2_10"><b>suppose </b></a><a NAME="E1:15_2_3_9_2_2_10"/><i><font color="Green">E195</font></i>: 
( <font color="Maroon">f</font> <a href="funct_2.html#K3">.</a> <font color="Maroon">x</font> <a href="hidden.html#R1">=</a> <font color="Maroon">b</font> &amp; <font color="Maroon">f</font> <a href="funct_2.html#K3">.</a> <font color="Maroon">y</font> <a href="hidden.html#R1">=</a> <font color="Maroon">e</font> )
 ;<br/><div class="add"><a NAME="E2:15_2_3_9_2_2_10"/>
( <font color="Maroon">f</font> <a href="funct_2.html#K3">.</a> <font color="Maroon">j</font> <a href="hidden.html#R1">=</a> <font color="Maroon">b</font> &amp; <font color="Maroon">f</font> <a href="funct_2.html#K3">.</a> <font color="Maroon">t</font> <a href="hidden.html#R1">=</a> <font color="Maroon">e</font> )
 <b>by </b><i><a class="ref" href="yellow11.html#T1" target="_self">Th1</a></i>;<br/><a NAME="E3:15_2_3_9_2_2_10"/><b>then </b>
( <font color="Maroon">j</font> <a href="hidden.html#R1">=</a> <font color="Maroon">x</font> &amp; <font color="Maroon">t</font> <a href="hidden.html#R1">=</a> <font color="Maroon">y</font> )
 <b>by </b><i><a class="ref" href="yellow11.html#T2" target="_self">Th2</a>, , <a class="ref" href="waybel_1.html#D1">WAYBEL_1:def 1</a></i>;<br/><a NAME="E4:15_2_3_9_2_2_10"/><b>then </b>
<font color="Maroon">x</font> <a href="tarski.html#R1">c=</a> <font color="Maroon">y</font>
 <b>by </b><i><a class="ref" href="card_1.html#T56">CARD_1:56</a></i>;<br/><b>hence </b><a NAME="E5:15_2_3_9_2_2_10"/>
<font color="Maroon">x</font> <a href="orders_2.html#R3">&lt;=</a> <font color="Maroon">y</font>
 <b>by </b><i><a class="ref" href="yellow_1.html#T3">YELLOW_1:3</a></i>;<br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="15_2_3_9_2_2_11"><b>suppose </b></a><a NAME="E1:15_2_3_9_2_2_11"/>
( <font color="Maroon">f</font> <a href="funct_2.html#K3">.</a> <font color="Maroon">x</font> <a href="hidden.html#R1">=</a> <font color="Maroon">c</font> &amp; <font color="Maroon">f</font> <a href="funct_2.html#K3">.</a> <font color="Maroon">y</font> <a href="hidden.html#R1">=</a> <font color="Maroon">a</font> )
 ;<br/><div class="add"><a NAME="E2:15_2_3_9_2_2_11"/><b>then </b>
<font color="Maroon">c</font> <a href="orders_2.html#R3">&lt;=</a> <font color="Maroon">a</font>
 <b>by </b><i><a class="txt" href="yellow11.html#E5"><i><font color="Green">Lemma26</font></i></a>, <a class="ref" href="yellow_0.html#T60">YELLOW_0:60</a></i>;<br/><b>hence </b><a NAME="E3:15_2_3_9_2_2_11"/>
<font color="Maroon">x</font> <a href="orders_2.html#R3">&lt;=</a> <font color="Maroon">y</font>
 <b>by </b><i>, <a class="ref" href="yellow_0.html#T25">YELLOW_0:25</a></i>;<br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="15_2_3_9_2_2_12"><b>suppose </b></a><a NAME="E1:15_2_3_9_2_2_12"/>
( <font color="Maroon">f</font> <a href="funct_2.html#K3">.</a> <font color="Maroon">x</font> <a href="hidden.html#R1">=</a> <font color="Maroon">c</font> &amp; <font color="Maroon">f</font> <a href="funct_2.html#K3">.</a> <font color="Maroon">y</font> <a href="hidden.html#R1">=</a> <font color="Maroon">b</font> )
 ;<br/><div class="add"><a NAME="E2:15_2_3_9_2_2_12"/><b>then </b>
<font color="Maroon">c</font> <a href="orders_2.html#R3">&lt;=</a> <font color="Maroon">b</font>
 <b>by </b><i><a class="txt" href="yellow11.html#E5"><i><font color="Green">Lemma26</font></i></a>, <a class="ref" href="yellow_0.html#T60">YELLOW_0:60</a></i>;<br/><b>hence </b><a NAME="E3:15_2_3_9_2_2_12"/>
<font color="Maroon">x</font> <a href="orders_2.html#R3">&lt;=</a> <font color="Maroon">y</font>
 <b>by </b><i>, <a class="ref" href="yellow_0.html#T25">YELLOW_0:25</a></i>;<br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="15_2_3_9_2_2_13"><b>suppose </b></a><a NAME="E1:15_2_3_9_2_2_13"/>
( <font color="Maroon">f</font> <a href="funct_2.html#K3">.</a> <font color="Maroon">x</font> <a href="hidden.html#R1">=</a> <font color="Maroon">c</font> &amp; <font color="Maroon">f</font> <a href="funct_2.html#K3">.</a> <font color="Maroon">y</font> <a href="hidden.html#R1">=</a> <font color="Maroon">c</font> )
 ;<br/><div class="add"><b>hence </b><a NAME="E2:15_2_3_9_2_2_13"/>
<font color="Maroon">x</font> <a href="orders_2.html#R3">&lt;=</a> <font color="Maroon">y</font>
 <b>by </b><i><a class="ref" href="yellow11.html#T2" target="_self">Th2</a>, <a class="ref" href="waybel_1.html#D1">WAYBEL_1:def 1</a></i>;<br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="15_2_3_9_2_2_14"><b>suppose </b></a><a NAME="E1:15_2_3_9_2_2_14"/>
( <font color="Maroon">f</font> <a href="funct_2.html#K3">.</a> <font color="Maroon">x</font> <a href="hidden.html#R1">=</a> <font color="Maroon">c</font> &amp; <font color="Maroon">f</font> <a href="funct_2.html#K3">.</a> <font color="Maroon">y</font> <a href="hidden.html#R1">=</a> <font color="Maroon">d</font> )
 ;<br/><div class="add"><a NAME="E2:15_2_3_9_2_2_14"/><b>then </b>
<font color="Maroon">c</font> <a href="orders_2.html#R3">&lt;=</a> <font color="Maroon">d</font>
 <b>by </b><i><a class="txt" href="yellow11.html#E5"><i><font color="Green">Lemma26</font></i></a>, <a class="ref" href="yellow_0.html#T60">YELLOW_0:60</a></i>;<br/><b>hence </b><a NAME="E3:15_2_3_9_2_2_14"/>
<font color="Maroon">x</font> <a href="orders_2.html#R3">&lt;=</a> <font color="Maroon">y</font>
 <b>by </b><i>, <a class="ref" href="yellow_0.html#T25">YELLOW_0:25</a></i>;<br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="15_2_3_9_2_2_15"><b>suppose </b></a><a NAME="E1:15_2_3_9_2_2_15"/><i><font color="Green">E196</font></i>: 
( <font color="Maroon">f</font> <a href="funct_2.html#K3">.</a> <font color="Maroon">x</font> <a href="hidden.html#R1">=</a> <font color="Maroon">c</font> &amp; <font color="Maroon">f</font> <a href="funct_2.html#K3">.</a> <font color="Maroon">y</font> <a href="hidden.html#R1">=</a> <font color="Maroon">e</font> )
 ;<br/><div class="add"><a NAME="E2:15_2_3_9_2_2_15"/>
( <font color="Maroon">f</font> <a href="funct_2.html#K3">.</a> <font color="Maroon">dj</font> <a href="hidden.html#R1">=</a> <font color="Maroon">c</font> &amp; <font color="Maroon">f</font> <a href="funct_2.html#K3">.</a> <font color="Maroon">t</font> <a href="hidden.html#R1">=</a> <font color="Maroon">e</font> )
 <b>by </b><i><a class="ref" href="yellow11.html#T1" target="_self">Th1</a></i>;<br/><a NAME="E3:15_2_3_9_2_2_15"/><b>then </b>
( <font color="Maroon">dj</font> <a href="hidden.html#R1">=</a> <font color="Maroon">x</font> &amp; <font color="Maroon">t</font> <a href="hidden.html#R1">=</a> <font color="Maroon">y</font> )
 <b>by </b><i><a class="ref" href="yellow11.html#T2" target="_self">Th2</a>, , <a class="ref" href="waybel_1.html#D1">WAYBEL_1:def 1</a></i>;<br/><b>hence </b><a NAME="E4:15_2_3_9_2_2_15"/>
<font color="Maroon">x</font> <a href="orders_2.html#R3">&lt;=</a> <font color="Maroon">y</font>
 <b>by </b><i>, <a class="ref" href="yellow_1.html#T3">YELLOW_1:3</a></i>;<br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="15_2_3_9_2_2_16"><b>suppose </b></a><a NAME="E1:15_2_3_9_2_2_16"/>
( <font color="Maroon">f</font> <a href="funct_2.html#K3">.</a> <font color="Maroon">x</font> <a href="hidden.html#R1">=</a> <font color="Maroon">d</font> &amp; <font color="Maroon">f</font> <a href="funct_2.html#K3">.</a> <font color="Maroon">y</font> <a href="hidden.html#R1">=</a> <font color="Maroon">a</font> )
 ;<br/><div class="add"><a NAME="E2:15_2_3_9_2_2_16"/><b>then </b>
( <font color="Maroon">d</font> <a href="orders_2.html#R3">&lt;=</a> <font color="Maroon">a</font> &amp; <font color="Maroon">a</font> <a href="orders_2.html#R3">&lt;=</a> <font color="Maroon">b</font> )
 <b>by </b><i>, <a class="txt" href="yellow11.html#E5"><i><font color="Green">Lemma26</font></i></a>, <a class="ref" href="yellow_0.html#T25">YELLOW_0:25</a>, <a class="ref" href="yellow_0.html#T60">YELLOW_0:60</a></i>;<br/><b>hence </b><a NAME="E3:15_2_3_9_2_2_16"/>
<font color="Maroon">x</font> <a href="orders_2.html#R3">&lt;=</a> <font color="Maroon">y</font>
 <b>by </b><i>, <a class="ref" href="yellow_0.html#T25">YELLOW_0:25</a></i>;<br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="15_2_3_9_2_2_17"><b>suppose </b></a><a NAME="E1:15_2_3_9_2_2_17"/>
( <font color="Maroon">f</font> <a href="funct_2.html#K3">.</a> <font color="Maroon">x</font> <a href="hidden.html#R1">=</a> <font color="Maroon">d</font> &amp; <font color="Maroon">f</font> <a href="funct_2.html#K3">.</a> <font color="Maroon">y</font> <a href="hidden.html#R1">=</a> <font color="Maroon">b</font> )
 ;<br/><div class="add"><a NAME="E2:15_2_3_9_2_2_17"/><b>then </b>
<font color="Maroon">d</font> <a href="orders_2.html#R3">&lt;=</a> <font color="Maroon">b</font>
 <b>by </b><i><a class="txt" href="yellow11.html#E5"><i><font color="Green">Lemma26</font></i></a>, <a class="ref" href="yellow_0.html#T60">YELLOW_0:60</a></i>;<br/><b>hence </b><a NAME="E3:15_2_3_9_2_2_17"/>
<font color="Maroon">x</font> <a href="orders_2.html#R3">&lt;=</a> <font color="Maroon">y</font>
 <b>by </b><i>, <a class="ref" href="yellow_0.html#T25">YELLOW_0:25</a></i>;<br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="15_2_3_9_2_2_18"><b>suppose </b></a><a NAME="E1:15_2_3_9_2_2_18"/>
( <font color="Maroon">f</font> <a href="funct_2.html#K3">.</a> <font color="Maroon">x</font> <a href="hidden.html#R1">=</a> <font color="Maroon">d</font> &amp; <font color="Maroon">f</font> <a href="funct_2.html#K3">.</a> <font color="Maroon">y</font> <a href="hidden.html#R1">=</a> <font color="Maroon">c</font> )
 ;<br/><div class="add"><a NAME="E2:15_2_3_9_2_2_18"/><b>then </b>
<font color="Maroon">d</font> <a href="orders_2.html#R3">&lt;=</a> <font color="Maroon">c</font>
 <b>by </b><i><a class="txt" href="yellow11.html#E5"><i><font color="Green">Lemma26</font></i></a>, <a class="ref" href="yellow_0.html#T60">YELLOW_0:60</a></i>;<br/><b>hence </b><a NAME="E3:15_2_3_9_2_2_18"/>
<font color="Maroon">x</font> <a href="orders_2.html#R3">&lt;=</a> <font color="Maroon">y</font>
 <b>by </b><i>, <a class="ref" href="yellow_0.html#T25">YELLOW_0:25</a></i>;<br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="15_2_3_9_2_2_19"><b>suppose </b></a><a NAME="E1:15_2_3_9_2_2_19"/>
( <font color="Maroon">f</font> <a href="funct_2.html#K3">.</a> <font color="Maroon">x</font> <a href="hidden.html#R1">=</a> <font color="Maroon">d</font> &amp; <font color="Maroon">f</font> <a href="funct_2.html#K3">.</a> <font color="Maroon">y</font> <a href="hidden.html#R1">=</a> <font color="Maroon">d</font> )
 ;<br/><div class="add"><b>hence </b><a NAME="E2:15_2_3_9_2_2_19"/>
<font color="Maroon">x</font> <a href="orders_2.html#R3">&lt;=</a> <font color="Maroon">y</font>
 <b>by </b><i><a class="ref" href="yellow11.html#T2" target="_self">Th2</a>, <a class="ref" href="waybel_1.html#D1">WAYBEL_1:def 1</a></i>;<br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="15_2_3_9_2_2_20"><b>suppose </b></a><a NAME="E1:15_2_3_9_2_2_20"/><i><font color="Green">E197</font></i>: 
( <font color="Maroon">f</font> <a href="funct_2.html#K3">.</a> <font color="Maroon">x</font> <a href="hidden.html#R1">=</a> <font color="Maroon">d</font> &amp; <font color="Maroon">f</font> <a href="funct_2.html#K3">.</a> <font color="Maroon">y</font> <a href="hidden.html#R1">=</a> <font color="Maroon">e</font> )
 ;<br/><div class="add"><a NAME="E2:15_2_3_9_2_2_20"/>
( <font color="Maroon">f</font> <a href="funct_2.html#K3">.</a> <font color="Maroon">td</font> <a href="hidden.html#R1">=</a> <font color="Maroon">d</font> &amp; <font color="Maroon">f</font> <a href="funct_2.html#K3">.</a> <font color="Maroon">t</font> <a href="hidden.html#R1">=</a> <font color="Maroon">e</font> )
 <b>by </b><i><a class="ref" href="yellow11.html#T1" target="_self">Th1</a></i>;<br/><a NAME="E3:15_2_3_9_2_2_20"/><b>then </b>
( <font color="Maroon">td</font> <a href="hidden.html#R1">=</a> <font color="Maroon">x</font> &amp; <font color="Maroon">t</font> <a href="hidden.html#R1">=</a> <font color="Maroon">y</font> )
 <b>by </b><i><a class="ref" href="yellow11.html#T2" target="_self">Th2</a>, , <a class="ref" href="waybel_1.html#D1">WAYBEL_1:def 1</a></i>;<br/><b>hence </b><a NAME="E4:15_2_3_9_2_2_20"/>
<font color="Maroon">x</font> <a href="orders_2.html#R3">&lt;=</a> <font color="Maroon">y</font>
 <b>by </b><i><a class="ref" href="yellow_1.html#T3">YELLOW_1:3</a></i>;<br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="15_2_3_9_2_2_21"><b>suppose </b></a><a NAME="E1:15_2_3_9_2_2_21"/>
( <font color="Maroon">f</font> <a href="funct_2.html#K3">.</a> <font color="Maroon">x</font> <a href="hidden.html#R1">=</a> <font color="Maroon">e</font> &amp; <font color="Maroon">f</font> <a href="funct_2.html#K3">.</a> <font color="Maroon">y</font> <a href="hidden.html#R1">=</a> <font color="Maroon">a</font> )
 ;<br/><div class="add"><a NAME="E2:15_2_3_9_2_2_21"/><b>then </b>
( <font color="Maroon">e</font> <a href="orders_2.html#R3">&lt;=</a> <font color="Maroon">a</font> &amp; <font color="Maroon">a</font> <a href="orders_2.html#R3">&lt;=</a> <font color="Maroon">b</font> )
 <b>by </b><i>, <a class="txt" href="yellow11.html#E5"><i><font color="Green">Lemma26</font></i></a>, <a class="ref" href="yellow_0.html#T25">YELLOW_0:25</a>, <a class="ref" href="yellow_0.html#T60">YELLOW_0:60</a></i>;<br/><a NAME="E3:15_2_3_9_2_2_21"/><b>then </b>
<font color="Maroon">e</font> <a href="orders_2.html#R3">&lt;=</a> <font color="Maroon">b</font>
 <b>by </b><i><a class="ref" href="orders_2.html#T26">ORDERS_2:26</a></i>;<br/><b>hence </b><a NAME="E4:15_2_3_9_2_2_21"/>
<font color="Maroon">x</font> <a href="orders_2.html#R3">&lt;=</a> <font color="Maroon">y</font>
 <b>by </b><i>, <a class="ref" href="yellow_0.html#T25">YELLOW_0:25</a></i>;<br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="15_2_3_9_2_2_22"><b>suppose </b></a><a NAME="E1:15_2_3_9_2_2_22"/>
( <font color="Maroon">f</font> <a href="funct_2.html#K3">.</a> <font color="Maroon">x</font> <a href="hidden.html#R1">=</a> <font color="Maroon">e</font> &amp; <font color="Maroon">f</font> <a href="funct_2.html#K3">.</a> <font color="Maroon">y</font> <a href="hidden.html#R1">=</a> <font color="Maroon">b</font> )
 ;<br/><div class="add"><a NAME="E2:15_2_3_9_2_2_22"/><b>then </b>
<font color="Maroon">e</font> <a href="orders_2.html#R3">&lt;=</a> <font color="Maroon">b</font>
 <b>by </b><i><a class="txt" href="yellow11.html#E5"><i><font color="Green">Lemma26</font></i></a>, <a class="ref" href="yellow_0.html#T60">YELLOW_0:60</a></i>;<br/><b>hence </b><a NAME="E3:15_2_3_9_2_2_22"/>
<font color="Maroon">x</font> <a href="orders_2.html#R3">&lt;=</a> <font color="Maroon">y</font>
 <b>by </b><i>, <a class="ref" href="yellow_0.html#T25">YELLOW_0:25</a></i>;<br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="15_2_3_9_2_2_23"><b>suppose </b></a><a NAME="E1:15_2_3_9_2_2_23"/>
( <font color="Maroon">f</font> <a href="funct_2.html#K3">.</a> <font color="Maroon">x</font> <a href="hidden.html#R1">=</a> <font color="Maroon">e</font> &amp; <font color="Maroon">f</font> <a href="funct_2.html#K3">.</a> <font color="Maroon">y</font> <a href="hidden.html#R1">=</a> <font color="Maroon">c</font> )
 ;<br/><div class="add"><a NAME="E2:15_2_3_9_2_2_23"/><b>then </b>
<font color="Maroon">e</font> <a href="orders_2.html#R3">&lt;=</a> <font color="Maroon">c</font>
 <b>by </b><i><a class="txt" href="yellow11.html#E5"><i><font color="Green">Lemma26</font></i></a>, <a class="ref" href="yellow_0.html#T60">YELLOW_0:60</a></i>;<br/><b>hence </b><a NAME="E3:15_2_3_9_2_2_23"/>
<font color="Maroon">x</font> <a href="orders_2.html#R3">&lt;=</a> <font color="Maroon">y</font>
 <b>by </b><i>, <a class="ref" href="yellow_0.html#T25">YELLOW_0:25</a></i>;<br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="15_2_3_9_2_2_24"><b>suppose </b></a><a NAME="E1:15_2_3_9_2_2_24"/>
( <font color="Maroon">f</font> <a href="funct_2.html#K3">.</a> <font color="Maroon">x</font> <a href="hidden.html#R1">=</a> <font color="Maroon">e</font> &amp; <font color="Maroon">f</font> <a href="funct_2.html#K3">.</a> <font color="Maroon">y</font> <a href="hidden.html#R1">=</a> <font color="Maroon">d</font> )
 ;<br/><div class="add"><a NAME="E2:15_2_3_9_2_2_24"/><b>then </b>
<font color="Maroon">e</font> <a href="orders_2.html#R3">&lt;=</a> <font color="Maroon">d</font>
 <b>by </b><i><a class="txt" href="yellow11.html#E5"><i><font color="Green">Lemma26</font></i></a>, <a class="ref" href="yellow_0.html#T60">YELLOW_0:60</a></i>;<br/><b>hence </b><a NAME="E3:15_2_3_9_2_2_24"/>
<font color="Maroon">x</font> <a href="orders_2.html#R3">&lt;=</a> <font color="Maroon">y</font>
 <b>by </b><i>, <a class="ref" href="yellow_0.html#T25">YELLOW_0:25</a></i>;<br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="15_2_3_9_2_2_25"><b>suppose </b></a><a NAME="E1:15_2_3_9_2_2_25"/>
( <font color="Maroon">f</font> <a href="funct_2.html#K3">.</a> <font color="Maroon">x</font> <a href="hidden.html#R1">=</a> <font color="Maroon">e</font> &amp; <font color="Maroon">f</font> <a href="funct_2.html#K3">.</a> <font color="Maroon">y</font> <a href="hidden.html#R1">=</a> <font color="Maroon">e</font> )
 ;<br/><div class="add"><b>hence </b><a NAME="E2:15_2_3_9_2_2_25"/>
<font color="Maroon">x</font> <a href="orders_2.html#R3">&lt;=</a> <font color="Maroon">y</font>
 <b>by </b><i><a class="ref" href="yellow11.html#T2" target="_self">Th2</a>, <a class="ref" href="waybel_1.html#D1">WAYBEL_1:def 1</a></i>;<br/></div><b>end;</b></div></div><b>end;</b></div>

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


</div><b>end;</b></div>
<b>hence </b><a NAME="E19:15_2_3"/>
<font color="Maroon">f</font> is <a href="waybel_0.html#V23">isomorphic</a>
 <b>by </b><i>, <a class="ref" href="yellow11.html#T2" target="_self">Th2</a>, <a class="ref" href="yellow11.html#T4" target="_self">Th4</a>, <a class="ref" href="waybel_0.html#T66">WAYBEL_0:66</a></i>;<br/>


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


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


</div>
