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

<b>let </b><font color="Maroon" title="c1">L</font> be   <a href="waybel_0.html#NM8" title="WAYBEL_0:NM.8">LATTICE</a>;<br/>

<b>set </b><font color="Maroon" title="c2">cn</font> = the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <a href="yellow11.html#K2" title="YELLOW11:func.2">M_3</a> ;<br/>
<a NAME="E1:15"/><i><font color="Green" title="E12">A1</font></i>: 
the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <a href="yellow11.html#K2" title="YELLOW11:func.2">M_3</a>  <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1"><a href="enumset1.html#K3" title="ENUMSET1:func.3">{</a><span class="default">0,1,<span class="p2">(<span class="default">2 <a href="subset_1.html#K6" title="SUBSET_1:func.6">\</a> 1</span>)</span>,<span class="p2">(<span class="default">3 <a href="subset_1.html#K6" title="SUBSET_1:func.6">\</a> 2</span>)</span>,3</span><a href="enumset1.html#K3" title="ENUMSET1:func.3">}</a></span>
 
<b>by </b><i><a class="ref" href="yellow_1.html#T1" title="YELLOW_1:th.1">YELLOW_1:1</a></i>;<br/>
<b>thus </b><a NAME="E2:15"/>
(  ex <font color="Olive" title="b1">K</font> being <a href="yellow_0.html#V4" title="YELLOW_0:attr.4">full</a> <a href="lattice5.html#NM2" title="LATTICE5:NM.2">Sublattice</a> of <font color="Maroon" title="c1">L</font> st  <a href="yellow11.html#K2" title="YELLOW11:func.2">M_3</a> ,<font color="Olive" title="b1">K</font> <a href="waybel_1.html#R5" title="WAYBEL_1:pred.5">are_isomorphic</a>  implies  ex <font color="Olive" title="b1">a</font>, <font color="Olive" title="b2">b</font>, <font color="Olive" title="b3">c</font>, <font color="Olive" title="b4">d</font>, <font color="Olive" title="b5">e</font> being  <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Maroon" title="c1">L</font> st <br/>( <font color="Olive" title="b1">a</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Olive" title="b2">b</font> &amp; <font color="Olive" title="b1">a</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Olive" title="b3">c</font> &amp; <font color="Olive" title="b1">a</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Olive" title="b4">d</font> &amp; <font color="Olive" title="b1">a</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Olive" title="b5">e</font> &amp; <font color="Olive" title="b2">b</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Olive" title="b3">c</font> &amp; <font color="Olive" title="b2">b</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Olive" title="b4">d</font> &amp; <font color="Olive" title="b2">b</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Olive" title="b5">e</font> &amp; <font color="Olive" title="b3">c</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Olive" title="b4">d</font> &amp; <font color="Olive" title="b3">c</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Olive" title="b5">e</font> &amp; <font color="Olive" title="b4">d</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Olive" title="b5">e</font> &amp; <font color="Olive" title="b1">a</font> <a href="lattice3.html#K12" title="LATTICE3:func.12">"/\"</a> <font color="Olive" title="b2">b</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b1">a</font> &amp; <font color="Olive" title="b1">a</font> <a href="lattice3.html#K12" title="LATTICE3:func.12">"/\"</a> <font color="Olive" title="b3">c</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b1">a</font> &amp; <font color="Olive" title="b1">a</font> <a href="lattice3.html#K12" title="LATTICE3:func.12">"/\"</a> <font color="Olive" title="b4">d</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b1">a</font> &amp; <font color="Olive" title="b2">b</font> <a href="lattice3.html#K12" title="LATTICE3:func.12">"/\"</a> <font color="Olive" title="b5">e</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b2">b</font> &amp; <font color="Olive" title="b3">c</font> <a href="lattice3.html#K12" title="LATTICE3:func.12">"/\"</a> <font color="Olive" title="b5">e</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b3">c</font> &amp; <font color="Olive" title="b4">d</font> <a href="lattice3.html#K12" title="LATTICE3:func.12">"/\"</a> <font color="Olive" title="b5">e</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b4">d</font> &amp; <font color="Olive" title="b2">b</font> <a href="lattice3.html#K12" title="LATTICE3:func.12">"/\"</a> <font color="Olive" title="b3">c</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b1">a</font> &amp; <font color="Olive" title="b2">b</font> <a href="lattice3.html#K12" title="LATTICE3:func.12">"/\"</a> <font color="Olive" title="b4">d</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b1">a</font> &amp; <font color="Olive" title="b3">c</font> <a href="lattice3.html#K12" title="LATTICE3:func.12">"/\"</a> <font color="Olive" title="b4">d</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b1">a</font> &amp; <font color="Olive" title="b2">b</font> <a href="lattice3.html#K13" title="LATTICE3:func.13">"\/"</a> <font color="Olive" title="b3">c</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b5">e</font> &amp; <font color="Olive" title="b2">b</font> <a href="lattice3.html#K13" title="LATTICE3:func.13">"\/"</a> <font color="Olive" title="b4">d</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b5">e</font> &amp; <font color="Olive" title="b3">c</font> <a href="lattice3.html#K13" title="LATTICE3:func.13">"\/"</a> <font color="Olive" title="b4">d</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b5">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" title="c3">K</font> being  <a href="yellow_0.html#V4" title="YELLOW_0:attr.4">full</a> <a href="lattice5.html#NM2" title="LATTICE5:NM.2">Sublattice</a> of <font color="Maroon" title="c1">L</font><b> such that </b><a NAME="E2:15_1"/><i><font color="Green" title="E13">A2</font></i>: 
 <a href="yellow11.html#K2" title="YELLOW11:func.2">M_3</a> ,<font color="Maroon" title="c3">K</font> <a href="waybel_1.html#R5" title="WAYBEL_1:pred.5">are_isomorphic</a> 
 ;<br/>

<b>consider </b><font color="Maroon" title="c4">f</font> being   <a href="struct_0.html#NM6" title="STRUCT_0:NM.6">Function</a> of <a href="yellow11.html#K2" title="YELLOW11:func.2">M_3</a> ,<font color="Maroon" title="c3">K</font><b> such that </b><br/><a NAME="E4:15_1"/><i><font color="Green" title="E14">A3</font></i>: 
<font color="Maroon" title="c4">f</font> is <a href="waybel_0.html#V23" title="WAYBEL_0:attr.23">isomorphic</a>
 <b>by </b><i><a class="txt" href="yellow11.html#E2:15_1"><i><font color="Green" title="E13">A2</font></i></a>, <a class="ref" href="waybel_1.html#D8" title="WAYBEL_1:def.8">WAYBEL_1:def 8</a></i>;<br/>
<a NAME="E5:15_1"/><i><font color="Green" title="E15">A4</font></i>: 
not <font color="Maroon" title="c3">K</font> is <a href="struct_0.html#V2" title="STRUCT_0:attr.2">empty</a>
 
<b>by </b><i><a class="txt" href="yellow11.html#E4:15_1"><i><font color="Green" title="E14">A3</font></i></a>, <a class="ref" href="waybel_0.html#D38" title="WAYBEL_0:def.38">WAYBEL_0:def 38</a></i>;<br/>
<b>reconsider </b><font color="Maroon" title="c5">K</font> = <font color="Maroon" title="c3">K</font> as  non <a href="struct_0.html#V2" title="STRUCT_0:attr.2">empty</a>  <a href="yellow_0.html#M1" title="YELLOW_0:mode.1">SubRelStr</a> of <font color="Maroon" title="c1">L</font> <b>by </b><i><a class="txt" href="yellow11.html#E4:15_1"><i><font color="Green" title="E14">A3</font></i></a>, <a class="ref" href="waybel_0.html#D38" title="WAYBEL_0:def.38">WAYBEL_0:def 38</a></i>;<br/>
<a NAME="E7:15_1"/><i><font color="Green" title="E16">A5</font></i>: 
( <font color="Maroon" title="c4">f</font> is <a href="funct_1.html#V2" title="FUNCT_1:attr.2">one-to-one</a> &amp; <font color="Maroon" title="c4">f</font> is <a href="orders_3.html#V5" title="ORDERS_3:attr.5">monotone</a> )
 
<b>by </b><i><a class="txt" href="yellow11.html#E4:15_1"><i><font color="Green" title="E14">A3</font></i></a>, <a class="txt" href="yellow11.html#E5:15_1"><i><font color="Green" title="E15">A4</font></i></a>, <a class="ref" href="waybel_0.html#D38" title="WAYBEL_0:def.38">WAYBEL_0:def 38</a></i>;<br/>
<b>reconsider </b><font color="Maroon" title="c6">z</font> = 0 as   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <a href="yellow11.html#K2" title="YELLOW11:func.2">M_3</a>  <b>by </b><i><a class="txt" href="yellow11.html#E1:15"><i><font color="Green" title="E12">A1</font></i></a>, <a class="ref" href="enumset1.html#D3" title="ENUMSET1:def.3">ENUMSET1:def 3</a></i>;<br/>
<b>reconsider </b><font color="Maroon" title="c7">j</font> = 1 as   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <a href="yellow11.html#K2" title="YELLOW11:func.2">M_3</a>  <b>by </b><i><a class="txt" href="yellow11.html#E1:15"><i><font color="Green" title="E12">A1</font></i></a>, <a class="ref" href="enumset1.html#D3" title="ENUMSET1:def.3">ENUMSET1:def 3</a></i>;<br/>
<b>reconsider </b><font color="Maroon" title="c8">dj</font> = 2 <a href="subset_1.html#K6" title="SUBSET_1:func.6">\</a> 1 as   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <a href="yellow11.html#K2" title="YELLOW11:func.2">M_3</a>  <b>by </b><i><a class="txt" href="yellow11.html#E1:15"><i><font color="Green" title="E12">A1</font></i></a>, <a class="ref" href="enumset1.html#D3" title="ENUMSET1:def.3">ENUMSET1:def 3</a></i>;<br/>
<b>reconsider </b><font color="Maroon" title="c9">td</font> = 3 <a href="subset_1.html#K6" title="SUBSET_1:func.6">\</a> 2 as   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <a href="yellow11.html#K2" title="YELLOW11:func.2">M_3</a>  <b>by </b><i><a class="txt" href="yellow11.html#E1:15"><i><font color="Green" title="E12">A1</font></i></a>, <a class="ref" href="enumset1.html#D3" title="ENUMSET1:def.3">ENUMSET1:def 3</a></i>;<br/>
<b>reconsider </b><font color="Maroon" title="c10">t</font> = 3 as   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <a href="yellow11.html#K2" title="YELLOW11:func.2">M_3</a>  <b>by </b><i><a class="txt" href="yellow11.html#E1:15"><i><font color="Green" title="E12">A1</font></i></a>, <a class="ref" href="enumset1.html#D3" title="ENUMSET1:def.3">ENUMSET1:def 3</a></i>;<br/>
<b>reconsider </b><font color="Maroon" title="c11">cl</font> = the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c1">L</font> as  non <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a>  <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a>  ;<br/>
<b>reconsider </b><font color="Maroon" title="c12">ck</font> = the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c5">K</font> as  non <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a>  <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a>  ;<br/>
<a NAME="E15:15_1"/><i><font color="Green" title="E17">A6</font></i>: 
<font color="Maroon" title="c12">ck</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="relset_1.html#K5" title="RELSET_1:func.5">rng</a> <font color="Maroon" title="c4">f</font>
 
<b>by </b><i><a class="txt" href="yellow11.html#E4:15_1"><i><font color="Green" title="E14">A3</font></i></a>, <a class="ref" href="waybel_0.html#T66" title="WAYBEL_0:th.66">WAYBEL_0:66</a></i>;<br/>
<b>reconsider </b><font color="Maroon" title="c13">g</font> = <font color="Maroon" title="c4">f</font> as   <a href="funct_2.html#NM1" title="FUNCT_2:NM.1">Function</a> of the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <a href="yellow11.html#K2" title="YELLOW11:func.2">M_3</a> ,<font color="Maroon" title="c12">ck</font> ;<br/>
<b>reconsider </b><font color="Maroon" title="c14">a</font> = <font color="Maroon" title="c13">g</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c6">z</font>, <font color="Maroon" title="c15">b</font> = <font color="Maroon" title="c13">g</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c7">j</font>, <font color="Maroon" title="c16">c</font> = <font color="Maroon" title="c13">g</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c8">dj</font>, <font color="Maroon" title="c17">d</font> = <font color="Maroon" title="c13">g</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c9">td</font>, <font color="Maroon" title="c18">e</font> = <font color="Maroon" title="c13">g</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c10">t</font> as   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Maroon" title="c5">K</font> ;<br/>
<b>reconsider </b><font color="Maroon" title="c19">ck</font> = <font color="Maroon" title="c12">ck</font> as  non <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a> <a href="subset_1.html#NM2" title="SUBSET_1:NM.2">Subset</a> of <font color="Maroon" title="c11">cl</font> <b>by </b><i><a class="ref" href="yellow_0.html#D13" title="YELLOW_0:def.13">YELLOW_0:def 13</a></i>;<br/>
<a NAME="E19:15_1"/>
( <font color="Maroon" title="c14">a</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c19">ck</font> &amp; <font color="Maroon" title="c15">b</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c19">ck</font> &amp; <font color="Maroon" title="c16">c</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c19">ck</font> &amp; <font color="Maroon" title="c17">d</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c19">ck</font> &amp; <font color="Maroon" title="c18">e</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c19">ck</font> )
 
;<br/>
<b>then reconsider </b><font color="Maroon" title="c20">A</font> = <font color="Maroon" title="c14">a</font>, <font color="Maroon" title="c21">B</font> = <font color="Maroon" title="c15">b</font>, <font color="Maroon" title="c22">C</font> = <font color="Maroon" title="c16">c</font>, <font color="Maroon" title="c23">D</font> = <font color="Maroon" title="c17">d</font>, <font color="Maroon" title="c24">E</font> = <font color="Maroon" title="c18">e</font> as   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Maroon" title="c1">L</font> ;<br/>
<b>take </b>
<font color="Maroon" title="c20">A</font>
;<br/>

<b>take </b>
<font color="Maroon" title="c21">B</font>
;<br/>

<b>take </b>
<font color="Maroon" title="c22">C</font>
;<br/>

<b>take </b>
<font color="Maroon" title="c23">D</font>
;<br/>

<b>take </b>
<font color="Maroon" title="c24">E</font>
;<br/>

<b>thus </b><a NAME="E21:15_1"/>
<font color="Maroon" title="c20">A</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c21">B</font>
 <b>by </b><i><a class="txt" href="yellow11.html#E7:15_1"><i><font color="Green" title="E16">A5</font></i></a>, <a class="ref" href="waybel_1.html#D1" title="WAYBEL_1:def.1">WAYBEL_1:def 1</a></i>;<br/>

<b>thus </b><a NAME="E22:15_1"/>
<font color="Maroon" title="c20">A</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c22">C</font>
 <b>by </b><i><a class="txt" href="yellow11.html#E7:15_1"><i><font color="Green" title="E16">A5</font></i></a>, <a class="ref" href="yellow11.html#T2" target="_self" title="YELLOW11:th.2">Th2</a>, <a class="ref" href="waybel_1.html#D1" title="WAYBEL_1:def.1">WAYBEL_1:def 1</a></i>;<br/>

<b>thus </b><a NAME="E23:15_1"/>
<font color="Maroon" title="c20">A</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c23">D</font>
 <b>by </b><i><a class="txt" href="yellow11.html#E7:15_1"><i><font color="Green" title="E16">A5</font></i></a>, <a class="ref" href="yellow11.html#T4" target="_self" title="YELLOW11:th.4">Th4</a>, <a class="ref" href="waybel_1.html#D1" title="WAYBEL_1:def.1">WAYBEL_1:def 1</a></i>;<br/>

<b>thus </b><a NAME="E24:15_1"/>
<font color="Maroon" title="c20">A</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c24">E</font>
 <b>by </b><i><a class="txt" href="yellow11.html#E7:15_1"><i><font color="Green" title="E16">A5</font></i></a>, <a class="ref" href="waybel_1.html#D1" title="WAYBEL_1:def.1">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" title="c4">f</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c7">j</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c4">f</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c8">dj</font>
 ;<br/><a NAME="E2:15_1_1"/><b>then </b>
<font color="Maroon" title="c7">j</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c8">dj</font>
 <b>by </b><i><a class="txt" href="yellow11.html#E5:15_1"><i><font color="Green" title="E15">A4</font></i></a>, <a class="txt" href="yellow11.html#E7:15_1"><i><font color="Green" title="E16">A5</font></i></a>, <a class="ref" href="waybel_1.html#D1" title="WAYBEL_1:def.1">WAYBEL_1:def 1</a></i>;<br/><a NAME="E3:15_1_1"/><b>then </b>
1 <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> 1
 <b>by </b><i><a class="ref" href="yellow11.html#T2" target="_self" title="YELLOW11:th.2">Th2</a>, <a class="ref" href="tarski.html#D1" title="TARSKI:def.1">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="E26:15_1"/>
<font color="Maroon" title="c21">B</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c22">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" title="c4">f</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c7">j</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c4">f</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c9">td</font>
 ;<br/><a NAME="E2:15_1_2"/><b>then </b><i><font color="Green" title="E18">A7</font></i>: 
<font color="Maroon" title="c7">j</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c9">td</font>
 <b>by </b><i><a class="txt" href="yellow11.html#E5:15_1"><i><font color="Green" title="E15">A4</font></i></a>, <a class="txt" href="yellow11.html#E7:15_1"><i><font color="Green" title="E16">A5</font></i></a>, <a class="ref" href="waybel_1.html#D1" title="WAYBEL_1:def.1">WAYBEL_1:def 1</a></i>;<br/><a NAME="E3:15_1_2"/>
( 0 <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c7">j</font> &amp; 0 <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> 2 )
 <b>by </b><i><a class="ref" href="card_5.html#T1" title="CARD_5:th.1">CARD_5:1</a>, <a class="ref" href="tarski.html#D1" title="TARSKI:def.1">TARSKI:def 1</a></i>;<br/><b>hence </b><a NAME="E4:15_1_2"/>
contradiction
 <b>by </b><i><a class="txt" href="yellow11.html#E2:15_1_2"><i><font color="Green" title="E18">A7</font></i></a>, <a class="ref" href="yellow11.html#T4" target="_self" title="YELLOW11:th.4">Th4</a>, <a class="ref" href="tarski.html#D1" title="TARSKI:def.1">TARSKI:def 1</a></i>;<br/></div><b>end;</b></div>
<b>hence </b><a NAME="E28:15_1"/>
<font color="Maroon" title="c21">B</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c23">D</font>
 ;<br/>

<b>thus </b><a NAME="E29:15_1"/>
<font color="Maroon" title="c21">B</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c24">E</font>
 <b>by </b><i><a class="txt" href="yellow11.html#E7:15_1"><i><font color="Green" title="E16">A5</font></i></a>, <a class="ref" href="waybel_1.html#D1" title="WAYBEL_1:def.1">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" title="c4">f</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c8">dj</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c4">f</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c9">td</font>
 ;<br/><a NAME="E2:15_1_3"/><b>then </b><i><font color="Green" title="E18">A8</font></i>: 
<font color="Maroon" title="c8">dj</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c9">td</font>
 <b>by </b><i><a class="txt" href="yellow11.html#E5:15_1"><i><font color="Green" title="E15">A4</font></i></a>, <a class="txt" href="yellow11.html#E7:15_1"><i><font color="Green" title="E16">A5</font></i></a>, <a class="ref" href="waybel_1.html#D1" title="WAYBEL_1:def.1">WAYBEL_1:def 1</a></i>;<br/><a NAME="E3:15_1_3"/>
( 1 <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c8">dj</font> &amp; 1 <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> 2 )
 <b>by </b><i><a class="ref" href="yellow11.html#T2" target="_self" title="YELLOW11:th.2">Th2</a>, <a class="ref" href="tarski.html#D1" title="TARSKI:def.1">TARSKI:def 1</a></i>;<br/><b>hence </b><a NAME="E4:15_1_3"/>
contradiction
 <b>by </b><i><a class="txt" href="yellow11.html#E2:15_1_3"><i><font color="Green" title="E18">A8</font></i></a>, <a class="ref" href="yellow11.html#T4" target="_self" title="YELLOW11:th.4">Th4</a>, <a class="ref" href="tarski.html#D1" title="TARSKI:def.1">TARSKI:def 1</a></i>;<br/></div><b>end;</b></div>
<b>hence </b><a NAME="E31:15_1"/>
<font color="Maroon" title="c22">C</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c23">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" title="c4">f</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c8">dj</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c4">f</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c10">t</font>
 ;<br/><a NAME="E2:15_1_4"/><b>then </b><i><font color="Green" title="E18">A9</font></i>: 
<font color="Maroon" title="c8">dj</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c10">t</font>
 <b>by </b><i><a class="txt" href="yellow11.html#E5:15_1"><i><font color="Green" title="E15">A4</font></i></a>, <a class="txt" href="yellow11.html#E7:15_1"><i><font color="Green" title="E16">A5</font></i></a>, <a class="ref" href="waybel_1.html#D1" title="WAYBEL_1:def.1">WAYBEL_1:def 1</a></i>;<br/><a NAME="E3:15_1_4"/>
( 0 <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c10">t</font> &amp; 0 <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> 1 )
 <b>by </b><i><a class="ref" href="yellow11.html#T1" target="_self" title="YELLOW11:th.1">Th1</a>, <a class="ref" href="enumset1.html#D1" title="ENUMSET1:def.1">ENUMSET1:def 1</a></i>;<br/><b>hence </b><a NAME="E4:15_1_4"/>
contradiction
 <b>by </b><i><a class="txt" href="yellow11.html#E2:15_1_4"><i><font color="Green" title="E18">A9</font></i></a>, <a class="ref" href="yellow11.html#T2" target="_self" title="YELLOW11:th.2">Th2</a>, <a class="ref" href="tarski.html#D1" title="TARSKI:def.1">TARSKI:def 1</a></i>;<br/></div><b>end;</b></div>
<b>hence </b><a NAME="E33:15_1"/>
<font color="Maroon" title="c22">C</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c24">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" title="c4">f</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c9">td</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c4">f</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c10">t</font>
 ;<br/><a NAME="E2:15_1_5"/><b>then </b><i><font color="Green" title="E18">A10</font></i>: 
<font color="Maroon" title="c9">td</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c10">t</font>
 <b>by </b><i><a class="txt" href="yellow11.html#E5:15_1"><i><font color="Green" title="E15">A4</font></i></a>, <a class="txt" href="yellow11.html#E7:15_1"><i><font color="Green" title="E16">A5</font></i></a>, <a class="ref" href="waybel_1.html#D1" title="WAYBEL_1:def.1">WAYBEL_1:def 1</a></i>;<br/><a NAME="E3:15_1_5"/>
( 0 <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c10">t</font> &amp; 0 <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> 2 )
 <b>by </b><i><a class="ref" href="yellow11.html#T1" target="_self" title="YELLOW11:th.1">Th1</a>, <a class="ref" href="enumset1.html#D1" title="ENUMSET1:def.1">ENUMSET1:def 1</a></i>;<br/><b>hence </b><a NAME="E4:15_1_5"/>
contradiction
 <b>by </b><i><a class="txt" href="yellow11.html#E2:15_1_5"><i><font color="Green" title="E18">A10</font></i></a>, <a class="ref" href="yellow11.html#T4" target="_self" title="YELLOW11:th.4">Th4</a>, <a class="ref" href="tarski.html#D1" title="TARSKI:def.1">TARSKI:def 1</a></i>;<br/></div><b>end;</b></div>
<b>hence </b><a NAME="E35:15_1"/>
<font color="Maroon" title="c23">D</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c24">E</font>
 ;<br/>

<a NAME="E36:15_1"/>
<font color="Maroon" title="c6">z</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <font color="Maroon" title="c7">j</font>
 
<b>by </b><i><a class="ref" href="xboole_1.html#T2" title="XBOOLE_1:th.2">XBOOLE_1:2</a></i>;<br/>
<a NAME="E37:15_1"/><b>then </b>
<font color="Maroon" title="c6">z</font> <a href="orders_2.html#R3" title="ORDERS_2:pred.3">&lt;=</a> <font color="Maroon" title="c7">j</font>
 
<b>by </b><i><a class="ref" href="yellow_1.html#T3" title="YELLOW_1:th.3">YELLOW_1:3</a></i>;<br/>
<a NAME="E38:15_1"/><b>then </b>
<font color="Maroon" title="c14">a</font> <a href="orders_2.html#R1" title="ORDERS_2:pred.1">&lt;=</a> <font color="Maroon" title="c15">b</font>
 
<b>by </b><i><a class="txt" href="yellow11.html#E4:15_1"><i><font color="Green" title="E14">A3</font></i></a>, <a class="ref" href="waybel_0.html#T66" title="WAYBEL_0:th.66">WAYBEL_0:66</a></i>;<br/>
<a NAME="E39:15_1"/><b>then </b>
<font color="Maroon" title="c20">A</font> <a href="orders_2.html#R3" title="ORDERS_2:pred.3">&lt;=</a> <font color="Maroon" title="c21">B</font>
 
<b>by </b><i><a class="ref" href="yellow_0.html#T60" title="YELLOW_0:th.60">YELLOW_0:60</a></i>;<br/>
<b>hence </b><a NAME="E40:15_1"/>
<font color="Maroon" title="c20">A</font> <a href="lattice3.html#K12" title="LATTICE3:func.12">"/\"</a> <font color="Maroon" title="c21">B</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c20">A</font>
 <b>by </b><i><a class="ref" href="yellow_0.html#T25" title="YELLOW_0:th.25">YELLOW_0:25</a></i>;<br/>

<a NAME="E41:15_1"/>
<font color="Maroon" title="c6">z</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <font color="Maroon" title="c8">dj</font>
 
<b>by </b><i><a class="ref" href="xboole_1.html#T2" title="XBOOLE_1:th.2">XBOOLE_1:2</a></i>;<br/>
<a NAME="E42:15_1"/><b>then </b>
<font color="Maroon" title="c6">z</font> <a href="orders_2.html#R3" title="ORDERS_2:pred.3">&lt;=</a> <font color="Maroon" title="c8">dj</font>
 
<b>by </b><i><a class="ref" href="yellow_1.html#T3" title="YELLOW_1:th.3">YELLOW_1:3</a></i>;<br/>
<a NAME="E43:15_1"/><b>then </b>
<font color="Maroon" title="c14">a</font> <a href="orders_2.html#R1" title="ORDERS_2:pred.1">&lt;=</a> <font color="Maroon" title="c16">c</font>
 
<b>by </b><i><a class="txt" href="yellow11.html#E4:15_1"><i><font color="Green" title="E14">A3</font></i></a>, <a class="ref" href="waybel_0.html#T66" title="WAYBEL_0:th.66">WAYBEL_0:66</a></i>;<br/>
<a NAME="E44:15_1"/><b>then </b>
<font color="Maroon" title="c20">A</font> <a href="orders_2.html#R3" title="ORDERS_2:pred.3">&lt;=</a> <font color="Maroon" title="c22">C</font>
 
<b>by </b><i><a class="ref" href="yellow_0.html#T60" title="YELLOW_0:th.60">YELLOW_0:60</a></i>;<br/>
<b>hence </b><a NAME="E45:15_1"/>
<font color="Maroon" title="c20">A</font> <a href="lattice3.html#K12" title="LATTICE3:func.12">"/\"</a> <font color="Maroon" title="c22">C</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c20">A</font>
 <b>by </b><i><a class="ref" href="yellow_0.html#T25" title="YELLOW_0:th.25">YELLOW_0:25</a></i>;<br/>

<a NAME="E46:15_1"/>
<font color="Maroon" title="c6">z</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <font color="Maroon" title="c9">td</font>
 
<b>by </b><i><a class="ref" href="xboole_1.html#T2" title="XBOOLE_1:th.2">XBOOLE_1:2</a></i>;<br/>
<a NAME="E47:15_1"/><b>then </b>
<font color="Maroon" title="c6">z</font> <a href="orders_2.html#R3" title="ORDERS_2:pred.3">&lt;=</a> <font color="Maroon" title="c9">td</font>
 
<b>by </b><i><a class="ref" href="yellow_1.html#T3" title="YELLOW_1:th.3">YELLOW_1:3</a></i>;<br/>
<a NAME="E48:15_1"/><b>then </b>
<font color="Maroon" title="c14">a</font> <a href="orders_2.html#R1" title="ORDERS_2:pred.1">&lt;=</a> <font color="Maroon" title="c17">d</font>
 
<b>by </b><i><a class="txt" href="yellow11.html#E4:15_1"><i><font color="Green" title="E14">A3</font></i></a>, <a class="ref" href="waybel_0.html#T66" title="WAYBEL_0:th.66">WAYBEL_0:66</a></i>;<br/>
<a NAME="E49:15_1"/><b>then </b>
<font color="Maroon" title="c20">A</font> <a href="orders_2.html#R3" title="ORDERS_2:pred.3">&lt;=</a> <font color="Maroon" title="c23">D</font>
 
<b>by </b><i><a class="ref" href="yellow_0.html#T60" title="YELLOW_0:th.60">YELLOW_0:60</a></i>;<br/>
<b>hence </b><a NAME="E50:15_1"/>
<font color="Maroon" title="c20">A</font> <a href="lattice3.html#K12" title="LATTICE3:func.12">"/\"</a> <font color="Maroon" title="c23">D</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c20">A</font>
 <b>by </b><i><a class="ref" href="yellow_0.html#T25" title="YELLOW_0:th.25">YELLOW_0:25</a></i>;<br/>

<a NAME="E51:15_1"/>
<font color="Maroon" title="c7">j</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <font color="Maroon" title="c10">t</font>
 
<b>by </b><i><a class="ref" href="card_1.html#T56" title="CARD_1:th.56">CARD_1:56</a></i>;<br/>
<a NAME="E52:15_1"/><b>then </b>
<font color="Maroon" title="c7">j</font> <a href="orders_2.html#R3" title="ORDERS_2:pred.3">&lt;=</a> <font color="Maroon" title="c10">t</font>
 
<b>by </b><i><a class="ref" href="yellow_1.html#T3" title="YELLOW_1:th.3">YELLOW_1:3</a></i>;<br/>
<a NAME="E53:15_1"/><b>then </b>
<font color="Maroon" title="c15">b</font> <a href="orders_2.html#R1" title="ORDERS_2:pred.1">&lt;=</a> <font color="Maroon" title="c18">e</font>
 
<b>by </b><i><a class="txt" href="yellow11.html#E4:15_1"><i><font color="Green" title="E14">A3</font></i></a>, <a class="ref" href="waybel_0.html#T66" title="WAYBEL_0:th.66">WAYBEL_0:66</a></i>;<br/>
<a NAME="E54:15_1"/><b>then </b>
<font color="Maroon" title="c21">B</font> <a href="orders_2.html#R3" title="ORDERS_2:pred.3">&lt;=</a> <font color="Maroon" title="c24">E</font>
 
<b>by </b><i><a class="ref" href="yellow_0.html#T60" title="YELLOW_0:th.60">YELLOW_0:60</a></i>;<br/>
<b>hence </b><a NAME="E55:15_1"/>
<font color="Maroon" title="c21">B</font> <a href="lattice3.html#K12" title="LATTICE3:func.12">"/\"</a> <font color="Maroon" title="c24">E</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c21">B</font>
 <b>by </b><i><a class="ref" href="yellow_0.html#T25" title="YELLOW_0:th.25">YELLOW_0:25</a></i>;<br/>

<a NAME="E56:15_1"/>
<font color="Maroon" title="c8">dj</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <font color="Maroon" title="c10">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" title="c25">x</font> be    <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a> ; <i><font color="Red">:: according to </font></i><a class="ref" href="tarski.html#D3" title="TARSKI:def.3">TARSKI:def 3</a><br/>

<b>assume </b><a NAME="E1:15_1_6"/>
<font color="Maroon" title="c25">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c8">dj</font>
 ;<br/>

<a NAME="E2:15_1_6"/><b>then </b>
<font color="Maroon" title="c25">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 1
 
<b>by </b><i><a class="ref" href="yellow11.html#T2" target="_self" title="YELLOW11:th.2">Th2</a>, <a class="ref" href="tarski.html#D1" title="TARSKI:def.1">TARSKI:def 1</a></i>;<br/>
<b>hence </b><a NAME="E3:15_1_6"/>
<font color="Maroon" title="c25">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c10">t</font>
 <b>by </b><i><a class="ref" href="yellow11.html#T1" target="_self" title="YELLOW11:th.1">Th1</a>, <a class="ref" href="enumset1.html#D1" title="ENUMSET1:def.1">ENUMSET1:def 1</a></i>;<br/>


</div><b>end;</b></div>
<a NAME="E57:15_1"/><b>then </b>
<font color="Maroon" title="c8">dj</font> <a href="orders_2.html#R3" title="ORDERS_2:pred.3">&lt;=</a> <font color="Maroon" title="c10">t</font>
 
<b>by </b><i><a class="ref" href="yellow_1.html#T3" title="YELLOW_1:th.3">YELLOW_1:3</a></i>;<br/>
<a NAME="E58:15_1"/><b>then </b>
<font color="Maroon" title="c16">c</font> <a href="orders_2.html#R1" title="ORDERS_2:pred.1">&lt;=</a> <font color="Maroon" title="c18">e</font>
 
<b>by </b><i><a class="txt" href="yellow11.html#E4:15_1"><i><font color="Green" title="E14">A3</font></i></a>, <a class="ref" href="waybel_0.html#T66" title="WAYBEL_0:th.66">WAYBEL_0:66</a></i>;<br/>
<a NAME="E59:15_1"/><b>then </b>
<font color="Maroon" title="c22">C</font> <a href="orders_2.html#R3" title="ORDERS_2:pred.3">&lt;=</a> <font color="Maroon" title="c24">E</font>
 
<b>by </b><i><a class="ref" href="yellow_0.html#T60" title="YELLOW_0:th.60">YELLOW_0:60</a></i>;<br/>
<b>hence </b><a NAME="E60:15_1"/>
<font color="Maroon" title="c22">C</font> <a href="lattice3.html#K12" title="LATTICE3:func.12">"/\"</a> <font color="Maroon" title="c24">E</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c22">C</font>
 <b>by </b><i><a class="ref" href="yellow_0.html#T25" title="YELLOW_0:th.25">YELLOW_0:25</a></i>;<br/>

<a NAME="E61:15_1"/>
<font color="Maroon" title="c9">td</font> <a href="orders_2.html#R3" title="ORDERS_2:pred.3">&lt;=</a> <font color="Maroon" title="c10">t</font>
 
<b>by </b><i><a class="ref" href="yellow_1.html#T3" title="YELLOW_1:th.3">YELLOW_1:3</a></i>;<br/>
<a NAME="E62:15_1"/><b>then </b>
<font color="Maroon" title="c17">d</font> <a href="orders_2.html#R1" title="ORDERS_2:pred.1">&lt;=</a> <font color="Maroon" title="c18">e</font>
 
<b>by </b><i><a class="txt" href="yellow11.html#E4:15_1"><i><font color="Green" title="E14">A3</font></i></a>, <a class="ref" href="waybel_0.html#T66" title="WAYBEL_0:th.66">WAYBEL_0:66</a></i>;<br/>
<a NAME="E63:15_1"/><b>then </b>
<font color="Maroon" title="c23">D</font> <a href="orders_2.html#R3" title="ORDERS_2:pred.3">&lt;=</a> <font color="Maroon" title="c24">E</font>
 
<b>by </b><i><a class="ref" href="yellow_0.html#T60" title="YELLOW_0:th.60">YELLOW_0:60</a></i>;<br/>
<b>hence </b><a NAME="E64:15_1"/>
<font color="Maroon" title="c23">D</font> <a href="lattice3.html#K12" title="LATTICE3:func.12">"/\"</a> <font color="Maroon" title="c24">E</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c23">D</font>
 <b>by </b><i><a class="ref" href="yellow_0.html#T25" title="YELLOW_0:th.25">YELLOW_0:25</a></i>;<br/>

<b>thus </b><a NAME="E65:15_1"/>
<font color="Maroon" title="c21">B</font> <a href="lattice3.html#K12" title="LATTICE3:func.12">"/\"</a> <font color="Maroon" title="c22">C</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c20">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" title="c21">B</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c5">K</font> &amp; <font color="Maroon" title="c22">C</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c5">K</font> &amp;  <a href="yellow_0.html#R2" title="YELLOW_0:pred.2">ex_inf_of</a> <span class="p1"><a href="domain_1.html#K7" title="DOMAIN_1:func.7">{</a><span class="default"><font color="Maroon" title="c21">B</font>,<font color="Maroon" title="c22">C</font></span><a href="domain_1.html#K7" title="DOMAIN_1:func.7">}</a></span>,<font color="Maroon" title="c1">L</font> )
 
<b>by </b><i><a class="ref" href="yellow_0.html#T21" title="YELLOW_0:th.21">YELLOW_0:21</a></i>;<br/>
<a NAME="E2:15_1_7"/><b>then </b>
 <a href="yellow_0.html#NK4" title="YELLOW_0:NK.4">inf</a> <span class="p1"><a href="domain_1.html#K7" title="DOMAIN_1:func.7">{</a><span class="default"><font color="Maroon" title="c21">B</font>,<font color="Maroon" title="c22">C</font></span><a href="domain_1.html#K7" title="DOMAIN_1:func.7">}</a></span> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c5">K</font>
 
<b>by </b><i><a class="ref" href="yellow_0.html#D16" title="YELLOW_0:def.16">YELLOW_0:def 16</a></i>;<br/>
<a NAME="E3:15_1_7"/><b>then </b>
<font color="Maroon" title="c21">B</font> <a href="lattice3.html#K12" title="LATTICE3:func.12">"/\"</a> <font color="Maroon" title="c22">C</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="relset_1.html#K5" title="RELSET_1:func.5">rng</a> <font color="Maroon" title="c4">f</font>
 
<b>by </b><i><a class="txt" href="yellow11.html#E15:15_1"><i><font color="Green" title="E17">A6</font></i></a>, <a class="ref" href="yellow_0.html#T40" title="YELLOW_0:th.40">YELLOW_0:40</a></i>;<br/>
<b>then consider </b><font color="Maroon" title="c25">x</font> being    <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a> <b> such that </b><br/><a NAME="E5:15_1_7"/><i><font color="Green" title="E18">A11</font></i>: 
( <font color="Maroon" title="c25">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="relset_1.html#K4" title="RELSET_1:func.4">dom</a> <font color="Maroon" title="c4">f</font> &amp; <font color="Maroon" title="c21">B</font> <a href="lattice3.html#K12" title="LATTICE3:func.12">"/\"</a> <font color="Maroon" title="c22">C</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c4">f</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c25">x</font> )
 <b>by </b><i><a class="ref" href="funct_1.html#D5" title="FUNCT_1:def.5">FUNCT_1:def 5</a></i>;<br/>
<b>reconsider </b><font color="Maroon" title="c26">x</font> = <font color="Maroon" title="c25">x</font> as   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <a href="yellow11.html#K2" title="YELLOW11:func.2">M_3</a>  <b>by </b><i><a class="txt" href="yellow11.html#E5:15_1_7"><i><font color="Green" title="E18">A11</font></i></a></i>;<br/>
<div><i><font color="Green" title="E19">A12</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" title="c21">B</font> <a href="lattice3.html#K12" title="LATTICE3:func.12">"/\"</a> <font color="Maroon" title="c22">C</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c21">B</font>
 ;<br/><a NAME="E2:15_1_7_1"/><b>then </b>
<font color="Maroon" title="c21">B</font> <a href="orders_2.html#R3" title="ORDERS_2:pred.3">&lt;=</a> <font color="Maroon" title="c22">C</font>
 <b>by </b><i><a class="ref" href="yellow_0.html#T25" title="YELLOW_0:th.25">YELLOW_0:25</a></i>;<br/><a NAME="E3:15_1_7_1"/><b>then </b>
<font color="Maroon" title="c15">b</font> <a href="orders_2.html#R1" title="ORDERS_2:pred.1">&lt;=</a> <font color="Maroon" title="c16">c</font>
 <b>by </b><i><a class="ref" href="yellow_0.html#T61" title="YELLOW_0:th.61">YELLOW_0:61</a></i>;<br/><a NAME="E4:15_1_7_1"/><b>then </b>
<font color="Maroon" title="c7">j</font> <a href="orders_2.html#R3" title="ORDERS_2:pred.3">&lt;=</a> <font color="Maroon" title="c8">dj</font>
 <b>by </b><i><a class="txt" href="yellow11.html#E4:15_1"><i><font color="Green" title="E14">A3</font></i></a>, <a class="ref" href="waybel_0.html#T66" title="WAYBEL_0:th.66">WAYBEL_0:66</a></i>;<br/><a NAME="E5:15_1_7_1"/><b>then </b><i><font color="Green" title="E20">A13</font></i>: 
<font color="Maroon" title="c7">j</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <font color="Maroon" title="c8">dj</font>
 <b>by </b><i><a class="ref" href="yellow_1.html#T3" title="YELLOW_1:th.3">YELLOW_1:3</a></i>;<br/><a NAME="E6:15_1_7_1"/>
0 <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c7">j</font>
 <b>by </b><i><a class="ref" href="card_5.html#T1" title="CARD_5:th.1">CARD_5:1</a>, <a class="ref" href="tarski.html#D1" title="TARSKI:def.1">TARSKI:def 1</a></i>;<br/><b>hence </b><a NAME="E7:15_1_7_1"/>
contradiction
 <b>by </b><i><a class="txt" href="yellow11.html#E5:15_1_7_1"><i><font color="Green" title="E20">A13</font></i></a>, <a class="ref" href="yellow11.html#T2" target="_self" title="YELLOW11:th.2">Th2</a>, <a class="ref" href="tarski.html#D1" title="TARSKI:def.1">TARSKI:def 1</a></i>;<br/></div><b>end;</b></div>
<div><i><font color="Green" title="E20">A14</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" title="c21">B</font> <a href="lattice3.html#K12" title="LATTICE3:func.12">"/\"</a> <font color="Maroon" title="c22">C</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c22">C</font>
 ;<br/><a NAME="E2:15_1_7_2"/><b>then </b>
<font color="Maroon" title="c22">C</font> <a href="orders_2.html#R3" title="ORDERS_2:pred.3">&lt;=</a> <font color="Maroon" title="c21">B</font>
 <b>by </b><i><a class="ref" href="yellow_0.html#T25" title="YELLOW_0:th.25">YELLOW_0:25</a></i>;<br/><a NAME="E3:15_1_7_2"/><b>then </b>
<font color="Maroon" title="c16">c</font> <a href="orders_2.html#R1" title="ORDERS_2:pred.1">&lt;=</a> <font color="Maroon" title="c15">b</font>
 <b>by </b><i><a class="ref" href="yellow_0.html#T61" title="YELLOW_0:th.61">YELLOW_0:61</a></i>;<br/><a NAME="E4:15_1_7_2"/><b>then </b>
<font color="Maroon" title="c8">dj</font> <a href="orders_2.html#R3" title="ORDERS_2:pred.3">&lt;=</a> <font color="Maroon" title="c7">j</font>
 <b>by </b><i><a class="txt" href="yellow11.html#E4:15_1"><i><font color="Green" title="E14">A3</font></i></a>, <a class="ref" href="waybel_0.html#T66" title="WAYBEL_0:th.66">WAYBEL_0:66</a></i>;<br/><a NAME="E5:15_1_7_2"/><b>then </b><i><font color="Green" title="E21">A15</font></i>: 
<font color="Maroon" title="c8">dj</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <font color="Maroon" title="c7">j</font>
 <b>by </b><i><a class="ref" href="yellow_1.html#T3" title="YELLOW_1:th.3">YELLOW_1:3</a></i>;<br/><a NAME="E6:15_1_7_2"/>
( 1 <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c8">dj</font> &amp; 0 <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> 1 )
 <b>by </b><i><a class="ref" href="yellow11.html#T2" target="_self" title="YELLOW11:th.2">Th2</a>, <a class="ref" href="tarski.html#D1" title="TARSKI:def.1">TARSKI:def 1</a></i>;<br/><b>hence </b><a NAME="E7:15_1_7_2"/>
contradiction
 <b>by </b><i><a class="txt" href="yellow11.html#E5:15_1_7_2"><i><font color="Green" title="E21">A15</font></i></a>, <a class="ref" href="card_5.html#T1" title="CARD_5:th.1">CARD_5:1</a>, <a class="ref" href="tarski.html#D1" title="TARSKI:def.1">TARSKI:def 1</a></i>;<br/></div><b>end;</b></div>
<div><i><font color="Green" title="E21">A16</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" title="c21">B</font> <a href="lattice3.html#K12" title="LATTICE3:func.12">"/\"</a> <font color="Maroon" title="c22">C</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c23">D</font>
 ;<br/><a NAME="E2:15_1_7_3"/><b>then </b>
<font color="Maroon" title="c23">D</font> <a href="orders_2.html#R3" title="ORDERS_2:pred.3">&lt;=</a> <font color="Maroon" title="c22">C</font>
 <b>by </b><i><a class="ref" href="yellow_0.html#T23" title="YELLOW_0:th.23">YELLOW_0:23</a></i>;<br/><a NAME="E3:15_1_7_3"/><b>then </b>
<font color="Maroon" title="c17">d</font> <a href="orders_2.html#R1" title="ORDERS_2:pred.1">&lt;=</a> <font color="Maroon" title="c16">c</font>
 <b>by </b><i><a class="ref" href="yellow_0.html#T61" title="YELLOW_0:th.61">YELLOW_0:61</a></i>;<br/><a NAME="E4:15_1_7_3"/><b>then </b>
<font color="Maroon" title="c9">td</font> <a href="orders_2.html#R3" title="ORDERS_2:pred.3">&lt;=</a> <font color="Maroon" title="c8">dj</font>
 <b>by </b><i><a class="txt" href="yellow11.html#E4:15_1"><i><font color="Green" title="E14">A3</font></i></a>, <a class="ref" href="waybel_0.html#T66" title="WAYBEL_0:th.66">WAYBEL_0:66</a></i>;<br/><a NAME="E5:15_1_7_3"/><b>then </b><i><font color="Green" title="E22">A17</font></i>: 
<font color="Maroon" title="c9">td</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <font color="Maroon" title="c8">dj</font>
 <b>by </b><i><a class="ref" href="yellow_1.html#T3" title="YELLOW_1:th.3">YELLOW_1:3</a></i>;<br/><a NAME="E6:15_1_7_3"/>
2 <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c9">td</font>
 <b>by </b><i><a class="ref" href="yellow11.html#T4" target="_self" title="YELLOW11:th.4">Th4</a>, <a class="ref" href="tarski.html#D1" title="TARSKI:def.1">TARSKI:def 1</a></i>;<br/><b>hence </b><a NAME="E7:15_1_7_3"/>
contradiction
 <b>by </b><i><a class="txt" href="yellow11.html#E5:15_1_7_3"><i><font color="Green" title="E22">A17</font></i></a>, <a class="ref" href="yellow11.html#T2" target="_self" title="YELLOW11:th.2">Th2</a>, <a class="ref" href="tarski.html#D1" title="TARSKI:def.1">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" title="c21">B</font> <a href="lattice3.html#K12" title="LATTICE3:func.12">"/\"</a> <font color="Maroon" title="c22">C</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c24">E</font>
 ;<br/><a NAME="E2:15_1_7_4"/><b>then </b>
<font color="Maroon" title="c24">E</font> <a href="orders_2.html#R3" title="ORDERS_2:pred.3">&lt;=</a> <font color="Maroon" title="c22">C</font>
 <b>by </b><i><a class="ref" href="yellow_0.html#T23" title="YELLOW_0:th.23">YELLOW_0:23</a></i>;<br/><a NAME="E3:15_1_7_4"/><b>then </b>
<font color="Maroon" title="c18">e</font> <a href="orders_2.html#R1" title="ORDERS_2:pred.1">&lt;=</a> <font color="Maroon" title="c16">c</font>
 <b>by </b><i><a class="ref" href="yellow_0.html#T61" title="YELLOW_0:th.61">YELLOW_0:61</a></i>;<br/><a NAME="E4:15_1_7_4"/><b>then </b>
<font color="Maroon" title="c10">t</font> <a href="orders_2.html#R3" title="ORDERS_2:pred.3">&lt;=</a> <font color="Maroon" title="c8">dj</font>
 <b>by </b><i><a class="txt" href="yellow11.html#E4:15_1"><i><font color="Green" title="E14">A3</font></i></a>, <a class="ref" href="waybel_0.html#T66" title="WAYBEL_0:th.66">WAYBEL_0:66</a></i>;<br/><a NAME="E5:15_1_7_4"/><b>then </b><i><font color="Green" title="E22">A18</font></i>: 
<font color="Maroon" title="c10">t</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <font color="Maroon" title="c8">dj</font>
 <b>by </b><i><a class="ref" href="yellow_1.html#T3" title="YELLOW_1:th.3">YELLOW_1:3</a></i>;<br/><a NAME="E6:15_1_7_4"/>
2 <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c10">t</font>
 <b>by </b><i><a class="ref" href="yellow11.html#T1" target="_self" title="YELLOW11:th.1">Th1</a>, <a class="ref" href="enumset1.html#D1" title="ENUMSET1:def.1">ENUMSET1:def 1</a></i>;<br/><b>hence </b><a NAME="E7:15_1_7_4"/>
contradiction
 <b>by </b><i><a class="txt" href="yellow11.html#E5:15_1_7_4"><i><font color="Green" title="E22">A18</font></i></a>, <a class="ref" href="yellow11.html#T2" target="_self" title="YELLOW11:th.2">Th2</a>, <a class="ref" href="tarski.html#D1" title="TARSKI:def.1">TARSKI:def 1</a></i>;<br/></div><b>end;</b></div>
<b>hence </b><a NAME="E11:15_1_7"/>
<font color="Maroon" title="c21">B</font> <a href="lattice3.html#K12" title="LATTICE3:func.12">"/\"</a> <font color="Maroon" title="c22">C</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c20">A</font>
 <b>by </b><i><a class="txt" href="yellow11.html#E1:15"><i><font color="Green" title="E12">A1</font></i></a>, <a class="txt" href="yellow11.html#E5:15_1_7"><i><font color="Green" title="E18">A11</font></i></a>, <a class="txt" href="yellow11.html#E7:15_1_7"><i><font color="Green" title="E19">A12</font></i></a>, <a class="txt" href="yellow11.html#E8:15_1_7"><i><font color="Green" title="E20">A14</font></i></a>, <a class="txt" href="yellow11.html#E9:15_1_7"><i><font color="Green" title="E21">A16</font></i></a>, <a class="ref" href="enumset1.html#D3" title="ENUMSET1:def.3">ENUMSET1:def 3</a></i>;<br/>


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

<b>thus </b><a NAME="E66:15_1"/>
<font color="Maroon" title="c21">B</font> <a href="lattice3.html#K12" title="LATTICE3:func.12">"/\"</a> <font color="Maroon" title="c23">D</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c20">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" title="c21">B</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c5">K</font> &amp; <font color="Maroon" title="c23">D</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c5">K</font> &amp;  <a href="yellow_0.html#R2" title="YELLOW_0:pred.2">ex_inf_of</a> <span class="p1"><a href="domain_1.html#K7" title="DOMAIN_1:func.7">{</a><span class="default"><font color="Maroon" title="c21">B</font>,<font color="Maroon" title="c23">D</font></span><a href="domain_1.html#K7" title="DOMAIN_1:func.7">}</a></span>,<font color="Maroon" title="c1">L</font> )
 
<b>by </b><i><a class="ref" href="yellow_0.html#T21" title="YELLOW_0:th.21">YELLOW_0:21</a></i>;<br/>
<a NAME="E2:15_1_8"/><b>then </b>
 <a href="yellow_0.html#NK4" title="YELLOW_0:NK.4">inf</a> <span class="p1"><a href="domain_1.html#K7" title="DOMAIN_1:func.7">{</a><span class="default"><font color="Maroon" title="c21">B</font>,<font color="Maroon" title="c23">D</font></span><a href="domain_1.html#K7" title="DOMAIN_1:func.7">}</a></span> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c5">K</font>
 
<b>by </b><i><a class="ref" href="yellow_0.html#D16" title="YELLOW_0:def.16">YELLOW_0:def 16</a></i>;<br/>
<a NAME="E3:15_1_8"/><b>then </b>
<font color="Maroon" title="c21">B</font> <a href="lattice3.html#K12" title="LATTICE3:func.12">"/\"</a> <font color="Maroon" title="c23">D</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="relset_1.html#K5" title="RELSET_1:func.5">rng</a> <font color="Maroon" title="c4">f</font>
 
<b>by </b><i><a class="txt" href="yellow11.html#E15:15_1"><i><font color="Green" title="E17">A6</font></i></a>, <a class="ref" href="yellow_0.html#T40" title="YELLOW_0:th.40">YELLOW_0:40</a></i>;<br/>
<b>then consider </b><font color="Maroon" title="c25">x</font> being    <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a> <b> such that </b><br/><a NAME="E5:15_1_8"/><i><font color="Green" title="E18">A19</font></i>: 
( <font color="Maroon" title="c25">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="relset_1.html#K4" title="RELSET_1:func.4">dom</a> <font color="Maroon" title="c4">f</font> &amp; <font color="Maroon" title="c21">B</font> <a href="lattice3.html#K12" title="LATTICE3:func.12">"/\"</a> <font color="Maroon" title="c23">D</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c4">f</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c25">x</font> )
 <b>by </b><i><a class="ref" href="funct_1.html#D5" title="FUNCT_1:def.5">FUNCT_1:def 5</a></i>;<br/>
<b>reconsider </b><font color="Maroon" title="c26">x</font> = <font color="Maroon" title="c25">x</font> as   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <a href="yellow11.html#K2" title="YELLOW11:func.2">M_3</a>  <b>by </b><i><a class="txt" href="yellow11.html#E5:15_1_8"><i><font color="Green" title="E18">A19</font></i></a></i>;<br/>
<div><i><font color="Green" title="E19">A20</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" title="c21">B</font> <a href="lattice3.html#K12" title="LATTICE3:func.12">"/\"</a> <font color="Maroon" title="c23">D</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c21">B</font>
 ;<br/><a NAME="E2:15_1_8_1"/><b>then </b>
<font color="Maroon" title="c21">B</font> <a href="orders_2.html#R3" title="ORDERS_2:pred.3">&lt;=</a> <font color="Maroon" title="c23">D</font>
 <b>by </b><i><a class="ref" href="yellow_0.html#T25" title="YELLOW_0:th.25">YELLOW_0:25</a></i>;<br/><a NAME="E3:15_1_8_1"/><b>then </b>
<font color="Maroon" title="c15">b</font> <a href="orders_2.html#R1" title="ORDERS_2:pred.1">&lt;=</a> <font color="Maroon" title="c17">d</font>
 <b>by </b><i><a class="ref" href="yellow_0.html#T61" title="YELLOW_0:th.61">YELLOW_0:61</a></i>;<br/><a NAME="E4:15_1_8_1"/><b>then </b>
<font color="Maroon" title="c7">j</font> <a href="orders_2.html#R3" title="ORDERS_2:pred.3">&lt;=</a> <font color="Maroon" title="c9">td</font>
 <b>by </b><i><a class="txt" href="yellow11.html#E4:15_1"><i><font color="Green" title="E14">A3</font></i></a>, <a class="ref" href="waybel_0.html#T66" title="WAYBEL_0:th.66">WAYBEL_0:66</a></i>;<br/><a NAME="E5:15_1_8_1"/><b>then </b><i><font color="Green" title="E20">A21</font></i>: 
<font color="Maroon" title="c7">j</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <font color="Maroon" title="c9">td</font>
 <b>by </b><i><a class="ref" href="yellow_1.html#T3" title="YELLOW_1:th.3">YELLOW_1:3</a></i>;<br/><a NAME="E6:15_1_8_1"/>
0 <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c7">j</font>
 <b>by </b><i><a class="ref" href="card_5.html#T1" title="CARD_5:th.1">CARD_5:1</a>, <a class="ref" href="tarski.html#D1" title="TARSKI:def.1">TARSKI:def 1</a></i>;<br/><b>hence </b><a NAME="E7:15_1_8_1"/>
contradiction
 <b>by </b><i><a class="txt" href="yellow11.html#E5:15_1_8_1"><i><font color="Green" title="E20">A21</font></i></a>, <a class="ref" href="yellow11.html#T4" target="_self" title="YELLOW11:th.4">Th4</a>, <a class="ref" href="tarski.html#D1" title="TARSKI:def.1">TARSKI:def 1</a></i>;<br/></div><b>end;</b></div>
<div><i><font color="Green" title="E20">A22</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" title="c21">B</font> <a href="lattice3.html#K12" title="LATTICE3:func.12">"/\"</a> <font color="Maroon" title="c23">D</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c22">C</font>
 ;<br/><a NAME="E2:15_1_8_2"/><b>then </b>
<font color="Maroon" title="c22">C</font> <a href="orders_2.html#R3" title="ORDERS_2:pred.3">&lt;=</a> <font color="Maroon" title="c21">B</font>
 <b>by </b><i><a class="ref" href="yellow_0.html#T23" title="YELLOW_0:th.23">YELLOW_0:23</a></i>;<br/><a NAME="E3:15_1_8_2"/><b>then </b>
<font color="Maroon" title="c16">c</font> <a href="orders_2.html#R1" title="ORDERS_2:pred.1">&lt;=</a> <font color="Maroon" title="c15">b</font>
 <b>by </b><i><a class="ref" href="yellow_0.html#T61" title="YELLOW_0:th.61">YELLOW_0:61</a></i>;<br/><a NAME="E4:15_1_8_2"/><b>then </b>
<font color="Maroon" title="c8">dj</font> <a href="orders_2.html#R3" title="ORDERS_2:pred.3">&lt;=</a> <font color="Maroon" title="c7">j</font>
 <b>by </b><i><a class="txt" href="yellow11.html#E4:15_1"><i><font color="Green" title="E14">A3</font></i></a>, <a class="ref" href="waybel_0.html#T66" title="WAYBEL_0:th.66">WAYBEL_0:66</a></i>;<br/><a NAME="E5:15_1_8_2"/><b>then </b><i><font color="Green" title="E21">A23</font></i>: 
<font color="Maroon" title="c8">dj</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <font color="Maroon" title="c7">j</font>
 <b>by </b><i><a class="ref" href="yellow_1.html#T3" title="YELLOW_1:th.3">YELLOW_1:3</a></i>;<br/><a NAME="E6:15_1_8_2"/>
( 1 <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c8">dj</font> &amp; 0 <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> 1 )
 <b>by </b><i><a class="ref" href="yellow11.html#T2" target="_self" title="YELLOW11:th.2">Th2</a>, <a class="ref" href="tarski.html#D1" title="TARSKI:def.1">TARSKI:def 1</a></i>;<br/><b>hence </b><a NAME="E7:15_1_8_2"/>
contradiction
 <b>by </b><i><a class="txt" href="yellow11.html#E5:15_1_8_2"><i><font color="Green" title="E21">A23</font></i></a>, <a class="ref" href="card_5.html#T1" title="CARD_5:th.1">CARD_5:1</a>, <a class="ref" href="tarski.html#D1" title="TARSKI:def.1">TARSKI:def 1</a></i>;<br/></div><b>end;</b></div>
<div><i><font color="Green" title="E21">A24</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" title="c21">B</font> <a href="lattice3.html#K12" title="LATTICE3:func.12">"/\"</a> <font color="Maroon" title="c23">D</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c23">D</font>
 ;<br/><a NAME="E2:15_1_8_3"/><b>then </b>
<font color="Maroon" title="c23">D</font> <a href="orders_2.html#R3" title="ORDERS_2:pred.3">&lt;=</a> <font color="Maroon" title="c21">B</font>
 <b>by </b><i><a class="ref" href="yellow_0.html#T23" title="YELLOW_0:th.23">YELLOW_0:23</a></i>;<br/><a NAME="E3:15_1_8_3"/><b>then </b>
<font color="Maroon" title="c17">d</font> <a href="orders_2.html#R1" title="ORDERS_2:pred.1">&lt;=</a> <font color="Maroon" title="c15">b</font>
 <b>by </b><i><a class="ref" href="yellow_0.html#T61" title="YELLOW_0:th.61">YELLOW_0:61</a></i>;<br/><a NAME="E4:15_1_8_3"/><b>then </b>
<font color="Maroon" title="c9">td</font> <a href="orders_2.html#R3" title="ORDERS_2:pred.3">&lt;=</a> <font color="Maroon" title="c7">j</font>
 <b>by </b><i><a class="txt" href="yellow11.html#E4:15_1"><i><font color="Green" title="E14">A3</font></i></a>, <a class="ref" href="waybel_0.html#T66" title="WAYBEL_0:th.66">WAYBEL_0:66</a></i>;<br/><a NAME="E5:15_1_8_3"/><b>then </b><i><font color="Green" title="E22">A25</font></i>: 
<font color="Maroon" title="c9">td</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <font color="Maroon" title="c7">j</font>
 <b>by </b><i><a class="ref" href="yellow_1.html#T3" title="YELLOW_1:th.3">YELLOW_1:3</a></i>;<br/><a NAME="E6:15_1_8_3"/>
2 <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c9">td</font>
 <b>by </b><i><a class="ref" href="yellow11.html#T4" target="_self" title="YELLOW11:th.4">Th4</a>, <a class="ref" href="tarski.html#D1" title="TARSKI:def.1">TARSKI:def 1</a></i>;<br/><b>hence </b><a NAME="E7:15_1_8_3"/>
contradiction
 <b>by </b><i><a class="txt" href="yellow11.html#E5:15_1_8_3"><i><font color="Green" title="E22">A25</font></i></a>, <a class="ref" href="card_5.html#T1" title="CARD_5:th.1">CARD_5:1</a>, <a class="ref" href="tarski.html#D1" title="TARSKI:def.1">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" title="c21">B</font> <a href="lattice3.html#K12" title="LATTICE3:func.12">"/\"</a> <font color="Maroon" title="c23">D</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c24">E</font>
 ;<br/><a NAME="E2:15_1_8_4"/><b>then </b>
<font color="Maroon" title="c24">E</font> <a href="orders_2.html#R3" title="ORDERS_2:pred.3">&lt;=</a> <font color="Maroon" title="c21">B</font>
 <b>by </b><i><a class="ref" href="yellow_0.html#T23" title="YELLOW_0:th.23">YELLOW_0:23</a></i>;<br/><a NAME="E3:15_1_8_4"/><b>then </b>
<font color="Maroon" title="c18">e</font> <a href="orders_2.html#R1" title="ORDERS_2:pred.1">&lt;=</a> <font color="Maroon" title="c15">b</font>
 <b>by </b><i><a class="ref" href="yellow_0.html#T61" title="YELLOW_0:th.61">YELLOW_0:61</a></i>;<br/><a NAME="E4:15_1_8_4"/><b>then </b>
<font color="Maroon" title="c10">t</font> <a href="orders_2.html#R3" title="ORDERS_2:pred.3">&lt;=</a> <font color="Maroon" title="c7">j</font>
 <b>by </b><i><a class="txt" href="yellow11.html#E4:15_1"><i><font color="Green" title="E14">A3</font></i></a>, <a class="ref" href="waybel_0.html#T66" title="WAYBEL_0:th.66">WAYBEL_0:66</a></i>;<br/><a NAME="E5:15_1_8_4"/><b>then </b><i><font color="Green" title="E22">A26</font></i>: 
<font color="Maroon" title="c10">t</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <font color="Maroon" title="c7">j</font>
 <b>by </b><i><a class="ref" href="yellow_1.html#T3" title="YELLOW_1:th.3">YELLOW_1:3</a></i>;<br/><a NAME="E6:15_1_8_4"/>
2 <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c10">t</font>
 <b>by </b><i><a class="ref" href="yellow11.html#T1" target="_self" title="YELLOW11:th.1">Th1</a>, <a class="ref" href="enumset1.html#D1" title="ENUMSET1:def.1">ENUMSET1:def 1</a></i>;<br/><b>hence </b><a NAME="E7:15_1_8_4"/>
contradiction
 <b>by </b><i><a class="txt" href="yellow11.html#E5:15_1_8_4"><i><font color="Green" title="E22">A26</font></i></a>, <a class="ref" href="card_5.html#T1" title="CARD_5:th.1">CARD_5:1</a>, <a class="ref" href="tarski.html#D1" title="TARSKI:def.1">TARSKI:def 1</a></i>;<br/></div><b>end;</b></div>
<b>hence </b><a NAME="E11:15_1_8"/>
<font color="Maroon" title="c21">B</font> <a href="lattice3.html#K12" title="LATTICE3:func.12">"/\"</a> <font color="Maroon" title="c23">D</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c20">A</font>
 <b>by </b><i><a class="txt" href="yellow11.html#E1:15"><i><font color="Green" title="E12">A1</font></i></a>, <a class="txt" href="yellow11.html#E5:15_1_8"><i><font color="Green" title="E18">A19</font></i></a>, <a class="txt" href="yellow11.html#E7:15_1_8"><i><font color="Green" title="E19">A20</font></i></a>, <a class="txt" href="yellow11.html#E8:15_1_8"><i><font color="Green" title="E20">A22</font></i></a>, <a class="txt" href="yellow11.html#E9:15_1_8"><i><font color="Green" title="E21">A24</font></i></a>, <a class="ref" href="enumset1.html#D3" title="ENUMSET1:def.3">ENUMSET1:def 3</a></i>;<br/>


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

<b>thus </b><a NAME="E67:15_1"/>
<font color="Maroon" title="c22">C</font> <a href="lattice3.html#K12" title="LATTICE3:func.12">"/\"</a> <font color="Maroon" title="c23">D</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c20">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" title="c22">C</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c5">K</font> &amp; <font color="Maroon" title="c23">D</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c5">K</font> &amp;  <a href="yellow_0.html#R2" title="YELLOW_0:pred.2">ex_inf_of</a> <span class="p1"><a href="domain_1.html#K7" title="DOMAIN_1:func.7">{</a><span class="default"><font color="Maroon" title="c22">C</font>,<font color="Maroon" title="c23">D</font></span><a href="domain_1.html#K7" title="DOMAIN_1:func.7">}</a></span>,<font color="Maroon" title="c1">L</font> )
 
<b>by </b><i><a class="ref" href="yellow_0.html#T21" title="YELLOW_0:th.21">YELLOW_0:21</a></i>;<br/>
<a NAME="E2:15_1_9"/><b>then </b>
 <a href="yellow_0.html#NK4" title="YELLOW_0:NK.4">inf</a> <span class="p1"><a href="domain_1.html#K7" title="DOMAIN_1:func.7">{</a><span class="default"><font color="Maroon" title="c22">C</font>,<font color="Maroon" title="c23">D</font></span><a href="domain_1.html#K7" title="DOMAIN_1:func.7">}</a></span> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c5">K</font>
 
<b>by </b><i><a class="ref" href="yellow_0.html#D16" title="YELLOW_0:def.16">YELLOW_0:def 16</a></i>;<br/>
<a NAME="E3:15_1_9"/><b>then </b>
<font color="Maroon" title="c22">C</font> <a href="lattice3.html#K12" title="LATTICE3:func.12">"/\"</a> <font color="Maroon" title="c23">D</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="relset_1.html#K5" title="RELSET_1:func.5">rng</a> <font color="Maroon" title="c4">f</font>
 
<b>by </b><i><a class="txt" href="yellow11.html#E15:15_1"><i><font color="Green" title="E17">A6</font></i></a>, <a class="ref" href="yellow_0.html#T40" title="YELLOW_0:th.40">YELLOW_0:40</a></i>;<br/>
<b>then consider </b><font color="Maroon" title="c25">x</font> being    <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a> <b> such that </b><br/><a NAME="E5:15_1_9"/><i><font color="Green" title="E18">A27</font></i>: 
( <font color="Maroon" title="c25">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="relset_1.html#K4" title="RELSET_1:func.4">dom</a> <font color="Maroon" title="c4">f</font> &amp; <font color="Maroon" title="c22">C</font> <a href="lattice3.html#K12" title="LATTICE3:func.12">"/\"</a> <font color="Maroon" title="c23">D</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c4">f</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c25">x</font> )
 <b>by </b><i><a class="ref" href="funct_1.html#D5" title="FUNCT_1:def.5">FUNCT_1:def 5</a></i>;<br/>
<b>reconsider </b><font color="Maroon" title="c26">x</font> = <font color="Maroon" title="c25">x</font> as   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <a href="yellow11.html#K2" title="YELLOW11:func.2">M_3</a>  <b>by </b><i><a class="txt" href="yellow11.html#E5:15_1_9"><i><font color="Green" title="E18">A27</font></i></a></i>;<br/>
<div><i><font color="Green" title="E19">A28</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" title="c22">C</font> <a href="lattice3.html#K12" title="LATTICE3:func.12">"/\"</a> <font color="Maroon" title="c23">D</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c21">B</font>
 ;<br/><a NAME="E2:15_1_9_1"/><b>then </b>
<font color="Maroon" title="c21">B</font> <a href="orders_2.html#R3" title="ORDERS_2:pred.3">&lt;=</a> <font color="Maroon" title="c22">C</font>
 <b>by </b><i><a class="ref" href="yellow_0.html#T23" title="YELLOW_0:th.23">YELLOW_0:23</a></i>;<br/><a NAME="E3:15_1_9_1"/><b>then </b>
<font color="Maroon" title="c15">b</font> <a href="orders_2.html#R1" title="ORDERS_2:pred.1">&lt;=</a> <font color="Maroon" title="c16">c</font>
 <b>by </b><i><a class="ref" href="yellow_0.html#T61" title="YELLOW_0:th.61">YELLOW_0:61</a></i>;<br/><a NAME="E4:15_1_9_1"/><b>then </b>
<font color="Maroon" title="c7">j</font> <a href="orders_2.html#R3" title="ORDERS_2:pred.3">&lt;=</a> <font color="Maroon" title="c8">dj</font>
 <b>by </b><i><a class="txt" href="yellow11.html#E4:15_1"><i><font color="Green" title="E14">A3</font></i></a>, <a class="ref" href="waybel_0.html#T66" title="WAYBEL_0:th.66">WAYBEL_0:66</a></i>;<br/><a NAME="E5:15_1_9_1"/><b>then </b><i><font color="Green" title="E20">A29</font></i>: 
<font color="Maroon" title="c7">j</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <font color="Maroon" title="c8">dj</font>
 <b>by </b><i><a class="ref" href="yellow_1.html#T3" title="YELLOW_1:th.3">YELLOW_1:3</a></i>;<br/><a NAME="E6:15_1_9_1"/>
0 <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c7">j</font>
 <b>by </b><i><a class="ref" href="card_5.html#T1" title="CARD_5:th.1">CARD_5:1</a>, <a class="ref" href="tarski.html#D1" title="TARSKI:def.1">TARSKI:def 1</a></i>;<br/><b>hence </b><a NAME="E7:15_1_9_1"/>
contradiction
 <b>by </b><i><a class="txt" href="yellow11.html#E5:15_1_9_1"><i><font color="Green" title="E20">A29</font></i></a>, <a class="ref" href="yellow11.html#T2" target="_self" title="YELLOW11:th.2">Th2</a>, <a class="ref" href="tarski.html#D1" title="TARSKI:def.1">TARSKI:def 1</a></i>;<br/></div><b>end;</b></div>
<div><i><font color="Green" title="E20">A30</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" title="c22">C</font> <a href="lattice3.html#K12" title="LATTICE3:func.12">"/\"</a> <font color="Maroon" title="c23">D</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c22">C</font>
 ;<br/><a NAME="E2:15_1_9_2"/><b>then </b>
<font color="Maroon" title="c22">C</font> <a href="orders_2.html#R3" title="ORDERS_2:pred.3">&lt;=</a> <font color="Maroon" title="c23">D</font>
 <b>by </b><i><a class="ref" href="yellow_0.html#T25" title="YELLOW_0:th.25">YELLOW_0:25</a></i>;<br/><a NAME="E3:15_1_9_2"/><b>then </b>
<font color="Maroon" title="c16">c</font> <a href="orders_2.html#R1" title="ORDERS_2:pred.1">&lt;=</a> <font color="Maroon" title="c17">d</font>
 <b>by </b><i><a class="ref" href="yellow_0.html#T61" title="YELLOW_0:th.61">YELLOW_0:61</a></i>;<br/><a NAME="E4:15_1_9_2"/><b>then </b>
<font color="Maroon" title="c8">dj</font> <a href="orders_2.html#R3" title="ORDERS_2:pred.3">&lt;=</a> <font color="Maroon" title="c9">td</font>
 <b>by </b><i><a class="txt" href="yellow11.html#E4:15_1"><i><font color="Green" title="E14">A3</font></i></a>, <a class="ref" href="waybel_0.html#T66" title="WAYBEL_0:th.66">WAYBEL_0:66</a></i>;<br/><a NAME="E5:15_1_9_2"/><b>then </b><i><font color="Green" title="E21">A31</font></i>: 
<font color="Maroon" title="c8">dj</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <font color="Maroon" title="c9">td</font>
 <b>by </b><i><a class="ref" href="yellow_1.html#T3" title="YELLOW_1:th.3">YELLOW_1:3</a></i>;<br/><a NAME="E6:15_1_9_2"/>
( 1 <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c8">dj</font> &amp; 1 <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> 2 )
 <b>by </b><i><a class="ref" href="yellow11.html#T2" target="_self" title="YELLOW11:th.2">Th2</a>, <a class="ref" href="tarski.html#D1" title="TARSKI:def.1">TARSKI:def 1</a></i>;<br/><b>hence </b><a NAME="E7:15_1_9_2"/>
contradiction
 <b>by </b><i><a class="txt" href="yellow11.html#E5:15_1_9_2"><i><font color="Green" title="E21">A31</font></i></a>, <a class="ref" href="yellow11.html#T4" target="_self" title="YELLOW11:th.4">Th4</a>, <a class="ref" href="tarski.html#D1" title="TARSKI:def.1">TARSKI:def 1</a></i>;<br/></div><b>end;</b></div>
<div><i><font color="Green" title="E21">A32</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" title="c22">C</font> <a href="lattice3.html#K12" title="LATTICE3:func.12">"/\"</a> <font color="Maroon" title="c23">D</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c23">D</font>
 ;<br/><a NAME="E2:15_1_9_3"/><b>then </b>
<font color="Maroon" title="c23">D</font> <a href="orders_2.html#R3" title="ORDERS_2:pred.3">&lt;=</a> <font color="Maroon" title="c22">C</font>
 <b>by </b><i><a class="ref" href="yellow_0.html#T23" title="YELLOW_0:th.23">YELLOW_0:23</a></i>;<br/><a NAME="E3:15_1_9_3"/><b>then </b>
<font color="Maroon" title="c17">d</font> <a href="orders_2.html#R1" title="ORDERS_2:pred.1">&lt;=</a> <font color="Maroon" title="c16">c</font>
 <b>by </b><i><a class="ref" href="yellow_0.html#T61" title="YELLOW_0:th.61">YELLOW_0:61</a></i>;<br/><a NAME="E4:15_1_9_3"/><b>then </b>
<font color="Maroon" title="c9">td</font> <a href="orders_2.html#R3" title="ORDERS_2:pred.3">&lt;=</a> <font color="Maroon" title="c8">dj</font>
 <b>by </b><i><a class="txt" href="yellow11.html#E4:15_1"><i><font color="Green" title="E14">A3</font></i></a>, <a class="ref" href="waybel_0.html#T66" title="WAYBEL_0:th.66">WAYBEL_0:66</a></i>;<br/><a NAME="E5:15_1_9_3"/><b>then </b><i><font color="Green" title="E22">A33</font></i>: 
<font color="Maroon" title="c9">td</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <font color="Maroon" title="c8">dj</font>
 <b>by </b><i><a class="ref" href="yellow_1.html#T3" title="YELLOW_1:th.3">YELLOW_1:3</a></i>;<br/><a NAME="E6:15_1_9_3"/>
2 <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c9">td</font>
 <b>by </b><i><a class="ref" href="yellow11.html#T4" target="_self" title="YELLOW11:th.4">Th4</a>, <a class="ref" href="tarski.html#D1" title="TARSKI:def.1">TARSKI:def 1</a></i>;<br/><b>hence </b><a NAME="E7:15_1_9_3"/>
contradiction
 <b>by </b><i><a class="txt" href="yellow11.html#E5:15_1_9_3"><i><font color="Green" title="E22">A33</font></i></a>, <a class="ref" href="yellow11.html#T2" target="_self" title="YELLOW11:th.2">Th2</a>, <a class="ref" href="tarski.html#D1" title="TARSKI:def.1">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" title="c22">C</font> <a href="lattice3.html#K12" title="LATTICE3:func.12">"/\"</a> <font color="Maroon" title="c23">D</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c24">E</font>
 ;<br/><a NAME="E2:15_1_9_4"/><b>then </b>
<font color="Maroon" title="c24">E</font> <a href="orders_2.html#R3" title="ORDERS_2:pred.3">&lt;=</a> <font color="Maroon" title="c22">C</font>
 <b>by </b><i><a class="ref" href="yellow_0.html#T23" title="YELLOW_0:th.23">YELLOW_0:23</a></i>;<br/><a NAME="E3:15_1_9_4"/><b>then </b>
<font color="Maroon" title="c18">e</font> <a href="orders_2.html#R1" title="ORDERS_2:pred.1">&lt;=</a> <font color="Maroon" title="c16">c</font>
 <b>by </b><i><a class="ref" href="yellow_0.html#T61" title="YELLOW_0:th.61">YELLOW_0:61</a></i>;<br/><a NAME="E4:15_1_9_4"/><b>then </b>
<font color="Maroon" title="c10">t</font> <a href="orders_2.html#R3" title="ORDERS_2:pred.3">&lt;=</a> <font color="Maroon" title="c8">dj</font>
 <b>by </b><i><a class="txt" href="yellow11.html#E4:15_1"><i><font color="Green" title="E14">A3</font></i></a>, <a class="ref" href="waybel_0.html#T66" title="WAYBEL_0:th.66">WAYBEL_0:66</a></i>;<br/><a NAME="E5:15_1_9_4"/><b>then </b><i><font color="Green" title="E22">A34</font></i>: 
<font color="Maroon" title="c10">t</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <font color="Maroon" title="c8">dj</font>
 <b>by </b><i><a class="ref" href="yellow_1.html#T3" title="YELLOW_1:th.3">YELLOW_1:3</a></i>;<br/><a NAME="E6:15_1_9_4"/>
2 <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c10">t</font>
 <b>by </b><i><a class="ref" href="yellow11.html#T1" target="_self" title="YELLOW11:th.1">Th1</a>, <a class="ref" href="enumset1.html#D1" title="ENUMSET1:def.1">ENUMSET1:def 1</a></i>;<br/><b>hence </b><a NAME="E7:15_1_9_4"/>
contradiction
 <b>by </b><i><a class="txt" href="yellow11.html#E5:15_1_9_4"><i><font color="Green" title="E22">A34</font></i></a>, <a class="ref" href="yellow11.html#T2" target="_self" title="YELLOW11:th.2">Th2</a>, <a class="ref" href="tarski.html#D1" title="TARSKI:def.1">TARSKI:def 1</a></i>;<br/></div><b>end;</b></div>
<b>hence </b><a NAME="E11:15_1_9"/>
<font color="Maroon" title="c22">C</font> <a href="lattice3.html#K12" title="LATTICE3:func.12">"/\"</a> <font color="Maroon" title="c23">D</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c20">A</font>
 <b>by </b><i><a class="txt" href="yellow11.html#E1:15"><i><font color="Green" title="E12">A1</font></i></a>, <a class="txt" href="yellow11.html#E5:15_1_9"><i><font color="Green" title="E18">A27</font></i></a>, <a class="txt" href="yellow11.html#E7:15_1_9"><i><font color="Green" title="E19">A28</font></i></a>, <a class="txt" href="yellow11.html#E8:15_1_9"><i><font color="Green" title="E20">A30</font></i></a>, <a class="txt" href="yellow11.html#E9:15_1_9"><i><font color="Green" title="E21">A32</font></i></a>, <a class="ref" href="enumset1.html#D3" title="ENUMSET1:def.3">ENUMSET1:def 3</a></i>;<br/>


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

<b>thus </b><a NAME="E68:15_1"/>
<font color="Maroon" title="c21">B</font> <a href="lattice3.html#K13" title="LATTICE3:func.13">"\/"</a> <font color="Maroon" title="c22">C</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c24">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" title="c21">B</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c5">K</font> &amp; <font color="Maroon" title="c21">B</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c5">K</font> &amp;  <a href="yellow_0.html#R1" title="YELLOW_0:pred.1">ex_sup_of</a> <span class="p1"><a href="domain_1.html#K7" title="DOMAIN_1:func.7">{</a><span class="default"><font color="Maroon" title="c21">B</font>,<font color="Maroon" title="c22">C</font></span><a href="domain_1.html#K7" title="DOMAIN_1:func.7">}</a></span>,<font color="Maroon" title="c1">L</font> )
 
<b>by </b><i><a class="ref" href="yellow_0.html#T20" title="YELLOW_0:th.20">YELLOW_0:20</a></i>;<br/>
<a NAME="E2:15_1_10"/><b>then </b>
 <a href="yellow_0.html#NK3" title="YELLOW_0:NK.3">sup</a> <span class="p1"><a href="domain_1.html#K7" title="DOMAIN_1:func.7">{</a><span class="default"><font color="Maroon" title="c21">B</font>,<font color="Maroon" title="c22">C</font></span><a href="domain_1.html#K7" title="DOMAIN_1:func.7">}</a></span> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c5">K</font>
 
<b>by </b><i><a class="ref" href="yellow_0.html#D17" title="YELLOW_0:def.17">YELLOW_0:def 17</a></i>;<br/>
<a NAME="E3:15_1_10"/><b>then </b>
<font color="Maroon" title="c21">B</font> <a href="lattice3.html#K13" title="LATTICE3:func.13">"\/"</a> <font color="Maroon" title="c22">C</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="relset_1.html#K5" title="RELSET_1:func.5">rng</a> <font color="Maroon" title="c4">f</font>
 
<b>by </b><i><a class="txt" href="yellow11.html#E15:15_1"><i><font color="Green" title="E17">A6</font></i></a>, <a class="ref" href="yellow_0.html#T41" title="YELLOW_0:th.41">YELLOW_0:41</a></i>;<br/>
<b>then consider </b><font color="Maroon" title="c25">x</font> being    <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a> <b> such that </b><br/><a NAME="E5:15_1_10"/><i><font color="Green" title="E18">A35</font></i>: 
( <font color="Maroon" title="c25">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="relset_1.html#K4" title="RELSET_1:func.4">dom</a> <font color="Maroon" title="c4">f</font> &amp; <font color="Maroon" title="c21">B</font> <a href="lattice3.html#K13" title="LATTICE3:func.13">"\/"</a> <font color="Maroon" title="c22">C</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c4">f</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c25">x</font> )
 <b>by </b><i><a class="ref" href="funct_1.html#D5" title="FUNCT_1:def.5">FUNCT_1:def 5</a></i>;<br/>
<b>reconsider </b><font color="Maroon" title="c26">x</font> = <font color="Maroon" title="c25">x</font> as   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <a href="yellow11.html#K2" title="YELLOW11:func.2">M_3</a>  <b>by </b><i><a class="txt" href="yellow11.html#E5:15_1_10"><i><font color="Green" title="E18">A35</font></i></a></i>;<br/>
<div><i><font color="Green" title="E19">A36</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" title="c21">B</font> <a href="lattice3.html#K13" title="LATTICE3:func.13">"\/"</a> <font color="Maroon" title="c22">C</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c21">B</font>
 ;<br/><a NAME="E2:15_1_10_1"/><b>then </b>
<font color="Maroon" title="c21">B</font> <a href="orders_2.html#NR2" title="ORDERS_2:NR.2">&gt;=</a> <font color="Maroon" title="c22">C</font>
 <b>by </b><i><a class="ref" href="yellow_0.html#T24" title="YELLOW_0:th.24">YELLOW_0:24</a></i>;<br/><a NAME="E3:15_1_10_1"/><b>then </b>
<font color="Maroon" title="c15">b</font> <a href="orders_2.html#NR2" title="ORDERS_2:NR.2">&gt;=</a> <font color="Maroon" title="c16">c</font>
 <b>by </b><i><a class="ref" href="yellow_0.html#T61" title="YELLOW_0:th.61">YELLOW_0:61</a></i>;<br/><a NAME="E4:15_1_10_1"/><b>then </b>
<font color="Maroon" title="c7">j</font> <a href="orders_2.html#NR2" title="ORDERS_2:NR.2">&gt;=</a> <font color="Maroon" title="c8">dj</font>
 <b>by </b><i><a class="txt" href="yellow11.html#E4:15_1"><i><font color="Green" title="E14">A3</font></i></a>, <a class="ref" href="waybel_0.html#T66" title="WAYBEL_0:th.66">WAYBEL_0:66</a></i>;<br/><a NAME="E5:15_1_10_1"/><b>then </b><i><font color="Green" title="E20">A37</font></i>: 
<font color="Maroon" title="c8">dj</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <font color="Maroon" title="c7">j</font>
 <b>by </b><i><a class="ref" href="yellow_1.html#T3" title="YELLOW_1:th.3">YELLOW_1:3</a></i>;<br/><a NAME="E6:15_1_10_1"/>
( 1 <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c8">dj</font> &amp; 0 <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> 1 )
 <b>by </b><i><a class="ref" href="yellow11.html#T2" target="_self" title="YELLOW11:th.2">Th2</a>, <a class="ref" href="tarski.html#D1" title="TARSKI:def.1">TARSKI:def 1</a></i>;<br/><b>hence </b><a NAME="E7:15_1_10_1"/>
contradiction
 <b>by </b><i><a class="txt" href="yellow11.html#E5:15_1_10_1"><i><font color="Green" title="E20">A37</font></i></a>, <a class="ref" href="card_5.html#T1" title="CARD_5:th.1">CARD_5:1</a>, <a class="ref" href="tarski.html#D1" title="TARSKI:def.1">TARSKI:def 1</a></i>;<br/></div><b>end;</b></div>
<div><i><font color="Green" title="E20">A38</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" title="c21">B</font> <a href="lattice3.html#K13" title="LATTICE3:func.13">"\/"</a> <font color="Maroon" title="c22">C</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c22">C</font>
 ;<br/><a NAME="E2:15_1_10_2"/><b>then </b>
<font color="Maroon" title="c22">C</font> <a href="orders_2.html#NR2" title="ORDERS_2:NR.2">&gt;=</a> <font color="Maroon" title="c21">B</font>
 <b>by </b><i><a class="ref" href="yellow_0.html#T24" title="YELLOW_0:th.24">YELLOW_0:24</a></i>;<br/><a NAME="E3:15_1_10_2"/><b>then </b>
<font color="Maroon" title="c16">c</font> <a href="orders_2.html#NR2" title="ORDERS_2:NR.2">&gt;=</a> <font color="Maroon" title="c15">b</font>
 <b>by </b><i><a class="ref" href="yellow_0.html#T61" title="YELLOW_0:th.61">YELLOW_0:61</a></i>;<br/><a NAME="E4:15_1_10_2"/><b>then </b>
<font color="Maroon" title="c8">dj</font> <a href="orders_2.html#NR2" title="ORDERS_2:NR.2">&gt;=</a> <font color="Maroon" title="c7">j</font>
 <b>by </b><i><a class="txt" href="yellow11.html#E4:15_1"><i><font color="Green" title="E14">A3</font></i></a>, <a class="ref" href="waybel_0.html#T66" title="WAYBEL_0:th.66">WAYBEL_0:66</a></i>;<br/><a NAME="E5:15_1_10_2"/><b>then </b><i><font color="Green" title="E21">A39</font></i>: 
<font color="Maroon" title="c7">j</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <font color="Maroon" title="c8">dj</font>
 <b>by </b><i><a class="ref" href="yellow_1.html#T3" title="YELLOW_1:th.3">YELLOW_1:3</a></i>;<br/><a NAME="E6:15_1_10_2"/>
0 <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c7">j</font>
 <b>by </b><i><a class="ref" href="card_5.html#T1" title="CARD_5:th.1">CARD_5:1</a>, <a class="ref" href="tarski.html#D1" title="TARSKI:def.1">TARSKI:def 1</a></i>;<br/><b>hence </b><a NAME="E7:15_1_10_2"/>
contradiction
 <b>by </b><i><a class="txt" href="yellow11.html#E5:15_1_10_2"><i><font color="Green" title="E21">A39</font></i></a>, <a class="ref" href="yellow11.html#T2" target="_self" title="YELLOW11:th.2">Th2</a>, <a class="ref" href="tarski.html#D1" title="TARSKI:def.1">TARSKI:def 1</a></i>;<br/></div><b>end;</b></div>
<div><i><font color="Green" title="E21">A40</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" title="c21">B</font> <a href="lattice3.html#K13" title="LATTICE3:func.13">"\/"</a> <font color="Maroon" title="c22">C</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c23">D</font>
 ;<br/><a NAME="E2:15_1_10_3"/><b>then </b>
<font color="Maroon" title="c23">D</font> <a href="orders_2.html#NR2" title="ORDERS_2:NR.2">&gt;=</a> <font color="Maroon" title="c22">C</font>
 <b>by </b><i><a class="ref" href="yellow_0.html#T22" title="YELLOW_0:th.22">YELLOW_0:22</a></i>;<br/><a NAME="E3:15_1_10_3"/><b>then </b>
<font color="Maroon" title="c17">d</font> <a href="orders_2.html#NR2" title="ORDERS_2:NR.2">&gt;=</a> <font color="Maroon" title="c16">c</font>
 <b>by </b><i><a class="ref" href="yellow_0.html#T61" title="YELLOW_0:th.61">YELLOW_0:61</a></i>;<br/><a NAME="E4:15_1_10_3"/><b>then </b>
<font color="Maroon" title="c9">td</font> <a href="orders_2.html#NR2" title="ORDERS_2:NR.2">&gt;=</a> <font color="Maroon" title="c8">dj</font>
 <b>by </b><i><a class="txt" href="yellow11.html#E4:15_1"><i><font color="Green" title="E14">A3</font></i></a>, <a class="ref" href="waybel_0.html#T66" title="WAYBEL_0:th.66">WAYBEL_0:66</a></i>;<br/><a NAME="E5:15_1_10_3"/><b>then </b><i><font color="Green" title="E22">A41</font></i>: 
<font color="Maroon" title="c8">dj</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <font color="Maroon" title="c9">td</font>
 <b>by </b><i><a class="ref" href="yellow_1.html#T3" title="YELLOW_1:th.3">YELLOW_1:3</a></i>;<br/><a NAME="E6:15_1_10_3"/>
( 1 <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c8">dj</font> &amp; 2 <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> 1 )
 <b>by </b><i><a class="ref" href="yellow11.html#T2" target="_self" title="YELLOW11:th.2">Th2</a>, <a class="ref" href="tarski.html#D1" title="TARSKI:def.1">TARSKI:def 1</a></i>;<br/><b>hence </b><a NAME="E7:15_1_10_3"/>
contradiction
 <b>by </b><i><a class="txt" href="yellow11.html#E5:15_1_10_3"><i><font color="Green" title="E22">A41</font></i></a>, <a class="ref" href="yellow11.html#T4" target="_self" title="YELLOW11:th.4">Th4</a>, <a class="ref" href="tarski.html#D1" title="TARSKI:def.1">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" title="c21">B</font> <a href="lattice3.html#K13" title="LATTICE3:func.13">"\/"</a> <font color="Maroon" title="c22">C</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c20">A</font>
 ;<br/><a NAME="E2:15_1_10_4"/><b>then </b>
<font color="Maroon" title="c20">A</font> <a href="orders_2.html#NR2" title="ORDERS_2:NR.2">&gt;=</a> <font color="Maroon" title="c22">C</font>
 <b>by </b><i><a class="ref" href="yellow_0.html#T22" title="YELLOW_0:th.22">YELLOW_0:22</a></i>;<br/><a NAME="E3:15_1_10_4"/><b>then </b>
<font color="Maroon" title="c14">a</font> <a href="orders_2.html#NR2" title="ORDERS_2:NR.2">&gt;=</a> <font color="Maroon" title="c16">c</font>
 <b>by </b><i><a class="ref" href="yellow_0.html#T61" title="YELLOW_0:th.61">YELLOW_0:61</a></i>;<br/><a NAME="E4:15_1_10_4"/><b>then </b>
<font color="Maroon" title="c6">z</font> <a href="orders_2.html#NR2" title="ORDERS_2:NR.2">&gt;=</a> <font color="Maroon" title="c8">dj</font>
 <b>by </b><i><a class="txt" href="yellow11.html#E4:15_1"><i><font color="Green" title="E14">A3</font></i></a>, <a class="ref" href="waybel_0.html#T66" title="WAYBEL_0:th.66">WAYBEL_0:66</a></i>;<br/><a NAME="E5:15_1_10_4"/><b>then </b>
<font color="Maroon" title="c8">dj</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <font color="Maroon" title="c6">z</font>
 <b>by </b><i><a class="ref" href="yellow_1.html#T3" title="YELLOW_1:th.3">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="yellow11.html#T2" target="_self" title="YELLOW11:th.2">Th2</a>, <a class="ref" href="xboole_1.html#T3" title="XBOOLE_1:th.3">XBOOLE_1:3</a></i>;<br/></div><b>end;</b></div>
<b>hence </b><a NAME="E11:15_1_10"/>
<font color="Maroon" title="c21">B</font> <a href="lattice3.html#K13" title="LATTICE3:func.13">"\/"</a> <font color="Maroon" title="c22">C</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c24">E</font>
 <b>by </b><i><a class="txt" href="yellow11.html#E1:15"><i><font color="Green" title="E12">A1</font></i></a>, <a class="txt" href="yellow11.html#E5:15_1_10"><i><font color="Green" title="E18">A35</font></i></a>, <a class="txt" href="yellow11.html#E7:15_1_10"><i><font color="Green" title="E19">A36</font></i></a>, <a class="txt" href="yellow11.html#E8:15_1_10"><i><font color="Green" title="E20">A38</font></i></a>, <a class="txt" href="yellow11.html#E9:15_1_10"><i><font color="Green" title="E21">A40</font></i></a>, <a class="ref" href="enumset1.html#D3" title="ENUMSET1:def.3">ENUMSET1:def 3</a></i>;<br/>


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

<b>thus </b><a NAME="E69:15_1"/>
<font color="Maroon" title="c21">B</font> <a href="lattice3.html#K13" title="LATTICE3:func.13">"\/"</a> <font color="Maroon" title="c23">D</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c24">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" title="c21">B</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c5">K</font> &amp; <font color="Maroon" title="c23">D</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c5">K</font> &amp;  <a href="yellow_0.html#R1" title="YELLOW_0:pred.1">ex_sup_of</a> <span class="p1"><a href="domain_1.html#K7" title="DOMAIN_1:func.7">{</a><span class="default"><font color="Maroon" title="c21">B</font>,<font color="Maroon" title="c23">D</font></span><a href="domain_1.html#K7" title="DOMAIN_1:func.7">}</a></span>,<font color="Maroon" title="c1">L</font> )
 
<b>by </b><i><a class="ref" href="yellow_0.html#T20" title="YELLOW_0:th.20">YELLOW_0:20</a></i>;<br/>
<a NAME="E2:15_1_11"/><b>then </b>
 <a href="yellow_0.html#NK3" title="YELLOW_0:NK.3">sup</a> <span class="p1"><a href="domain_1.html#K7" title="DOMAIN_1:func.7">{</a><span class="default"><font color="Maroon" title="c21">B</font>,<font color="Maroon" title="c23">D</font></span><a href="domain_1.html#K7" title="DOMAIN_1:func.7">}</a></span> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c5">K</font>
 
<b>by </b><i><a class="ref" href="yellow_0.html#D17" title="YELLOW_0:def.17">YELLOW_0:def 17</a></i>;<br/>
<a NAME="E3:15_1_11"/><b>then </b>
<font color="Maroon" title="c21">B</font> <a href="lattice3.html#K13" title="LATTICE3:func.13">"\/"</a> <font color="Maroon" title="c23">D</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="relset_1.html#K5" title="RELSET_1:func.5">rng</a> <font color="Maroon" title="c4">f</font>
 
<b>by </b><i><a class="txt" href="yellow11.html#E15:15_1"><i><font color="Green" title="E17">A6</font></i></a>, <a class="ref" href="yellow_0.html#T41" title="YELLOW_0:th.41">YELLOW_0:41</a></i>;<br/>
<b>then consider </b><font color="Maroon" title="c25">x</font> being    <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a> <b> such that </b><br/><a NAME="E5:15_1_11"/><i><font color="Green" title="E18">A42</font></i>: 
( <font color="Maroon" title="c25">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="relset_1.html#K4" title="RELSET_1:func.4">dom</a> <font color="Maroon" title="c4">f</font> &amp; <font color="Maroon" title="c21">B</font> <a href="lattice3.html#K13" title="LATTICE3:func.13">"\/"</a> <font color="Maroon" title="c23">D</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c4">f</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c25">x</font> )
 <b>by </b><i><a class="ref" href="funct_1.html#D5" title="FUNCT_1:def.5">FUNCT_1:def 5</a></i>;<br/>
<b>reconsider </b><font color="Maroon" title="c26">x</font> = <font color="Maroon" title="c25">x</font> as   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <a href="yellow11.html#K2" title="YELLOW11:func.2">M_3</a>  <b>by </b><i><a class="txt" href="yellow11.html#E5:15_1_11"><i><font color="Green" title="E18">A42</font></i></a></i>;<br/>
<div><i><font color="Green" title="E19">A43</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" title="c21">B</font> <a href="lattice3.html#K13" title="LATTICE3:func.13">"\/"</a> <font color="Maroon" title="c23">D</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c21">B</font>
 ;<br/><a NAME="E2:15_1_11_1"/><b>then </b>
<font color="Maroon" title="c21">B</font> <a href="orders_2.html#NR2" title="ORDERS_2:NR.2">&gt;=</a> <font color="Maroon" title="c23">D</font>
 <b>by </b><i><a class="ref" href="yellow_0.html#T22" title="YELLOW_0:th.22">YELLOW_0:22</a></i>;<br/><a NAME="E3:15_1_11_1"/><b>then </b>
<font color="Maroon" title="c15">b</font> <a href="orders_2.html#NR2" title="ORDERS_2:NR.2">&gt;=</a> <font color="Maroon" title="c17">d</font>
 <b>by </b><i><a class="ref" href="yellow_0.html#T61" title="YELLOW_0:th.61">YELLOW_0:61</a></i>;<br/><a NAME="E4:15_1_11_1"/><b>then </b>
<font color="Maroon" title="c7">j</font> <a href="orders_2.html#NR2" title="ORDERS_2:NR.2">&gt;=</a> <font color="Maroon" title="c9">td</font>
 <b>by </b><i><a class="txt" href="yellow11.html#E4:15_1"><i><font color="Green" title="E14">A3</font></i></a>, <a class="ref" href="waybel_0.html#T66" title="WAYBEL_0:th.66">WAYBEL_0:66</a></i>;<br/><a NAME="E5:15_1_11_1"/><b>then </b><i><font color="Green" title="E20">A44</font></i>: 
<font color="Maroon" title="c9">td</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <font color="Maroon" title="c7">j</font>
 <b>by </b><i><a class="ref" href="yellow_1.html#T3" title="YELLOW_1:th.3">YELLOW_1:3</a></i>;<br/><a NAME="E6:15_1_11_1"/>
( 2 <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c9">td</font> &amp; 2 <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> 0 )
 <b>by </b><i><a class="ref" href="yellow11.html#T4" target="_self" title="YELLOW11:th.4">Th4</a>, <a class="ref" href="tarski.html#D1" title="TARSKI:def.1">TARSKI:def 1</a></i>;<br/><b>hence </b><a NAME="E7:15_1_11_1"/>
contradiction
 <b>by </b><i><a class="txt" href="yellow11.html#E5:15_1_11_1"><i><font color="Green" title="E20">A44</font></i></a>, <a class="ref" href="card_5.html#T1" title="CARD_5:th.1">CARD_5:1</a>, <a class="ref" href="tarski.html#D1" title="TARSKI:def.1">TARSKI:def 1</a></i>;<br/></div><b>end;</b></div>
<div><i><font color="Green" title="E20">A45</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" title="c21">B</font> <a href="lattice3.html#K13" title="LATTICE3:func.13">"\/"</a> <font color="Maroon" title="c23">D</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c22">C</font>
 ;<br/><a NAME="E2:15_1_11_2"/><b>then </b>
<font color="Maroon" title="c22">C</font> <a href="orders_2.html#NR2" title="ORDERS_2:NR.2">&gt;=</a> <font color="Maroon" title="c23">D</font>
 <b>by </b><i><a class="ref" href="yellow_0.html#T22" title="YELLOW_0:th.22">YELLOW_0:22</a></i>;<br/><a NAME="E3:15_1_11_2"/><b>then </b>
<font color="Maroon" title="c16">c</font> <a href="orders_2.html#NR2" title="ORDERS_2:NR.2">&gt;=</a> <font color="Maroon" title="c17">d</font>
 <b>by </b><i><a class="ref" href="yellow_0.html#T61" title="YELLOW_0:th.61">YELLOW_0:61</a></i>;<br/><a NAME="E4:15_1_11_2"/><b>then </b>
<font color="Maroon" title="c8">dj</font> <a href="orders_2.html#NR2" title="ORDERS_2:NR.2">&gt;=</a> <font color="Maroon" title="c9">td</font>
 <b>by </b><i><a class="txt" href="yellow11.html#E4:15_1"><i><font color="Green" title="E14">A3</font></i></a>, <a class="ref" href="waybel_0.html#T66" title="WAYBEL_0:th.66">WAYBEL_0:66</a></i>;<br/><a NAME="E5:15_1_11_2"/><b>then </b><i><font color="Green" title="E21">A46</font></i>: 
<font color="Maroon" title="c9">td</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <font color="Maroon" title="c8">dj</font>
 <b>by </b><i><a class="ref" href="yellow_1.html#T3" title="YELLOW_1:th.3">YELLOW_1:3</a></i>;<br/><a NAME="E6:15_1_11_2"/>
( 2 <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c9">td</font> &amp; 2 <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> 1 )
 <b>by </b><i><a class="ref" href="yellow11.html#T4" target="_self" title="YELLOW11:th.4">Th4</a>, <a class="ref" href="tarski.html#D1" title="TARSKI:def.1">TARSKI:def 1</a></i>;<br/><b>hence </b><a NAME="E7:15_1_11_2"/>
contradiction
 <b>by </b><i><a class="txt" href="yellow11.html#E5:15_1_11_2"><i><font color="Green" title="E21">A46</font></i></a>, <a class="ref" href="yellow11.html#T2" target="_self" title="YELLOW11:th.2">Th2</a>, <a class="ref" href="tarski.html#D1" title="TARSKI:def.1">TARSKI:def 1</a></i>;<br/></div><b>end;</b></div>
<div><i><font color="Green" title="E21">A47</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" title="c21">B</font> <a href="lattice3.html#K13" title="LATTICE3:func.13">"\/"</a> <font color="Maroon" title="c23">D</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c23">D</font>
 ;<br/><a NAME="E2:15_1_11_3"/><b>then </b>
<font color="Maroon" title="c23">D</font> <a href="orders_2.html#NR2" title="ORDERS_2:NR.2">&gt;=</a> <font color="Maroon" title="c21">B</font>
 <b>by </b><i><a class="ref" href="yellow_0.html#T22" title="YELLOW_0:th.22">YELLOW_0:22</a></i>;<br/><a NAME="E3:15_1_11_3"/><b>then </b>
<font color="Maroon" title="c17">d</font> <a href="orders_2.html#NR2" title="ORDERS_2:NR.2">&gt;=</a> <font color="Maroon" title="c15">b</font>
 <b>by </b><i><a class="ref" href="yellow_0.html#T61" title="YELLOW_0:th.61">YELLOW_0:61</a></i>;<br/><a NAME="E4:15_1_11_3"/><b>then </b>
<font color="Maroon" title="c9">td</font> <a href="orders_2.html#NR2" title="ORDERS_2:NR.2">&gt;=</a> <font color="Maroon" title="c7">j</font>
 <b>by </b><i><a class="txt" href="yellow11.html#E4:15_1"><i><font color="Green" title="E14">A3</font></i></a>, <a class="ref" href="waybel_0.html#T66" title="WAYBEL_0:th.66">WAYBEL_0:66</a></i>;<br/><a NAME="E5:15_1_11_3"/><b>then </b><i><font color="Green" title="E22">A48</font></i>: 
<font color="Maroon" title="c7">j</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <font color="Maroon" title="c9">td</font>
 <b>by </b><i><a class="ref" href="yellow_1.html#T3" title="YELLOW_1:th.3">YELLOW_1:3</a></i>;<br/><a NAME="E6:15_1_11_3"/>
( 0 <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c7">j</font> &amp; 0 <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> 2 )
 <b>by </b><i><a class="ref" href="card_5.html#T1" title="CARD_5:th.1">CARD_5:1</a>, <a class="ref" href="tarski.html#D1" title="TARSKI:def.1">TARSKI:def 1</a></i>;<br/><b>hence </b><a NAME="E7:15_1_11_3"/>
contradiction
 <b>by </b><i><a class="txt" href="yellow11.html#E5:15_1_11_3"><i><font color="Green" title="E22">A48</font></i></a>, <a class="ref" href="yellow11.html#T4" target="_self" title="YELLOW11:th.4">Th4</a>, <a class="ref" href="tarski.html#D1" title="TARSKI:def.1">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" title="c21">B</font> <a href="lattice3.html#K13" title="LATTICE3:func.13">"\/"</a> <font color="Maroon" title="c23">D</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c20">A</font>
 ;<br/><a NAME="E2:15_1_11_4"/><b>then </b>
<font color="Maroon" title="c20">A</font> <a href="orders_2.html#NR2" title="ORDERS_2:NR.2">&gt;=</a> <font color="Maroon" title="c21">B</font>
 <b>by </b><i><a class="ref" href="yellow_0.html#T22" title="YELLOW_0:th.22">YELLOW_0:22</a></i>;<br/><a NAME="E3:15_1_11_4"/><b>then </b>
<font color="Maroon" title="c14">a</font> <a href="orders_2.html#NR2" title="ORDERS_2:NR.2">&gt;=</a> <font color="Maroon" title="c15">b</font>
 <b>by </b><i><a class="ref" href="yellow_0.html#T61" title="YELLOW_0:th.61">YELLOW_0:61</a></i>;<br/><a NAME="E4:15_1_11_4"/><b>then </b>
<font color="Maroon" title="c6">z</font> <a href="orders_2.html#NR2" title="ORDERS_2:NR.2">&gt;=</a> <font color="Maroon" title="c7">j</font>
 <b>by </b><i><a class="txt" href="yellow11.html#E4:15_1"><i><font color="Green" title="E14">A3</font></i></a>, <a class="ref" href="waybel_0.html#T66" title="WAYBEL_0:th.66">WAYBEL_0:66</a></i>;<br/><a NAME="E5:15_1_11_4"/><b>then </b>
<font color="Maroon" title="c7">j</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <font color="Maroon" title="c6">z</font>
 <b>by </b><i><a class="ref" href="yellow_1.html#T3" title="YELLOW_1:th.3">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" title="XBOOLE_1:th.3">XBOOLE_1:3</a></i>;<br/></div><b>end;</b></div>
<b>hence </b><a NAME="E11:15_1_11"/>
<font color="Maroon" title="c21">B</font> <a href="lattice3.html#K13" title="LATTICE3:func.13">"\/"</a> <font color="Maroon" title="c23">D</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c24">E</font>
 <b>by </b><i><a class="txt" href="yellow11.html#E1:15"><i><font color="Green" title="E12">A1</font></i></a>, <a class="txt" href="yellow11.html#E5:15_1_11"><i><font color="Green" title="E18">A42</font></i></a>, <a class="txt" href="yellow11.html#E7:15_1_11"><i><font color="Green" title="E19">A43</font></i></a>, <a class="txt" href="yellow11.html#E8:15_1_11"><i><font color="Green" title="E20">A45</font></i></a>, <a class="txt" href="yellow11.html#E9:15_1_11"><i><font color="Green" title="E21">A47</font></i></a>, <a class="ref" href="enumset1.html#D3" title="ENUMSET1:def.3">ENUMSET1:def 3</a></i>;<br/>


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

<b>thus </b><a NAME="E70:15_1"/>
<font color="Maroon" title="c22">C</font> <a href="lattice3.html#K13" title="LATTICE3:func.13">"\/"</a> <font color="Maroon" title="c23">D</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c24">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" title="c22">C</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c5">K</font> &amp; <font color="Maroon" title="c23">D</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c5">K</font> &amp;  <a href="yellow_0.html#R1" title="YELLOW_0:pred.1">ex_sup_of</a> <span class="p1"><a href="domain_1.html#K7" title="DOMAIN_1:func.7">{</a><span class="default"><font color="Maroon" title="c22">C</font>,<font color="Maroon" title="c23">D</font></span><a href="domain_1.html#K7" title="DOMAIN_1:func.7">}</a></span>,<font color="Maroon" title="c1">L</font> )
 
<b>by </b><i><a class="ref" href="yellow_0.html#T20" title="YELLOW_0:th.20">YELLOW_0:20</a></i>;<br/>
<a NAME="E2:15_1_12"/><b>then </b>
 <a href="yellow_0.html#NK3" title="YELLOW_0:NK.3">sup</a> <span class="p1"><a href="domain_1.html#K7" title="DOMAIN_1:func.7">{</a><span class="default"><font color="Maroon" title="c22">C</font>,<font color="Maroon" title="c23">D</font></span><a href="domain_1.html#K7" title="DOMAIN_1:func.7">}</a></span> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c5">K</font>
 
<b>by </b><i><a class="ref" href="yellow_0.html#D17" title="YELLOW_0:def.17">YELLOW_0:def 17</a></i>;<br/>
<a NAME="E3:15_1_12"/><b>then </b>
<font color="Maroon" title="c22">C</font> <a href="lattice3.html#K13" title="LATTICE3:func.13">"\/"</a> <font color="Maroon" title="c23">D</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="relset_1.html#K5" title="RELSET_1:func.5">rng</a> <font color="Maroon" title="c4">f</font>
 
<b>by </b><i><a class="txt" href="yellow11.html#E15:15_1"><i><font color="Green" title="E17">A6</font></i></a>, <a class="ref" href="yellow_0.html#T41" title="YELLOW_0:th.41">YELLOW_0:41</a></i>;<br/>
<b>then consider </b><font color="Maroon" title="c25">x</font> being    <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a> <b> such that </b><br/><a NAME="E5:15_1_12"/><i><font color="Green" title="E18">A49</font></i>: 
( <font color="Maroon" title="c25">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="relset_1.html#K4" title="RELSET_1:func.4">dom</a> <font color="Maroon" title="c4">f</font> &amp; <font color="Maroon" title="c22">C</font> <a href="lattice3.html#K13" title="LATTICE3:func.13">"\/"</a> <font color="Maroon" title="c23">D</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c4">f</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c25">x</font> )
 <b>by </b><i><a class="ref" href="funct_1.html#D5" title="FUNCT_1:def.5">FUNCT_1:def 5</a></i>;<br/>
<b>reconsider </b><font color="Maroon" title="c26">x</font> = <font color="Maroon" title="c25">x</font> as   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <a href="yellow11.html#K2" title="YELLOW11:func.2">M_3</a>  <b>by </b><i><a class="txt" href="yellow11.html#E5:15_1_12"><i><font color="Green" title="E18">A49</font></i></a></i>;<br/>
<div><i><font color="Green" title="E19">A50</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" title="c22">C</font> <a href="lattice3.html#K13" title="LATTICE3:func.13">"\/"</a> <font color="Maroon" title="c23">D</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c21">B</font>
 ;<br/><a NAME="E2:15_1_12_1"/><b>then </b>
<font color="Maroon" title="c21">B</font> <a href="orders_2.html#NR2" title="ORDERS_2:NR.2">&gt;=</a> <font color="Maroon" title="c22">C</font>
 <b>by </b><i><a class="ref" href="yellow_0.html#T22" title="YELLOW_0:th.22">YELLOW_0:22</a></i>;<br/><a NAME="E3:15_1_12_1"/><b>then </b>
<font color="Maroon" title="c15">b</font> <a href="orders_2.html#NR2" title="ORDERS_2:NR.2">&gt;=</a> <font color="Maroon" title="c16">c</font>
 <b>by </b><i><a class="ref" href="yellow_0.html#T61" title="YELLOW_0:th.61">YELLOW_0:61</a></i>;<br/><a NAME="E4:15_1_12_1"/><b>then </b>
<font color="Maroon" title="c7">j</font> <a href="orders_2.html#NR2" title="ORDERS_2:NR.2">&gt;=</a> <font color="Maroon" title="c8">dj</font>
 <b>by </b><i><a class="txt" href="yellow11.html#E4:15_1"><i><font color="Green" title="E14">A3</font></i></a>, <a class="ref" href="waybel_0.html#T66" title="WAYBEL_0:th.66">WAYBEL_0:66</a></i>;<br/><a NAME="E5:15_1_12_1"/><b>then </b><i><font color="Green" title="E20">A51</font></i>: 
<font color="Maroon" title="c8">dj</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <font color="Maroon" title="c7">j</font>
 <b>by </b><i><a class="ref" href="yellow_1.html#T3" title="YELLOW_1:th.3">YELLOW_1:3</a></i>;<br/><a NAME="E6:15_1_12_1"/>
1 <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c8">dj</font>
 <b>by </b><i><a class="ref" href="yellow11.html#T2" target="_self" title="YELLOW11:th.2">Th2</a>, <a class="ref" href="tarski.html#D1" title="TARSKI:def.1">TARSKI:def 1</a></i>;<br/><a NAME="E7:15_1_12_1"/><b>then </b>
1 <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> 1
 <b>by </b><i><a class="txt" href="yellow11.html#E5:15_1_12_1"><i><font color="Green" title="E20">A51</font></i></a></i>;<br/><b>hence </b><a NAME="E8:15_1_12_1"/>
contradiction
 ;<br/></div><b>end;</b></div>
<div><i><font color="Green" title="E20">A52</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" title="c22">C</font> <a href="lattice3.html#K13" title="LATTICE3:func.13">"\/"</a> <font color="Maroon" title="c23">D</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c22">C</font>
 ;<br/><a NAME="E2:15_1_12_2"/><b>then </b>
<font color="Maroon" title="c22">C</font> <a href="orders_2.html#NR2" title="ORDERS_2:NR.2">&gt;=</a> <font color="Maroon" title="c23">D</font>
 <b>by </b><i><a class="ref" href="yellow_0.html#T24" title="YELLOW_0:th.24">YELLOW_0:24</a></i>;<br/><a NAME="E3:15_1_12_2"/><b>then </b>
<font color="Maroon" title="c16">c</font> <a href="orders_2.html#NR2" title="ORDERS_2:NR.2">&gt;=</a> <font color="Maroon" title="c17">d</font>
 <b>by </b><i><a class="ref" href="yellow_0.html#T61" title="YELLOW_0:th.61">YELLOW_0:61</a></i>;<br/><a NAME="E4:15_1_12_2"/><b>then </b>
<font color="Maroon" title="c8">dj</font> <a href="orders_2.html#NR2" title="ORDERS_2:NR.2">&gt;=</a> <font color="Maroon" title="c9">td</font>
 <b>by </b><i><a class="txt" href="yellow11.html#E4:15_1"><i><font color="Green" title="E14">A3</font></i></a>, <a class="ref" href="waybel_0.html#T66" title="WAYBEL_0:th.66">WAYBEL_0:66</a></i>;<br/><a NAME="E5:15_1_12_2"/><b>then </b><i><font color="Green" title="E21">A53</font></i>: 
<font color="Maroon" title="c9">td</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <font color="Maroon" title="c8">dj</font>
 <b>by </b><i><a class="ref" href="yellow_1.html#T3" title="YELLOW_1:th.3">YELLOW_1:3</a></i>;<br/><a NAME="E6:15_1_12_2"/>
( 2 <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c9">td</font> &amp; 2 <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> 1 )
 <b>by </b><i><a class="ref" href="yellow11.html#T4" target="_self" title="YELLOW11:th.4">Th4</a>, <a class="ref" href="tarski.html#D1" title="TARSKI:def.1">TARSKI:def 1</a></i>;<br/><b>hence </b><a NAME="E7:15_1_12_2"/>
contradiction
 <b>by </b><i><a class="txt" href="yellow11.html#E5:15_1_12_2"><i><font color="Green" title="E21">A53</font></i></a>, <a class="ref" href="yellow11.html#T2" target="_self" title="YELLOW11:th.2">Th2</a>, <a class="ref" href="tarski.html#D1" title="TARSKI:def.1">TARSKI:def 1</a></i>;<br/></div><b>end;</b></div>
<div><i><font color="Green" title="E21">A54</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" title="c22">C</font> <a href="lattice3.html#K13" title="LATTICE3:func.13">"\/"</a> <font color="Maroon" title="c23">D</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c23">D</font>
 ;<br/><a NAME="E2:15_1_12_3"/><b>then </b>
<font color="Maroon" title="c23">D</font> <a href="orders_2.html#NR2" title="ORDERS_2:NR.2">&gt;=</a> <font color="Maroon" title="c22">C</font>
 <b>by </b><i><a class="ref" href="yellow_0.html#T22" title="YELLOW_0:th.22">YELLOW_0:22</a></i>;<br/><a NAME="E3:15_1_12_3"/><b>then </b>
<font color="Maroon" title="c17">d</font> <a href="orders_2.html#NR2" title="ORDERS_2:NR.2">&gt;=</a> <font color="Maroon" title="c16">c</font>
 <b>by </b><i><a class="ref" href="yellow_0.html#T61" title="YELLOW_0:th.61">YELLOW_0:61</a></i>;<br/><a NAME="E4:15_1_12_3"/><b>then </b>
<font color="Maroon" title="c9">td</font> <a href="orders_2.html#NR2" title="ORDERS_2:NR.2">&gt;=</a> <font color="Maroon" title="c8">dj</font>
 <b>by </b><i><a class="txt" href="yellow11.html#E4:15_1"><i><font color="Green" title="E14">A3</font></i></a>, <a class="ref" href="waybel_0.html#T66" title="WAYBEL_0:th.66">WAYBEL_0:66</a></i>;<br/><a NAME="E5:15_1_12_3"/><b>then </b><i><font color="Green" title="E22">A55</font></i>: 
<font color="Maroon" title="c8">dj</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <font color="Maroon" title="c9">td</font>
 <b>by </b><i><a class="ref" href="yellow_1.html#T3" title="YELLOW_1:th.3">YELLOW_1:3</a></i>;<br/><a NAME="E6:15_1_12_3"/>
( 1 <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c8">dj</font> &amp; 1 <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> 2 )
 <b>by </b><i><a class="ref" href="yellow11.html#T2" target="_self" title="YELLOW11:th.2">Th2</a>, <a class="ref" href="tarski.html#D1" title="TARSKI:def.1">TARSKI:def 1</a></i>;<br/><b>hence </b><a NAME="E7:15_1_12_3"/>
contradiction
 <b>by </b><i><a class="txt" href="yellow11.html#E5:15_1_12_3"><i><font color="Green" title="E22">A55</font></i></a>, <a class="ref" href="yellow11.html#T4" target="_self" title="YELLOW11:th.4">Th4</a>, <a class="ref" href="tarski.html#D1" title="TARSKI:def.1">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" title="c22">C</font> <a href="lattice3.html#K13" title="LATTICE3:func.13">"\/"</a> <font color="Maroon" title="c23">D</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c20">A</font>
 ;<br/><a NAME="E2:15_1_12_4"/><b>then </b>
<font color="Maroon" title="c20">A</font> <a href="orders_2.html#NR2" title="ORDERS_2:NR.2">&gt;=</a> <font color="Maroon" title="c22">C</font>
 <b>by </b><i><a class="ref" href="yellow_0.html#T22" title="YELLOW_0:th.22">YELLOW_0:22</a></i>;<br/><a NAME="E3:15_1_12_4"/><b>then </b>
<font color="Maroon" title="c14">a</font> <a href="orders_2.html#NR2" title="ORDERS_2:NR.2">&gt;=</a> <font color="Maroon" title="c16">c</font>
 <b>by </b><i><a class="ref" href="yellow_0.html#T61" title="YELLOW_0:th.61">YELLOW_0:61</a></i>;<br/><a NAME="E4:15_1_12_4"/><b>then </b>
<font color="Maroon" title="c6">z</font> <a href="orders_2.html#NR2" title="ORDERS_2:NR.2">&gt;=</a> <font color="Maroon" title="c8">dj</font>
 <b>by </b><i><a class="txt" href="yellow11.html#E4:15_1"><i><font color="Green" title="E14">A3</font></i></a>, <a class="ref" href="waybel_0.html#T66" title="WAYBEL_0:th.66">WAYBEL_0:66</a></i>;<br/><a NAME="E5:15_1_12_4"/><b>then </b>
<font color="Maroon" title="c8">dj</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <font color="Maroon" title="c6">z</font>
 <b>by </b><i><a class="ref" href="yellow_1.html#T3" title="YELLOW_1:th.3">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="yellow11.html#T2" target="_self" title="YELLOW11:th.2">Th2</a>, <a class="ref" href="xboole_1.html#T3" title="XBOOLE_1:th.3">XBOOLE_1:3</a></i>;<br/></div><b>end;</b></div>
<b>hence </b><a NAME="E11:15_1_12"/>
<font color="Maroon" title="c22">C</font> <a href="lattice3.html#K13" title="LATTICE3:func.13">"\/"</a> <font color="Maroon" title="c23">D</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c24">E</font>
 <b>by </b><i><a class="txt" href="yellow11.html#E1:15"><i><font color="Green" title="E12">A1</font></i></a>, <a class="txt" href="yellow11.html#E5:15_1_12"><i><font color="Green" title="E18">A49</font></i></a>, <a class="txt" href="yellow11.html#E7:15_1_12"><i><font color="Green" title="E19">A50</font></i></a>, <a class="txt" href="yellow11.html#E8:15_1_12"><i><font color="Green" title="E20">A52</font></i></a>, <a class="txt" href="yellow11.html#E9:15_1_12"><i><font color="Green" title="E21">A54</font></i></a>, <a class="ref" href="enumset1.html#D3" title="ENUMSET1:def.3">ENUMSET1:def 3</a></i>;<br/>


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


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

<b>thus </b><a NAME="E3:15"/>
(  ex <font color="Olive" title="b1">a</font>, <font color="Olive" title="b2">b</font>, <font color="Olive" title="b3">c</font>, <font color="Olive" title="b4">d</font>, <font color="Olive" title="b5">e</font> being  <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Maroon" title="c1">L</font> st <br/>( <font color="Olive" title="b1">a</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Olive" title="b2">b</font> &amp; <font color="Olive" title="b1">a</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Olive" title="b3">c</font> &amp; <font color="Olive" title="b1">a</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Olive" title="b4">d</font> &amp; <font color="Olive" title="b1">a</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Olive" title="b5">e</font> &amp; <font color="Olive" title="b2">b</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Olive" title="b3">c</font> &amp; <font color="Olive" title="b2">b</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Olive" title="b4">d</font> &amp; <font color="Olive" title="b2">b</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Olive" title="b5">e</font> &amp; <font color="Olive" title="b3">c</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Olive" title="b4">d</font> &amp; <font color="Olive" title="b3">c</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Olive" title="b5">e</font> &amp; <font color="Olive" title="b4">d</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Olive" title="b5">e</font> &amp; <font color="Olive" title="b1">a</font> <a href="lattice3.html#K12" title="LATTICE3:func.12">"/\"</a> <font color="Olive" title="b2">b</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b1">a</font> &amp; <font color="Olive" title="b1">a</font> <a href="lattice3.html#K12" title="LATTICE3:func.12">"/\"</a> <font color="Olive" title="b3">c</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b1">a</font> &amp; <font color="Olive" title="b1">a</font> <a href="lattice3.html#K12" title="LATTICE3:func.12">"/\"</a> <font color="Olive" title="b4">d</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b1">a</font> &amp; <font color="Olive" title="b2">b</font> <a href="lattice3.html#K12" title="LATTICE3:func.12">"/\"</a> <font color="Olive" title="b5">e</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b2">b</font> &amp; <font color="Olive" title="b3">c</font> <a href="lattice3.html#K12" title="LATTICE3:func.12">"/\"</a> <font color="Olive" title="b5">e</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b3">c</font> &amp; <font color="Olive" title="b4">d</font> <a href="lattice3.html#K12" title="LATTICE3:func.12">"/\"</a> <font color="Olive" title="b5">e</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b4">d</font> &amp; <font color="Olive" title="b2">b</font> <a href="lattice3.html#K12" title="LATTICE3:func.12">"/\"</a> <font color="Olive" title="b3">c</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b1">a</font> &amp; <font color="Olive" title="b2">b</font> <a href="lattice3.html#K12" title="LATTICE3:func.12">"/\"</a> <font color="Olive" title="b4">d</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b1">a</font> &amp; <font color="Olive" title="b3">c</font> <a href="lattice3.html#K12" title="LATTICE3:func.12">"/\"</a> <font color="Olive" title="b4">d</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b1">a</font> &amp; <font color="Olive" title="b2">b</font> <a href="lattice3.html#K13" title="LATTICE3:func.13">"\/"</a> <font color="Olive" title="b3">c</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b5">e</font> &amp; <font color="Olive" title="b2">b</font> <a href="lattice3.html#K13" title="LATTICE3:func.13">"\/"</a> <font color="Olive" title="b4">d</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b5">e</font> &amp; <font color="Olive" title="b3">c</font> <a href="lattice3.html#K13" title="LATTICE3:func.13">"\/"</a> <font color="Olive" title="b4">d</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b5">e</font> ) implies  ex <font color="Olive" title="b1">K</font> being <a href="yellow_0.html#V4" title="YELLOW_0:attr.4">full</a> <a href="lattice5.html#NM2" title="LATTICE5:NM.2">Sublattice</a> of <font color="Maroon" title="c1">L</font> st  <a href="yellow11.html#K2" title="YELLOW11:func.2">M_3</a> ,<font color="Olive" title="b1">K</font> <a href="waybel_1.html#R5" title="WAYBEL_1:pred.5">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" title="c3">a</font>, <font color="Maroon" title="c4">b</font>, <font color="Maroon" title="c5">c</font>, <font color="Maroon" title="c6">d</font>, <font color="Maroon" title="c7">e</font> being   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Maroon" title="c1">L</font><b> such that </b><a NAME="E2:15_2"/><i><font color="Green" title="E13">A56</font></i>: 
( <font color="Maroon" title="c3">a</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c4">b</font> &amp; <font color="Maroon" title="c3">a</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c5">c</font> &amp; <font color="Maroon" title="c3">a</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c6">d</font> &amp; <font color="Maroon" title="c3">a</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c7">e</font> &amp; <font color="Maroon" title="c4">b</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c5">c</font> &amp; <font color="Maroon" title="c4">b</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c6">d</font> &amp; <font color="Maroon" title="c4">b</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c7">e</font> &amp; <font color="Maroon" title="c5">c</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c6">d</font> &amp; <font color="Maroon" title="c5">c</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c7">e</font> &amp; <font color="Maroon" title="c6">d</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c7">e</font> &amp; <font color="Maroon" title="c3">a</font> <a href="lattice3.html#K12" title="LATTICE3:func.12">"/\"</a> <font color="Maroon" title="c4">b</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c3">a</font> &amp; <font color="Maroon" title="c3">a</font> <a href="lattice3.html#K12" title="LATTICE3:func.12">"/\"</a> <font color="Maroon" title="c5">c</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c3">a</font> &amp; <font color="Maroon" title="c3">a</font> <a href="lattice3.html#K12" title="LATTICE3:func.12">"/\"</a> <font color="Maroon" title="c6">d</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c3">a</font> &amp; <font color="Maroon" title="c4">b</font> <a href="lattice3.html#K12" title="LATTICE3:func.12">"/\"</a> <font color="Maroon" title="c7">e</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c4">b</font> &amp; <font color="Maroon" title="c5">c</font> <a href="lattice3.html#K12" title="LATTICE3:func.12">"/\"</a> <font color="Maroon" title="c7">e</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c5">c</font> &amp; <font color="Maroon" title="c6">d</font> <a href="lattice3.html#K12" title="LATTICE3:func.12">"/\"</a> <font color="Maroon" title="c7">e</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c6">d</font> &amp; <font color="Maroon" title="c4">b</font> <a href="lattice3.html#K12" title="LATTICE3:func.12">"/\"</a> <font color="Maroon" title="c5">c</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c3">a</font> &amp; <font color="Maroon" title="c4">b</font> <a href="lattice3.html#K12" title="LATTICE3:func.12">"/\"</a> <font color="Maroon" title="c6">d</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c3">a</font> &amp; <font color="Maroon" title="c5">c</font> <a href="lattice3.html#K12" title="LATTICE3:func.12">"/\"</a> <font color="Maroon" title="c6">d</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c3">a</font> &amp; <font color="Maroon" title="c4">b</font> <a href="lattice3.html#K13" title="LATTICE3:func.13">"\/"</a> <font color="Maroon" title="c5">c</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c7">e</font> &amp; <font color="Maroon" title="c4">b</font> <a href="lattice3.html#K13" title="LATTICE3:func.13">"\/"</a> <font color="Maroon" title="c6">d</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c7">e</font> &amp; <font color="Maroon" title="c5">c</font> <a href="lattice3.html#K13" title="LATTICE3:func.13">"\/"</a> <font color="Maroon" title="c6">d</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c7">e</font> )
 ;<br/>

<b>set </b><font color="Maroon" title="c8">ck</font> = <span class="p1"><a href="domain_1.html#K10" title="DOMAIN_1:func.10">{</a><span class="default"><font color="Maroon" title="c3">a</font>,<font color="Maroon" title="c4">b</font>,<font color="Maroon" title="c5">c</font>,<font color="Maroon" title="c6">d</font>,<font color="Maroon" title="c7">e</font></span><a href="domain_1.html#K10" title="DOMAIN_1:func.10">}</a></span>;<br/>
<b>reconsider </b><font color="Maroon" title="c9">ck</font> = <span class="p1"><a href="domain_1.html#K10" title="DOMAIN_1:func.10">{</a><span class="default"><font color="Maroon" title="c3">a</font>,<font color="Maroon" title="c4">b</font>,<font color="Maroon" title="c5">c</font>,<font color="Maroon" title="c6">d</font>,<font color="Maroon" title="c7">e</font></span><a href="domain_1.html#K10" title="DOMAIN_1:func.10">}</a></span> as   <a href="struct_0.html#NM2" title="STRUCT_0:NM.2">Subset</a> of <font color="Maroon" title="c1">L</font> ;<br/>
<b>set </b><font color="Maroon" title="c10">K</font> =  <a href="yellow_0.html#K5" title="YELLOW_0:func.5">subrelstr</a> <font color="Maroon" title="c9">ck</font>;<br/>
<a NAME="E4:15_2"/><i><font color="Green" title="E14">A57</font></i>: 
the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <span class="p1">(<span class="default"><a href="yellow_0.html#K5" title="YELLOW_0:func.5">subrelstr</a> <font color="Maroon" title="c9">ck</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c9">ck</font>
 
<b>by </b><i><a class="ref" href="yellow_0.html#D15" title="YELLOW_0:def.15">YELLOW_0:def 15</a></i>;<br/>
<a NAME="E5:15_2"/><i><font color="Green" title="E15">A58</font></i>: 
 <a href="yellow_0.html#K5" title="YELLOW_0:func.5">subrelstr</a> <font color="Maroon" title="c9">ck</font> is <a href="yellow_0.html#V5" title="YELLOW_0:attr.5">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" title="c11">x</font>, <font color="Maroon" title="c12">y</font> be   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Maroon" title="c1">L</font>; <i><font color="Red">:: according to </font></i><a class="ref" href="yellow_0.html#D16" title="YELLOW_0:def.16">YELLOW_0:def 16</a><br/>

<b>assume </b><a NAME="E1:15_2_1"/><i><font color="Green" title="E16">A59</font></i>: 
( <font color="Maroon" title="c11">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <span class="p1">(<span class="default"><a href="yellow_0.html#K5" title="YELLOW_0:func.5">subrelstr</a> <font color="Maroon" title="c9">ck</font></span>)</span> &amp; <font color="Maroon" title="c12">y</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <span class="p1">(<span class="default"><a href="yellow_0.html#K5" title="YELLOW_0:func.5">subrelstr</a> <font color="Maroon" title="c9">ck</font></span>)</span> &amp;  <a href="yellow_0.html#R2" title="YELLOW_0:pred.2">ex_inf_of</a> <span class="p1"><a href="domain_1.html#K7" title="DOMAIN_1:func.7">{</a><span class="default"><font color="Maroon" title="c11">x</font>,<font color="Maroon" title="c12">y</font></span><a href="domain_1.html#K7" title="DOMAIN_1:func.7">}</a></span>,<font color="Maroon" title="c1">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" title="c11">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c3">a</font> &amp; <font color="Maroon" title="c12">y</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c3">a</font> ) or ( <font color="Maroon" title="c11">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c3">a</font> &amp; <font color="Maroon" title="c12">y</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c4">b</font> ) or ( <font color="Maroon" title="c11">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c3">a</font> &amp; <font color="Maroon" title="c12">y</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c5">c</font> ) or ( <font color="Maroon" title="c11">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c3">a</font> &amp; <font color="Maroon" title="c12">y</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c6">d</font> ) or ( <font color="Maroon" title="c11">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c3">a</font> &amp; <font color="Maroon" title="c12">y</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c7">e</font> ) or ( <font color="Maroon" title="c11">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c4">b</font> &amp; <font color="Maroon" title="c12">y</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c3">a</font> ) or ( <font color="Maroon" title="c11">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c4">b</font> &amp; <font color="Maroon" title="c12">y</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c4">b</font> ) or ( <font color="Maroon" title="c11">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c4">b</font> &amp; <font color="Maroon" title="c12">y</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c5">c</font> ) or ( <font color="Maroon" title="c11">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c4">b</font> &amp; <font color="Maroon" title="c12">y</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c6">d</font> ) or ( <font color="Maroon" title="c11">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c4">b</font> &amp; <font color="Maroon" title="c12">y</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c7">e</font> ) or ( <font color="Maroon" title="c11">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c5">c</font> &amp; <font color="Maroon" title="c12">y</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c3">a</font> ) or ( <font color="Maroon" title="c11">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c5">c</font> &amp; <font color="Maroon" title="c12">y</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c4">b</font> ) or ( <font color="Maroon" title="c11">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c5">c</font> &amp; <font color="Maroon" title="c12">y</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c5">c</font> ) or ( <font color="Maroon" title="c11">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c5">c</font> &amp; <font color="Maroon" title="c12">y</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c6">d</font> ) or ( <font color="Maroon" title="c11">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c5">c</font> &amp; <font color="Maroon" title="c12">y</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c7">e</font> ) or ( <font color="Maroon" title="c11">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c6">d</font> &amp; <font color="Maroon" title="c12">y</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c3">a</font> ) or ( <font color="Maroon" title="c11">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c6">d</font> &amp; <font color="Maroon" title="c12">y</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c4">b</font> ) or ( <font color="Maroon" title="c11">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c6">d</font> &amp; <font color="Maroon" title="c12">y</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c5">c</font> ) or ( <font color="Maroon" title="c11">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c6">d</font> &amp; <font color="Maroon" title="c12">y</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c6">d</font> ) or ( <font color="Maroon" title="c11">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c6">d</font> &amp; <font color="Maroon" title="c12">y</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c7">e</font> ) or ( <font color="Maroon" title="c11">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c7">e</font> &amp; <font color="Maroon" title="c12">y</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c3">a</font> ) or ( <font color="Maroon" title="c11">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c7">e</font> &amp; <font color="Maroon" title="c12">y</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c4">b</font> ) or ( <font color="Maroon" title="c11">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c7">e</font> &amp; <font color="Maroon" title="c12">y</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c5">c</font> ) or ( <font color="Maroon" title="c11">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c7">e</font> &amp; <font color="Maroon" title="c12">y</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c6">d</font> ) or ( <font color="Maroon" title="c11">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c7">e</font> &amp; <font color="Maroon" title="c12">y</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c7">e</font> ) )
 </span><b>by </b><i><a class="txt" href="yellow11.html#E4:15_2"><i><font color="Green" title="E14">A57</font></i></a>, <a class="txt" href="yellow11.html#E1:15_2_1"><i><font color="Green" title="E16">A59</font></i></a>, <a class="ref" href="enumset1.html#D3" title="ENUMSET1:def.3">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" title="c11">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c3">a</font> &amp; <font color="Maroon" title="c12">y</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c3">a</font> )
 ;<br/><div class="add"><a NAME="E2:15_2_1_1_1"/><b>then </b>
 <a href="yellow_0.html#NK4" title="YELLOW_0:NK.4">inf</a> <span class="p1"><a href="domain_1.html#K7" title="DOMAIN_1:func.7">{</a><span class="default"><font color="Maroon" title="c11">x</font>,<font color="Maroon" title="c12">y</font></span><a href="domain_1.html#K7" title="DOMAIN_1:func.7">}</a></span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c3">a</font> <a href="lattice3.html#K12" title="LATTICE3:func.12">"/\"</a> <font color="Maroon" title="c3">a</font>
 <b>by </b><i><a class="ref" href="yellow_0.html#T40" title="YELLOW_0:th.40">YELLOW_0:40</a></i>;<br/><a NAME="E3:15_2_1_1_1"/><b>then </b>
 <a href="yellow_0.html#NK4" title="YELLOW_0:NK.4">inf</a> <span class="p1"><a href="domain_1.html#K7" title="DOMAIN_1:func.7">{</a><span class="default"><font color="Maroon" title="c11">x</font>,<font color="Maroon" title="c12">y</font></span><a href="domain_1.html#K7" title="DOMAIN_1:func.7">}</a></span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c3">a</font>
 <b>by </b><i><a class="ref" href="yellow_5.html#T2" title="YELLOW_5:th.2">YELLOW_5:2</a></i>;<br/><b>hence </b><a NAME="E4:15_2_1_1_1"/>
 <a href="yellow_0.html#K2" title="YELLOW_0:func.2">"/\"</a> <span class="p1"><a href="domain_1.html#K7" title="DOMAIN_1:func.7">{</a><span class="default"><font color="Maroon" title="c11">x</font>,<font color="Maroon" title="c12">y</font></span><a href="domain_1.html#K7" title="DOMAIN_1:func.7">}</a></span>,<font color="Maroon" title="c1">L</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <span class="p1">(<span class="default"><a href="yellow_0.html#K5" title="YELLOW_0:func.5">subrelstr</a> <font color="Maroon" title="c9">ck</font></span>)</span>
 <b>by </b><i><a class="txt" href="yellow11.html#E4:15_2"><i><font color="Green" title="E14">A57</font></i></a>, <a class="ref" href="enumset1.html#D3" title="ENUMSET1:def.3">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" title="c11">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c3">a</font> &amp; <font color="Maroon" title="c12">y</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c4">b</font> )
 ;<br/><div class="add"><a NAME="E2:15_2_1_1_2"/><b>then </b>
 <a href="yellow_0.html#NK4" title="YELLOW_0:NK.4">inf</a> <span class="p1"><a href="domain_1.html#K7" title="DOMAIN_1:func.7">{</a><span class="default"><font color="Maroon" title="c11">x</font>,<font color="Maroon" title="c12">y</font></span><a href="domain_1.html#K7" title="DOMAIN_1:func.7">}</a></span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c3">a</font> <a href="lattice3.html#K12" title="LATTICE3:func.12">"/\"</a> <font color="Maroon" title="c4">b</font>
 <b>by </b><i><a class="ref" href="yellow_0.html#T40" title="YELLOW_0:th.40">YELLOW_0:40</a></i>;<br/><b>hence </b><a NAME="E3:15_2_1_1_2"/>
 <a href="yellow_0.html#K2" title="YELLOW_0:func.2">"/\"</a> <span class="p1"><a href="domain_1.html#K7" title="DOMAIN_1:func.7">{</a><span class="default"><font color="Maroon" title="c11">x</font>,<font color="Maroon" title="c12">y</font></span><a href="domain_1.html#K7" title="DOMAIN_1:func.7">}</a></span>,<font color="Maroon" title="c1">L</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <span class="p1">(<span class="default"><a href="yellow_0.html#K5" title="YELLOW_0:func.5">subrelstr</a> <font color="Maroon" title="c9">ck</font></span>)</span>
 <b>by </b><i><a class="txt" href="yellow11.html#E2:15_2"><i><font color="Green" title="E13">A56</font></i></a>, <a class="txt" href="yellow11.html#E4:15_2"><i><font color="Green" title="E14">A57</font></i></a>, <a class="ref" href="enumset1.html#D3" title="ENUMSET1:def.3">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" title="c11">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c3">a</font> &amp; <font color="Maroon" title="c12">y</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c5">c</font> )
 ;<br/><div class="add"><a NAME="E2:15_2_1_1_3"/><b>then </b>
 <a href="yellow_0.html#NK4" title="YELLOW_0:NK.4">inf</a> <span class="p1"><a href="domain_1.html#K7" title="DOMAIN_1:func.7">{</a><span class="default"><font color="Maroon" title="c11">x</font>,<font color="Maroon" title="c12">y</font></span><a href="domain_1.html#K7" title="DOMAIN_1:func.7">}</a></span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c3">a</font> <a href="lattice3.html#K12" title="LATTICE3:func.12">"/\"</a> <font color="Maroon" title="c5">c</font>
 <b>by </b><i><a class="ref" href="yellow_0.html#T40" title="YELLOW_0:th.40">YELLOW_0:40</a></i>;<br/><b>hence </b><a NAME="E3:15_2_1_1_3"/>
 <a href="yellow_0.html#K2" title="YELLOW_0:func.2">"/\"</a> <span class="p1"><a href="domain_1.html#K7" title="DOMAIN_1:func.7">{</a><span class="default"><font color="Maroon" title="c11">x</font>,<font color="Maroon" title="c12">y</font></span><a href="domain_1.html#K7" title="DOMAIN_1:func.7">}</a></span>,<font color="Maroon" title="c1">L</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <span class="p1">(<span class="default"><a href="yellow_0.html#K5" title="YELLOW_0:func.5">subrelstr</a> <font color="Maroon" title="c9">ck</font></span>)</span>
 <b>by </b><i><a class="txt" href="yellow11.html#E2:15_2"><i><font color="Green" title="E13">A56</font></i></a>, <a class="txt" href="yellow11.html#E4:15_2"><i><font color="Green" title="E14">A57</font></i></a>, <a class="ref" href="enumset1.html#D3" title="ENUMSET1:def.3">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" title="c11">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c3">a</font> &amp; <font color="Maroon" title="c12">y</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c6">d</font> )
 ;<br/><div class="add"><a NAME="E2:15_2_1_1_4"/><b>then </b>
 <a href="yellow_0.html#NK4" title="YELLOW_0:NK.4">inf</a> <span class="p1"><a href="domain_1.html#K7" title="DOMAIN_1:func.7">{</a><span class="default"><font color="Maroon" title="c11">x</font>,<font color="Maroon" title="c12">y</font></span><a href="domain_1.html#K7" title="DOMAIN_1:func.7">}</a></span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c3">a</font> <a href="lattice3.html#K12" title="LATTICE3:func.12">"/\"</a> <font color="Maroon" title="c6">d</font>
 <b>by </b><i><a class="ref" href="yellow_0.html#T40" title="YELLOW_0:th.40">YELLOW_0:40</a></i>;<br/><b>hence </b><a NAME="E3:15_2_1_1_4"/>
 <a href="yellow_0.html#K2" title="YELLOW_0:func.2">"/\"</a> <span class="p1"><a href="domain_1.html#K7" title="DOMAIN_1:func.7">{</a><span class="default"><font color="Maroon" title="c11">x</font>,<font color="Maroon" title="c12">y</font></span><a href="domain_1.html#K7" title="DOMAIN_1:func.7">}</a></span>,<font color="Maroon" title="c1">L</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <span class="p1">(<span class="default"><a href="yellow_0.html#K5" title="YELLOW_0:func.5">subrelstr</a> <font color="Maroon" title="c9">ck</font></span>)</span>
 <b>by </b><i><a class="txt" href="yellow11.html#E2:15_2"><i><font color="Green" title="E13">A56</font></i></a>, <a class="txt" href="yellow11.html#E4:15_2"><i><font color="Green" title="E14">A57</font></i></a>, <a class="ref" href="enumset1.html#D3" title="ENUMSET1:def.3">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" title="E17">A60</font></i>: 
( <font color="Maroon" title="c11">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c3">a</font> &amp; <font color="Maroon" title="c12">y</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c7">e</font> )
 ;<br/><div class="add"><a NAME="E2:15_2_1_1_5"/>
( <font color="Maroon" title="c3">a</font> <a href="orders_2.html#R3" title="ORDERS_2:pred.3">&lt;=</a> <font color="Maroon" title="c5">c</font> &amp; <font color="Maroon" title="c5">c</font> <a href="orders_2.html#R3" title="ORDERS_2:pred.3">&lt;=</a> <font color="Maroon" title="c7">e</font> )
 <b>by </b><i><a class="txt" href="yellow11.html#E2:15_2"><i><font color="Green" title="E13">A56</font></i></a>, <a class="ref" href="yellow_0.html#T25" title="YELLOW_0:th.25">YELLOW_0:25</a></i>;<br/><a NAME="E3:15_2_1_1_5"/><b>then </b>
<font color="Maroon" title="c3">a</font> <a href="orders_2.html#R3" title="ORDERS_2:pred.3">&lt;=</a> <font color="Maroon" title="c7">e</font>
 <b>by </b><i><a class="ref" href="orders_2.html#T26" title="ORDERS_2:th.26">ORDERS_2:26</a></i>;<br/><a NAME="E4:15_2_1_1_5"/><b>then </b>
<font color="Maroon" title="c3">a</font> <a href="lattice3.html#K12" title="LATTICE3:func.12">"/\"</a> <font color="Maroon" title="c7">e</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c3">a</font>
 <b>by </b><i><a class="ref" href="yellow_0.html#T25" title="YELLOW_0:th.25">YELLOW_0:25</a></i>;<br/><a NAME="E5:15_2_1_1_5"/><b>then </b>
 <a href="yellow_0.html#NK4" title="YELLOW_0:NK.4">inf</a> <span class="p1"><a href="domain_1.html#K7" title="DOMAIN_1:func.7">{</a><span class="default"><font color="Maroon" title="c11">x</font>,<font color="Maroon" title="c12">y</font></span><a href="domain_1.html#K7" title="DOMAIN_1:func.7">}</a></span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c3">a</font>
 <b>by </b><i><a class="txt" href="yellow11.html#E1:15_2_1_1_5"><i><font color="Green" title="E17">A60</font></i></a>, <a class="ref" href="yellow_0.html#T40" title="YELLOW_0:th.40">YELLOW_0:40</a></i>;<br/><b>hence </b><a NAME="E6:15_2_1_1_5"/>
 <a href="yellow_0.html#K2" title="YELLOW_0:func.2">"/\"</a> <span class="p1"><a href="domain_1.html#K7" title="DOMAIN_1:func.7">{</a><span class="default"><font color="Maroon" title="c11">x</font>,<font color="Maroon" title="c12">y</font></span><a href="domain_1.html#K7" title="DOMAIN_1:func.7">}</a></span>,<font color="Maroon" title="c1">L</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <span class="p1">(<span class="default"><a href="yellow_0.html#K5" title="YELLOW_0:func.5">subrelstr</a> <font color="Maroon" title="c9">ck</font></span>)</span>
 <b>by </b><i><a class="txt" href="yellow11.html#E4:15_2"><i><font color="Green" title="E14">A57</font></i></a>, <a class="ref" href="enumset1.html#D3" title="ENUMSET1:def.3">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" title="c11">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c4">b</font> &amp; <font color="Maroon" title="c12">y</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c3">a</font> )
 ;<br/><div class="add"><a NAME="E2:15_2_1_1_6"/><b>then </b>
 <a href="yellow_0.html#NK4" title="YELLOW_0:NK.4">inf</a> <span class="p1"><a href="domain_1.html#K7" title="DOMAIN_1:func.7">{</a><span class="default"><font color="Maroon" title="c11">x</font>,<font color="Maroon" title="c12">y</font></span><a href="domain_1.html#K7" title="DOMAIN_1:func.7">}</a></span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c3">a</font> <a href="lattice3.html#K12" title="LATTICE3:func.12">"/\"</a> <font color="Maroon" title="c4">b</font>
 <b>by </b><i><a class="ref" href="yellow_0.html#T40" title="YELLOW_0:th.40">YELLOW_0:40</a></i>;<br/><b>hence </b><a NAME="E3:15_2_1_1_6"/>
 <a href="yellow_0.html#K2" title="YELLOW_0:func.2">"/\"</a> <span class="p1"><a href="domain_1.html#K7" title="DOMAIN_1:func.7">{</a><span class="default"><font color="Maroon" title="c11">x</font>,<font color="Maroon" title="c12">y</font></span><a href="domain_1.html#K7" title="DOMAIN_1:func.7">}</a></span>,<font color="Maroon" title="c1">L</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <span class="p1">(<span class="default"><a href="yellow_0.html#K5" title="YELLOW_0:func.5">subrelstr</a> <font color="Maroon" title="c9">ck</font></span>)</span>
 <b>by </b><i><a class="txt" href="yellow11.html#E2:15_2"><i><font color="Green" title="E13">A56</font></i></a>, <a class="txt" href="yellow11.html#E4:15_2"><i><font color="Green" title="E14">A57</font></i></a>, <a class="ref" href="enumset1.html#D3" title="ENUMSET1:def.3">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" title="c11">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c4">b</font> &amp; <font color="Maroon" title="c12">y</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c4">b</font> )
 ;<br/><div class="add"><a NAME="E2:15_2_1_1_7"/><b>then </b>
 <a href="yellow_0.html#NK4" title="YELLOW_0:NK.4">inf</a> <span class="p1"><a href="domain_1.html#K7" title="DOMAIN_1:func.7">{</a><span class="default"><font color="Maroon" title="c11">x</font>,<font color="Maroon" title="c12">y</font></span><a href="domain_1.html#K7" title="DOMAIN_1:func.7">}</a></span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c4">b</font> <a href="lattice3.html#K12" title="LATTICE3:func.12">"/\"</a> <font color="Maroon" title="c4">b</font>
 <b>by </b><i><a class="ref" href="yellow_0.html#T40" title="YELLOW_0:th.40">YELLOW_0:40</a></i>;<br/><a NAME="E3:15_2_1_1_7"/><b>then </b>
 <a href="yellow_0.html#NK4" title="YELLOW_0:NK.4">inf</a> <span class="p1"><a href="domain_1.html#K7" title="DOMAIN_1:func.7">{</a><span class="default"><font color="Maroon" title="c11">x</font>,<font color="Maroon" title="c12">y</font></span><a href="domain_1.html#K7" title="DOMAIN_1:func.7">}</a></span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c4">b</font>
 <b>by </b><i><a class="ref" href="yellow_5.html#T2" title="YELLOW_5:th.2">YELLOW_5:2</a></i>;<br/><b>hence </b><a NAME="E4:15_2_1_1_7"/>
 <a href="yellow_0.html#K2" title="YELLOW_0:func.2">"/\"</a> <span class="p1"><a href="domain_1.html#K7" title="DOMAIN_1:func.7">{</a><span class="default"><font color="Maroon" title="c11">x</font>,<font color="Maroon" title="c12">y</font></span><a href="domain_1.html#K7" title="DOMAIN_1:func.7">}</a></span>,<font color="Maroon" title="c1">L</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <span class="p1">(<span class="default"><a href="yellow_0.html#K5" title="YELLOW_0:func.5">subrelstr</a> <font color="Maroon" title="c9">ck</font></span>)</span>
 <b>by </b><i><a class="txt" href="yellow11.html#E4:15_2"><i><font color="Green" title="E14">A57</font></i></a>, <a class="ref" href="enumset1.html#D3" title="ENUMSET1:def.3">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" title="c11">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c4">b</font> &amp; <font color="Maroon" title="c12">y</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c5">c</font> )
 ;<br/><div class="add"><a NAME="E2:15_2_1_1_8"/><b>then </b>
 <a href="yellow_0.html#NK4" title="YELLOW_0:NK.4">inf</a> <span class="p1"><a href="domain_1.html#K7" title="DOMAIN_1:func.7">{</a><span class="default"><font color="Maroon" title="c11">x</font>,<font color="Maroon" title="c12">y</font></span><a href="domain_1.html#K7" title="DOMAIN_1:func.7">}</a></span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c4">b</font> <a href="lattice3.html#K12" title="LATTICE3:func.12">"/\"</a> <font color="Maroon" title="c5">c</font>
 <b>by </b><i><a class="ref" href="yellow_0.html#T40" title="YELLOW_0:th.40">YELLOW_0:40</a></i>;<br/><b>hence </b><a NAME="E3:15_2_1_1_8"/>
 <a href="yellow_0.html#K2" title="YELLOW_0:func.2">"/\"</a> <span class="p1"><a href="domain_1.html#K7" title="DOMAIN_1:func.7">{</a><span class="default"><font color="Maroon" title="c11">x</font>,<font color="Maroon" title="c12">y</font></span><a href="domain_1.html#K7" title="DOMAIN_1:func.7">}</a></span>,<font color="Maroon" title="c1">L</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <span class="p1">(<span class="default"><a href="yellow_0.html#K5" title="YELLOW_0:func.5">subrelstr</a> <font color="Maroon" title="c9">ck</font></span>)</span>
 <b>by </b><i><a class="txt" href="yellow11.html#E2:15_2"><i><font color="Green" title="E13">A56</font></i></a>, <a class="txt" href="yellow11.html#E4:15_2"><i><font color="Green" title="E14">A57</font></i></a>, <a class="ref" href="enumset1.html#D3" title="ENUMSET1:def.3">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" title="c11">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c4">b</font> &amp; <font color="Maroon" title="c12">y</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c6">d</font> )
 ;<br/><div class="add"><a NAME="E2:15_2_1_1_9"/><b>then </b>
 <a href="yellow_0.html#NK4" title="YELLOW_0:NK.4">inf</a> <span class="p1"><a href="domain_1.html#K7" title="DOMAIN_1:func.7">{</a><span class="default"><font color="Maroon" title="c11">x</font>,<font color="Maroon" title="c12">y</font></span><a href="domain_1.html#K7" title="DOMAIN_1:func.7">}</a></span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c4">b</font> <a href="lattice3.html#K12" title="LATTICE3:func.12">"/\"</a> <font color="Maroon" title="c6">d</font>
 <b>by </b><i><a class="ref" href="yellow_0.html#T40" title="YELLOW_0:th.40">YELLOW_0:40</a></i>;<br/><b>hence </b><a NAME="E3:15_2_1_1_9"/>
 <a href="yellow_0.html#K2" title="YELLOW_0:func.2">"/\"</a> <span class="p1"><a href="domain_1.html#K7" title="DOMAIN_1:func.7">{</a><span class="default"><font color="Maroon" title="c11">x</font>,<font color="Maroon" title="c12">y</font></span><a href="domain_1.html#K7" title="DOMAIN_1:func.7">}</a></span>,<font color="Maroon" title="c1">L</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <span class="p1">(<span class="default"><a href="yellow_0.html#K5" title="YELLOW_0:func.5">subrelstr</a> <font color="Maroon" title="c9">ck</font></span>)</span>
 <b>by </b><i><a class="txt" href="yellow11.html#E2:15_2"><i><font color="Green" title="E13">A56</font></i></a>, <a class="txt" href="yellow11.html#E4:15_2"><i><font color="Green" title="E14">A57</font></i></a>, <a class="ref" href="enumset1.html#D3" title="ENUMSET1:def.3">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" title="c11">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c4">b</font> &amp; <font color="Maroon" title="c12">y</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c7">e</font> )
 ;<br/><div class="add"><a NAME="E2:15_2_1_1_10"/><b>then </b>
 <a href="yellow_0.html#NK4" title="YELLOW_0:NK.4">inf</a> <span class="p1"><a href="domain_1.html#K7" title="DOMAIN_1:func.7">{</a><span class="default"><font color="Maroon" title="c11">x</font>,<font color="Maroon" title="c12">y</font></span><a href="domain_1.html#K7" title="DOMAIN_1:func.7">}</a></span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c4">b</font> <a href="lattice3.html#K12" title="LATTICE3:func.12">"/\"</a> <font color="Maroon" title="c7">e</font>
 <b>by </b><i><a class="ref" href="yellow_0.html#T40" title="YELLOW_0:th.40">YELLOW_0:40</a></i>;<br/><b>hence </b><a NAME="E3:15_2_1_1_10"/>
 <a href="yellow_0.html#K2" title="YELLOW_0:func.2">"/\"</a> <span class="p1"><a href="domain_1.html#K7" title="DOMAIN_1:func.7">{</a><span class="default"><font color="Maroon" title="c11">x</font>,<font color="Maroon" title="c12">y</font></span><a href="domain_1.html#K7" title="DOMAIN_1:func.7">}</a></span>,<font color="Maroon" title="c1">L</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <span class="p1">(<span class="default"><a href="yellow_0.html#K5" title="YELLOW_0:func.5">subrelstr</a> <font color="Maroon" title="c9">ck</font></span>)</span>
 <b>by </b><i><a class="txt" href="yellow11.html#E2:15_2"><i><font color="Green" title="E13">A56</font></i></a>, <a class="txt" href="yellow11.html#E4:15_2"><i><font color="Green" title="E14">A57</font></i></a>, <a class="ref" href="enumset1.html#D3" title="ENUMSET1:def.3">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" title="c11">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c5">c</font> &amp; <font color="Maroon" title="c12">y</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c3">a</font> )
 ;<br/><div class="add"><a NAME="E2:15_2_1_1_11"/><b>then </b>
 <a href="yellow_0.html#NK4" title="YELLOW_0:NK.4">inf</a> <span class="p1"><a href="domain_1.html#K7" title="DOMAIN_1:func.7">{</a><span class="default"><font color="Maroon" title="c11">x</font>,<font color="Maroon" title="c12">y</font></span><a href="domain_1.html#K7" title="DOMAIN_1:func.7">}</a></span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c3">a</font> <a href="lattice3.html#K12" title="LATTICE3:func.12">"/\"</a> <font color="Maroon" title="c5">c</font>
 <b>by </b><i><a class="ref" href="yellow_0.html#T40" title="YELLOW_0:th.40">YELLOW_0:40</a></i>;<br/><b>hence </b><a NAME="E3:15_2_1_1_11"/>
 <a href="yellow_0.html#K2" title="YELLOW_0:func.2">"/\"</a> <span class="p1"><a href="domain_1.html#K7" title="DOMAIN_1:func.7">{</a><span class="default"><font color="Maroon" title="c11">x</font>,<font color="Maroon" title="c12">y</font></span><a href="domain_1.html#K7" title="DOMAIN_1:func.7">}</a></span>,<font color="Maroon" title="c1">L</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <span class="p1">(<span class="default"><a href="yellow_0.html#K5" title="YELLOW_0:func.5">subrelstr</a> <font color="Maroon" title="c9">ck</font></span>)</span>
 <b>by </b><i><a class="txt" href="yellow11.html#E2:15_2"><i><font color="Green" title="E13">A56</font></i></a>, <a class="txt" href="yellow11.html#E4:15_2"><i><font color="Green" title="E14">A57</font></i></a>, <a class="ref" href="enumset1.html#D3" title="ENUMSET1:def.3">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" title="c11">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c5">c</font> &amp; <font color="Maroon" title="c12">y</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c4">b</font> )
 ;<br/><div class="add"><a NAME="E2:15_2_1_1_12"/><b>then </b>
 <a href="yellow_0.html#NK4" title="YELLOW_0:NK.4">inf</a> <span class="p1"><a href="domain_1.html#K7" title="DOMAIN_1:func.7">{</a><span class="default"><font color="Maroon" title="c11">x</font>,<font color="Maroon" title="c12">y</font></span><a href="domain_1.html#K7" title="DOMAIN_1:func.7">}</a></span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c4">b</font> <a href="lattice3.html#K12" title="LATTICE3:func.12">"/\"</a> <font color="Maroon" title="c5">c</font>
 <b>by </b><i><a class="ref" href="yellow_0.html#T40" title="YELLOW_0:th.40">YELLOW_0:40</a></i>;<br/><b>hence </b><a NAME="E3:15_2_1_1_12"/>
 <a href="yellow_0.html#K2" title="YELLOW_0:func.2">"/\"</a> <span class="p1"><a href="domain_1.html#K7" title="DOMAIN_1:func.7">{</a><span class="default"><font color="Maroon" title="c11">x</font>,<font color="Maroon" title="c12">y</font></span><a href="domain_1.html#K7" title="DOMAIN_1:func.7">}</a></span>,<font color="Maroon" title="c1">L</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <span class="p1">(<span class="default"><a href="yellow_0.html#K5" title="YELLOW_0:func.5">subrelstr</a> <font color="Maroon" title="c9">ck</font></span>)</span>
 <b>by </b><i><a class="txt" href="yellow11.html#E2:15_2"><i><font color="Green" title="E13">A56</font></i></a>, <a class="txt" href="yellow11.html#E4:15_2"><i><font color="Green" title="E14">A57</font></i></a>, <a class="ref" href="enumset1.html#D3" title="ENUMSET1:def.3">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" title="c11">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c5">c</font> &amp; <font color="Maroon" title="c12">y</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c5">c</font> )
 ;<br/><div class="add"><a NAME="E2:15_2_1_1_13"/><b>then </b>
 <a href="yellow_0.html#NK4" title="YELLOW_0:NK.4">inf</a> <span class="p1"><a href="domain_1.html#K7" title="DOMAIN_1:func.7">{</a><span class="default"><font color="Maroon" title="c11">x</font>,<font color="Maroon" title="c12">y</font></span><a href="domain_1.html#K7" title="DOMAIN_1:func.7">}</a></span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c5">c</font> <a href="lattice3.html#K12" title="LATTICE3:func.12">"/\"</a> <font color="Maroon" title="c5">c</font>
 <b>by </b><i><a class="ref" href="yellow_0.html#T40" title="YELLOW_0:th.40">YELLOW_0:40</a></i>;<br/><a NAME="E3:15_2_1_1_13"/><b>then </b>
 <a href="yellow_0.html#NK4" title="YELLOW_0:NK.4">inf</a> <span class="p1"><a href="domain_1.html#K7" title="DOMAIN_1:func.7">{</a><span class="default"><font color="Maroon" title="c11">x</font>,<font color="Maroon" title="c12">y</font></span><a href="domain_1.html#K7" title="DOMAIN_1:func.7">}</a></span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c5">c</font>
 <b>by </b><i><a class="ref" href="yellow_5.html#T2" title="YELLOW_5:th.2">YELLOW_5:2</a></i>;<br/><b>hence </b><a NAME="E4:15_2_1_1_13"/>
 <a href="yellow_0.html#K2" title="YELLOW_0:func.2">"/\"</a> <span class="p1"><a href="domain_1.html#K7" title="DOMAIN_1:func.7">{</a><span class="default"><font color="Maroon" title="c11">x</font>,<font color="Maroon" title="c12">y</font></span><a href="domain_1.html#K7" title="DOMAIN_1:func.7">}</a></span>,<font color="Maroon" title="c1">L</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <span class="p1">(<span class="default"><a href="yellow_0.html#K5" title="YELLOW_0:func.5">subrelstr</a> <font color="Maroon" title="c9">ck</font></span>)</span>
 <b>by </b><i><a class="txt" href="yellow11.html#E4:15_2"><i><font color="Green" title="E14">A57</font></i></a>, <a class="ref" href="enumset1.html#D3" title="ENUMSET1:def.3">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" title="c11">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c5">c</font> &amp; <font color="Maroon" title="c12">y</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c6">d</font> )
 ;<br/><div class="add"><a NAME="E2:15_2_1_1_14"/><b>then </b>
 <a href="yellow_0.html#NK4" title="YELLOW_0:NK.4">inf</a> <span class="p1"><a href="domain_1.html#K7" title="DOMAIN_1:func.7">{</a><span class="default"><font color="Maroon" title="c11">x</font>,<font color="Maroon" title="c12">y</font></span><a href="domain_1.html#K7" title="DOMAIN_1:func.7">}</a></span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c5">c</font> <a href="lattice3.html#K12" title="LATTICE3:func.12">"/\"</a> <font color="Maroon" title="c6">d</font>
 <b>by </b><i><a class="ref" href="yellow_0.html#T40" title="YELLOW_0:th.40">YELLOW_0:40</a></i>;<br/><b>hence </b><a NAME="E3:15_2_1_1_14"/>
 <a href="yellow_0.html#K2" title="YELLOW_0:func.2">"/\"</a> <span class="p1"><a href="domain_1.html#K7" title="DOMAIN_1:func.7">{</a><span class="default"><font color="Maroon" title="c11">x</font>,<font color="Maroon" title="c12">y</font></span><a href="domain_1.html#K7" title="DOMAIN_1:func.7">}</a></span>,<font color="Maroon" title="c1">L</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <span class="p1">(<span class="default"><a href="yellow_0.html#K5" title="YELLOW_0:func.5">subrelstr</a> <font color="Maroon" title="c9">ck</font></span>)</span>
 <b>by </b><i><a class="txt" href="yellow11.html#E2:15_2"><i><font color="Green" title="E13">A56</font></i></a>, <a class="txt" href="yellow11.html#E4:15_2"><i><font color="Green" title="E14">A57</font></i></a>, <a class="ref" href="enumset1.html#D3" title="ENUMSET1:def.3">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" title="c11">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c5">c</font> &amp; <font color="Maroon" title="c12">y</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c7">e</font> )
 ;<br/><div class="add"><a NAME="E2:15_2_1_1_15"/><b>then </b>
 <a href="yellow_0.html#NK4" title="YELLOW_0:NK.4">inf</a> <span class="p1"><a href="domain_1.html#K7" title="DOMAIN_1:func.7">{</a><span class="default"><font color="Maroon" title="c11">x</font>,<font color="Maroon" title="c12">y</font></span><a href="domain_1.html#K7" title="DOMAIN_1:func.7">}</a></span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c5">c</font> <a href="lattice3.html#K12" title="LATTICE3:func.12">"/\"</a> <font color="Maroon" title="c7">e</font>
 <b>by </b><i><a class="ref" href="yellow_0.html#T40" title="YELLOW_0:th.40">YELLOW_0:40</a></i>;<br/><b>hence </b><a NAME="E3:15_2_1_1_15"/>
 <a href="yellow_0.html#K2" title="YELLOW_0:func.2">"/\"</a> <span class="p1"><a href="domain_1.html#K7" title="DOMAIN_1:func.7">{</a><span class="default"><font color="Maroon" title="c11">x</font>,<font color="Maroon" title="c12">y</font></span><a href="domain_1.html#K7" title="DOMAIN_1:func.7">}</a></span>,<font color="Maroon" title="c1">L</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <span class="p1">(<span class="default"><a href="yellow_0.html#K5" title="YELLOW_0:func.5">subrelstr</a> <font color="Maroon" title="c9">ck</font></span>)</span>
 <b>by </b><i><a class="txt" href="yellow11.html#E2:15_2"><i><font color="Green" title="E13">A56</font></i></a>, <a class="txt" href="yellow11.html#E4:15_2"><i><font color="Green" title="E14">A57</font></i></a>, <a class="ref" href="enumset1.html#D3" title="ENUMSET1:def.3">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" title="c11">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c6">d</font> &amp; <font color="Maroon" title="c12">y</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c3">a</font> )
 ;<br/><div class="add"><a NAME="E2:15_2_1_1_16"/><b>then </b>
 <a href="yellow_0.html#NK4" title="YELLOW_0:NK.4">inf</a> <span class="p1"><a href="domain_1.html#K7" title="DOMAIN_1:func.7">{</a><span class="default"><font color="Maroon" title="c11">x</font>,<font color="Maroon" title="c12">y</font></span><a href="domain_1.html#K7" title="DOMAIN_1:func.7">}</a></span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c3">a</font> <a href="lattice3.html#K12" title="LATTICE3:func.12">"/\"</a> <font color="Maroon" title="c6">d</font>
 <b>by </b><i><a class="ref" href="yellow_0.html#T40" title="YELLOW_0:th.40">YELLOW_0:40</a></i>;<br/><b>hence </b><a NAME="E3:15_2_1_1_16"/>
 <a href="yellow_0.html#K2" title="YELLOW_0:func.2">"/\"</a> <span class="p1"><a href="domain_1.html#K7" title="DOMAIN_1:func.7">{</a><span class="default"><font color="Maroon" title="c11">x</font>,<font color="Maroon" title="c12">y</font></span><a href="domain_1.html#K7" title="DOMAIN_1:func.7">}</a></span>,<font color="Maroon" title="c1">L</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <span class="p1">(<span class="default"><a href="yellow_0.html#K5" title="YELLOW_0:func.5">subrelstr</a> <font color="Maroon" title="c9">ck</font></span>)</span>
 <b>by </b><i><a class="txt" href="yellow11.html#E2:15_2"><i><font color="Green" title="E13">A56</font></i></a>, <a class="txt" href="yellow11.html#E4:15_2"><i><font color="Green" title="E14">A57</font></i></a>, <a class="ref" href="enumset1.html#D3" title="ENUMSET1:def.3">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" title="c11">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c6">d</font> &amp; <font color="Maroon" title="c12">y</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c4">b</font> )
 ;<br/><div class="add"><a NAME="E2:15_2_1_1_17"/><b>then </b>
 <a href="yellow_0.html#NK4" title="YELLOW_0:NK.4">inf</a> <span class="p1"><a href="domain_1.html#K7" title="DOMAIN_1:func.7">{</a><span class="default"><font color="Maroon" title="c11">x</font>,<font color="Maroon" title="c12">y</font></span><a href="domain_1.html#K7" title="DOMAIN_1:func.7">}</a></span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c4">b</font> <a href="lattice3.html#K12" title="LATTICE3:func.12">"/\"</a> <font color="Maroon" title="c6">d</font>
 <b>by </b><i><a class="ref" href="yellow_0.html#T40" title="YELLOW_0:th.40">YELLOW_0:40</a></i>;<br/><b>hence </b><a NAME="E3:15_2_1_1_17"/>
 <a href="yellow_0.html#K2" title="YELLOW_0:func.2">"/\"</a> <span class="p1"><a href="domain_1.html#K7" title="DOMAIN_1:func.7">{</a><span class="default"><font color="Maroon" title="c11">x</font>,<font color="Maroon" title="c12">y</font></span><a href="domain_1.html#K7" title="DOMAIN_1:func.7">}</a></span>,<font color="Maroon" title="c1">L</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <span class="p1">(<span class="default"><a href="yellow_0.html#K5" title="YELLOW_0:func.5">subrelstr</a> <font color="Maroon" title="c9">ck</font></span>)</span>
 <b>by </b><i><a class="txt" href="yellow11.html#E2:15_2"><i><font color="Green" title="E13">A56</font></i></a>, <a class="txt" href="yellow11.html#E4:15_2"><i><font color="Green" title="E14">A57</font></i></a>, <a class="ref" href="enumset1.html#D3" title="ENUMSET1:def.3">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" title="c11">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c6">d</font> &amp; <font color="Maroon" title="c12">y</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c5">c</font> )
 ;<br/><div class="add"><a NAME="E2:15_2_1_1_18"/><b>then </b>
 <a href="yellow_0.html#NK4" title="YELLOW_0:NK.4">inf</a> <span class="p1"><a href="domain_1.html#K7" title="DOMAIN_1:func.7">{</a><span class="default"><font color="Maroon" title="c11">x</font>,<font color="Maroon" title="c12">y</font></span><a href="domain_1.html#K7" title="DOMAIN_1:func.7">}</a></span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c5">c</font> <a href="lattice3.html#K12" title="LATTICE3:func.12">"/\"</a> <font color="Maroon" title="c6">d</font>
 <b>by </b><i><a class="ref" href="yellow_0.html#T40" title="YELLOW_0:th.40">YELLOW_0:40</a></i>;<br/><b>hence </b><a NAME="E3:15_2_1_1_18"/>
 <a href="yellow_0.html#K2" title="YELLOW_0:func.2">"/\"</a> <span class="p1"><a href="domain_1.html#K7" title="DOMAIN_1:func.7">{</a><span class="default"><font color="Maroon" title="c11">x</font>,<font color="Maroon" title="c12">y</font></span><a href="domain_1.html#K7" title="DOMAIN_1:func.7">}</a></span>,<font color="Maroon" title="c1">L</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <span class="p1">(<span class="default"><a href="yellow_0.html#K5" title="YELLOW_0:func.5">subrelstr</a> <font color="Maroon" title="c9">ck</font></span>)</span>
 <b>by </b><i><a class="txt" href="yellow11.html#E2:15_2"><i><font color="Green" title="E13">A56</font></i></a>, <a class="txt" href="yellow11.html#E4:15_2"><i><font color="Green" title="E14">A57</font></i></a>, <a class="ref" href="enumset1.html#D3" title="ENUMSET1:def.3">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" title="c11">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c6">d</font> &amp; <font color="Maroon" title="c12">y</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c6">d</font> )
 ;<br/><div class="add"><a NAME="E2:15_2_1_1_19"/><b>then </b>
 <a href="yellow_0.html#NK4" title="YELLOW_0:NK.4">inf</a> <span class="p1"><a href="domain_1.html#K7" title="DOMAIN_1:func.7">{</a><span class="default"><font color="Maroon" title="c11">x</font>,<font color="Maroon" title="c12">y</font></span><a href="domain_1.html#K7" title="DOMAIN_1:func.7">}</a></span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c6">d</font> <a href="lattice3.html#K12" title="LATTICE3:func.12">"/\"</a> <font color="Maroon" title="c6">d</font>
 <b>by </b><i><a class="ref" href="yellow_0.html#T40" title="YELLOW_0:th.40">YELLOW_0:40</a></i>;<br/><a NAME="E3:15_2_1_1_19"/><b>then </b>
 <a href="yellow_0.html#NK4" title="YELLOW_0:NK.4">inf</a> <span class="p1"><a href="domain_1.html#K7" title="DOMAIN_1:func.7">{</a><span class="default"><font color="Maroon" title="c11">x</font>,<font color="Maroon" title="c12">y</font></span><a href="domain_1.html#K7" title="DOMAIN_1:func.7">}</a></span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c6">d</font>
 <b>by </b><i><a class="ref" href="yellow_5.html#T2" title="YELLOW_5:th.2">YELLOW_5:2</a></i>;<br/><b>hence </b><a NAME="E4:15_2_1_1_19"/>
 <a href="yellow_0.html#K2" title="YELLOW_0:func.2">"/\"</a> <span class="p1"><a href="domain_1.html#K7" title="DOMAIN_1:func.7">{</a><span class="default"><font color="Maroon" title="c11">x</font>,<font color="Maroon" title="c12">y</font></span><a href="domain_1.html#K7" title="DOMAIN_1:func.7">}</a></span>,<font color="Maroon" title="c1">L</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <span class="p1">(<span class="default"><a href="yellow_0.html#K5" title="YELLOW_0:func.5">subrelstr</a> <font color="Maroon" title="c9">ck</font></span>)</span>
 <b>by </b><i><a class="txt" href="yellow11.html#E4:15_2"><i><font color="Green" title="E14">A57</font></i></a>, <a class="ref" href="enumset1.html#D3" title="ENUMSET1:def.3">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" title="c11">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c6">d</font> &amp; <font color="Maroon" title="c12">y</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c7">e</font> )
 ;<br/><div class="add"><a NAME="E2:15_2_1_1_20"/><b>then </b>
 <a href="yellow_0.html#NK4" title="YELLOW_0:NK.4">inf</a> <span class="p1"><a href="domain_1.html#K7" title="DOMAIN_1:func.7">{</a><span class="default"><font color="Maroon" title="c11">x</font>,<font color="Maroon" title="c12">y</font></span><a href="domain_1.html#K7" title="DOMAIN_1:func.7">}</a></span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c6">d</font> <a href="lattice3.html#K12" title="LATTICE3:func.12">"/\"</a> <font color="Maroon" title="c7">e</font>
 <b>by </b><i><a class="ref" href="yellow_0.html#T40" title="YELLOW_0:th.40">YELLOW_0:40</a></i>;<br/><b>hence </b><a NAME="E3:15_2_1_1_20"/>
 <a href="yellow_0.html#K2" title="YELLOW_0:func.2">"/\"</a> <span class="p1"><a href="domain_1.html#K7" title="DOMAIN_1:func.7">{</a><span class="default"><font color="Maroon" title="c11">x</font>,<font color="Maroon" title="c12">y</font></span><a href="domain_1.html#K7" title="DOMAIN_1:func.7">}</a></span>,<font color="Maroon" title="c1">L</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <span class="p1">(<span class="default"><a href="yellow_0.html#K5" title="YELLOW_0:func.5">subrelstr</a> <font color="Maroon" title="c9">ck</font></span>)</span>
 <b>by </b><i><a class="txt" href="yellow11.html#E2:15_2"><i><font color="Green" title="E13">A56</font></i></a>, <a class="txt" href="yellow11.html#E4:15_2"><i><font color="Green" title="E14">A57</font></i></a>, <a class="ref" href="enumset1.html#D3" title="ENUMSET1:def.3">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" title="E17">A61</font></i>: 
( <font color="Maroon" title="c11">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c7">e</font> &amp; <font color="Maroon" title="c12">y</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c3">a</font> )
 ;<br/><div class="add"><a NAME="E2:15_2_1_1_21"/>
( <font color="Maroon" title="c3">a</font> <a href="orders_2.html#R3" title="ORDERS_2:pred.3">&lt;=</a> <font color="Maroon" title="c5">c</font> &amp; <font color="Maroon" title="c5">c</font> <a href="orders_2.html#R3" title="ORDERS_2:pred.3">&lt;=</a> <font color="Maroon" title="c7">e</font> )
 <b>by </b><i><a class="txt" href="yellow11.html#E2:15_2"><i><font color="Green" title="E13">A56</font></i></a>, <a class="ref" href="yellow_0.html#T25" title="YELLOW_0:th.25">YELLOW_0:25</a></i>;<br/><a NAME="E3:15_2_1_1_21"/><b>then </b>
<font color="Maroon" title="c3">a</font> <a href="orders_2.html#R3" title="ORDERS_2:pred.3">&lt;=</a> <font color="Maroon" title="c7">e</font>
 <b>by </b><i><a class="ref" href="orders_2.html#T26" title="ORDERS_2:th.26">ORDERS_2:26</a></i>;<br/><a NAME="E4:15_2_1_1_21"/><b>then </b>
<font color="Maroon" title="c3">a</font> <a href="lattice3.html#K12" title="LATTICE3:func.12">"/\"</a> <font color="Maroon" title="c7">e</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c3">a</font>
 <b>by </b><i><a class="ref" href="yellow_0.html#T25" title="YELLOW_0:th.25">YELLOW_0:25</a></i>;<br/><a NAME="E5:15_2_1_1_21"/><b>then </b>
 <a href="yellow_0.html#NK4" title="YELLOW_0:NK.4">inf</a> <span class="p1"><a href="domain_1.html#K7" title="DOMAIN_1:func.7">{</a><span class="default"><font color="Maroon" title="c11">x</font>,<font color="Maroon" title="c12">y</font></span><a href="domain_1.html#K7" title="DOMAIN_1:func.7">}</a></span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c3">a</font>
 <b>by </b><i><a class="txt" href="yellow11.html#E1:15_2_1_1_21"><i><font color="Green" title="E17">A61</font></i></a>, <a class="ref" href="yellow_0.html#T40" title="YELLOW_0:th.40">YELLOW_0:40</a></i>;<br/><b>hence </b><a NAME="E6:15_2_1_1_21"/>
 <a href="yellow_0.html#K2" title="YELLOW_0:func.2">"/\"</a> <span class="p1"><a href="domain_1.html#K7" title="DOMAIN_1:func.7">{</a><span class="default"><font color="Maroon" title="c11">x</font>,<font color="Maroon" title="c12">y</font></span><a href="domain_1.html#K7" title="DOMAIN_1:func.7">}</a></span>,<font color="Maroon" title="c1">L</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <span class="p1">(<span class="default"><a href="yellow_0.html#K5" title="YELLOW_0:func.5">subrelstr</a> <font color="Maroon" title="c9">ck</font></span>)</span>
 <b>by </b><i><a class="txt" href="yellow11.html#E4:15_2"><i><font color="Green" title="E14">A57</font></i></a>, <a class="ref" href="enumset1.html#D3" title="ENUMSET1:def.3">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" title="c11">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c7">e</font> &amp; <font color="Maroon" title="c12">y</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c4">b</font> )
 ;<br/><div class="add"><a NAME="E2:15_2_1_1_22"/><b>then </b>
 <a href="yellow_0.html#NK4" title="YELLOW_0:NK.4">inf</a> <span class="p1"><a href="domain_1.html#K7" title="DOMAIN_1:func.7">{</a><span class="default"><font color="Maroon" title="c11">x</font>,<font color="Maroon" title="c12">y</font></span><a href="domain_1.html#K7" title="DOMAIN_1:func.7">}</a></span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c4">b</font> <a href="lattice3.html#K12" title="LATTICE3:func.12">"/\"</a> <font color="Maroon" title="c7">e</font>
 <b>by </b><i><a class="ref" href="yellow_0.html#T40" title="YELLOW_0:th.40">YELLOW_0:40</a></i>;<br/><b>hence </b><a NAME="E3:15_2_1_1_22"/>
 <a href="yellow_0.html#K2" title="YELLOW_0:func.2">"/\"</a> <span class="p1"><a href="domain_1.html#K7" title="DOMAIN_1:func.7">{</a><span class="default"><font color="Maroon" title="c11">x</font>,<font color="Maroon" title="c12">y</font></span><a href="domain_1.html#K7" title="DOMAIN_1:func.7">}</a></span>,<font color="Maroon" title="c1">L</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <span class="p1">(<span class="default"><a href="yellow_0.html#K5" title="YELLOW_0:func.5">subrelstr</a> <font color="Maroon" title="c9">ck</font></span>)</span>
 <b>by </b><i><a class="txt" href="yellow11.html#E2:15_2"><i><font color="Green" title="E13">A56</font></i></a>, <a class="txt" href="yellow11.html#E4:15_2"><i><font color="Green" title="E14">A57</font></i></a>, <a class="ref" href="enumset1.html#D3" title="ENUMSET1:def.3">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" title="c11">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c7">e</font> &amp; <font color="Maroon" title="c12">y</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c5">c</font> )
 ;<br/><div class="add"><a NAME="E2:15_2_1_1_23"/><b>then </b>
 <a href="yellow_0.html#NK4" title="YELLOW_0:NK.4">inf</a> <span class="p1"><a href="domain_1.html#K7" title="DOMAIN_1:func.7">{</a><span class="default"><font color="Maroon" title="c11">x</font>,<font color="Maroon" title="c12">y</font></span><a href="domain_1.html#K7" title="DOMAIN_1:func.7">}</a></span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c5">c</font> <a href="lattice3.html#K12" title="LATTICE3:func.12">"/\"</a> <font color="Maroon" title="c7">e</font>
 <b>by </b><i><a class="ref" href="yellow_0.html#T40" title="YELLOW_0:th.40">YELLOW_0:40</a></i>;<br/><b>hence </b><a NAME="E3:15_2_1_1_23"/>
 <a href="yellow_0.html#K2" title="YELLOW_0:func.2">"/\"</a> <span class="p1"><a href="domain_1.html#K7" title="DOMAIN_1:func.7">{</a><span class="default"><font color="Maroon" title="c11">x</font>,<font color="Maroon" title="c12">y</font></span><a href="domain_1.html#K7" title="DOMAIN_1:func.7">}</a></span>,<font color="Maroon" title="c1">L</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <span class="p1">(<span class="default"><a href="yellow_0.html#K5" title="YELLOW_0:func.5">subrelstr</a> <font color="Maroon" title="c9">ck</font></span>)</span>
 <b>by </b><i><a class="txt" href="yellow11.html#E2:15_2"><i><font color="Green" title="E13">A56</font></i></a>, <a class="txt" href="yellow11.html#E4:15_2"><i><font color="Green" title="E14">A57</font></i></a>, <a class="ref" href="enumset1.html#D3" title="ENUMSET1:def.3">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" title="c11">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c7">e</font> &amp; <font color="Maroon" title="c12">y</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c6">d</font> )
 ;<br/><div class="add"><a NAME="E2:15_2_1_1_24"/><b>then </b>
 <a href="yellow_0.html#NK4" title="YELLOW_0:NK.4">inf</a> <span class="p1"><a href="domain_1.html#K7" title="DOMAIN_1:func.7">{</a><span class="default"><font color="Maroon" title="c11">x</font>,<font color="Maroon" title="c12">y</font></span><a href="domain_1.html#K7" title="DOMAIN_1:func.7">}</a></span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c6">d</font> <a href="lattice3.html#K12" title="LATTICE3:func.12">"/\"</a> <font color="Maroon" title="c7">e</font>
 <b>by </b><i><a class="ref" href="yellow_0.html#T40" title="YELLOW_0:th.40">YELLOW_0:40</a></i>;<br/><b>hence </b><a NAME="E3:15_2_1_1_24"/>
 <a href="yellow_0.html#K2" title="YELLOW_0:func.2">"/\"</a> <span class="p1"><a href="domain_1.html#K7" title="DOMAIN_1:func.7">{</a><span class="default"><font color="Maroon" title="c11">x</font>,<font color="Maroon" title="c12">y</font></span><a href="domain_1.html#K7" title="DOMAIN_1:func.7">}</a></span>,<font color="Maroon" title="c1">L</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <span class="p1">(<span class="default"><a href="yellow_0.html#K5" title="YELLOW_0:func.5">subrelstr</a> <font color="Maroon" title="c9">ck</font></span>)</span>
 <b>by </b><i><a class="txt" href="yellow11.html#E2:15_2"><i><font color="Green" title="E13">A56</font></i></a>, <a class="txt" href="yellow11.html#E4:15_2"><i><font color="Green" title="E14">A57</font></i></a>, <a class="ref" href="enumset1.html#D3" title="ENUMSET1:def.3">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" title="c11">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c7">e</font> &amp; <font color="Maroon" title="c12">y</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c7">e</font> )
 ;<br/><div class="add"><a NAME="E2:15_2_1_1_25"/><b>then </b>
 <a href="yellow_0.html#NK4" title="YELLOW_0:NK.4">inf</a> <span class="p1"><a href="domain_1.html#K7" title="DOMAIN_1:func.7">{</a><span class="default"><font color="Maroon" title="c11">x</font>,<font color="Maroon" title="c12">y</font></span><a href="domain_1.html#K7" title="DOMAIN_1:func.7">}</a></span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c7">e</font> <a href="lattice3.html#K12" title="LATTICE3:func.12">"/\"</a> <font color="Maroon" title="c7">e</font>
 <b>by </b><i><a class="ref" href="yellow_0.html#T40" title="YELLOW_0:th.40">YELLOW_0:40</a></i>;<br/><a NAME="E3:15_2_1_1_25"/><b>then </b>
 <a href="yellow_0.html#NK4" title="YELLOW_0:NK.4">inf</a> <span class="p1"><a href="domain_1.html#K7" title="DOMAIN_1:func.7">{</a><span class="default"><font color="Maroon" title="c11">x</font>,<font color="Maroon" title="c12">y</font></span><a href="domain_1.html#K7" title="DOMAIN_1:func.7">}</a></span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c7">e</font>
 <b>by </b><i><a class="ref" href="yellow_5.html#T2" title="YELLOW_5:th.2">YELLOW_5:2</a></i>;<br/><b>hence </b><a NAME="E4:15_2_1_1_25"/>
 <a href="yellow_0.html#K2" title="YELLOW_0:func.2">"/\"</a> <span class="p1"><a href="domain_1.html#K7" title="DOMAIN_1:func.7">{</a><span class="default"><font color="Maroon" title="c11">x</font>,<font color="Maroon" title="c12">y</font></span><a href="domain_1.html#K7" title="DOMAIN_1:func.7">}</a></span>,<font color="Maroon" title="c1">L</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <span class="p1">(<span class="default"><a href="yellow_0.html#K5" title="YELLOW_0:func.5">subrelstr</a> <font color="Maroon" title="c9">ck</font></span>)</span>
 <b>by </b><i><a class="txt" href="yellow11.html#E4:15_2"><i><font color="Green" title="E14">A57</font></i></a>, <a class="ref" href="enumset1.html#D3" title="ENUMSET1:def.3">ENUMSET1:def 3</a></i>;<br/></div><b>end;</b></div></div><b>end;</b></div>

</div><b>end;</b></div>
<a NAME="E6:15_2"/>
 <a href="yellow_0.html#K5" title="YELLOW_0:func.5">subrelstr</a> <font color="Maroon" title="c9">ck</font> is <a href="yellow_0.html#V6" title="YELLOW_0:attr.6">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" title="c11">x</font>, <font color="Maroon" title="c12">y</font> be   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Maroon" title="c1">L</font>; <i><font color="Red">:: according to </font></i><a class="ref" href="yellow_0.html#D17" title="YELLOW_0:def.17">YELLOW_0:def 17</a><br/>

<b>assume </b><a NAME="E1:15_2_2"/><i><font color="Green" title="E16">A62</font></i>: 
( <font color="Maroon" title="c11">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <span class="p1">(<span class="default"><a href="yellow_0.html#K5" title="YELLOW_0:func.5">subrelstr</a> <font color="Maroon" title="c9">ck</font></span>)</span> &amp; <font color="Maroon" title="c12">y</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <span class="p1">(<span class="default"><a href="yellow_0.html#K5" title="YELLOW_0:func.5">subrelstr</a> <font color="Maroon" title="c9">ck</font></span>)</span> &amp;  <a href="yellow_0.html#R1" title="YELLOW_0:pred.1">ex_sup_of</a> <span class="p1"><a href="domain_1.html#K7" title="DOMAIN_1:func.7">{</a><span class="default"><font color="Maroon" title="c11">x</font>,<font color="Maroon" title="c12">y</font></span><a href="domain_1.html#K7" title="DOMAIN_1:func.7">}</a></span>,<font color="Maroon" title="c1">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" title="c11">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c3">a</font> &amp; <font color="Maroon" title="c12">y</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c3">a</font> ) or ( <font color="Maroon" title="c11">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c3">a</font> &amp; <font color="Maroon" title="c12">y</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c4">b</font> ) or ( <font color="Maroon" title="c11">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c3">a</font> &amp; <font color="Maroon" title="c12">y</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c5">c</font> ) or ( <font color="Maroon" title="c11">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c3">a</font> &amp; <font color="Maroon" title="c12">y</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c6">d</font> ) or ( <font color="Maroon" title="c11">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c3">a</font> &amp; <font color="Maroon" title="c12">y</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c7">e</font> ) or ( <font color="Maroon" title="c11">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c4">b</font> &amp; <font color="Maroon" title="c12">y</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c3">a</font> ) or ( <font color="Maroon" title="c11">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c4">b</font> &amp; <font color="Maroon" title="c12">y</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c4">b</font> ) or ( <font color="Maroon" title="c11">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c4">b</font> &amp; <font color="Maroon" title="c12">y</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c5">c</font> ) or ( <font color="Maroon" title="c11">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c4">b</font> &amp; <font color="Maroon" title="c12">y</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c6">d</font> ) or ( <font color="Maroon" title="c11">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c4">b</font> &amp; <font color="Maroon" title="c12">y</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c7">e</font> ) or ( <font color="Maroon" title="c11">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c5">c</font> &amp; <font color="Maroon" title="c12">y</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c3">a</font> ) or ( <font color="Maroon" title="c11">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c5">c</font> &amp; <font color="Maroon" title="c12">y</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c4">b</font> ) or ( <font color="Maroon" title="c11">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c5">c</font> &amp; <font color="Maroon" title="c12">y</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c5">c</font> ) or ( <font color="Maroon" title="c11">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c5">c</font> &amp; <font color="Maroon" title="c12">y</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c6">d</font> ) or ( <font color="Maroon" title="c11">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c5">c</font> &amp; <font color="Maroon" title="c12">y</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c7">e</font> ) or ( <font color="Maroon" title="c11">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c6">d</font> &amp; <font color="Maroon" title="c12">y</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c3">a</font> ) or ( <font color="Maroon" title="c11">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c6">d</font> &amp; <font color="Maroon" title="c12">y</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c4">b</font> ) or ( <font color="Maroon" title="c11">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c6">d</font> &amp; <font color="Maroon" title="c12">y</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c5">c</font> ) or ( <font color="Maroon" title="c11">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c6">d</font> &amp; <font color="Maroon" title="c12">y</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c6">d</font> ) or ( <font color="Maroon" title="c11">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c6">d</font> &amp; <font color="Maroon" title="c12">y</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c7">e</font> ) or ( <font color="Maroon" title="c11">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c7">e</font> &amp; <font color="Maroon" title="c12">y</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c3">a</font> ) or ( <font color="Maroon" title="c11">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c7">e</font> &amp; <font color="Maroon" title="c12">y</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c4">b</font> ) or ( <font color="Maroon" title="c11">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c7">e</font> &amp; <font color="Maroon" title="c12">y</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c5">c</font> ) or ( <font color="Maroon" title="c11">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c7">e</font> &amp; <font color="Maroon" title="c12">y</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c6">d</font> ) or ( <font color="Maroon" title="c11">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c7">e</font> &amp; <font color="Maroon" title="c12">y</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c7">e</font> ) )
 </span><b>by </b><i><a class="txt" href="yellow11.html#E4:15_2"><i><font color="Green" title="E14">A57</font></i></a>, <a class="txt" href="yellow11.html#E1:15_2_2"><i><font color="Green" title="E16">A62</font></i></a>, <a class="ref" href="enumset1.html#D3" title="ENUMSET1:def.3">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" title="c11">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c3">a</font> &amp; <font color="Maroon" title="c12">y</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c3">a</font> )
 ;<br/><div class="add"><a NAME="E2:15_2_2_1_1"/><b>then </b>
 <a href="yellow_0.html#NK3" title="YELLOW_0:NK.3">sup</a> <span class="p1"><a href="domain_1.html#K7" title="DOMAIN_1:func.7">{</a><span class="default"><font color="Maroon" title="c11">x</font>,<font color="Maroon" title="c12">y</font></span><a href="domain_1.html#K7" title="DOMAIN_1:func.7">}</a></span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c3">a</font> <a href="lattice3.html#K13" title="LATTICE3:func.13">"\/"</a> <font color="Maroon" title="c3">a</font>
 <b>by </b><i><a class="ref" href="yellow_0.html#T41" title="YELLOW_0:th.41">YELLOW_0:41</a></i>;<br/><a NAME="E3:15_2_2_1_1"/><b>then </b>
 <a href="yellow_0.html#NK3" title="YELLOW_0:NK.3">sup</a> <span class="p1"><a href="domain_1.html#K7" title="DOMAIN_1:func.7">{</a><span class="default"><font color="Maroon" title="c11">x</font>,<font color="Maroon" title="c12">y</font></span><a href="domain_1.html#K7" title="DOMAIN_1:func.7">}</a></span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c3">a</font>
 <b>by </b><i><a class="ref" href="yellow_5.html#T1" title="YELLOW_5:th.1">YELLOW_5:1</a></i>;<br/><b>hence </b><a NAME="E4:15_2_2_1_1"/>
 <a href="yellow_0.html#K1" title="YELLOW_0:func.1">"\/"</a> <span class="p1"><a href="domain_1.html#K7" title="DOMAIN_1:func.7">{</a><span class="default"><font color="Maroon" title="c11">x</font>,<font color="Maroon" title="c12">y</font></span><a href="domain_1.html#K7" title="DOMAIN_1:func.7">}</a></span>,<font color="Maroon" title="c1">L</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <span class="p1">(<span class="default"><a href="yellow_0.html#K5" title="YELLOW_0:func.5">subrelstr</a> <font color="Maroon" title="c9">ck</font></span>)</span>
 <b>by </b><i><a class="txt" href="yellow11.html#E4:15_2"><i><font color="Green" title="E14">A57</font></i></a>, <a class="ref" href="enumset1.html#D3" title="ENUMSET1:def.3">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" title="c11">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c3">a</font> &amp; <font color="Maroon" title="c12">y</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c4">b</font> )
 ;<br/><div class="add"><a NAME="E2:15_2_2_1_2"/><b>then </b>
<font color="Maroon" title="c11">x</font> <a href="lattice3.html#K13" title="LATTICE3:func.13">"\/"</a> <font color="Maroon" title="c12">y</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c4">b</font>
 <b>by </b><i><a class="txt" href="yellow11.html#E2:15_2"><i><font color="Green" title="E13">A56</font></i></a>, <a class="ref" href="yellow11.html#T5" target="_self" title="YELLOW11:th.5">Th5</a></i>;<br/><a NAME="E3:15_2_2_1_2"/><b>then </b>
 <a href="yellow_0.html#NK3" title="YELLOW_0:NK.3">sup</a> <span class="p1"><a href="domain_1.html#K7" title="DOMAIN_1:func.7">{</a><span class="default"><font color="Maroon" title="c11">x</font>,<font color="Maroon" title="c12">y</font></span><a href="domain_1.html#K7" title="DOMAIN_1:func.7">}</a></span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c4">b</font>
 <b>by </b><i><a class="ref" href="yellow_0.html#T41" title="YELLOW_0:th.41">YELLOW_0:41</a></i>;<br/><b>hence </b><a NAME="E4:15_2_2_1_2"/>
 <a href="yellow_0.html#K1" title="YELLOW_0:func.1">"\/"</a> <span class="p1"><a href="domain_1.html#K7" title="DOMAIN_1:func.7">{</a><span class="default"><font color="Maroon" title="c11">x</font>,<font color="Maroon" title="c12">y</font></span><a href="domain_1.html#K7" title="DOMAIN_1:func.7">}</a></span>,<font color="Maroon" title="c1">L</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <span class="p1">(<span class="default"><a href="yellow_0.html#K5" title="YELLOW_0:func.5">subrelstr</a> <font color="Maroon" title="c9">ck</font></span>)</span>
 <b>by </b><i><a class="txt" href="yellow11.html#E4:15_2"><i><font color="Green" title="E14">A57</font></i></a>, <a class="ref" href="enumset1.html#D3" title="ENUMSET1:def.3">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" title="c11">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c3">a</font> &amp; <font color="Maroon" title="c12">y</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c5">c</font> )
 ;<br/><div class="add"><a NAME="E2:15_2_2_1_3"/><b>then </b>
<font color="Maroon" title="c11">x</font> <a href="lattice3.html#K13" title="LATTICE3:func.13">"\/"</a> <font color="Maroon" title="c12">y</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c5">c</font>
 <b>by </b><i><a class="txt" href="yellow11.html#E2:15_2"><i><font color="Green" title="E13">A56</font></i></a>, <a class="ref" href="yellow11.html#T5" target="_self" title="YELLOW11:th.5">Th5</a></i>;<br/><a NAME="E3:15_2_2_1_3"/><b>then </b>
 <a href="yellow_0.html#NK3" title="YELLOW_0:NK.3">sup</a> <span class="p1"><a href="domain_1.html#K7" title="DOMAIN_1:func.7">{</a><span class="default"><font color="Maroon" title="c11">x</font>,<font color="Maroon" title="c12">y</font></span><a href="domain_1.html#K7" title="DOMAIN_1:func.7">}</a></span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c5">c</font>
 <b>by </b><i><a class="ref" href="yellow_0.html#T41" title="YELLOW_0:th.41">YELLOW_0:41</a></i>;<br/><b>hence </b><a NAME="E4:15_2_2_1_3"/>
 <a href="yellow_0.html#K1" title="YELLOW_0:func.1">"\/"</a> <span class="p1"><a href="domain_1.html#K7" title="DOMAIN_1:func.7">{</a><span class="default"><font color="Maroon" title="c11">x</font>,<font color="Maroon" title="c12">y</font></span><a href="domain_1.html#K7" title="DOMAIN_1:func.7">}</a></span>,<font color="Maroon" title="c1">L</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <span class="p1">(<span class="default"><a href="yellow_0.html#K5" title="YELLOW_0:func.5">subrelstr</a> <font color="Maroon" title="c9">ck</font></span>)</span>
 <b>by </b><i><a class="txt" href="yellow11.html#E4:15_2"><i><font color="Green" title="E14">A57</font></i></a>, <a class="ref" href="enumset1.html#D3" title="ENUMSET1:def.3">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" title="c11">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c3">a</font> &amp; <font color="Maroon" title="c12">y</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c6">d</font> )
 ;<br/><div class="add"><a NAME="E2:15_2_2_1_4"/><b>then </b>
<font color="Maroon" title="c11">x</font> <a href="lattice3.html#K13" title="LATTICE3:func.13">"\/"</a> <font color="Maroon" title="c12">y</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c6">d</font>
 <b>by </b><i><a class="txt" href="yellow11.html#E2:15_2"><i><font color="Green" title="E13">A56</font></i></a>, <a class="ref" href="yellow11.html#T5" target="_self" title="YELLOW11:th.5">Th5</a></i>;<br/><a NAME="E3:15_2_2_1_4"/><b>then </b>
 <a href="yellow_0.html#NK3" title="YELLOW_0:NK.3">sup</a> <span class="p1"><a href="domain_1.html#K7" title="DOMAIN_1:func.7">{</a><span class="default"><font color="Maroon" title="c11">x</font>,<font color="Maroon" title="c12">y</font></span><a href="domain_1.html#K7" title="DOMAIN_1:func.7">}</a></span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c6">d</font>
 <b>by </b><i><a class="ref" href="yellow_0.html#T41" title="YELLOW_0:th.41">YELLOW_0:41</a></i>;<br/><b>hence </b><a NAME="E4:15_2_2_1_4"/>
 <a href="yellow_0.html#K1" title="YELLOW_0:func.1">"\/"</a> <span class="p1"><a href="domain_1.html#K7" title="DOMAIN_1:func.7">{</a><span class="default"><font color="Maroon" title="c11">x</font>,<font color="Maroon" title="c12">y</font></span><a href="domain_1.html#K7" title="DOMAIN_1:func.7">}</a></span>,<font color="Maroon" title="c1">L</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <span class="p1">(<span class="default"><a href="yellow_0.html#K5" title="YELLOW_0:func.5">subrelstr</a> <font color="Maroon" title="c9">ck</font></span>)</span>
 <b>by </b><i><a class="txt" href="yellow11.html#E4:15_2"><i><font color="Green" title="E14">A57</font></i></a>, <a class="ref" href="enumset1.html#D3" title="ENUMSET1:def.3">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" title="E17">A63</font></i>: 
( <font color="Maroon" title="c11">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c3">a</font> &amp; <font color="Maroon" title="c12">y</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c7">e</font> )
 ;<br/><div class="add"><a NAME="E2:15_2_2_1_5"/>
( <font color="Maroon" title="c3">a</font> <a href="orders_2.html#R3" title="ORDERS_2:pred.3">&lt;=</a> <font color="Maroon" title="c5">c</font> &amp; <font color="Maroon" title="c5">c</font> <a href="orders_2.html#R3" title="ORDERS_2:pred.3">&lt;=</a> <font color="Maroon" title="c7">e</font> )
 <b>by </b><i><a class="txt" href="yellow11.html#E2:15_2"><i><font color="Green" title="E13">A56</font></i></a>, <a class="ref" href="yellow_0.html#T25" title="YELLOW_0:th.25">YELLOW_0:25</a></i>;<br/><a NAME="E3:15_2_2_1_5"/><b>then </b>
<font color="Maroon" title="c3">a</font> <a href="orders_2.html#R3" title="ORDERS_2:pred.3">&lt;=</a> <font color="Maroon" title="c7">e</font>
 <b>by </b><i><a class="ref" href="orders_2.html#T26" title="ORDERS_2:th.26">ORDERS_2:26</a></i>;<br/><a NAME="E4:15_2_2_1_5"/><b>then </b>
<font color="Maroon" title="c3">a</font> <a href="lattice3.html#K12" title="LATTICE3:func.12">"/\"</a> <font color="Maroon" title="c7">e</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c3">a</font>
 <b>by </b><i><a class="ref" href="yellow_0.html#T25" title="YELLOW_0:th.25">YELLOW_0:25</a></i>;<br/><a NAME="E5:15_2_2_1_5"/><b>then </b>
<font color="Maroon" title="c3">a</font> <a href="lattice3.html#K13" title="LATTICE3:func.13">"\/"</a> <font color="Maroon" title="c7">e</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c7">e</font>
 <b>by </b><i><a class="ref" href="yellow11.html#T5" target="_self" title="YELLOW11:th.5">Th5</a></i>;<br/><a NAME="E6:15_2_2_1_5"/><b>then </b>
 <a href="yellow_0.html#NK3" title="YELLOW_0:NK.3">sup</a> <span class="p1"><a href="domain_1.html#K7" title="DOMAIN_1:func.7">{</a><span class="default"><font color="Maroon" title="c11">x</font>,<font color="Maroon" title="c12">y</font></span><a href="domain_1.html#K7" title="DOMAIN_1:func.7">}</a></span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c7">e</font>
 <b>by </b><i><a class="txt" href="yellow11.html#E1:15_2_2_1_5"><i><font color="Green" title="E17">A63</font></i></a>, <a class="ref" href="yellow_0.html#T41" title="YELLOW_0:th.41">YELLOW_0:41</a></i>;<br/><b>hence </b><a NAME="E7:15_2_2_1_5"/>
 <a href="yellow_0.html#K1" title="YELLOW_0:func.1">"\/"</a> <span class="p1"><a href="domain_1.html#K7" title="DOMAIN_1:func.7">{</a><span class="default"><font color="Maroon" title="c11">x</font>,<font color="Maroon" title="c12">y</font></span><a href="domain_1.html#K7" title="DOMAIN_1:func.7">}</a></span>,<font color="Maroon" title="c1">L</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <span class="p1">(<span class="default"><a href="yellow_0.html#K5" title="YELLOW_0:func.5">subrelstr</a> <font color="Maroon" title="c9">ck</font></span>)</span>
 <b>by </b><i><a class="txt" href="yellow11.html#E4:15_2"><i><font color="Green" title="E14">A57</font></i></a>, <a class="ref" href="enumset1.html#D3" title="ENUMSET1:def.3">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" title="E17">A64</font></i>: 
( <font color="Maroon" title="c11">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c4">b</font> &amp; <font color="Maroon" title="c12">y</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c3">a</font> )
 ;<br/><div class="add"><a NAME="E2:15_2_2_1_6"/>
<font color="Maroon" title="c3">a</font> <a href="lattice3.html#K13" title="LATTICE3:func.13">"\/"</a> <font color="Maroon" title="c4">b</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c4">b</font>
 <b>by </b><i><a class="txt" href="yellow11.html#E2:15_2"><i><font color="Green" title="E13">A56</font></i></a>, <a class="ref" href="yellow11.html#T5" target="_self" title="YELLOW11:th.5">Th5</a></i>;<br/><a NAME="E3:15_2_2_1_6"/><b>then </b>
 <a href="yellow_0.html#NK3" title="YELLOW_0:NK.3">sup</a> <span class="p1"><a href="domain_1.html#K7" title="DOMAIN_1:func.7">{</a><span class="default"><font color="Maroon" title="c11">x</font>,<font color="Maroon" title="c12">y</font></span><a href="domain_1.html#K7" title="DOMAIN_1:func.7">}</a></span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c4">b</font>
 <b>by </b><i><a class="txt" href="yellow11.html#E1:15_2_2_1_6"><i><font color="Green" title="E17">A64</font></i></a>, <a class="ref" href="yellow_0.html#T41" title="YELLOW_0:th.41">YELLOW_0:41</a></i>;<br/><b>hence </b><a NAME="E4:15_2_2_1_6"/>
 <a href="yellow_0.html#K1" title="YELLOW_0:func.1">"\/"</a> <span class="p1"><a href="domain_1.html#K7" title="DOMAIN_1:func.7">{</a><span class="default"><font color="Maroon" title="c11">x</font>,<font color="Maroon" title="c12">y</font></span><a href="domain_1.html#K7" title="DOMAIN_1:func.7">}</a></span>,<font color="Maroon" title="c1">L</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <span class="p1">(<span class="default"><a href="yellow_0.html#K5" title="YELLOW_0:func.5">subrelstr</a> <font color="Maroon" title="c9">ck</font></span>)</span>
 <b>by </b><i><a class="txt" href="yellow11.html#E4:15_2"><i><font color="Green" title="E14">A57</font></i></a>, <a class="ref" href="enumset1.html#D3" title="ENUMSET1:def.3">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" title="c11">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c4">b</font> &amp; <font color="Maroon" title="c12">y</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c4">b</font> )
 ;<br/><div class="add"><a NAME="E2:15_2_2_1_7"/><b>then </b>
 <a href="yellow_0.html#NK3" title="YELLOW_0:NK.3">sup</a> <span class="p1"><a href="domain_1.html#K7" title="DOMAIN_1:func.7">{</a><span class="default"><font color="Maroon" title="c11">x</font>,<font color="Maroon" title="c12">y</font></span><a href="domain_1.html#K7" title="DOMAIN_1:func.7">}</a></span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c4">b</font> <a href="lattice3.html#K13" title="LATTICE3:func.13">"\/"</a> <font color="Maroon" title="c4">b</font>
 <b>by </b><i><a class="ref" href="yellow_0.html#T41" title="YELLOW_0:th.41">YELLOW_0:41</a></i>;<br/><a NAME="E3:15_2_2_1_7"/><b>then </b>
 <a href="yellow_0.html#NK3" title="YELLOW_0:NK.3">sup</a> <span class="p1"><a href="domain_1.html#K7" title="DOMAIN_1:func.7">{</a><span class="default"><font color="Maroon" title="c11">x</font>,<font color="Maroon" title="c12">y</font></span><a href="domain_1.html#K7" title="DOMAIN_1:func.7">}</a></span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c4">b</font>
 <b>by </b><i><a class="ref" href="yellow_5.html#T1" title="YELLOW_5:th.1">YELLOW_5:1</a></i>;<br/><b>hence </b><a NAME="E4:15_2_2_1_7"/>
 <a href="yellow_0.html#K1" title="YELLOW_0:func.1">"\/"</a> <span class="p1"><a href="domain_1.html#K7" title="DOMAIN_1:func.7">{</a><span class="default"><font color="Maroon" title="c11">x</font>,<font color="Maroon" title="c12">y</font></span><a href="domain_1.html#K7" title="DOMAIN_1:func.7">}</a></span>,<font color="Maroon" title="c1">L</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <span class="p1">(<span class="default"><a href="yellow_0.html#K5" title="YELLOW_0:func.5">subrelstr</a> <font color="Maroon" title="c9">ck</font></span>)</span>
 <b>by </b><i><a class="txt" href="yellow11.html#E4:15_2"><i><font color="Green" title="E14">A57</font></i></a>, <a class="ref" href="enumset1.html#D3" title="ENUMSET1:def.3">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" title="c11">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c4">b</font> &amp; <font color="Maroon" title="c12">y</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c5">c</font> )
 ;<br/><div class="add"><a NAME="E2:15_2_2_1_8"/><b>then </b>
 <a href="yellow_0.html#NK3" title="YELLOW_0:NK.3">sup</a> <span class="p1"><a href="domain_1.html#K7" title="DOMAIN_1:func.7">{</a><span class="default"><font color="Maroon" title="c11">x</font>,<font color="Maroon" title="c12">y</font></span><a href="domain_1.html#K7" title="DOMAIN_1:func.7">}</a></span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c4">b</font> <a href="lattice3.html#K13" title="LATTICE3:func.13">"\/"</a> <font color="Maroon" title="c5">c</font>
 <b>by </b><i><a class="ref" href="yellow_0.html#T41" title="YELLOW_0:th.41">YELLOW_0:41</a></i>;<br/><b>hence </b><a NAME="E3:15_2_2_1_8"/>
 <a href="yellow_0.html#K1" title="YELLOW_0:func.1">"\/"</a> <span class="p1"><a href="domain_1.html#K7" title="DOMAIN_1:func.7">{</a><span class="default"><font color="Maroon" title="c11">x</font>,<font color="Maroon" title="c12">y</font></span><a href="domain_1.html#K7" title="DOMAIN_1:func.7">}</a></span>,<font color="Maroon" title="c1">L</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <span class="p1">(<span class="default"><a href="yellow_0.html#K5" title="YELLOW_0:func.5">subrelstr</a> <font color="Maroon" title="c9">ck</font></span>)</span>
 <b>by </b><i><a class="txt" href="yellow11.html#E2:15_2"><i><font color="Green" title="E13">A56</font></i></a>, <a class="txt" href="yellow11.html#E4:15_2"><i><font color="Green" title="E14">A57</font></i></a>, <a class="ref" href="enumset1.html#D3" title="ENUMSET1:def.3">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" title="c11">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c4">b</font> &amp; <font color="Maroon" title="c12">y</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c6">d</font> )
 ;<br/><div class="add"><a NAME="E2:15_2_2_1_9"/><b>then </b>
 <a href="yellow_0.html#NK3" title="YELLOW_0:NK.3">sup</a> <span class="p1"><a href="domain_1.html#K7" title="DOMAIN_1:func.7">{</a><span class="default"><font color="Maroon" title="c11">x</font>,<font color="Maroon" title="c12">y</font></span><a href="domain_1.html#K7" title="DOMAIN_1:func.7">}</a></span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c4">b</font> <a href="lattice3.html#K13" title="LATTICE3:func.13">"\/"</a> <font color="Maroon" title="c6">d</font>
 <b>by </b><i><a class="ref" href="yellow_0.html#T41" title="YELLOW_0:th.41">YELLOW_0:41</a></i>;<br/><b>hence </b><a NAME="E3:15_2_2_1_9"/>
 <a href="yellow_0.html#K1" title="YELLOW_0:func.1">"\/"</a> <span class="p1"><a href="domain_1.html#K7" title="DOMAIN_1:func.7">{</a><span class="default"><font color="Maroon" title="c11">x</font>,<font color="Maroon" title="c12">y</font></span><a href="domain_1.html#K7" title="DOMAIN_1:func.7">}</a></span>,<font color="Maroon" title="c1">L</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <span class="p1">(<span class="default"><a href="yellow_0.html#K5" title="YELLOW_0:func.5">subrelstr</a> <font color="Maroon" title="c9">ck</font></span>)</span>
 <b>by </b><i><a class="txt" href="yellow11.html#E2:15_2"><i><font color="Green" title="E13">A56</font></i></a>, <a class="txt" href="yellow11.html#E4:15_2"><i><font color="Green" title="E14">A57</font></i></a>, <a class="ref" href="enumset1.html#D3" title="ENUMSET1:def.3">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" title="E17">A65</font></i>: 
( <font color="Maroon" title="c11">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c4">b</font> &amp; <font color="Maroon" title="c12">y</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c7">e</font> )
 ;<br/><div class="add"><a NAME="E2:15_2_2_1_10"/>
<font color="Maroon" title="c4">b</font> <a href="lattice3.html#K13" title="LATTICE3:func.13">"\/"</a> <font color="Maroon" title="c7">e</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c7">e</font>
 <b>by </b><i><a class="txt" href="yellow11.html#E2:15_2"><i><font color="Green" title="E13">A56</font></i></a>, <a class="ref" href="yellow11.html#T5" target="_self" title="YELLOW11:th.5">Th5</a></i>;<br/><a NAME="E3:15_2_2_1_10"/><b>then </b>
 <a href="yellow_0.html#NK3" title="YELLOW_0:NK.3">sup</a> <span class="p1"><a href="domain_1.html#K7" title="DOMAIN_1:func.7">{</a><span class="default"><font color="Maroon" title="c11">x</font>,<font color="Maroon" title="c12">y</font></span><a href="domain_1.html#K7" title="DOMAIN_1:func.7">}</a></span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c7">e</font>
 <b>by </b><i><a class="txt" href="yellow11.html#E1:15_2_2_1_10"><i><font color="Green" title="E17">A65</font></i></a>, <a class="ref" href="yellow_0.html#T41" title="YELLOW_0:th.41">YELLOW_0:41</a></i>;<br/><b>hence </b><a NAME="E4:15_2_2_1_10"/>
 <a href="yellow_0.html#K1" title="YELLOW_0:func.1">"\/"</a> <span class="p1"><a href="domain_1.html#K7" title="DOMAIN_1:func.7">{</a><span class="default"><font color="Maroon" title="c11">x</font>,<font color="Maroon" title="c12">y</font></span><a href="domain_1.html#K7" title="DOMAIN_1:func.7">}</a></span>,<font color="Maroon" title="c1">L</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <span class="p1">(<span class="default"><a href="yellow_0.html#K5" title="YELLOW_0:func.5">subrelstr</a> <font color="Maroon" title="c9">ck</font></span>)</span>
 <b>by </b><i><a class="txt" href="yellow11.html#E4:15_2"><i><font color="Green" title="E14">A57</font></i></a>, <a class="ref" href="enumset1.html#D3" title="ENUMSET1:def.3">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" title="E17">A66</font></i>: 
( <font color="Maroon" title="c11">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c5">c</font> &amp; <font color="Maroon" title="c12">y</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c3">a</font> )
 ;<br/><div class="add"><a NAME="E2:15_2_2_1_11"/>
<font color="Maroon" title="c5">c</font> <a href="lattice3.html#K13" title="LATTICE3:func.13">"\/"</a> <font color="Maroon" title="c3">a</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c5">c</font>
 <b>by </b><i><a class="txt" href="yellow11.html#E2:15_2"><i><font color="Green" title="E13">A56</font></i></a>, <a class="ref" href="yellow11.html#T5" target="_self" title="YELLOW11:th.5">Th5</a></i>;<br/><a NAME="E3:15_2_2_1_11"/><b>then </b>
 <a href="yellow_0.html#NK3" title="YELLOW_0:NK.3">sup</a> <span class="p1"><a href="domain_1.html#K7" title="DOMAIN_1:func.7">{</a><span class="default"><font color="Maroon" title="c11">x</font>,<font color="Maroon" title="c12">y</font></span><a href="domain_1.html#K7" title="DOMAIN_1:func.7">}</a></span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c5">c</font>
 <b>by </b><i><a class="txt" href="yellow11.html#E1:15_2_2_1_11"><i><font color="Green" title="E17">A66</font></i></a>, <a class="ref" href="yellow_0.html#T41" title="YELLOW_0:th.41">YELLOW_0:41</a></i>;<br/><b>hence </b><a NAME="E4:15_2_2_1_11"/>
 <a href="yellow_0.html#K1" title="YELLOW_0:func.1">"\/"</a> <span class="p1"><a href="domain_1.html#K7" title="DOMAIN_1:func.7">{</a><span class="default"><font color="Maroon" title="c11">x</font>,<font color="Maroon" title="c12">y</font></span><a href="domain_1.html#K7" title="DOMAIN_1:func.7">}</a></span>,<font color="Maroon" title="c1">L</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <span class="p1">(<span class="default"><a href="yellow_0.html#K5" title="YELLOW_0:func.5">subrelstr</a> <font color="Maroon" title="c9">ck</font></span>)</span>
 <b>by </b><i><a class="txt" href="yellow11.html#E4:15_2"><i><font color="Green" title="E14">A57</font></i></a>, <a class="ref" href="enumset1.html#D3" title="ENUMSET1:def.3">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" title="c11">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c5">c</font> &amp; <font color="Maroon" title="c12">y</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c4">b</font> )
 ;<br/><div class="add"><a NAME="E2:15_2_2_1_12"/><b>then </b>
 <a href="yellow_0.html#NK3" title="YELLOW_0:NK.3">sup</a> <span class="p1"><a href="domain_1.html#K7" title="DOMAIN_1:func.7">{</a><span class="default"><font color="Maroon" title="c11">x</font>,<font color="Maroon" title="c12">y</font></span><a href="domain_1.html#K7" title="DOMAIN_1:func.7">}</a></span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c4">b</font> <a href="lattice3.html#K13" title="LATTICE3:func.13">"\/"</a> <font color="Maroon" title="c5">c</font>
 <b>by </b><i><a class="ref" href="yellow_0.html#T41" title="YELLOW_0:th.41">YELLOW_0:41</a></i>;<br/><b>hence </b><a NAME="E3:15_2_2_1_12"/>
 <a href="yellow_0.html#K1" title="YELLOW_0:func.1">"\/"</a> <span class="p1"><a href="domain_1.html#K7" title="DOMAIN_1:func.7">{</a><span class="default"><font color="Maroon" title="c11">x</font>,<font color="Maroon" title="c12">y</font></span><a href="domain_1.html#K7" title="DOMAIN_1:func.7">}</a></span>,<font color="Maroon" title="c1">L</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <span class="p1">(<span class="default"><a href="yellow_0.html#K5" title="YELLOW_0:func.5">subrelstr</a> <font color="Maroon" title="c9">ck</font></span>)</span>
 <b>by </b><i><a class="txt" href="yellow11.html#E2:15_2"><i><font color="Green" title="E13">A56</font></i></a>, <a class="txt" href="yellow11.html#E4:15_2"><i><font color="Green" title="E14">A57</font></i></a>, <a class="ref" href="enumset1.html#D3" title="ENUMSET1:def.3">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" title="c11">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c5">c</font> &amp; <font color="Maroon" title="c12">y</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c5">c</font> )
 ;<br/><div class="add"><a NAME="E2:15_2_2_1_13"/><b>then </b>
 <a href="yellow_0.html#NK3" title="YELLOW_0:NK.3">sup</a> <span class="p1"><a href="domain_1.html#K7" title="DOMAIN_1:func.7">{</a><span class="default"><font color="Maroon" title="c11">x</font>,<font color="Maroon" title="c12">y</font></span><a href="domain_1.html#K7" title="DOMAIN_1:func.7">}</a></span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c5">c</font> <a href="lattice3.html#K13" title="LATTICE3:func.13">"\/"</a> <font color="Maroon" title="c5">c</font>
 <b>by </b><i><a class="ref" href="yellow_0.html#T41" title="YELLOW_0:th.41">YELLOW_0:41</a></i>;<br/><a NAME="E3:15_2_2_1_13"/><b>then </b>
 <a href="yellow_0.html#NK3" title="YELLOW_0:NK.3">sup</a> <span class="p1"><a href="domain_1.html#K7" title="DOMAIN_1:func.7">{</a><span class="default"><font color="Maroon" title="c11">x</font>,<font color="Maroon" title="c12">y</font></span><a href="domain_1.html#K7" title="DOMAIN_1:func.7">}</a></span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c5">c</font>
 <b>by </b><i><a class="ref" href="yellow_5.html#T1" title="YELLOW_5:th.1">YELLOW_5:1</a></i>;<br/><b>hence </b><a NAME="E4:15_2_2_1_13"/>
 <a href="yellow_0.html#K1" title="YELLOW_0:func.1">"\/"</a> <span class="p1"><a href="domain_1.html#K7" title="DOMAIN_1:func.7">{</a><span class="default"><font color="Maroon" title="c11">x</font>,<font color="Maroon" title="c12">y</font></span><a href="domain_1.html#K7" title="DOMAIN_1:func.7">}</a></span>,<font color="Maroon" title="c1">L</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <span class="p1">(<span class="default"><a href="yellow_0.html#K5" title="YELLOW_0:func.5">subrelstr</a> <font color="Maroon" title="c9">ck</font></span>)</span>
 <b>by </b><i><a class="txt" href="yellow11.html#E4:15_2"><i><font color="Green" title="E14">A57</font></i></a>, <a class="ref" href="enumset1.html#D3" title="ENUMSET1:def.3">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" title="c11">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c5">c</font> &amp; <font color="Maroon" title="c12">y</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c6">d</font> )
 ;<br/><div class="add"><a NAME="E2:15_2_2_1_14"/><b>then </b>
 <a href="yellow_0.html#NK3" title="YELLOW_0:NK.3">sup</a> <span class="p1"><a href="domain_1.html#K7" title="DOMAIN_1:func.7">{</a><span class="default"><font color="Maroon" title="c11">x</font>,<font color="Maroon" title="c12">y</font></span><a href="domain_1.html#K7" title="DOMAIN_1:func.7">}</a></span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c5">c</font> <a href="lattice3.html#K13" title="LATTICE3:func.13">"\/"</a> <font color="Maroon" title="c6">d</font>
 <b>by </b><i><a class="ref" href="yellow_0.html#T41" title="YELLOW_0:th.41">YELLOW_0:41</a></i>;<br/><b>hence </b><a NAME="E3:15_2_2_1_14"/>
 <a href="yellow_0.html#K1" title="YELLOW_0:func.1">"\/"</a> <span class="p1"><a href="domain_1.html#K7" title="DOMAIN_1:func.7">{</a><span class="default"><font color="Maroon" title="c11">x</font>,<font color="Maroon" title="c12">y</font></span><a href="domain_1.html#K7" title="DOMAIN_1:func.7">}</a></span>,<font color="Maroon" title="c1">L</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <span class="p1">(<span class="default"><a href="yellow_0.html#K5" title="YELLOW_0:func.5">subrelstr</a> <font color="Maroon" title="c9">ck</font></span>)</span>
 <b>by </b><i><a class="txt" href="yellow11.html#E2:15_2"><i><font color="Green" title="E13">A56</font></i></a>, <a class="txt" href="yellow11.html#E4:15_2"><i><font color="Green" title="E14">A57</font></i></a>, <a class="ref" href="enumset1.html#D3" title="ENUMSET1:def.3">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" title="E17">A67</font></i>: 
( <font color="Maroon" title="c11">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c5">c</font> &amp; <font color="Maroon" title="c12">y</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c7">e</font> )
 ;<br/><div class="add"><a NAME="E2:15_2_2_1_15"/>
<font color="Maroon" title="c5">c</font> <a href="lattice3.html#K13" title="LATTICE3:func.13">"\/"</a> <font color="Maroon" title="c7">e</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c7">e</font>
 <b>by </b><i><a class="txt" href="yellow11.html#E2:15_2"><i><font color="Green" title="E13">A56</font></i></a>, <a class="ref" href="yellow11.html#T5" target="_self" title="YELLOW11:th.5">Th5</a></i>;<br/><a NAME="E3:15_2_2_1_15"/><b>then </b>
 <a href="yellow_0.html#NK3" title="YELLOW_0:NK.3">sup</a> <span class="p1"><a href="domain_1.html#K7" title="DOMAIN_1:func.7">{</a><span class="default"><font color="Maroon" title="c11">x</font>,<font color="Maroon" title="c12">y</font></span><a href="domain_1.html#K7" title="DOMAIN_1:func.7">}</a></span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c7">e</font>
 <b>by </b><i><a class="txt" href="yellow11.html#E1:15_2_2_1_15"><i><font color="Green" title="E17">A67</font></i></a>, <a class="ref" href="yellow_0.html#T41" title="YELLOW_0:th.41">YELLOW_0:41</a></i>;<br/><b>hence </b><a NAME="E4:15_2_2_1_15"/>
 <a href="yellow_0.html#K1" title="YELLOW_0:func.1">"\/"</a> <span class="p1"><a href="domain_1.html#K7" title="DOMAIN_1:func.7">{</a><span class="default"><font color="Maroon" title="c11">x</font>,<font color="Maroon" title="c12">y</font></span><a href="domain_1.html#K7" title="DOMAIN_1:func.7">}</a></span>,<font color="Maroon" title="c1">L</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <span class="p1">(<span class="default"><a href="yellow_0.html#K5" title="YELLOW_0:func.5">subrelstr</a> <font color="Maroon" title="c9">ck</font></span>)</span>
 <b>by </b><i><a class="txt" href="yellow11.html#E4:15_2"><i><font color="Green" title="E14">A57</font></i></a>, <a class="ref" href="enumset1.html#D3" title="ENUMSET1:def.3">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" title="c11">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c6">d</font> &amp; <font color="Maroon" title="c12">y</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c3">a</font> )
 ;<br/><div class="add"><a NAME="E2:15_2_2_1_16"/><b>then </b>
<font color="Maroon" title="c11">x</font> <a href="lattice3.html#K13" title="LATTICE3:func.13">"\/"</a> <font color="Maroon" title="c12">y</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c6">d</font>
 <b>by </b><i><a class="txt" href="yellow11.html#E2:15_2"><i><font color="Green" title="E13">A56</font></i></a>, <a class="ref" href="yellow11.html#T5" target="_self" title="YELLOW11:th.5">Th5</a></i>;<br/><a NAME="E3:15_2_2_1_16"/><b>then </b>
 <a href="yellow_0.html#NK3" title="YELLOW_0:NK.3">sup</a> <span class="p1"><a href="domain_1.html#K7" title="DOMAIN_1:func.7">{</a><span class="default"><font color="Maroon" title="c11">x</font>,<font color="Maroon" title="c12">y</font></span><a href="domain_1.html#K7" title="DOMAIN_1:func.7">}</a></span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c6">d</font>
 <b>by </b><i><a class="ref" href="yellow_0.html#T41" title="YELLOW_0:th.41">YELLOW_0:41</a></i>;<br/><b>hence </b><a NAME="E4:15_2_2_1_16"/>
 <a href="yellow_0.html#K1" title="YELLOW_0:func.1">"\/"</a> <span class="p1"><a href="domain_1.html#K7" title="DOMAIN_1:func.7">{</a><span class="default"><font color="Maroon" title="c11">x</font>,<font color="Maroon" title="c12">y</font></span><a href="domain_1.html#K7" title="DOMAIN_1:func.7">}</a></span>,<font color="Maroon" title="c1">L</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <span class="p1">(<span class="default"><a href="yellow_0.html#K5" title="YELLOW_0:func.5">subrelstr</a> <font color="Maroon" title="c9">ck</font></span>)</span>
 <b>by </b><i><a class="txt" href="yellow11.html#E4:15_2"><i><font color="Green" title="E14">A57</font></i></a>, <a class="ref" href="enumset1.html#D3" title="ENUMSET1:def.3">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" title="c11">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c6">d</font> &amp; <font color="Maroon" title="c12">y</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c4">b</font> )
 ;<br/><div class="add"><a NAME="E2:15_2_2_1_17"/><b>then </b>
 <a href="yellow_0.html#NK3" title="YELLOW_0:NK.3">sup</a> <span class="p1"><a href="domain_1.html#K7" title="DOMAIN_1:func.7">{</a><span class="default"><font color="Maroon" title="c11">x</font>,<font color="Maroon" title="c12">y</font></span><a href="domain_1.html#K7" title="DOMAIN_1:func.7">}</a></span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c4">b</font> <a href="lattice3.html#K13" title="LATTICE3:func.13">"\/"</a> <font color="Maroon" title="c6">d</font>
 <b>by </b><i><a class="ref" href="yellow_0.html#T41" title="YELLOW_0:th.41">YELLOW_0:41</a></i>;<br/><b>hence </b><a NAME="E3:15_2_2_1_17"/>
 <a href="yellow_0.html#K1" title="YELLOW_0:func.1">"\/"</a> <span class="p1"><a href="domain_1.html#K7" title="DOMAIN_1:func.7">{</a><span class="default"><font color="Maroon" title="c11">x</font>,<font color="Maroon" title="c12">y</font></span><a href="domain_1.html#K7" title="DOMAIN_1:func.7">}</a></span>,<font color="Maroon" title="c1">L</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <span class="p1">(<span class="default"><a href="yellow_0.html#K5" title="YELLOW_0:func.5">subrelstr</a> <font color="Maroon" title="c9">ck</font></span>)</span>
 <b>by </b><i><a class="txt" href="yellow11.html#E2:15_2"><i><font color="Green" title="E13">A56</font></i></a>, <a class="txt" href="yellow11.html#E4:15_2"><i><font color="Green" title="E14">A57</font></i></a>, <a class="ref" href="enumset1.html#D3" title="ENUMSET1:def.3">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" title="c11">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c6">d</font> &amp; <font color="Maroon" title="c12">y</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c5">c</font> )
 ;<br/><div class="add"><a NAME="E2:15_2_2_1_18"/><b>then </b>
 <a href="yellow_0.html#NK3" title="YELLOW_0:NK.3">sup</a> <span class="p1"><a href="domain_1.html#K7" title="DOMAIN_1:func.7">{</a><span class="default"><font color="Maroon" title="c11">x</font>,<font color="Maroon" title="c12">y</font></span><a href="domain_1.html#K7" title="DOMAIN_1:func.7">}</a></span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c5">c</font> <a href="lattice3.html#K13" title="LATTICE3:func.13">"\/"</a> <font color="Maroon" title="c6">d</font>
 <b>by </b><i><a class="ref" href="yellow_0.html#T41" title="YELLOW_0:th.41">YELLOW_0:41</a></i>;<br/><b>hence </b><a NAME="E3:15_2_2_1_18"/>
 <a href="yellow_0.html#K1" title="YELLOW_0:func.1">"\/"</a> <span class="p1"><a href="domain_1.html#K7" title="DOMAIN_1:func.7">{</a><span class="default"><font color="Maroon" title="c11">x</font>,<font color="Maroon" title="c12">y</font></span><a href="domain_1.html#K7" title="DOMAIN_1:func.7">}</a></span>,<font color="Maroon" title="c1">L</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <span class="p1">(<span class="default"><a href="yellow_0.html#K5" title="YELLOW_0:func.5">subrelstr</a> <font color="Maroon" title="c9">ck</font></span>)</span>
 <b>by </b><i><a class="txt" href="yellow11.html#E2:15_2"><i><font color="Green" title="E13">A56</font></i></a>, <a class="txt" href="yellow11.html#E4:15_2"><i><font color="Green" title="E14">A57</font></i></a>, <a class="ref" href="enumset1.html#D3" title="ENUMSET1:def.3">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" title="c11">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c6">d</font> &amp; <font color="Maroon" title="c12">y</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c6">d</font> )
 ;<br/><div class="add"><a NAME="E2:15_2_2_1_19"/><b>then </b>
 <a href="yellow_0.html#NK3" title="YELLOW_0:NK.3">sup</a> <span class="p1"><a href="domain_1.html#K7" title="DOMAIN_1:func.7">{</a><span class="default"><font color="Maroon" title="c11">x</font>,<font color="Maroon" title="c12">y</font></span><a href="domain_1.html#K7" title="DOMAIN_1:func.7">}</a></span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c6">d</font> <a href="lattice3.html#K13" title="LATTICE3:func.13">"\/"</a> <font color="Maroon" title="c6">d</font>
 <b>by </b><i><a class="ref" href="yellow_0.html#T41" title="YELLOW_0:th.41">YELLOW_0:41</a></i>;<br/><a NAME="E3:15_2_2_1_19"/><b>then </b>
 <a href="yellow_0.html#NK3" title="YELLOW_0:NK.3">sup</a> <span class="p1"><a href="domain_1.html#K7" title="DOMAIN_1:func.7">{</a><span class="default"><font color="Maroon" title="c11">x</font>,<font color="Maroon" title="c12">y</font></span><a href="domain_1.html#K7" title="DOMAIN_1:func.7">}</a></span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c6">d</font>
 <b>by </b><i><a class="ref" href="yellow_5.html#T1" title="YELLOW_5:th.1">YELLOW_5:1</a></i>;<br/><b>hence </b><a NAME="E4:15_2_2_1_19"/>
 <a href="yellow_0.html#K1" title="YELLOW_0:func.1">"\/"</a> <span class="p1"><a href="domain_1.html#K7" title="DOMAIN_1:func.7">{</a><span class="default"><font color="Maroon" title="c11">x</font>,<font color="Maroon" title="c12">y</font></span><a href="domain_1.html#K7" title="DOMAIN_1:func.7">}</a></span>,<font color="Maroon" title="c1">L</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <span class="p1">(<span class="default"><a href="yellow_0.html#K5" title="YELLOW_0:func.5">subrelstr</a> <font color="Maroon" title="c9">ck</font></span>)</span>
 <b>by </b><i><a class="txt" href="yellow11.html#E4:15_2"><i><font color="Green" title="E14">A57</font></i></a>, <a class="ref" href="enumset1.html#D3" title="ENUMSET1:def.3">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" title="E17">A68</font></i>: 
( <font color="Maroon" title="c11">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c6">d</font> &amp; <font color="Maroon" title="c12">y</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c7">e</font> )
 ;<br/><div class="add"><a NAME="E2:15_2_2_1_20"/>
<font color="Maroon" title="c6">d</font> <a href="lattice3.html#K13" title="LATTICE3:func.13">"\/"</a> <font color="Maroon" title="c7">e</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c7">e</font>
 <b>by </b><i><a class="txt" href="yellow11.html#E2:15_2"><i><font color="Green" title="E13">A56</font></i></a>, <a class="ref" href="yellow11.html#T5" target="_self" title="YELLOW11:th.5">Th5</a></i>;<br/><a NAME="E3:15_2_2_1_20"/><b>then </b>
 <a href="yellow_0.html#NK3" title="YELLOW_0:NK.3">sup</a> <span class="p1"><a href="domain_1.html#K7" title="DOMAIN_1:func.7">{</a><span class="default"><font color="Maroon" title="c11">x</font>,<font color="Maroon" title="c12">y</font></span><a href="domain_1.html#K7" title="DOMAIN_1:func.7">}</a></span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c7">e</font>
 <b>by </b><i><a class="txt" href="yellow11.html#E1:15_2_2_1_20"><i><font color="Green" title="E17">A68</font></i></a>, <a class="ref" href="yellow_0.html#T41" title="YELLOW_0:th.41">YELLOW_0:41</a></i>;<br/><b>hence </b><a NAME="E4:15_2_2_1_20"/>
 <a href="yellow_0.html#K1" title="YELLOW_0:func.1">"\/"</a> <span class="p1"><a href="domain_1.html#K7" title="DOMAIN_1:func.7">{</a><span class="default"><font color="Maroon" title="c11">x</font>,<font color="Maroon" title="c12">y</font></span><a href="domain_1.html#K7" title="DOMAIN_1:func.7">}</a></span>,<font color="Maroon" title="c1">L</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <span class="p1">(<span class="default"><a href="yellow_0.html#K5" title="YELLOW_0:func.5">subrelstr</a> <font color="Maroon" title="c9">ck</font></span>)</span>
 <b>by </b><i><a class="txt" href="yellow11.html#E4:15_2"><i><font color="Green" title="E14">A57</font></i></a>, <a class="ref" href="enumset1.html#D3" title="ENUMSET1:def.3">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" title="E17">A69</font></i>: 
( <font color="Maroon" title="c11">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c7">e</font> &amp; <font color="Maroon" title="c12">y</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c3">a</font> )
 ;<br/><div class="add"><a NAME="E2:15_2_2_1_21"/>
( <font color="Maroon" title="c3">a</font> <a href="orders_2.html#R3" title="ORDERS_2:pred.3">&lt;=</a> <font color="Maroon" title="c5">c</font> &amp; <font color="Maroon" title="c5">c</font> <a href="orders_2.html#R3" title="ORDERS_2:pred.3">&lt;=</a> <font color="Maroon" title="c7">e</font> )
 <b>by </b><i><a class="txt" href="yellow11.html#E2:15_2"><i><font color="Green" title="E13">A56</font></i></a>, <a class="ref" href="yellow_0.html#T25" title="YELLOW_0:th.25">YELLOW_0:25</a></i>;<br/><a NAME="E3:15_2_2_1_21"/><b>then </b>
<font color="Maroon" title="c3">a</font> <a href="orders_2.html#R3" title="ORDERS_2:pred.3">&lt;=</a> <font color="Maroon" title="c7">e</font>
 <b>by </b><i><a class="ref" href="orders_2.html#T26" title="ORDERS_2:th.26">ORDERS_2:26</a></i>;<br/><a NAME="E4:15_2_2_1_21"/><b>then </b>
<font color="Maroon" title="c3">a</font> <a href="lattice3.html#K12" title="LATTICE3:func.12">"/\"</a> <font color="Maroon" title="c7">e</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c3">a</font>
 <b>by </b><i><a class="ref" href="yellow_0.html#T25" title="YELLOW_0:th.25">YELLOW_0:25</a></i>;<br/><a NAME="E5:15_2_2_1_21"/><b>then </b>
<font color="Maroon" title="c3">a</font> <a href="lattice3.html#K13" title="LATTICE3:func.13">"\/"</a> <font color="Maroon" title="c7">e</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c7">e</font>
 <b>by </b><i><a class="ref" href="yellow11.html#T5" target="_self" title="YELLOW11:th.5">Th5</a></i>;<br/><a NAME="E6:15_2_2_1_21"/><b>then </b>
 <a href="yellow_0.html#NK3" title="YELLOW_0:NK.3">sup</a> <span class="p1"><a href="domain_1.html#K7" title="DOMAIN_1:func.7">{</a><span class="default"><font color="Maroon" title="c11">x</font>,<font color="Maroon" title="c12">y</font></span><a href="domain_1.html#K7" title="DOMAIN_1:func.7">}</a></span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c7">e</font>
 <b>by </b><i><a class="txt" href="yellow11.html#E1:15_2_2_1_21"><i><font color="Green" title="E17">A69</font></i></a>, <a class="ref" href="yellow_0.html#T41" title="YELLOW_0:th.41">YELLOW_0:41</a></i>;<br/><b>hence </b><a NAME="E7:15_2_2_1_21"/>
 <a href="yellow_0.html#K1" title="YELLOW_0:func.1">"\/"</a> <span class="p1"><a href="domain_1.html#K7" title="DOMAIN_1:func.7">{</a><span class="default"><font color="Maroon" title="c11">x</font>,<font color="Maroon" title="c12">y</font></span><a href="domain_1.html#K7" title="DOMAIN_1:func.7">}</a></span>,<font color="Maroon" title="c1">L</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <span class="p1">(<span class="default"><a href="yellow_0.html#K5" title="YELLOW_0:func.5">subrelstr</a> <font color="Maroon" title="c9">ck</font></span>)</span>
 <b>by </b><i><a class="txt" href="yellow11.html#E4:15_2"><i><font color="Green" title="E14">A57</font></i></a>, <a class="ref" href="enumset1.html#D3" title="ENUMSET1:def.3">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" title="E17">A70</font></i>: 
( <font color="Maroon" title="c11">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c7">e</font> &amp; <font color="Maroon" title="c12">y</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c4">b</font> )
 ;<br/><div class="add"><a NAME="E2:15_2_2_1_22"/>
<font color="Maroon" title="c4">b</font> <a href="lattice3.html#K13" title="LATTICE3:func.13">"\/"</a> <font color="Maroon" title="c7">e</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c7">e</font>
 <b>by </b><i><a class="txt" href="yellow11.html#E2:15_2"><i><font color="Green" title="E13">A56</font></i></a>, <a class="ref" href="yellow11.html#T5" target="_self" title="YELLOW11:th.5">Th5</a></i>;<br/><a NAME="E3:15_2_2_1_22"/><b>then </b>
 <a href="yellow_0.html#NK3" title="YELLOW_0:NK.3">sup</a> <span class="p1"><a href="domain_1.html#K7" title="DOMAIN_1:func.7">{</a><span class="default"><font color="Maroon" title="c11">x</font>,<font color="Maroon" title="c12">y</font></span><a href="domain_1.html#K7" title="DOMAIN_1:func.7">}</a></span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c7">e</font>
 <b>by </b><i><a class="txt" href="yellow11.html#E1:15_2_2_1_22"><i><font color="Green" title="E17">A70</font></i></a>, <a class="ref" href="yellow_0.html#T41" title="YELLOW_0:th.41">YELLOW_0:41</a></i>;<br/><b>hence </b><a NAME="E4:15_2_2_1_22"/>
 <a href="yellow_0.html#K1" title="YELLOW_0:func.1">"\/"</a> <span class="p1"><a href="domain_1.html#K7" title="DOMAIN_1:func.7">{</a><span class="default"><font color="Maroon" title="c11">x</font>,<font color="Maroon" title="c12">y</font></span><a href="domain_1.html#K7" title="DOMAIN_1:func.7">}</a></span>,<font color="Maroon" title="c1">L</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <span class="p1">(<span class="default"><a href="yellow_0.html#K5" title="YELLOW_0:func.5">subrelstr</a> <font color="Maroon" title="c9">ck</font></span>)</span>
 <b>by </b><i><a class="txt" href="yellow11.html#E4:15_2"><i><font color="Green" title="E14">A57</font></i></a>, <a class="ref" href="enumset1.html#D3" title="ENUMSET1:def.3">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" title="E17">A71</font></i>: 
( <font color="Maroon" title="c11">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c7">e</font> &amp; <font color="Maroon" title="c12">y</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c5">c</font> )
 ;<br/><div class="add"><a NAME="E2:15_2_2_1_23"/>
<font color="Maroon" title="c5">c</font> <a href="lattice3.html#K13" title="LATTICE3:func.13">"\/"</a> <font color="Maroon" title="c7">e</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c7">e</font>
 <b>by </b><i><a class="txt" href="yellow11.html#E2:15_2"><i><font color="Green" title="E13">A56</font></i></a>, <a class="ref" href="yellow11.html#T5" target="_self" title="YELLOW11:th.5">Th5</a></i>;<br/><a NAME="E3:15_2_2_1_23"/><b>then </b>
 <a href="yellow_0.html#NK3" title="YELLOW_0:NK.3">sup</a> <span class="p1"><a href="domain_1.html#K7" title="DOMAIN_1:func.7">{</a><span class="default"><font color="Maroon" title="c11">x</font>,<font color="Maroon" title="c12">y</font></span><a href="domain_1.html#K7" title="DOMAIN_1:func.7">}</a></span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c7">e</font>
 <b>by </b><i><a class="txt" href="yellow11.html#E1:15_2_2_1_23"><i><font color="Green" title="E17">A71</font></i></a>, <a class="ref" href="yellow_0.html#T41" title="YELLOW_0:th.41">YELLOW_0:41</a></i>;<br/><b>hence </b><a NAME="E4:15_2_2_1_23"/>
 <a href="yellow_0.html#K1" title="YELLOW_0:func.1">"\/"</a> <span class="p1"><a href="domain_1.html#K7" title="DOMAIN_1:func.7">{</a><span class="default"><font color="Maroon" title="c11">x</font>,<font color="Maroon" title="c12">y</font></span><a href="domain_1.html#K7" title="DOMAIN_1:func.7">}</a></span>,<font color="Maroon" title="c1">L</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <span class="p1">(<span class="default"><a href="yellow_0.html#K5" title="YELLOW_0:func.5">subrelstr</a> <font color="Maroon" title="c9">ck</font></span>)</span>
 <b>by </b><i><a class="txt" href="yellow11.html#E4:15_2"><i><font color="Green" title="E14">A57</font></i></a>, <a class="ref" href="enumset1.html#D3" title="ENUMSET1:def.3">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" title="E17">A72</font></i>: 
( <font color="Maroon" title="c11">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c7">e</font> &amp; <font color="Maroon" title="c12">y</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c6">d</font> )
 ;<br/><div class="add"><a NAME="E2:15_2_2_1_24"/>
<font color="Maroon" title="c6">d</font> <a href="lattice3.html#K13" title="LATTICE3:func.13">"\/"</a> <font color="Maroon" title="c7">e</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c7">e</font>
 <b>by </b><i><a class="txt" href="yellow11.html#E2:15_2"><i><font color="Green" title="E13">A56</font></i></a>, <a class="ref" href="yellow11.html#T5" target="_self" title="YELLOW11:th.5">Th5</a></i>;<br/><a NAME="E3:15_2_2_1_24"/><b>then </b>
 <a href="yellow_0.html#NK3" title="YELLOW_0:NK.3">sup</a> <span class="p1"><a href="domain_1.html#K7" title="DOMAIN_1:func.7">{</a><span class="default"><font color="Maroon" title="c11">x</font>,<font color="Maroon" title="c12">y</font></span><a href="domain_1.html#K7" title="DOMAIN_1:func.7">}</a></span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c7">e</font>
 <b>by </b><i><a class="txt" href="yellow11.html#E1:15_2_2_1_24"><i><font color="Green" title="E17">A72</font></i></a>, <a class="ref" href="yellow_0.html#T41" title="YELLOW_0:th.41">YELLOW_0:41</a></i>;<br/><b>hence </b><a NAME="E4:15_2_2_1_24"/>
 <a href="yellow_0.html#K1" title="YELLOW_0:func.1">"\/"</a> <span class="p1"><a href="domain_1.html#K7" title="DOMAIN_1:func.7">{</a><span class="default"><font color="Maroon" title="c11">x</font>,<font color="Maroon" title="c12">y</font></span><a href="domain_1.html#K7" title="DOMAIN_1:func.7">}</a></span>,<font color="Maroon" title="c1">L</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <span class="p1">(<span class="default"><a href="yellow_0.html#K5" title="YELLOW_0:func.5">subrelstr</a> <font color="Maroon" title="c9">ck</font></span>)</span>
 <b>by </b><i><a class="txt" href="yellow11.html#E4:15_2"><i><font color="Green" title="E14">A57</font></i></a>, <a class="ref" href="enumset1.html#D3" title="ENUMSET1:def.3">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" title="c11">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c7">e</font> &amp; <font color="Maroon" title="c12">y</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c7">e</font> )
 ;<br/><div class="add"><a NAME="E2:15_2_2_1_25"/><b>then </b>
 <a href="yellow_0.html#NK3" title="YELLOW_0:NK.3">sup</a> <span class="p1"><a href="domain_1.html#K7" title="DOMAIN_1:func.7">{</a><span class="default"><font color="Maroon" title="c11">x</font>,<font color="Maroon" title="c12">y</font></span><a href="domain_1.html#K7" title="DOMAIN_1:func.7">}</a></span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c7">e</font> <a href="lattice3.html#K13" title="LATTICE3:func.13">"\/"</a> <font color="Maroon" title="c7">e</font>
 <b>by </b><i><a class="ref" href="yellow_0.html#T41" title="YELLOW_0:th.41">YELLOW_0:41</a></i>;<br/><a NAME="E3:15_2_2_1_25"/><b>then </b>
 <a href="yellow_0.html#NK3" title="YELLOW_0:NK.3">sup</a> <span class="p1"><a href="domain_1.html#K7" title="DOMAIN_1:func.7">{</a><span class="default"><font color="Maroon" title="c11">x</font>,<font color="Maroon" title="c12">y</font></span><a href="domain_1.html#K7" title="DOMAIN_1:func.7">}</a></span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c7">e</font>
 <b>by </b><i><a class="ref" href="yellow_5.html#T1" title="YELLOW_5:th.1">YELLOW_5:1</a></i>;<br/><b>hence </b><a NAME="E4:15_2_2_1_25"/>
 <a href="yellow_0.html#K1" title="YELLOW_0:func.1">"\/"</a> <span class="p1"><a href="domain_1.html#K7" title="DOMAIN_1:func.7">{</a><span class="default"><font color="Maroon" title="c11">x</font>,<font color="Maroon" title="c12">y</font></span><a href="domain_1.html#K7" title="DOMAIN_1:func.7">}</a></span>,<font color="Maroon" title="c1">L</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <span class="p1">(<span class="default"><a href="yellow_0.html#K5" title="YELLOW_0:func.5">subrelstr</a> <font color="Maroon" title="c9">ck</font></span>)</span>
 <b>by </b><i><a class="txt" href="yellow11.html#E4:15_2"><i><font color="Green" title="E14">A57</font></i></a>, <a class="ref" href="enumset1.html#D3" title="ENUMSET1:def.3">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" title="c11">K</font> =  <a href="yellow_0.html#K5" title="YELLOW_0:func.5">subrelstr</a> <font color="Maroon" title="c9">ck</font> as  non <a href="struct_0.html#V2" title="STRUCT_0:attr.2">empty</a> <a href="yellow_0.html#V4" title="YELLOW_0:attr.4">full</a> <a href="lattice5.html#NM2" title="LATTICE5:NM.2">Sublattice</a> of <font color="Maroon" title="c1">L</font> <b>by </b><i><a class="txt" href="yellow11.html#E4:15_2"><i><font color="Green" title="E14">A57</font></i></a>, <a class="txt" href="yellow11.html#E5:15_2"><i><font color="Green" title="E15">A58</font></i></a>, <a class="ref" href="struct_0.html#D1" title="STRUCT_0:def.1">STRUCT_0:def 1</a></i>;<br/>
<b>take </b>
<font color="Maroon" title="c11">K</font>
;<br/>

<b>thus </b><a NAME="E8:15_2"/>
 <a href="yellow11.html#K2" title="YELLOW11:func.2">M_3</a> ,<font color="Maroon" title="c11">K</font> <a href="waybel_1.html#R5" title="WAYBEL_1:pred.5">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" title="c12">z</font> = 0 as   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <a href="yellow11.html#K2" title="YELLOW11:func.2">M_3</a>  <b>by </b><i><a class="txt" href="yellow11.html#E1:15"><i><font color="Green" title="E12">A1</font></i></a>, <a class="ref" href="enumset1.html#D3" title="ENUMSET1:def.3">ENUMSET1:def 3</a></i>;<br/>
<b>reconsider </b><font color="Maroon" title="c13">j</font> = 1 as   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <a href="yellow11.html#K2" title="YELLOW11:func.2">M_3</a>  <b>by </b><i><a class="txt" href="yellow11.html#E1:15"><i><font color="Green" title="E12">A1</font></i></a>, <a class="ref" href="enumset1.html#D3" title="ENUMSET1:def.3">ENUMSET1:def 3</a></i>;<br/>
<b>reconsider </b><font color="Maroon" title="c14">dj</font> = 2 <a href="subset_1.html#K6" title="SUBSET_1:func.6">\</a> 1 as   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <a href="yellow11.html#K2" title="YELLOW11:func.2">M_3</a>  <b>by </b><i><a class="txt" href="yellow11.html#E1:15"><i><font color="Green" title="E12">A1</font></i></a>, <a class="ref" href="enumset1.html#D3" title="ENUMSET1:def.3">ENUMSET1:def 3</a></i>;<br/>
<b>reconsider </b><font color="Maroon" title="c15">td</font> = 3 <a href="subset_1.html#K6" title="SUBSET_1:func.6">\</a> 2 as   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <a href="yellow11.html#K2" title="YELLOW11:func.2">M_3</a>  <b>by </b><i><a class="txt" href="yellow11.html#E1:15"><i><font color="Green" title="E12">A1</font></i></a>, <a class="ref" href="enumset1.html#D3" title="ENUMSET1:def.3">ENUMSET1:def 3</a></i>;<br/>
<b>reconsider </b><font color="Maroon" title="c16">t</font> = 3 as   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <a href="yellow11.html#K2" title="YELLOW11:func.2">M_3</a>  <b>by </b><i><a class="txt" href="yellow11.html#E1:15"><i><font color="Green" title="E12">A1</font></i></a>, <a class="ref" href="enumset1.html#D3" title="ENUMSET1:def.3">ENUMSET1:def 3</a></i>;<br/>
<div><i><font color="Green" title="E16">A73</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" title="E17">A74</font></i>: 
<font color="Maroon" title="c13">j</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c14">dj</font>
 ;<br/><a NAME="E2:15_2_3_1"/>
1 <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c14">dj</font>
 <b>by </b><i><a class="ref" href="yellow11.html#T2" target="_self" title="YELLOW11:th.2">Th2</a>, <a class="ref" href="tarski.html#D1" title="TARSKI:def.1">TARSKI:def 1</a></i>;<br/><b>hence </b><a NAME="E3:15_2_3_1"/>
contradiction
 <b>by </b><i><a class="txt" href="yellow11.html#E1:15_2_3_1"><i><font color="Green" title="E17">A74</font></i></a></i>;<br/></div><b>end;</b></div>
<div><i><font color="Green" title="E17">A75</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" title="E18">A76</font></i>: 
<font color="Maroon" title="c13">j</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c15">td</font>
 ;<br/><a NAME="E2:15_2_3_2"/>
( 2 <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c15">td</font> &amp; 0 <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> 2 )
 <b>by </b><i><a class="ref" href="yellow11.html#T4" target="_self" title="YELLOW11:th.4">Th4</a>, <a class="ref" href="tarski.html#D1" title="TARSKI:def.1">TARSKI:def 1</a></i>;<br/><b>hence </b><a NAME="E3:15_2_3_2"/>
contradiction
 <b>by </b><i><a class="txt" href="yellow11.html#E1:15_2_3_2"><i><font color="Green" title="E18">A76</font></i></a>, <a class="ref" href="card_5.html#T1" title="CARD_5:th.1">CARD_5:1</a>, <a class="ref" href="tarski.html#D1" title="TARSKI:def.1">TARSKI:def 1</a></i>;<br/></div><b>end;</b></div>
<div><i><font color="Green" title="E18">A77</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" title="E19">A78</font></i>: 
<font color="Maroon" title="c14">dj</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c15">td</font>
 ;<br/><a NAME="E2:15_2_3_3"/>
( 2 <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c15">td</font> &amp; 1 <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> 2 )
 <b>by </b><i><a class="ref" href="yellow11.html#T4" target="_self" title="YELLOW11:th.4">Th4</a>, <a class="ref" href="tarski.html#D1" title="TARSKI:def.1">TARSKI:def 1</a></i>;<br/><b>hence </b><a NAME="E3:15_2_3_3"/>
contradiction
 <b>by </b><i><a class="txt" href="yellow11.html#E1:15_2_3_3"><i><font color="Green" title="E19">A78</font></i></a>, <a class="ref" href="yellow11.html#T2" target="_self" title="YELLOW11:th.2">Th2</a>, <a class="ref" href="tarski.html#D1" title="TARSKI:def.1">TARSKI:def 1</a></i>;<br/></div><b>end;</b></div>
<div><i><font color="Green" title="E19">A79</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" title="E20">A80</font></i>: 
<font color="Maroon" title="c14">dj</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c16">t</font>
 ;<br/><a NAME="E2:15_2_3_4"/>
( 2 <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c16">t</font> &amp; 1 <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> 2 )
 <b>by </b><i><a class="ref" href="yellow11.html#T1" target="_self" title="YELLOW11:th.1">Th1</a>, <a class="ref" href="enumset1.html#D1" title="ENUMSET1:def.1">ENUMSET1:def 1</a></i>;<br/><b>hence </b><a NAME="E3:15_2_3_4"/>
contradiction
 <b>by </b><i><a class="txt" href="yellow11.html#E1:15_2_3_4"><i><font color="Green" title="E20">A80</font></i></a>, <a class="ref" href="yellow11.html#T2" target="_self" title="YELLOW11:th.2">Th2</a>, <a class="ref" href="tarski.html#D1" title="TARSKI:def.1">TARSKI:def 1</a></i>;<br/></div><b>end;</b></div>
<div><i><font color="Green" title="E20">A81</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" title="E21">A82</font></i>: 
<font color="Maroon" title="c15">td</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c16">t</font>
 ;<br/><a NAME="E2:15_2_3_5"/>
( 0 <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c16">t</font> &amp; 0 <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> 2 )
 <b>by </b><i><a class="ref" href="yellow11.html#T1" target="_self" title="YELLOW11:th.1">Th1</a>, <a class="ref" href="enumset1.html#D1" title="ENUMSET1:def.1">ENUMSET1:def 1</a></i>;<br/><b>hence </b><a NAME="E3:15_2_3_5"/>
contradiction
 <b>by </b><i><a class="txt" href="yellow11.html#E1:15_2_3_5"><i><font color="Green" title="E21">A82</font></i></a>, <a class="ref" href="yellow11.html#T4" target="_self" title="YELLOW11:th.4">Th4</a>, <a class="ref" href="tarski.html#D1" title="TARSKI:def.1">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" title="HIDDEN:mode.1">set</a> ,   <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a> ] <b>means </b>for <font color="Olive" title="b1">X</font> being  <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <a href="yellow11.html#K2" title="YELLOW11:func.2">M_3</a>   st <font color="Olive" title="b1">X</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> $1 holds <br/>( ( <font color="Olive" title="b1">X</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c12">z</font> implies $2 <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c3">a</font> ) &amp; ( <font color="Olive" title="b1">X</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c13">j</font> implies $2 <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c4">b</font> ) &amp; ( <font color="Olive" title="b1">X</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c14">dj</font> implies $2 <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c5">c</font> ) &amp; ( <font color="Olive" title="b1">X</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c15">td</font> implies $2 <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c6">d</font> ) &amp; ( <font color="Olive" title="b1">X</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c16">t</font> implies $2 <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c7">e</font> ) );<br/>
<a NAME="E11:15_2_3"/><i><font color="Green" title="E21">A83</font></i>: 
for <font color="Olive" title="b1">x</font> being   <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a>   st <font color="Olive" title="b1">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <a href="yellow11.html#K2" title="YELLOW11:func.2">M_3</a>  holds <br/> ex <font color="Olive" title="b2">y</font> being   <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a>  st <br/>( <font color="Olive" title="b2">y</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c9">ck</font> &amp; <font color="Maroon">S<sub>1</sub></font>[<font color="Olive" title="b1">x</font>,<font color="Olive" title="b2">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" title="c17">x</font> be    <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a> ;<br/>

<b>assume </b><a NAME="E1:15_2_3_6"/><i><font color="Green" title="E22">A84</font></i>: 
<font color="Maroon" title="c17">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <a href="yellow11.html#K2" title="YELLOW11:func.2">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" title="c17">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 0 or <font color="Maroon" title="c17">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 1 or <font color="Maroon" title="c17">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 2 <a href="subset_1.html#K6" title="SUBSET_1:func.6">\</a> 1 or <font color="Maroon" title="c17">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 3 <a href="subset_1.html#K6" title="SUBSET_1:func.6">\</a> 2 or <font color="Maroon" title="c17">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 3 )
 </span><b>by </b><i><a class="txt" href="yellow11.html#E1:15"><i><font color="Green" title="E12">A1</font></i></a>, <a class="txt" href="yellow11.html#E1:15_2_3_6"><i><font color="Green" title="E22">A84</font></i></a>, <a class="ref" href="enumset1.html#D3" title="ENUMSET1:def.3">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" title="E23">A85</font></i>: 
<font color="Maroon" title="c17">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 0
 ;<br/><div class="add"><b>take </b><font color="Maroon" title="c18">y</font> = <font color="Maroon" title="c3">a</font>;<br/><b>thus </b><a NAME="E2:15_2_3_6_1_1"/>
<font color="Maroon" title="c18">y</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c9">ck</font>
 <b>by </b><i><a class="ref" href="enumset1.html#D3" title="ENUMSET1:def.3">ENUMSET1:def 3</a></i>;<br/><b>let </b><font color="Maroon" title="c19">X</font> be   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <a href="yellow11.html#K2" title="YELLOW11:func.2">M_3</a> ;<br/><b>thus </b><a NAME="E3:15_2_3_6_1_1"/>
( <font color="Maroon" title="c19">X</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c17">x</font> implies ( ( <font color="Maroon" title="c19">X</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c12">z</font> implies <font color="Maroon" title="c18">y</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c3">a</font> ) &amp; ( <font color="Maroon" title="c19">X</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c13">j</font> implies <font color="Maroon" title="c18">y</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c4">b</font> ) &amp; ( <font color="Maroon" title="c19">X</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c14">dj</font> implies <font color="Maroon" title="c18">y</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c5">c</font> ) &amp; ( <font color="Maroon" title="c19">X</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c15">td</font> implies <font color="Maroon" title="c18">y</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c6">d</font> ) &amp; ( <font color="Maroon" title="c19">X</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c16">t</font> implies <font color="Maroon" title="c18">y</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c7">e</font> ) ) )
 <b>by </b><i><a class="txt" href="yellow11.html#E1:15_2_3_6_1_1"><i><font color="Green" title="E23">A85</font></i></a>, <a class="ref" href="yellow11.html#T2" target="_self" title="YELLOW11:th.2">Th2</a>, <a class="ref" href="yellow11.html#T4" target="_self" title="YELLOW11:th.4">Th4</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" title="E23">A86</font></i>: 
<font color="Maroon" title="c17">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 1
 ;<br/><div class="add"><b>take </b><font color="Maroon" title="c18">y</font> = <font color="Maroon" title="c4">b</font>;<br/><b>thus </b><a NAME="E2:15_2_3_6_1_2"/>
<font color="Maroon" title="c18">y</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c9">ck</font>
 <b>by </b><i><a class="ref" href="enumset1.html#D3" title="ENUMSET1:def.3">ENUMSET1:def 3</a></i>;<br/><b>let </b><font color="Maroon" title="c19">X</font> be   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <a href="yellow11.html#K2" title="YELLOW11:func.2">M_3</a> ;<br/><b>thus </b><a NAME="E3:15_2_3_6_1_2"/>
( <font color="Maroon" title="c19">X</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c17">x</font> implies ( ( <font color="Maroon" title="c19">X</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c12">z</font> implies <font color="Maroon" title="c18">y</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c3">a</font> ) &amp; ( <font color="Maroon" title="c19">X</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c13">j</font> implies <font color="Maroon" title="c18">y</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c4">b</font> ) &amp; ( <font color="Maroon" title="c19">X</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c14">dj</font> implies <font color="Maroon" title="c18">y</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c5">c</font> ) &amp; ( <font color="Maroon" title="c19">X</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c15">td</font> implies <font color="Maroon" title="c18">y</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c6">d</font> ) &amp; ( <font color="Maroon" title="c19">X</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c16">t</font> implies <font color="Maroon" title="c18">y</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c7">e</font> ) ) )
 <b>by </b><i><a class="txt" href="yellow11.html#E6:15_2_3"><i><font color="Green" title="E16">A73</font></i></a>, <a class="txt" href="yellow11.html#E7:15_2_3"><i><font color="Green" title="E17">A75</font></i></a>, <a class="txt" href="yellow11.html#E1:15_2_3_6_1_2"><i><font color="Green" title="E23">A86</font></i></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" title="E23">A87</font></i>: 
<font color="Maroon" title="c17">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 2 <a href="subset_1.html#K6" title="SUBSET_1:func.6">\</a> 1
 ;<br/><div class="add"><b>take </b><font color="Maroon" title="c18">y</font> = <font color="Maroon" title="c5">c</font>;<br/><b>thus </b><a NAME="E2:15_2_3_6_1_3"/>
<font color="Maroon" title="c18">y</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c9">ck</font>
 <b>by </b><i><a class="ref" href="enumset1.html#D3" title="ENUMSET1:def.3">ENUMSET1:def 3</a></i>;<br/><b>let </b><font color="Maroon" title="c19">X</font> be   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <a href="yellow11.html#K2" title="YELLOW11:func.2">M_3</a> ;<br/><b>thus </b><a NAME="E3:15_2_3_6_1_3"/>
( <font color="Maroon" title="c19">X</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c17">x</font> implies ( ( <font color="Maroon" title="c19">X</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c12">z</font> implies <font color="Maroon" title="c18">y</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c3">a</font> ) &amp; ( <font color="Maroon" title="c19">X</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c13">j</font> implies <font color="Maroon" title="c18">y</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c4">b</font> ) &amp; ( <font color="Maroon" title="c19">X</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c14">dj</font> implies <font color="Maroon" title="c18">y</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c5">c</font> ) &amp; ( <font color="Maroon" title="c19">X</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c15">td</font> implies <font color="Maroon" title="c18">y</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c6">d</font> ) &amp; ( <font color="Maroon" title="c19">X</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c16">t</font> implies <font color="Maroon" title="c18">y</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c7">e</font> ) ) )
 <b>by </b><i><a class="txt" href="yellow11.html#E6:15_2_3"><i><font color="Green" title="E16">A73</font></i></a>, <a class="txt" href="yellow11.html#E8:15_2_3"><i><font color="Green" title="E18">A77</font></i></a>, <a class="txt" href="yellow11.html#E9:15_2_3"><i><font color="Green" title="E19">A79</font></i></a>, <a class="txt" href="yellow11.html#E1:15_2_3_6_1_3"><i><font color="Green" title="E23">A87</font></i></a>, <a class="ref" href="yellow11.html#T2" target="_self" title="YELLOW11:th.2">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" title="E23">A88</font></i>: 
<font color="Maroon" title="c17">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 3 <a href="subset_1.html#K6" title="SUBSET_1:func.6">\</a> 2
 ;<br/><div class="add"><b>take </b><font color="Maroon" title="c18">y</font> = <font color="Maroon" title="c6">d</font>;<br/><b>thus </b><a NAME="E2:15_2_3_6_1_4"/>
<font color="Maroon" title="c18">y</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c9">ck</font>
 <b>by </b><i><a class="ref" href="enumset1.html#D3" title="ENUMSET1:def.3">ENUMSET1:def 3</a></i>;<br/><b>let </b><font color="Maroon" title="c19">X</font> be   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <a href="yellow11.html#K2" title="YELLOW11:func.2">M_3</a> ;<br/><b>thus </b><a NAME="E3:15_2_3_6_1_4"/>
( <font color="Maroon" title="c19">X</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c17">x</font> implies ( ( <font color="Maroon" title="c19">X</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c12">z</font> implies <font color="Maroon" title="c18">y</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c3">a</font> ) &amp; ( <font color="Maroon" title="c19">X</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c13">j</font> implies <font color="Maroon" title="c18">y</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c4">b</font> ) &amp; ( <font color="Maroon" title="c19">X</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c14">dj</font> implies <font color="Maroon" title="c18">y</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c5">c</font> ) &amp; ( <font color="Maroon" title="c19">X</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c15">td</font> implies <font color="Maroon" title="c18">y</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c6">d</font> ) &amp; ( <font color="Maroon" title="c19">X</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c16">t</font> implies <font color="Maroon" title="c18">y</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c7">e</font> ) ) )
 <b>by </b><i><a class="txt" href="yellow11.html#E7:15_2_3"><i><font color="Green" title="E17">A75</font></i></a>, <a class="txt" href="yellow11.html#E8:15_2_3"><i><font color="Green" title="E18">A77</font></i></a>, <a class="txt" href="yellow11.html#E10:15_2_3"><i><font color="Green" title="E20">A81</font></i></a>, <a class="txt" href="yellow11.html#E1:15_2_3_6_1_4"><i><font color="Green" title="E23">A88</font></i></a>, <a class="ref" href="yellow11.html#T4" target="_self" title="YELLOW11:th.4">Th4</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" title="E23">A89</font></i>: 
<font color="Maroon" title="c17">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 3
 ;<br/><div class="add"><b>take </b><font color="Maroon" title="c18">y</font> = <font color="Maroon" title="c7">e</font>;<br/><b>thus </b><a NAME="E2:15_2_3_6_1_5"/>
<font color="Maroon" title="c18">y</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c9">ck</font>
 <b>by </b><i><a class="ref" href="enumset1.html#D3" title="ENUMSET1:def.3">ENUMSET1:def 3</a></i>;<br/><b>let </b><font color="Maroon" title="c19">X</font> be   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <a href="yellow11.html#K2" title="YELLOW11:func.2">M_3</a> ;<br/><b>thus </b><a NAME="E3:15_2_3_6_1_5"/>
( <font color="Maroon" title="c19">X</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c17">x</font> implies ( ( <font color="Maroon" title="c19">X</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c12">z</font> implies <font color="Maroon" title="c18">y</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c3">a</font> ) &amp; ( <font color="Maroon" title="c19">X</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c13">j</font> implies <font color="Maroon" title="c18">y</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c4">b</font> ) &amp; ( <font color="Maroon" title="c19">X</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c14">dj</font> implies <font color="Maroon" title="c18">y</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c5">c</font> ) &amp; ( <font color="Maroon" title="c19">X</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c15">td</font> implies <font color="Maroon" title="c18">y</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c6">d</font> ) &amp; ( <font color="Maroon" title="c19">X</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c16">t</font> implies <font color="Maroon" title="c18">y</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c7">e</font> ) ) )
 <b>by </b><i><a class="txt" href="yellow11.html#E9:15_2_3"><i><font color="Green" title="E19">A79</font></i></a>, <a class="txt" href="yellow11.html#E10:15_2_3"><i><font color="Green" title="E20">A81</font></i></a>, <a class="txt" href="yellow11.html#E1:15_2_3_6_1_5"><i><font color="Green" title="E23">A89</font></i></a></i>;<br/></div><b>end;</b></div></div><b>end;</b></div>

</div><b>end;</b></div>
<b>consider </b><font color="Maroon" title="c17">f</font> being   <a href="funct_2.html#NM1" title="FUNCT_2:NM.1">Function</a> of the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <a href="yellow11.html#K2" title="YELLOW11:func.2">M_3</a> ,<font color="Maroon" title="c9">ck</font><b> such that </b><br/><a NAME="E13:15_2_3"/><i><font color="Green" title="E22">A90</font></i>: 
for <font color="Olive" title="b1">x</font> being   <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a>   st <font color="Olive" title="b1">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <a href="yellow11.html#K2" title="YELLOW11:func.2">M_3</a>  holds <br/><font color="Maroon">S<sub>1</sub></font>[<font color="Olive" title="b1">x</font>,<font color="Maroon" title="c17">f</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Olive" title="b1">x</font>]
 <b>from </b><i><a class="ref" href="funct_2.html#S1" title="FUNCT_2:sch.1">FUNCT_2:sch 1</a>(<a class="txt" href="yellow11.html#E11:15_2_3"><i><font color="Green" title="E21">A83</font></i></a>);<br/></i>
<b>reconsider </b><font color="Maroon" title="c18">f</font> = <font color="Maroon" title="c17">f</font> as   <a href="struct_0.html#NM6" title="STRUCT_0:NM.6">Function</a> of <a href="yellow11.html#K2" title="YELLOW11:func.2">M_3</a> ,<font color="Maroon" title="c11">K</font> <b>by </b><i><a class="txt" href="yellow11.html#E4:15_2"><i><font color="Green" title="E14">A57</font></i></a></i>;<br/>
<b>take </b>
<font color="Maroon" title="c18">f</font>
; <i><font color="Red">:: according to </font></i><a class="ref" href="waybel_1.html#D8" title="WAYBEL_1:def.8">WAYBEL_1:def 8</a><br/>

<a NAME="E15:15_2_3"/><i><font color="Green" title="E23">A91</font></i>: 
<font color="Maroon" title="c18">f</font> is <a href="funct_1.html#V2" title="FUNCT_1:attr.2">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" title="c19">x</font>, <font color="Maroon" title="c20">y</font> be   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <a href="yellow11.html#K2" title="YELLOW11:func.2">M_3</a> ;<br/><b>assume </b><a NAME="E1:15_2_3_7_1"/><i><font color="Green" title="E24">A92</font></i>: 
<font color="Maroon" title="c18">f</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c19">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c18">f</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c20">y</font>
 ;<br/><b>thus </b><a NAME="E2:15_2_3_7_1"/>
<font color="Maroon" title="c19">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c20">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" title="c19">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c12">z</font> &amp; <font color="Maroon" title="c20">y</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c12">z</font> ) or ( <font color="Maroon" title="c19">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c13">j</font> &amp; <font color="Maroon" title="c20">y</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c13">j</font> ) or ( <font color="Maroon" title="c19">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c14">dj</font> &amp; <font color="Maroon" title="c20">y</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c14">dj</font> ) or ( <font color="Maroon" title="c19">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c15">td</font> &amp; <font color="Maroon" title="c20">y</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c15">td</font> ) or ( <font color="Maroon" title="c19">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c16">t</font> &amp; <font color="Maroon" title="c20">y</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c16">t</font> ) or ( <font color="Maroon" title="c19">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c12">z</font> &amp; <font color="Maroon" title="c20">y</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c13">j</font> ) or ( <font color="Maroon" title="c19">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c12">z</font> &amp; <font color="Maroon" title="c20">y</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c14">dj</font> ) or ( <font color="Maroon" title="c19">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c12">z</font> &amp; <font color="Maroon" title="c20">y</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c15">td</font> ) or ( <font color="Maroon" title="c19">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c12">z</font> &amp; <font color="Maroon" title="c20">y</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c16">t</font> ) or ( <font color="Maroon" title="c19">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c13">j</font> &amp; <font color="Maroon" title="c20">y</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c12">z</font> ) or ( <font color="Maroon" title="c19">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c13">j</font> &amp; <font color="Maroon" title="c20">y</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c14">dj</font> ) or ( <font color="Maroon" title="c19">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c13">j</font> &amp; <font color="Maroon" title="c20">y</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c15">td</font> ) or ( <font color="Maroon" title="c19">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c13">j</font> &amp; <font color="Maroon" title="c20">y</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c16">t</font> ) or ( <font color="Maroon" title="c19">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c14">dj</font> &amp; <font color="Maroon" title="c20">y</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c12">z</font> ) or ( <font color="Maroon" title="c19">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c14">dj</font> &amp; <font color="Maroon" title="c20">y</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c13">j</font> ) or ( <font color="Maroon" title="c19">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c14">dj</font> &amp; <font color="Maroon" title="c20">y</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c15">td</font> ) or ( <font color="Maroon" title="c19">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c14">dj</font> &amp; <font color="Maroon" title="c20">y</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c16">t</font> ) or ( <font color="Maroon" title="c19">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c15">td</font> &amp; <font color="Maroon" title="c20">y</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c12">z</font> ) or ( <font color="Maroon" title="c19">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c15">td</font> &amp; <font color="Maroon" title="c20">y</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c13">j</font> ) or ( <font color="Maroon" title="c19">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c15">td</font> &amp; <font color="Maroon" title="c20">y</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c14">dj</font> ) or ( <font color="Maroon" title="c19">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c15">td</font> &amp; <font color="Maroon" title="c20">y</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c16">t</font> ) or ( <font color="Maroon" title="c19">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c16">t</font> &amp; <font color="Maroon" title="c20">y</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c12">z</font> ) or ( <font color="Maroon" title="c19">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c16">t</font> &amp; <font color="Maroon" title="c20">y</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c13">j</font> ) or ( <font color="Maroon" title="c19">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c16">t</font> &amp; <font color="Maroon" title="c20">y</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c14">dj</font> ) or ( <font color="Maroon" title="c19">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c16">t</font> &amp; <font color="Maroon" title="c20">y</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c15">td</font> ) )
 </span><b>by </b><i><a class="txt" href="yellow11.html#E1:15"><i><font color="Green" title="E12">A1</font></i></a>, <a class="ref" href="enumset1.html#D3" title="ENUMSET1:def.3">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" title="c19">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c12">z</font> &amp; <font color="Maroon" title="c20">y</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c12">z</font> )
 ;<br/><div class="add"><b>hence </b><a NAME="E2:15_2_3_7_1_1_1_1"/>
<font color="Maroon" title="c19">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c20">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" title="c19">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c13">j</font> &amp; <font color="Maroon" title="c20">y</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c13">j</font> )
 ;<br/><div class="add"><b>hence </b><a NAME="E2:15_2_3_7_1_1_1_2"/>
<font color="Maroon" title="c19">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c20">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" title="c19">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c14">dj</font> &amp; <font color="Maroon" title="c20">y</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c14">dj</font> )
 ;<br/><div class="add"><b>hence </b><a NAME="E2:15_2_3_7_1_1_1_3"/>
<font color="Maroon" title="c19">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c20">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" title="c19">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c15">td</font> &amp; <font color="Maroon" title="c20">y</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c15">td</font> )
 ;<br/><div class="add"><b>hence </b><a NAME="E2:15_2_3_7_1_1_1_4"/>
<font color="Maroon" title="c19">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c20">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" title="c19">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c16">t</font> &amp; <font color="Maroon" title="c20">y</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c16">t</font> )
 ;<br/><div class="add"><b>hence </b><a NAME="E2:15_2_3_7_1_1_1_5"/>
<font color="Maroon" title="c19">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c20">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" title="c19">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c12">z</font> &amp; <font color="Maroon" title="c20">y</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c13">j</font> )
 ;<br/><div class="add"><a NAME="E2:15_2_3_7_1_1_1_6"/><b>then </b>
( <font color="Maroon" title="c18">f</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c19">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c3">a</font> &amp; <font color="Maroon" title="c18">f</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c20">y</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c4">b</font> )
 <b>by </b><i><a class="txt" href="yellow11.html#E13:15_2_3"><i><font color="Green" title="E22">A90</font></i></a></i>;<br/><b>hence </b><a NAME="E3:15_2_3_7_1_1_1_6"/>
<font color="Maroon" title="c19">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c20">y</font>
 <b>by </b><i><a class="txt" href="yellow11.html#E2:15_2"><i><font color="Green" title="E13">A56</font></i></a>, <a class="txt" href="yellow11.html#E1:15_2_3_7_1"><i><font color="Green" title="E24">A92</font></i></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" title="c19">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c12">z</font> &amp; <font color="Maroon" title="c20">y</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c14">dj</font> )
 ;<br/><div class="add"><a NAME="E2:15_2_3_7_1_1_1_7"/><b>then </b>
( <font color="Maroon" title="c18">f</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c19">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c3">a</font> &amp; <font color="Maroon" title="c18">f</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c20">y</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c5">c</font> )
 <b>by </b><i><a class="txt" href="yellow11.html#E13:15_2_3"><i><font color="Green" title="E22">A90</font></i></a></i>;<br/><b>hence </b><a NAME="E3:15_2_3_7_1_1_1_7"/>
<font color="Maroon" title="c19">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c20">y</font>
 <b>by </b><i><a class="txt" href="yellow11.html#E2:15_2"><i><font color="Green" title="E13">A56</font></i></a>, <a class="txt" href="yellow11.html#E1:15_2_3_7_1"><i><font color="Green" title="E24">A92</font></i></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" title="c19">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c12">z</font> &amp; <font color="Maroon" title="c20">y</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c15">td</font> )
 ;<br/><div class="add"><a NAME="E2:15_2_3_7_1_1_1_8"/><b>then </b>
( <font color="Maroon" title="c18">f</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c19">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c3">a</font> &amp; <font color="Maroon" title="c18">f</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c20">y</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c6">d</font> )
 <b>by </b><i><a class="txt" href="yellow11.html#E13:15_2_3"><i><font color="Green" title="E22">A90</font></i></a></i>;<br/><b>hence </b><a NAME="E3:15_2_3_7_1_1_1_8"/>
<font color="Maroon" title="c19">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c20">y</font>
 <b>by </b><i><a class="txt" href="yellow11.html#E2:15_2"><i><font color="Green" title="E13">A56</font></i></a>, <a class="txt" href="yellow11.html#E1:15_2_3_7_1"><i><font color="Green" title="E24">A92</font></i></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" title="c19">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c12">z</font> &amp; <font color="Maroon" title="c20">y</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c16">t</font> )
 ;<br/><div class="add"><a NAME="E2:15_2_3_7_1_1_1_9"/><b>then </b>
( <font color="Maroon" title="c18">f</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c19">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c3">a</font> &amp; <font color="Maroon" title="c18">f</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c20">y</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c7">e</font> )
 <b>by </b><i><a class="txt" href="yellow11.html#E13:15_2_3"><i><font color="Green" title="E22">A90</font></i></a></i>;<br/><b>hence </b><a NAME="E3:15_2_3_7_1_1_1_9"/>
<font color="Maroon" title="c19">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c20">y</font>
 <b>by </b><i><a class="txt" href="yellow11.html#E2:15_2"><i><font color="Green" title="E13">A56</font></i></a>, <a class="txt" href="yellow11.html#E1:15_2_3_7_1"><i><font color="Green" title="E24">A92</font></i></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" title="c19">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c13">j</font> &amp; <font color="Maroon" title="c20">y</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c12">z</font> )
 ;<br/><div class="add"><a NAME="E2:15_2_3_7_1_1_1_10"/><b>then </b>
( <font color="Maroon" title="c18">f</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c19">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c4">b</font> &amp; <font color="Maroon" title="c18">f</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c20">y</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c3">a</font> )
 <b>by </b><i><a class="txt" href="yellow11.html#E13:15_2_3"><i><font color="Green" title="E22">A90</font></i></a></i>;<br/><b>hence </b><a NAME="E3:15_2_3_7_1_1_1_10"/>
<font color="Maroon" title="c19">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c20">y</font>
 <b>by </b><i><a class="txt" href="yellow11.html#E2:15_2"><i><font color="Green" title="E13">A56</font></i></a>, <a class="txt" href="yellow11.html#E1:15_2_3_7_1"><i><font color="Green" title="E24">A92</font></i></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" title="c19">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c13">j</font> &amp; <font color="Maroon" title="c20">y</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c14">dj</font> )
 ;<br/><div class="add"><a NAME="E2:15_2_3_7_1_1_1_11"/><b>then </b>
( <font color="Maroon" title="c18">f</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c19">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c4">b</font> &amp; <font color="Maroon" title="c18">f</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c20">y</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c5">c</font> )
 <b>by </b><i><a class="txt" href="yellow11.html#E13:15_2_3"><i><font color="Green" title="E22">A90</font></i></a></i>;<br/><b>hence </b><a NAME="E3:15_2_3_7_1_1_1_11"/>
<font color="Maroon" title="c19">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c20">y</font>
 <b>by </b><i><a class="txt" href="yellow11.html#E2:15_2"><i><font color="Green" title="E13">A56</font></i></a>, <a class="txt" href="yellow11.html#E1:15_2_3_7_1"><i><font color="Green" title="E24">A92</font></i></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" title="c19">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c13">j</font> &amp; <font color="Maroon" title="c20">y</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c15">td</font> )
 ;<br/><div class="add"><a NAME="E2:15_2_3_7_1_1_1_12"/><b>then </b>
( <font color="Maroon" title="c18">f</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c19">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c4">b</font> &amp; <font color="Maroon" title="c18">f</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c20">y</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c6">d</font> )
 <b>by </b><i><a class="txt" href="yellow11.html#E13:15_2_3"><i><font color="Green" title="E22">A90</font></i></a></i>;<br/><b>hence </b><a NAME="E3:15_2_3_7_1_1_1_12"/>
<font color="Maroon" title="c19">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c20">y</font>
 <b>by </b><i><a class="txt" href="yellow11.html#E2:15_2"><i><font color="Green" title="E13">A56</font></i></a>, <a class="txt" href="yellow11.html#E1:15_2_3_7_1"><i><font color="Green" title="E24">A92</font></i></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" title="c19">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c13">j</font> &amp; <font color="Maroon" title="c20">y</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c16">t</font> )
 ;<br/><div class="add"><a NAME="E2:15_2_3_7_1_1_1_13"/><b>then </b>
( <font color="Maroon" title="c18">f</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c19">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c4">b</font> &amp; <font color="Maroon" title="c18">f</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c20">y</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c7">e</font> )
 <b>by </b><i><a class="txt" href="yellow11.html#E13:15_2_3"><i><font color="Green" title="E22">A90</font></i></a></i>;<br/><b>hence </b><a NAME="E3:15_2_3_7_1_1_1_13"/>
<font color="Maroon" title="c19">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c20">y</font>
 <b>by </b><i><a class="txt" href="yellow11.html#E2:15_2"><i><font color="Green" title="E13">A56</font></i></a>, <a class="txt" href="yellow11.html#E1:15_2_3_7_1"><i><font color="Green" title="E24">A92</font></i></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" title="c19">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c14">dj</font> &amp; <font color="Maroon" title="c20">y</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c12">z</font> )
 ;<br/><div class="add"><a NAME="E2:15_2_3_7_1_1_1_14"/><b>then </b>
( <font color="Maroon" title="c18">f</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c19">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c5">c</font> &amp; <font color="Maroon" title="c18">f</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c20">y</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c3">a</font> )
 <b>by </b><i><a class="txt" href="yellow11.html#E13:15_2_3"><i><font color="Green" title="E22">A90</font></i></a></i>;<br/><b>hence </b><a NAME="E3:15_2_3_7_1_1_1_14"/>
<font color="Maroon" title="c19">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c20">y</font>
 <b>by </b><i><a class="txt" href="yellow11.html#E2:15_2"><i><font color="Green" title="E13">A56</font></i></a>, <a class="txt" href="yellow11.html#E1:15_2_3_7_1"><i><font color="Green" title="E24">A92</font></i></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" title="c19">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c14">dj</font> &amp; <font color="Maroon" title="c20">y</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c13">j</font> )
 ;<br/><div class="add"><a NAME="E2:15_2_3_7_1_1_1_15"/><b>then </b>
( <font color="Maroon" title="c18">f</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c19">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c5">c</font> &amp; <font color="Maroon" title="c18">f</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c20">y</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c4">b</font> )
 <b>by </b><i><a class="txt" href="yellow11.html#E13:15_2_3"><i><font color="Green" title="E22">A90</font></i></a></i>;<br/><b>hence </b><a NAME="E3:15_2_3_7_1_1_1_15"/>
<font color="Maroon" title="c19">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c20">y</font>
 <b>by </b><i><a class="txt" href="yellow11.html#E2:15_2"><i><font color="Green" title="E13">A56</font></i></a>, <a class="txt" href="yellow11.html#E1:15_2_3_7_1"><i><font color="Green" title="E24">A92</font></i></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" title="c19">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c14">dj</font> &amp; <font color="Maroon" title="c20">y</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c15">td</font> )
 ;<br/><div class="add"><a NAME="E2:15_2_3_7_1_1_1_16"/><b>then </b>
( <font color="Maroon" title="c18">f</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c19">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c5">c</font> &amp; <font color="Maroon" title="c18">f</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c20">y</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c6">d</font> )
 <b>by </b><i><a class="txt" href="yellow11.html#E13:15_2_3"><i><font color="Green" title="E22">A90</font></i></a></i>;<br/><b>hence </b><a NAME="E3:15_2_3_7_1_1_1_16"/>
<font color="Maroon" title="c19">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c20">y</font>
 <b>by </b><i><a class="txt" href="yellow11.html#E2:15_2"><i><font color="Green" title="E13">A56</font></i></a>, <a class="txt" href="yellow11.html#E1:15_2_3_7_1"><i><font color="Green" title="E24">A92</font></i></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" title="c19">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c14">dj</font> &amp; <font color="Maroon" title="c20">y</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c16">t</font> )
 ;<br/><div class="add"><a NAME="E2:15_2_3_7_1_1_1_17"/><b>then </b>
( <font color="Maroon" title="c18">f</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c19">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c5">c</font> &amp; <font color="Maroon" title="c18">f</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c20">y</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c7">e</font> )
 <b>by </b><i><a class="txt" href="yellow11.html#E13:15_2_3"><i><font color="Green" title="E22">A90</font></i></a></i>;<br/><b>hence </b><a NAME="E3:15_2_3_7_1_1_1_17"/>
<font color="Maroon" title="c19">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c20">y</font>
 <b>by </b><i><a class="txt" href="yellow11.html#E2:15_2"><i><font color="Green" title="E13">A56</font></i></a>, <a class="txt" href="yellow11.html#E1:15_2_3_7_1"><i><font color="Green" title="E24">A92</font></i></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" title="c19">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c15">td</font> &amp; <font color="Maroon" title="c20">y</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c12">z</font> )
 ;<br/><div class="add"><a NAME="E2:15_2_3_7_1_1_1_18"/><b>then </b>
( <font color="Maroon" title="c18">f</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c19">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c6">d</font> &amp; <font color="Maroon" title="c18">f</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c20">y</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c3">a</font> )
 <b>by </b><i><a class="txt" href="yellow11.html#E13:15_2_3"><i><font color="Green" title="E22">A90</font></i></a></i>;<br/><b>hence </b><a NAME="E3:15_2_3_7_1_1_1_18"/>
<font color="Maroon" title="c19">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c20">y</font>
 <b>by </b><i><a class="txt" href="yellow11.html#E2:15_2"><i><font color="Green" title="E13">A56</font></i></a>, <a class="txt" href="yellow11.html#E1:15_2_3_7_1"><i><font color="Green" title="E24">A92</font></i></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" title="c19">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c15">td</font> &amp; <font color="Maroon" title="c20">y</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c13">j</font> )
 ;<br/><div class="add"><a NAME="E2:15_2_3_7_1_1_1_19"/><b>then </b>
( <font color="Maroon" title="c18">f</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c19">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c6">d</font> &amp; <font color="Maroon" title="c18">f</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c20">y</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c4">b</font> )
 <b>by </b><i><a class="txt" href="yellow11.html#E13:15_2_3"><i><font color="Green" title="E22">A90</font></i></a></i>;<br/><b>hence </b><a NAME="E3:15_2_3_7_1_1_1_19"/>
<font color="Maroon" title="c19">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c20">y</font>
 <b>by </b><i><a class="txt" href="yellow11.html#E2:15_2"><i><font color="Green" title="E13">A56</font></i></a>, <a class="txt" href="yellow11.html#E1:15_2_3_7_1"><i><font color="Green" title="E24">A92</font></i></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" title="c19">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c15">td</font> &amp; <font color="Maroon" title="c20">y</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c14">dj</font> )
 ;<br/><div class="add"><a NAME="E2:15_2_3_7_1_1_1_20"/><b>then </b>
( <font color="Maroon" title="c18">f</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c19">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c6">d</font> &amp; <font color="Maroon" title="c18">f</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c20">y</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c5">c</font> )
 <b>by </b><i><a class="txt" href="yellow11.html#E13:15_2_3"><i><font color="Green" title="E22">A90</font></i></a></i>;<br/><b>hence </b><a NAME="E3:15_2_3_7_1_1_1_20"/>
<font color="Maroon" title="c19">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c20">y</font>
 <b>by </b><i><a class="txt" href="yellow11.html#E2:15_2"><i><font color="Green" title="E13">A56</font></i></a>, <a class="txt" href="yellow11.html#E1:15_2_3_7_1"><i><font color="Green" title="E24">A92</font></i></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" title="c19">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c15">td</font> &amp; <font color="Maroon" title="c20">y</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c16">t</font> )
 ;<br/><div class="add"><a NAME="E2:15_2_3_7_1_1_1_21"/><b>then </b>
( <font color="Maroon" title="c18">f</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c19">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c6">d</font> &amp; <font color="Maroon" title="c18">f</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c20">y</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c7">e</font> )
 <b>by </b><i><a class="txt" href="yellow11.html#E13:15_2_3"><i><font color="Green" title="E22">A90</font></i></a></i>;<br/><b>hence </b><a NAME="E3:15_2_3_7_1_1_1_21"/>
<font color="Maroon" title="c19">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c20">y</font>
 <b>by </b><i><a class="txt" href="yellow11.html#E2:15_2"><i><font color="Green" title="E13">A56</font></i></a>, <a class="txt" href="yellow11.html#E1:15_2_3_7_1"><i><font color="Green" title="E24">A92</font></i></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" title="c19">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c16">t</font> &amp; <font color="Maroon" title="c20">y</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c12">z</font> )
 ;<br/><div class="add"><a NAME="E2:15_2_3_7_1_1_1_22"/><b>then </b>
( <font color="Maroon" title="c18">f</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c19">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c7">e</font> &amp; <font color="Maroon" title="c18">f</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c20">y</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c3">a</font> )
 <b>by </b><i><a class="txt" href="yellow11.html#E13:15_2_3"><i><font color="Green" title="E22">A90</font></i></a></i>;<br/><b>hence </b><a NAME="E3:15_2_3_7_1_1_1_22"/>
<font color="Maroon" title="c19">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c20">y</font>
 <b>by </b><i><a class="txt" href="yellow11.html#E2:15_2"><i><font color="Green" title="E13">A56</font></i></a>, <a class="txt" href="yellow11.html#E1:15_2_3_7_1"><i><font color="Green" title="E24">A92</font></i></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" title="c19">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c16">t</font> &amp; <font color="Maroon" title="c20">y</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c13">j</font> )
 ;<br/><div class="add"><a NAME="E2:15_2_3_7_1_1_1_23"/><b>then </b>
( <font color="Maroon" title="c18">f</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c19">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c7">e</font> &amp; <font color="Maroon" title="c18">f</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c20">y</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c4">b</font> )
 <b>by </b><i><a class="txt" href="yellow11.html#E13:15_2_3"><i><font color="Green" title="E22">A90</font></i></a></i>;<br/><b>hence </b><a NAME="E3:15_2_3_7_1_1_1_23"/>
<font color="Maroon" title="c19">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c20">y</font>
 <b>by </b><i><a class="txt" href="yellow11.html#E2:15_2"><i><font color="Green" title="E13">A56</font></i></a>, <a class="txt" href="yellow11.html#E1:15_2_3_7_1"><i><font color="Green" title="E24">A92</font></i></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" title="c19">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c16">t</font> &amp; <font color="Maroon" title="c20">y</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c14">dj</font> )
 ;<br/><div class="add"><a NAME="E2:15_2_3_7_1_1_1_24"/><b>then </b>
( <font color="Maroon" title="c18">f</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c19">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c7">e</font> &amp; <font color="Maroon" title="c18">f</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c20">y</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c5">c</font> )
 <b>by </b><i><a class="txt" href="yellow11.html#E13:15_2_3"><i><font color="Green" title="E22">A90</font></i></a></i>;<br/><b>hence </b><a NAME="E3:15_2_3_7_1_1_1_24"/>
<font color="Maroon" title="c19">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c20">y</font>
 <b>by </b><i><a class="txt" href="yellow11.html#E2:15_2"><i><font color="Green" title="E13">A56</font></i></a>, <a class="txt" href="yellow11.html#E1:15_2_3_7_1"><i><font color="Green" title="E24">A92</font></i></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" title="c19">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c16">t</font> &amp; <font color="Maroon" title="c20">y</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c15">td</font> )
 ;<br/><div class="add"><a NAME="E2:15_2_3_7_1_1_1_25"/><b>then </b>
( <font color="Maroon" title="c18">f</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c19">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c7">e</font> &amp; <font color="Maroon" title="c18">f</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c20">y</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c6">d</font> )
 <b>by </b><i><a class="txt" href="yellow11.html#E13:15_2_3"><i><font color="Green" title="E22">A90</font></i></a></i>;<br/><b>hence </b><a NAME="E3:15_2_3_7_1_1_1_25"/>
<font color="Maroon" title="c19">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c20">y</font>
 <b>by </b><i><a class="txt" href="yellow11.html#E2:15_2"><i><font color="Green" title="E13">A56</font></i></a>, <a class="txt" href="yellow11.html#E1:15_2_3_7_1"><i><font color="Green" title="E24">A92</font></i></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" title="c18">f</font> is <a href="funct_1.html#V2" title="FUNCT_1:attr.2">one-to-one</a>
 <b>by </b><i><a class="ref" href="waybel_1.html#D1" title="WAYBEL_1:def.1">WAYBEL_1:def 1</a></i>;<br/>


</div><b>end;</b></div>
<a NAME="E16:15_2_3"/><i><font color="Green" title="E24">A93</font></i>: 
 <a href="relset_1.html#K4" title="RELSET_1:func.4">dom</a> <font color="Maroon" title="c18">f</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <a href="yellow11.html#K2" title="YELLOW11:func.2">M_3</a> 
 
<b>by </b><i><a class="ref" href="funct_2.html#D1" title="FUNCT_2:def.1">FUNCT_2:def 1</a></i>;<br/>
<a NAME="E17:15_2_3"/><i><font color="Green" title="E25">A94</font></i>: 
 <a href="relset_1.html#K5" title="RELSET_1:func.5">rng</a> <font color="Maroon" title="c18">f</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c9">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" title="RELSET_1:func.5">rng</a> <font color="Maroon" title="c18">f</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <font color="Maroon" title="c9">ck</font>
  <i><font color="Red">:: according to </font></i><a class="ref" href="xboole_0.html#D10" title="XBOOLE_0:def.10">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" title="c19">y</font> be    <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a> ; <i><font color="Red">:: according to </font></i><a class="ref" href="tarski.html#D3" title="TARSKI:def.3">TARSKI:def 3</a><br/>

<b>assume </b><a NAME="E1:15_2_3_8_1"/>
<font color="Maroon" title="c19">y</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="relset_1.html#K5" title="RELSET_1:func.5">rng</a> <font color="Maroon" title="c18">f</font>
 ;<br/>

<b>then consider </b><font color="Maroon" title="c20">x</font> being    <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a> <b> such that </b><br/><a NAME="E3:15_2_3_8_1"/><i><font color="Green" title="E26">A95</font></i>: 
( <font color="Maroon" title="c20">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="relset_1.html#K4" title="RELSET_1:func.4">dom</a> <font color="Maroon" title="c18">f</font> &amp; <font color="Maroon" title="c19">y</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c18">f</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c20">x</font> )
 <b>by </b><i><a class="ref" href="funct_1.html#D5" title="FUNCT_1:def.5">FUNCT_1:def 5</a></i>;<br/>
<b>reconsider </b><font color="Maroon" title="c21">x</font> = <font color="Maroon" title="c20">x</font> as   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <a href="yellow11.html#K2" title="YELLOW11:func.2">M_3</a>  <b>by </b><i><a class="txt" href="yellow11.html#E3:15_2_3_8_1"><i><font color="Green" title="E26">A95</font></i></a></i>;<br/>
<a NAME="E5:15_2_3_8_1"/>
( <font color="Maroon" title="c21">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c12">z</font> or <font color="Maroon" title="c21">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c13">j</font> or <font color="Maroon" title="c21">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c14">dj</font> or <font color="Maroon" title="c21">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c15">td</font> or <font color="Maroon" title="c21">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c16">t</font> )
 
<b>by </b><i><a class="txt" href="yellow11.html#E1:15"><i><font color="Green" title="E12">A1</font></i></a>, <a class="ref" href="enumset1.html#D3" title="ENUMSET1:def.3">ENUMSET1:def 3</a></i>;<br/>
<a NAME="E6:15_2_3_8_1"/><b>then </b>
( <font color="Maroon" title="c19">y</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c3">a</font> or <font color="Maroon" title="c19">y</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c6">d</font> or <font color="Maroon" title="c19">y</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c5">c</font> or <font color="Maroon" title="c19">y</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c4">b</font> or <font color="Maroon" title="c19">y</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c7">e</font> )
 
<b>by </b><i><a class="txt" href="yellow11.html#E13:15_2_3"><i><font color="Green" title="E22">A90</font></i></a>, <a class="txt" href="yellow11.html#E3:15_2_3_8_1"><i><font color="Green" title="E26">A95</font></i></a></i>;<br/>
<b>hence </b><a NAME="E7:15_2_3_8_1"/>
<font color="Maroon" title="c19">y</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c9">ck</font>
 <b>by </b><i><a class="ref" href="enumset1.html#D3" title="ENUMSET1:def.3">ENUMSET1:def 3</a></i>;<br/>


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

<b>thus </b><a NAME="E2:15_2_3_8"/>
<font color="Maroon" title="c9">ck</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a>  <a href="relset_1.html#K5" title="RELSET_1:func.5">rng</a> <font color="Maroon" title="c18">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" title="c19">y</font> be    <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a> ; <i><font color="Red">:: according to </font></i><a class="ref" href="tarski.html#D3" title="TARSKI:def.3">TARSKI:def 3</a><br/>

<b>assume </b><a NAME="E1:15_2_3_8_2"/><i><font color="Green" title="E26">A96</font></i>: 
<font color="Maroon" title="c19">y</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c9">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" title="c19">y</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c3">a</font> or <font color="Maroon" title="c19">y</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c4">b</font> or <font color="Maroon" title="c19">y</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c5">c</font> or <font color="Maroon" title="c19">y</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c6">d</font> or <font color="Maroon" title="c19">y</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c7">e</font> )
 </span><b>by </b><i><a class="txt" href="yellow11.html#E1:15_2_3_8_2"><i><font color="Green" title="E26">A96</font></i></a>, <a class="ref" href="enumset1.html#D3" title="ENUMSET1:def.3">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" title="E27">A97</font></i>: 
<font color="Maroon" title="c19">y</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c3">a</font>
 ;<br/><div class="add"><a NAME="E2:15_2_3_8_2_1_1"/>
( <font color="Maroon" title="c12">z</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="relset_1.html#K4" title="RELSET_1:func.4">dom</a> <font color="Maroon" title="c18">f</font> &amp; <font color="Maroon" title="c3">a</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c18">f</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c12">z</font> )
 <b>by </b><i><a class="txt" href="yellow11.html#E13:15_2_3"><i><font color="Green" title="E22">A90</font></i></a>, <a class="txt" href="yellow11.html#E16:15_2_3"><i><font color="Green" title="E24">A93</font></i></a></i>;<br/><b>hence </b><a NAME="E3:15_2_3_8_2_1_1"/>
<font color="Maroon" title="c19">y</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="relset_1.html#K5" title="RELSET_1:func.5">rng</a> <font color="Maroon" title="c18">f</font>
 <b>by </b><i><a class="txt" href="yellow11.html#E1:15_2_3_8_2_1_1"><i><font color="Green" title="E27">A97</font></i></a>, <a class="ref" href="funct_1.html#D5" title="FUNCT_1:def.5">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" title="E27">A98</font></i>: 
<font color="Maroon" title="c19">y</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c4">b</font>
 ;<br/><div class="add"><a NAME="E2:15_2_3_8_2_1_2"/>
( <font color="Maroon" title="c13">j</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="relset_1.html#K4" title="RELSET_1:func.4">dom</a> <font color="Maroon" title="c18">f</font> &amp; <font color="Maroon" title="c4">b</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c18">f</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c13">j</font> )
 <b>by </b><i><a class="txt" href="yellow11.html#E13:15_2_3"><i><font color="Green" title="E22">A90</font></i></a>, <a class="txt" href="yellow11.html#E16:15_2_3"><i><font color="Green" title="E24">A93</font></i></a></i>;<br/><b>hence </b><a NAME="E3:15_2_3_8_2_1_2"/>
<font color="Maroon" title="c19">y</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="relset_1.html#K5" title="RELSET_1:func.5">rng</a> <font color="Maroon" title="c18">f</font>
 <b>by </b><i><a class="txt" href="yellow11.html#E1:15_2_3_8_2_1_2"><i><font color="Green" title="E27">A98</font></i></a>, <a class="ref" href="funct_1.html#D5" title="FUNCT_1:def.5">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" title="E27">A99</font></i>: 
<font color="Maroon" title="c19">y</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c5">c</font>
 ;<br/><div class="add"><a NAME="E2:15_2_3_8_2_1_3"/>
( <font color="Maroon" title="c14">dj</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="relset_1.html#K4" title="RELSET_1:func.4">dom</a> <font color="Maroon" title="c18">f</font> &amp; <font color="Maroon" title="c5">c</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c18">f</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c14">dj</font> )
 <b>by </b><i><a class="txt" href="yellow11.html#E13:15_2_3"><i><font color="Green" title="E22">A90</font></i></a>, <a class="txt" href="yellow11.html#E16:15_2_3"><i><font color="Green" title="E24">A93</font></i></a></i>;<br/><b>hence </b><a NAME="E3:15_2_3_8_2_1_3"/>
<font color="Maroon" title="c19">y</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="relset_1.html#K5" title="RELSET_1:func.5">rng</a> <font color="Maroon" title="c18">f</font>
 <b>by </b><i><a class="txt" href="yellow11.html#E1:15_2_3_8_2_1_3"><i><font color="Green" title="E27">A99</font></i></a>, <a class="ref" href="funct_1.html#D5" title="FUNCT_1:def.5">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" title="E27">A100</font></i>: 
<font color="Maroon" title="c19">y</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c6">d</font>
 ;<br/><div class="add"><a NAME="E2:15_2_3_8_2_1_4"/>
( <font color="Maroon" title="c15">td</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="relset_1.html#K4" title="RELSET_1:func.4">dom</a> <font color="Maroon" title="c18">f</font> &amp; <font color="Maroon" title="c6">d</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c18">f</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c15">td</font> )
 <b>by </b><i><a class="txt" href="yellow11.html#E13:15_2_3"><i><font color="Green" title="E22">A90</font></i></a>, <a class="txt" href="yellow11.html#E16:15_2_3"><i><font color="Green" title="E24">A93</font></i></a></i>;<br/><b>hence </b><a NAME="E3:15_2_3_8_2_1_4"/>
<font color="Maroon" title="c19">y</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="relset_1.html#K5" title="RELSET_1:func.5">rng</a> <font color="Maroon" title="c18">f</font>
 <b>by </b><i><a class="txt" href="yellow11.html#E1:15_2_3_8_2_1_4"><i><font color="Green" title="E27">A100</font></i></a>, <a class="ref" href="funct_1.html#D5" title="FUNCT_1:def.5">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" title="E27">A101</font></i>: 
<font color="Maroon" title="c19">y</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c7">e</font>
 ;<br/><div class="add"><a NAME="E2:15_2_3_8_2_1_5"/>
( <font color="Maroon" title="c16">t</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="relset_1.html#K4" title="RELSET_1:func.4">dom</a> <font color="Maroon" title="c18">f</font> &amp; <font color="Maroon" title="c7">e</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c18">f</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c16">t</font> )
 <b>by </b><i><a class="txt" href="yellow11.html#E13:15_2_3"><i><font color="Green" title="E22">A90</font></i></a>, <a class="txt" href="yellow11.html#E16:15_2_3"><i><font color="Green" title="E24">A93</font></i></a></i>;<br/><b>hence </b><a NAME="E3:15_2_3_8_2_1_5"/>
<font color="Maroon" title="c19">y</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="relset_1.html#K5" title="RELSET_1:func.5">rng</a> <font color="Maroon" title="c18">f</font>
 <b>by </b><i><a class="txt" href="yellow11.html#E1:15_2_3_8_2_1_5"><i><font color="Green" title="E27">A101</font></i></a>, <a class="ref" href="funct_1.html#D5" title="FUNCT_1:def.5">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" title="b1">x</font>, <font color="Olive" title="b2">y</font> being  <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <a href="yellow11.html#K2" title="YELLOW11:func.2">M_3</a>  holds <br/> ( <font color="Olive" title="b1">x</font> <a href="orders_2.html#R3" title="ORDERS_2:pred.3">&lt;=</a> <font color="Olive" title="b2">y</font> iff <font color="Maroon" title="c18">f</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Olive" title="b1">x</font> <a href="orders_2.html#R3" title="ORDERS_2:pred.3">&lt;=</a> <font color="Maroon" title="c18">f</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Olive" title="b2">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" title="c19">x</font>, <font color="Maroon" title="c20">y</font> be   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <a href="yellow11.html#K2" title="YELLOW11:func.2">M_3</a> ;<br/>

<b>thus </b><a NAME="E1:15_2_3_9"/>
( <font color="Maroon" title="c19">x</font> <a href="orders_2.html#R3" title="ORDERS_2:pred.3">&lt;=</a> <font color="Maroon" title="c20">y</font> implies <font color="Maroon" title="c18">f</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c19">x</font> <a href="orders_2.html#R3" title="ORDERS_2:pred.3">&lt;=</a> <font color="Maroon" title="c18">f</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c20">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" title="E26">A102</font></i>: 
<font color="Maroon" title="c19">x</font> <a href="orders_2.html#R3" title="ORDERS_2:pred.3">&lt;=</a> <font color="Maroon" title="c20">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" title="c19">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c12">z</font> &amp; <font color="Maroon" title="c20">y</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c12">z</font> ) or ( <font color="Maroon" title="c19">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c12">z</font> &amp; <font color="Maroon" title="c20">y</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c13">j</font> ) or ( <font color="Maroon" title="c19">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c12">z</font> &amp; <font color="Maroon" title="c20">y</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c14">dj</font> ) or ( <font color="Maroon" title="c19">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c12">z</font> &amp; <font color="Maroon" title="c20">y</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c15">td</font> ) or ( <font color="Maroon" title="c19">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c12">z</font> &amp; <font color="Maroon" title="c20">y</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c16">t</font> ) or ( <font color="Maroon" title="c19">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c13">j</font> &amp; <font color="Maroon" title="c20">y</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c12">z</font> ) or ( <font color="Maroon" title="c19">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c13">j</font> &amp; <font color="Maroon" title="c20">y</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c13">j</font> ) or ( <font color="Maroon" title="c19">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c13">j</font> &amp; <font color="Maroon" title="c20">y</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c14">dj</font> ) or ( <font color="Maroon" title="c19">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c13">j</font> &amp; <font color="Maroon" title="c20">y</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c15">td</font> ) or ( <font color="Maroon" title="c19">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c13">j</font> &amp; <font color="Maroon" title="c20">y</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c16">t</font> ) or ( <font color="Maroon" title="c19">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c14">dj</font> &amp; <font color="Maroon" title="c20">y</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c12">z</font> ) or ( <font color="Maroon" title="c19">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c14">dj</font> &amp; <font color="Maroon" title="c20">y</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c13">j</font> ) or ( <font color="Maroon" title="c19">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c14">dj</font> &amp; <font color="Maroon" title="c20">y</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c14">dj</font> ) or ( <font color="Maroon" title="c19">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c14">dj</font> &amp; <font color="Maroon" title="c20">y</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c15">td</font> ) or ( <font color="Maroon" title="c19">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c14">dj</font> &amp; <font color="Maroon" title="c20">y</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c16">t</font> ) or ( <font color="Maroon" title="c19">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c15">td</font> &amp; <font color="Maroon" title="c20">y</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c12">z</font> ) or ( <font color="Maroon" title="c19">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c15">td</font> &amp; <font color="Maroon" title="c20">y</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c13">j</font> ) or ( <font color="Maroon" title="c19">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c15">td</font> &amp; <font color="Maroon" title="c20">y</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c14">dj</font> ) or ( <font color="Maroon" title="c19">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c15">td</font> &amp; <font color="Maroon" title="c20">y</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c15">td</font> ) or ( <font color="Maroon" title="c19">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c15">td</font> &amp; <font color="Maroon" title="c20">y</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c16">t</font> ) or ( <font color="Maroon" title="c19">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c16">t</font> &amp; <font color="Maroon" title="c20">y</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c12">z</font> ) or ( <font color="Maroon" title="c19">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c16">t</font> &amp; <font color="Maroon" title="c20">y</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c13">j</font> ) or ( <font color="Maroon" title="c19">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c16">t</font> &amp; <font color="Maroon" title="c20">y</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c14">dj</font> ) or ( <font color="Maroon" title="c19">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c16">t</font> &amp; <font color="Maroon" title="c20">y</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c15">td</font> ) or ( <font color="Maroon" title="c19">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c16">t</font> &amp; <font color="Maroon" title="c20">y</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c16">t</font> ) )
 </span><b>by </b><i><a class="txt" href="yellow11.html#E1:15"><i><font color="Green" title="E12">A1</font></i></a>, <a class="ref" href="enumset1.html#D3" title="ENUMSET1:def.3">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" title="c19">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c12">z</font> &amp; <font color="Maroon" title="c20">y</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c12">z</font> )
 ;<br/><div class="add"><b>hence </b><a NAME="E2:15_2_3_9_1_1_1"/>
<font color="Maroon" title="c18">f</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c19">x</font> <a href="orders_2.html#R3" title="ORDERS_2:pred.3">&lt;=</a> <font color="Maroon" title="c18">f</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c20">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" title="c19">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c12">z</font> &amp; <font color="Maroon" title="c20">y</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c13">j</font> )
 ;<br/><div class="add"><a NAME="E2:15_2_3_9_1_1_2"/><b>then </b><i><font color="Green" title="E27">A103</font></i>: 
( <font color="Maroon" title="c18">f</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c19">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c3">a</font> &amp; <font color="Maroon" title="c18">f</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c20">y</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c4">b</font> )
 <b>by </b><i><a class="txt" href="yellow11.html#E13:15_2_3"><i><font color="Green" title="E22">A90</font></i></a></i>;<br/><b>reconsider </b><font color="Maroon" title="c21">A</font> = <font color="Maroon" title="c3">a</font>, <font color="Maroon" title="c22">B</font> = <font color="Maroon" title="c4">b</font> as   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Maroon" title="c11">K</font> <b>by </b><i><a class="txt" href="yellow11.html#E4:15_2"><i><font color="Green" title="E14">A57</font></i></a>, <a class="ref" href="enumset1.html#D3" title="ENUMSET1:def.3">ENUMSET1:def 3</a></i>;<br/><a NAME="E4:15_2_3_9_1_1_2"/>
( <font color="Maroon" title="c3">a</font> <a href="orders_2.html#R3" title="ORDERS_2:pred.3">&lt;=</a> <font color="Maroon" title="c4">b</font> &amp; <font color="Maroon" title="c21">A</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c11">K</font> &amp; <font color="Maroon" title="c22">B</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c11">K</font> )
 <b>by </b><i><a class="txt" href="yellow11.html#E2:15_2"><i><font color="Green" title="E13">A56</font></i></a>, <a class="ref" href="yellow_0.html#T25" title="YELLOW_0:th.25">YELLOW_0:25</a></i>;<br/><b>hence </b><a NAME="E5:15_2_3_9_1_1_2"/>
<font color="Maroon" title="c18">f</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c19">x</font> <a href="orders_2.html#R3" title="ORDERS_2:pred.3">&lt;=</a> <font color="Maroon" title="c18">f</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c20">y</font>
 <b>by </b><i><a class="txt" href="yellow11.html#E2:15_2_3_9_1_1_2"><i><font color="Green" title="E27">A103</font></i></a>, <a class="ref" href="yellow_0.html#T61" title="YELLOW_0:th.61">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" title="c19">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c12">z</font> &amp; <font color="Maroon" title="c20">y</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c14">dj</font> )
 ;<br/><div class="add"><a NAME="E2:15_2_3_9_1_1_3"/><b>then </b><i><font color="Green" title="E27">A104</font></i>: 
( <font color="Maroon" title="c18">f</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c19">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c3">a</font> &amp; <font color="Maroon" title="c18">f</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c20">y</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c5">c</font> )
 <b>by </b><i><a class="txt" href="yellow11.html#E13:15_2_3"><i><font color="Green" title="E22">A90</font></i></a></i>;<br/><b>reconsider </b><font color="Maroon" title="c21">A</font> = <font color="Maroon" title="c3">a</font>, <font color="Maroon" title="c22">C</font> = <font color="Maroon" title="c5">c</font> as   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Maroon" title="c11">K</font> <b>by </b><i><a class="txt" href="yellow11.html#E4:15_2"><i><font color="Green" title="E14">A57</font></i></a>, <a class="ref" href="enumset1.html#D3" title="ENUMSET1:def.3">ENUMSET1:def 3</a></i>;<br/><a NAME="E4:15_2_3_9_1_1_3"/>
( <font color="Maroon" title="c3">a</font> <a href="orders_2.html#R3" title="ORDERS_2:pred.3">&lt;=</a> <font color="Maroon" title="c5">c</font> &amp; <font color="Maroon" title="c21">A</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c11">K</font> &amp; <font color="Maroon" title="c22">C</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c11">K</font> )
 <b>by </b><i><a class="txt" href="yellow11.html#E2:15_2"><i><font color="Green" title="E13">A56</font></i></a>, <a class="ref" href="yellow_0.html#T25" title="YELLOW_0:th.25">YELLOW_0:25</a></i>;<br/><b>hence </b><a NAME="E5:15_2_3_9_1_1_3"/>
<font color="Maroon" title="c18">f</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c19">x</font> <a href="orders_2.html#R3" title="ORDERS_2:pred.3">&lt;=</a> <font color="Maroon" title="c18">f</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c20">y</font>
 <b>by </b><i><a class="txt" href="yellow11.html#E2:15_2_3_9_1_1_3"><i><font color="Green" title="E27">A104</font></i></a>, <a class="ref" href="yellow_0.html#T61" title="YELLOW_0:th.61">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" title="c19">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c12">z</font> &amp; <font color="Maroon" title="c20">y</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c15">td</font> )
 ;<br/><div class="add"><a NAME="E2:15_2_3_9_1_1_4"/><b>then </b><i><font color="Green" title="E27">A105</font></i>: 
( <font color="Maroon" title="c18">f</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c19">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c3">a</font> &amp; <font color="Maroon" title="c18">f</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c20">y</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c6">d</font> )
 <b>by </b><i><a class="txt" href="yellow11.html#E13:15_2_3"><i><font color="Green" title="E22">A90</font></i></a></i>;<br/><b>reconsider </b><font color="Maroon" title="c21">A</font> = <font color="Maroon" title="c3">a</font>, <font color="Maroon" title="c22">D</font> = <font color="Maroon" title="c6">d</font> as   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Maroon" title="c11">K</font> <b>by </b><i><a class="txt" href="yellow11.html#E4:15_2"><i><font color="Green" title="E14">A57</font></i></a>, <a class="ref" href="enumset1.html#D3" title="ENUMSET1:def.3">ENUMSET1:def 3</a></i>;<br/><a NAME="E4:15_2_3_9_1_1_4"/>
( <font color="Maroon" title="c3">a</font> <a href="orders_2.html#R3" title="ORDERS_2:pred.3">&lt;=</a> <font color="Maroon" title="c6">d</font> &amp; <font color="Maroon" title="c21">A</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c11">K</font> &amp; <font color="Maroon" title="c22">D</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c11">K</font> )
 <b>by </b><i><a class="txt" href="yellow11.html#E2:15_2"><i><font color="Green" title="E13">A56</font></i></a>, <a class="ref" href="yellow_0.html#T25" title="YELLOW_0:th.25">YELLOW_0:25</a></i>;<br/><b>hence </b><a NAME="E5:15_2_3_9_1_1_4"/>
<font color="Maroon" title="c18">f</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c19">x</font> <a href="orders_2.html#R3" title="ORDERS_2:pred.3">&lt;=</a> <font color="Maroon" title="c18">f</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c20">y</font>
 <b>by </b><i><a class="txt" href="yellow11.html#E2:15_2_3_9_1_1_4"><i><font color="Green" title="E27">A105</font></i></a>, <a class="ref" href="yellow_0.html#T61" title="YELLOW_0:th.61">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" title="c19">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c12">z</font> &amp; <font color="Maroon" title="c20">y</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c16">t</font> )
 ;<br/><div class="add"><a NAME="E2:15_2_3_9_1_1_5"/><b>then </b><i><font color="Green" title="E27">A106</font></i>: 
( <font color="Maroon" title="c18">f</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c19">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c3">a</font> &amp; <font color="Maroon" title="c18">f</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c20">y</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c7">e</font> )
 <b>by </b><i><a class="txt" href="yellow11.html#E13:15_2_3"><i><font color="Green" title="E22">A90</font></i></a></i>;<br/><b>reconsider </b><font color="Maroon" title="c21">A</font> = <font color="Maroon" title="c3">a</font>, <font color="Maroon" title="c22">E</font> = <font color="Maroon" title="c7">e</font> as   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Maroon" title="c11">K</font> <b>by </b><i><a class="txt" href="yellow11.html#E4:15_2"><i><font color="Green" title="E14">A57</font></i></a>, <a class="ref" href="enumset1.html#D3" title="ENUMSET1:def.3">ENUMSET1:def 3</a></i>;<br/><a NAME="E4:15_2_3_9_1_1_5"/>
( <font color="Maroon" title="c3">a</font> <a href="orders_2.html#R3" title="ORDERS_2:pred.3">&lt;=</a> <font color="Maroon" title="c5">c</font> &amp; <font color="Maroon" title="c5">c</font> <a href="orders_2.html#R3" title="ORDERS_2:pred.3">&lt;=</a> <font color="Maroon" title="c7">e</font> )
 <b>by </b><i><a class="txt" href="yellow11.html#E2:15_2"><i><font color="Green" title="E13">A56</font></i></a>, <a class="ref" href="yellow_0.html#T25" title="YELLOW_0:th.25">YELLOW_0:25</a></i>;<br/><a NAME="E5:15_2_3_9_1_1_5"/><b>then </b>
( <font color="Maroon" title="c3">a</font> <a href="orders_2.html#R3" title="ORDERS_2:pred.3">&lt;=</a> <font color="Maroon" title="c7">e</font> &amp; <font color="Maroon" title="c21">A</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c11">K</font> &amp; <font color="Maroon" title="c22">E</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c11">K</font> )
 <b>by </b><i><a class="ref" href="orders_2.html#T26" title="ORDERS_2:th.26">ORDERS_2:26</a></i>;<br/><b>hence </b><a NAME="E6:15_2_3_9_1_1_5"/>
<font color="Maroon" title="c18">f</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c19">x</font> <a href="orders_2.html#R3" title="ORDERS_2:pred.3">&lt;=</a> <font color="Maroon" title="c18">f</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c20">y</font>
 <b>by </b><i><a class="txt" href="yellow11.html#E2:15_2_3_9_1_1_5"><i><font color="Green" title="E27">A106</font></i></a>, <a class="ref" href="yellow_0.html#T61" title="YELLOW_0:th.61">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" title="c19">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c13">j</font> &amp; <font color="Maroon" title="c20">y</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c12">z</font> )
 ;<br/><div class="add"><a NAME="E2:15_2_3_9_1_1_6"/><b>then </b>
<font color="Maroon" title="c13">j</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <font color="Maroon" title="c12">z</font>
 <b>by </b><i><a class="txt" href="yellow11.html#E1:15_2_3_9_1"><i><font color="Green" title="E26">A102</font></i></a>, <a class="ref" href="yellow_1.html#T3" title="YELLOW_1:th.3">YELLOW_1:3</a></i>;<br/><b>hence </b><a NAME="E3:15_2_3_9_1_1_6"/>
<font color="Maroon" title="c18">f</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c19">x</font> <a href="orders_2.html#R3" title="ORDERS_2:pred.3">&lt;=</a> <font color="Maroon" title="c18">f</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c20">y</font>
 <b>by </b><i><a class="ref" href="xboole_1.html#T3" title="XBOOLE_1:th.3">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" title="c19">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c13">j</font> &amp; <font color="Maroon" title="c20">y</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c13">j</font> )
 ;<br/><div class="add"><b>hence </b><a NAME="E2:15_2_3_9_1_1_7"/>
<font color="Maroon" title="c18">f</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c19">x</font> <a href="orders_2.html#R3" title="ORDERS_2:pred.3">&lt;=</a> <font color="Maroon" title="c18">f</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c20">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" title="E27">A107</font></i>: 
( <font color="Maroon" title="c19">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c13">j</font> &amp; <font color="Maroon" title="c20">y</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c14">dj</font> )
 ;<br/><div class="add"><a NAME="E2:15_2_3_9_1_1_8"/>
( 0 <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c13">j</font> &amp; not 0 <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c14">dj</font> )
 <b>by </b><i><a class="ref" href="yellow11.html#T2" target="_self" title="YELLOW11:th.2">Th2</a>, <a class="ref" href="card_5.html#T1" title="CARD_5:th.1">CARD_5:1</a>, <a class="ref" href="tarski.html#D1" title="TARSKI:def.1">TARSKI:def 1</a></i>;<br/><a NAME="E3:15_2_3_9_1_1_8"/><b>then </b>
not <font color="Maroon" title="c13">j</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <font color="Maroon" title="c14">dj</font>
 ;<br/><b>hence </b><a NAME="E4:15_2_3_9_1_1_8"/>
<font color="Maroon" title="c18">f</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c19">x</font> <a href="orders_2.html#R3" title="ORDERS_2:pred.3">&lt;=</a> <font color="Maroon" title="c18">f</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c20">y</font>
 <b>by </b><i><a class="txt" href="yellow11.html#E1:15_2_3_9_1"><i><font color="Green" title="E26">A102</font></i></a>, <a class="txt" href="yellow11.html#E1:15_2_3_9_1_1_8"><i><font color="Green" title="E27">A107</font></i></a>, <a class="ref" href="yellow_1.html#T3" title="YELLOW_1:th.3">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" title="E27">A108</font></i>: 
( <font color="Maroon" title="c19">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c13">j</font> &amp; <font color="Maroon" title="c20">y</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c15">td</font> )
 ;<br/><div class="add"><a NAME="E2:15_2_3_9_1_1_9"/>
( 0 <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c13">j</font> &amp; not 0 <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c15">td</font> )
 <b>by </b><i><a class="ref" href="yellow11.html#T4" target="_self" title="YELLOW11:th.4">Th4</a>, <a class="ref" href="card_5.html#T1" title="CARD_5:th.1">CARD_5:1</a>, <a class="ref" href="tarski.html#D1" title="TARSKI:def.1">TARSKI:def 1</a></i>;<br/><a NAME="E3:15_2_3_9_1_1_9"/><b>then </b>
not <font color="Maroon" title="c13">j</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <font color="Maroon" title="c15">td</font>
 ;<br/><b>hence </b><a NAME="E4:15_2_3_9_1_1_9"/>
<font color="Maroon" title="c18">f</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c19">x</font> <a href="orders_2.html#R3" title="ORDERS_2:pred.3">&lt;=</a> <font color="Maroon" title="c18">f</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c20">y</font>
 <b>by </b><i><a class="txt" href="yellow11.html#E1:15_2_3_9_1"><i><font color="Green" title="E26">A102</font></i></a>, <a class="txt" href="yellow11.html#E1:15_2_3_9_1_1_9"><i><font color="Green" title="E27">A108</font></i></a>, <a class="ref" href="yellow_1.html#T3" title="YELLOW_1:th.3">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" title="c19">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c13">j</font> &amp; <font color="Maroon" title="c20">y</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c16">t</font> )
 ;<br/><div class="add"><a NAME="E2:15_2_3_9_1_1_10"/><b>then </b><i><font color="Green" title="E27">A109</font></i>: 
( <font color="Maroon" title="c18">f</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c19">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c4">b</font> &amp; <font color="Maroon" title="c18">f</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c20">y</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c7">e</font> )
 <b>by </b><i><a class="txt" href="yellow11.html#E13:15_2_3"><i><font color="Green" title="E22">A90</font></i></a></i>;<br/><b>reconsider </b><font color="Maroon" title="c21">B</font> = <font color="Maroon" title="c4">b</font>, <font color="Maroon" title="c22">E</font> = <font color="Maroon" title="c7">e</font> as   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Maroon" title="c11">K</font> <b>by </b><i><a class="txt" href="yellow11.html#E4:15_2"><i><font color="Green" title="E14">A57</font></i></a>, <a class="ref" href="enumset1.html#D3" title="ENUMSET1:def.3">ENUMSET1:def 3</a></i>;<br/><a NAME="E4:15_2_3_9_1_1_10"/>
( <font color="Maroon" title="c4">b</font> <a href="orders_2.html#R3" title="ORDERS_2:pred.3">&lt;=</a> <font color="Maroon" title="c7">e</font> &amp; <font color="Maroon" title="c21">B</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c11">K</font> &amp; <font color="Maroon" title="c22">E</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c11">K</font> )
 <b>by </b><i><a class="txt" href="yellow11.html#E2:15_2"><i><font color="Green" title="E13">A56</font></i></a>, <a class="ref" href="yellow_0.html#T25" title="YELLOW_0:th.25">YELLOW_0:25</a></i>;<br/><b>hence </b><a NAME="E5:15_2_3_9_1_1_10"/>
<font color="Maroon" title="c18">f</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c19">x</font> <a href="orders_2.html#R3" title="ORDERS_2:pred.3">&lt;=</a> <font color="Maroon" title="c18">f</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c20">y</font>
 <b>by </b><i><a class="txt" href="yellow11.html#E2:15_2_3_9_1_1_10"><i><font color="Green" title="E27">A109</font></i></a>, <a class="ref" href="yellow_0.html#T61" title="YELLOW_0:th.61">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" title="c19">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c14">dj</font> &amp; <font color="Maroon" title="c20">y</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c12">z</font> )
 ;<br/><div class="add"><a NAME="E2:15_2_3_9_1_1_11"/><b>then </b>
<font color="Maroon" title="c14">dj</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <font color="Maroon" title="c12">z</font>
 <b>by </b><i><a class="txt" href="yellow11.html#E1:15_2_3_9_1"><i><font color="Green" title="E26">A102</font></i></a>, <a class="ref" href="yellow_1.html#T3" title="YELLOW_1:th.3">YELLOW_1:3</a></i>;<br/><b>hence </b><a NAME="E3:15_2_3_9_1_1_11"/>
<font color="Maroon" title="c18">f</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c19">x</font> <a href="orders_2.html#R3" title="ORDERS_2:pred.3">&lt;=</a> <font color="Maroon" title="c18">f</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c20">y</font>
 <b>by </b><i><a class="ref" href="yellow11.html#T2" target="_self" title="YELLOW11:th.2">Th2</a>, <a class="ref" href="xboole_1.html#T3" title="XBOOLE_1:th.3">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" title="E27">A110</font></i>: 
( <font color="Maroon" title="c19">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c14">dj</font> &amp; <font color="Maroon" title="c20">y</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c13">j</font> )
 ;<br/><div class="add"><a NAME="E2:15_2_3_9_1_1_12"/>
( 1 <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c14">dj</font> &amp; not 1 <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c13">j</font> )
 <b>by </b><i><a class="ref" href="yellow11.html#T2" target="_self" title="YELLOW11:th.2">Th2</a>, <a class="ref" href="tarski.html#D1" title="TARSKI:def.1">TARSKI:def 1</a></i>;<br/><a NAME="E3:15_2_3_9_1_1_12"/><b>then </b>
not <font color="Maroon" title="c14">dj</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <font color="Maroon" title="c13">j</font>
 ;<br/><b>hence </b><a NAME="E4:15_2_3_9_1_1_12"/>
<font color="Maroon" title="c18">f</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c19">x</font> <a href="orders_2.html#R3" title="ORDERS_2:pred.3">&lt;=</a> <font color="Maroon" title="c18">f</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c20">y</font>
 <b>by </b><i><a class="txt" href="yellow11.html#E1:15_2_3_9_1"><i><font color="Green" title="E26">A102</font></i></a>, <a class="txt" href="yellow11.html#E1:15_2_3_9_1_1_12"><i><font color="Green" title="E27">A110</font></i></a>, <a class="ref" href="yellow_1.html#T3" title="YELLOW_1:th.3">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" title="c19">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c14">dj</font> &amp; <font color="Maroon" title="c20">y</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c14">dj</font> )
 ;<br/><div class="add"><b>hence </b><a NAME="E2:15_2_3_9_1_1_13"/>
<font color="Maroon" title="c18">f</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c19">x</font> <a href="orders_2.html#R3" title="ORDERS_2:pred.3">&lt;=</a> <font color="Maroon" title="c18">f</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c20">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" title="E27">A111</font></i>: 
( <font color="Maroon" title="c19">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c14">dj</font> &amp; <font color="Maroon" title="c20">y</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c15">td</font> )
 ;<br/><div class="add"><a NAME="E2:15_2_3_9_1_1_14"/>
( 1 <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c14">dj</font> &amp; not 1 <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c15">td</font> )
 <b>by </b><i><a class="ref" href="yellow11.html#T2" target="_self" title="YELLOW11:th.2">Th2</a>, <a class="ref" href="yellow11.html#T4" target="_self" title="YELLOW11:th.4">Th4</a>, <a class="ref" href="tarski.html#D1" title="TARSKI:def.1">TARSKI:def 1</a></i>;<br/><a NAME="E3:15_2_3_9_1_1_14"/><b>then </b>
not <font color="Maroon" title="c14">dj</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <font color="Maroon" title="c15">td</font>
 ;<br/><b>hence </b><a NAME="E4:15_2_3_9_1_1_14"/>
<font color="Maroon" title="c18">f</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c19">x</font> <a href="orders_2.html#R3" title="ORDERS_2:pred.3">&lt;=</a> <font color="Maroon" title="c18">f</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c20">y</font>
 <b>by </b><i><a class="txt" href="yellow11.html#E1:15_2_3_9_1"><i><font color="Green" title="E26">A102</font></i></a>, <a class="txt" href="yellow11.html#E1:15_2_3_9_1_1_14"><i><font color="Green" title="E27">A111</font></i></a>, <a class="ref" href="yellow_1.html#T3" title="YELLOW_1:th.3">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" title="c19">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c14">dj</font> &amp; <font color="Maroon" title="c20">y</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c16">t</font> )
 ;<br/><div class="add"><a NAME="E2:15_2_3_9_1_1_15"/><b>then </b><i><font color="Green" title="E27">A112</font></i>: 
( <font color="Maroon" title="c18">f</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c19">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c5">c</font> &amp; <font color="Maroon" title="c18">f</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c20">y</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c7">e</font> )
 <b>by </b><i><a class="txt" href="yellow11.html#E13:15_2_3"><i><font color="Green" title="E22">A90</font></i></a></i>;<br/><b>reconsider </b><font color="Maroon" title="c21">C</font> = <font color="Maroon" title="c5">c</font>, <font color="Maroon" title="c22">E</font> = <font color="Maroon" title="c7">e</font> as   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Maroon" title="c11">K</font> <b>by </b><i><a class="txt" href="yellow11.html#E4:15_2"><i><font color="Green" title="E14">A57</font></i></a>, <a class="ref" href="enumset1.html#D3" title="ENUMSET1:def.3">ENUMSET1:def 3</a></i>;<br/><a NAME="E4:15_2_3_9_1_1_15"/>
( <font color="Maroon" title="c5">c</font> <a href="orders_2.html#R3" title="ORDERS_2:pred.3">&lt;=</a> <font color="Maroon" title="c7">e</font> &amp; <font color="Maroon" title="c21">C</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c11">K</font> &amp; <font color="Maroon" title="c22">E</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c11">K</font> )
 <b>by </b><i><a class="txt" href="yellow11.html#E2:15_2"><i><font color="Green" title="E13">A56</font></i></a>, <a class="ref" href="yellow_0.html#T25" title="YELLOW_0:th.25">YELLOW_0:25</a></i>;<br/><b>hence </b><a NAME="E5:15_2_3_9_1_1_15"/>
<font color="Maroon" title="c18">f</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c19">x</font> <a href="orders_2.html#R3" title="ORDERS_2:pred.3">&lt;=</a> <font color="Maroon" title="c18">f</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c20">y</font>
 <b>by </b><i><a class="txt" href="yellow11.html#E2:15_2_3_9_1_1_15"><i><font color="Green" title="E27">A112</font></i></a>, <a class="ref" href="yellow_0.html#T61" title="YELLOW_0:th.61">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" title="c19">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c15">td</font> &amp; <font color="Maroon" title="c20">y</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c12">z</font> )
 ;<br/><div class="add"><a NAME="E2:15_2_3_9_1_1_16"/><b>then </b>
<font color="Maroon" title="c15">td</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <font color="Maroon" title="c12">z</font>
 <b>by </b><i><a class="txt" href="yellow11.html#E1:15_2_3_9_1"><i><font color="Green" title="E26">A102</font></i></a>, <a class="ref" href="yellow_1.html#T3" title="YELLOW_1:th.3">YELLOW_1:3</a></i>;<br/><b>hence </b><a NAME="E3:15_2_3_9_1_1_16"/>
<font color="Maroon" title="c18">f</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c19">x</font> <a href="orders_2.html#R3" title="ORDERS_2:pred.3">&lt;=</a> <font color="Maroon" title="c18">f</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c20">y</font>
 <b>by </b><i><a class="ref" href="yellow11.html#T4" target="_self" title="YELLOW11:th.4">Th4</a>, <a class="ref" href="xboole_1.html#T3" title="XBOOLE_1:th.3">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" title="E27">A113</font></i>: 
( <font color="Maroon" title="c19">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c15">td</font> &amp; <font color="Maroon" title="c20">y</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c13">j</font> )
 ;<br/><div class="add"><a NAME="E2:15_2_3_9_1_1_17"/>
( 2 <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c15">td</font> &amp; not 2 <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c13">j</font> )
 <b>by </b><i><a class="ref" href="yellow11.html#T4" target="_self" title="YELLOW11:th.4">Th4</a>, <a class="ref" href="card_5.html#T1" title="CARD_5:th.1">CARD_5:1</a>, <a class="ref" href="tarski.html#D1" title="TARSKI:def.1">TARSKI:def 1</a></i>;<br/><a NAME="E3:15_2_3_9_1_1_17"/><b>then </b>
not <font color="Maroon" title="c15">td</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <font color="Maroon" title="c13">j</font>
 ;<br/><b>hence </b><a NAME="E4:15_2_3_9_1_1_17"/>
<font color="Maroon" title="c18">f</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c19">x</font> <a href="orders_2.html#R3" title="ORDERS_2:pred.3">&lt;=</a> <font color="Maroon" title="c18">f</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c20">y</font>
 <b>by </b><i><a class="txt" href="yellow11.html#E1:15_2_3_9_1"><i><font color="Green" title="E26">A102</font></i></a>, <a class="txt" href="yellow11.html#E1:15_2_3_9_1_1_17"><i><font color="Green" title="E27">A113</font></i></a>, <a class="ref" href="yellow_1.html#T3" title="YELLOW_1:th.3">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" title="E27">A114</font></i>: 
( <font color="Maroon" title="c19">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c15">td</font> &amp; <font color="Maroon" title="c20">y</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c14">dj</font> )
 ;<br/><div class="add"><a NAME="E2:15_2_3_9_1_1_18"/>
( 2 <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c15">td</font> &amp; not 2 <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c14">dj</font> )
 <b>by </b><i><a class="ref" href="yellow11.html#T2" target="_self" title="YELLOW11:th.2">Th2</a>, <a class="ref" href="yellow11.html#T4" target="_self" title="YELLOW11:th.4">Th4</a>, <a class="ref" href="tarski.html#D1" title="TARSKI:def.1">TARSKI:def 1</a></i>;<br/><a NAME="E3:15_2_3_9_1_1_18"/><b>then </b>
not <font color="Maroon" title="c15">td</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <font color="Maroon" title="c14">dj</font>
 ;<br/><b>hence </b><a NAME="E4:15_2_3_9_1_1_18"/>
<font color="Maroon" title="c18">f</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c19">x</font> <a href="orders_2.html#R3" title="ORDERS_2:pred.3">&lt;=</a> <font color="Maroon" title="c18">f</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c20">y</font>
 <b>by </b><i><a class="txt" href="yellow11.html#E1:15_2_3_9_1"><i><font color="Green" title="E26">A102</font></i></a>, <a class="txt" href="yellow11.html#E1:15_2_3_9_1_1_18"><i><font color="Green" title="E27">A114</font></i></a>, <a class="ref" href="yellow_1.html#T3" title="YELLOW_1:th.3">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" title="c19">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c15">td</font> &amp; <font color="Maroon" title="c20">y</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c15">td</font> )
 ;<br/><div class="add"><b>hence </b><a NAME="E2:15_2_3_9_1_1_19"/>
<font color="Maroon" title="c18">f</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c19">x</font> <a href="orders_2.html#R3" title="ORDERS_2:pred.3">&lt;=</a> <font color="Maroon" title="c18">f</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c20">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" title="c19">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c15">td</font> &amp; <font color="Maroon" title="c20">y</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c16">t</font> )
 ;<br/><div class="add"><a NAME="E2:15_2_3_9_1_1_20"/><b>then </b><i><font color="Green" title="E27">A115</font></i>: 
( <font color="Maroon" title="c18">f</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c19">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c6">d</font> &amp; <font color="Maroon" title="c18">f</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c20">y</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c7">e</font> )
 <b>by </b><i><a class="txt" href="yellow11.html#E13:15_2_3"><i><font color="Green" title="E22">A90</font></i></a></i>;<br/><b>reconsider </b><font color="Maroon" title="c21">D</font> = <font color="Maroon" title="c6">d</font>, <font color="Maroon" title="c22">E</font> = <font color="Maroon" title="c7">e</font> as   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Maroon" title="c11">K</font> <b>by </b><i><a class="txt" href="yellow11.html#E4:15_2"><i><font color="Green" title="E14">A57</font></i></a>, <a class="ref" href="enumset1.html#D3" title="ENUMSET1:def.3">ENUMSET1:def 3</a></i>;<br/><a NAME="E4:15_2_3_9_1_1_20"/>
( <font color="Maroon" title="c6">d</font> <a href="orders_2.html#R3" title="ORDERS_2:pred.3">&lt;=</a> <font color="Maroon" title="c7">e</font> &amp; <font color="Maroon" title="c21">D</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c11">K</font> &amp; <font color="Maroon" title="c22">E</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c11">K</font> )
 <b>by </b><i><a class="txt" href="yellow11.html#E2:15_2"><i><font color="Green" title="E13">A56</font></i></a>, <a class="ref" href="yellow_0.html#T25" title="YELLOW_0:th.25">YELLOW_0:25</a></i>;<br/><b>hence </b><a NAME="E5:15_2_3_9_1_1_20"/>
<font color="Maroon" title="c18">f</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c19">x</font> <a href="orders_2.html#R3" title="ORDERS_2:pred.3">&lt;=</a> <font color="Maroon" title="c18">f</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c20">y</font>
 <b>by </b><i><a class="txt" href="yellow11.html#E2:15_2_3_9_1_1_20"><i><font color="Green" title="E27">A115</font></i></a>, <a class="ref" href="yellow_0.html#T61" title="YELLOW_0:th.61">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" title="c19">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c16">t</font> &amp; <font color="Maroon" title="c20">y</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c12">z</font> )
 ;<br/><div class="add"><a NAME="E2:15_2_3_9_1_1_21"/><b>then </b>
<font color="Maroon" title="c16">t</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <font color="Maroon" title="c12">z</font>
 <b>by </b><i><a class="txt" href="yellow11.html#E1:15_2_3_9_1"><i><font color="Green" title="E26">A102</font></i></a>, <a class="ref" href="yellow_1.html#T3" title="YELLOW_1:th.3">YELLOW_1:3</a></i>;<br/><b>hence </b><a NAME="E3:15_2_3_9_1_1_21"/>
<font color="Maroon" title="c18">f</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c19">x</font> <a href="orders_2.html#R3" title="ORDERS_2:pred.3">&lt;=</a> <font color="Maroon" title="c18">f</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c20">y</font>
 <b>by </b><i><a class="ref" href="xboole_1.html#T3" title="XBOOLE_1:th.3">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" title="E27">A116</font></i>: 
( <font color="Maroon" title="c19">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c16">t</font> &amp; <font color="Maroon" title="c20">y</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c13">j</font> )
 ;<br/><div class="add"><a NAME="E2:15_2_3_9_1_1_22"/>
( 1 <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c16">t</font> &amp; not 1 <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c13">j</font> )
 <b>by </b><i><a class="ref" href="yellow11.html#T1" target="_self" title="YELLOW11:th.1">Th1</a>, <a class="ref" href="enumset1.html#D1" title="ENUMSET1:def.1">ENUMSET1:def 1</a></i>;<br/><a NAME="E3:15_2_3_9_1_1_22"/><b>then </b>
not <font color="Maroon" title="c16">t</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <font color="Maroon" title="c13">j</font>
 ;<br/><b>hence </b><a NAME="E4:15_2_3_9_1_1_22"/>
<font color="Maroon" title="c18">f</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c19">x</font> <a href="orders_2.html#R3" title="ORDERS_2:pred.3">&lt;=</a> <font color="Maroon" title="c18">f</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c20">y</font>
 <b>by </b><i><a class="txt" href="yellow11.html#E1:15_2_3_9_1"><i><font color="Green" title="E26">A102</font></i></a>, <a class="txt" href="yellow11.html#E1:15_2_3_9_1_1_22"><i><font color="Green" title="E27">A116</font></i></a>, <a class="ref" href="yellow_1.html#T3" title="YELLOW_1:th.3">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" title="E27">A117</font></i>: 
( <font color="Maroon" title="c19">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c16">t</font> &amp; <font color="Maroon" title="c20">y</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c14">dj</font> )
 ;<br/><div class="add"><a NAME="E2:15_2_3_9_1_1_23"/>
( 2 <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c16">t</font> &amp; not 2 <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c14">dj</font> )
 <b>by </b><i><a class="ref" href="yellow11.html#T1" target="_self" title="YELLOW11:th.1">Th1</a>, <a class="ref" href="yellow11.html#T2" target="_self" title="YELLOW11:th.2">Th2</a>, <a class="ref" href="enumset1.html#D1" title="ENUMSET1:def.1">ENUMSET1:def 1</a>, <a class="ref" href="tarski.html#D1" title="TARSKI:def.1">TARSKI:def 1</a></i>;<br/><a NAME="E3:15_2_3_9_1_1_23"/><b>then </b>
not <font color="Maroon" title="c16">t</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <font color="Maroon" title="c14">dj</font>
 ;<br/><b>hence </b><a NAME="E4:15_2_3_9_1_1_23"/>
<font color="Maroon" title="c18">f</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c19">x</font> <a href="orders_2.html#R3" title="ORDERS_2:pred.3">&lt;=</a> <font color="Maroon" title="c18">f</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c20">y</font>
 <b>by </b><i><a class="txt" href="yellow11.html#E1:15_2_3_9_1"><i><font color="Green" title="E26">A102</font></i></a>, <a class="txt" href="yellow11.html#E1:15_2_3_9_1_1_23"><i><font color="Green" title="E27">A117</font></i></a>, <a class="ref" href="yellow_1.html#T3" title="YELLOW_1:th.3">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" title="E27">A118</font></i>: 
( <font color="Maroon" title="c19">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c16">t</font> &amp; <font color="Maroon" title="c20">y</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c15">td</font> )
 ;<br/><div class="add"><a NAME="E2:15_2_3_9_1_1_24"/>
( 0 <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c16">t</font> &amp; not 0 <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c15">td</font> )
 <b>by </b><i><a class="ref" href="yellow11.html#T1" target="_self" title="YELLOW11:th.1">Th1</a>, <a class="ref" href="yellow11.html#T4" target="_self" title="YELLOW11:th.4">Th4</a>, <a class="ref" href="enumset1.html#D1" title="ENUMSET1:def.1">ENUMSET1:def 1</a>, <a class="ref" href="tarski.html#D1" title="TARSKI:def.1">TARSKI:def 1</a></i>;<br/><a NAME="E3:15_2_3_9_1_1_24"/><b>then </b>
not <font color="Maroon" title="c16">t</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <font color="Maroon" title="c15">td</font>
 ;<br/><b>hence </b><a NAME="E4:15_2_3_9_1_1_24"/>
<font color="Maroon" title="c18">f</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c19">x</font> <a href="orders_2.html#R3" title="ORDERS_2:pred.3">&lt;=</a> <font color="Maroon" title="c18">f</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c20">y</font>
 <b>by </b><i><a class="txt" href="yellow11.html#E1:15_2_3_9_1"><i><font color="Green" title="E26">A102</font></i></a>, <a class="txt" href="yellow11.html#E1:15_2_3_9_1_1_24"><i><font color="Green" title="E27">A118</font></i></a>, <a class="ref" href="yellow_1.html#T3" title="YELLOW_1:th.3">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" title="c19">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c16">t</font> &amp; <font color="Maroon" title="c20">y</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c16">t</font> )
 ;<br/><div class="add"><b>hence </b><a NAME="E2:15_2_3_9_1_1_25"/>
<font color="Maroon" title="c18">f</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c19">x</font> <a href="orders_2.html#R3" title="ORDERS_2:pred.3">&lt;=</a> <font color="Maroon" title="c18">f</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c20">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" title="c18">f</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c19">x</font> <a href="orders_2.html#R3" title="ORDERS_2:pred.3">&lt;=</a> <font color="Maroon" title="c18">f</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c20">y</font> implies <font color="Maroon" title="c19">x</font> <a href="orders_2.html#R3" title="ORDERS_2:pred.3">&lt;=</a> <font color="Maroon" title="c20">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" title="E26">A119</font></i>: 
<font color="Maroon" title="c18">f</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c19">x</font> <a href="orders_2.html#R3" title="ORDERS_2:pred.3">&lt;=</a> <font color="Maroon" title="c18">f</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c20">y</font>
 ;<br/>

<a NAME="E2:15_2_3_9_2"/><i><font color="Green" title="E27">A120</font></i>: 
( <font color="Maroon" title="c18">f</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c19">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c9">ck</font> &amp; <font color="Maroon" title="c18">f</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c20">y</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c9">ck</font> )
 
<b>by </b><i><a class="txt" href="yellow11.html#E16:15_2_3"><i><font color="Green" title="E24">A93</font></i></a>, <a class="txt" href="yellow11.html#E17:15_2_3"><i><font color="Green" title="E25">A94</font></i></a>, <a class="ref" href="funct_1.html#D5" title="FUNCT_1:def.5">FUNCT_1:def 5</a></i>;<br/>
<a NAME="E3:15_2_3_9_2"/><i><font color="Green" title="E28">A121</font></i>: 
<font color="Maroon" title="c14">dj</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <font color="Maroon" title="c16">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" title="c21">X</font> be    <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a> ; <i><font color="Red">:: according to </font></i><a class="ref" href="tarski.html#D3" title="TARSKI:def.3">TARSKI:def 3</a><br/>

<b>assume </b><a NAME="E1:15_2_3_9_2_1"/>
<font color="Maroon" title="c21">X</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c14">dj</font>
 ;<br/>

<a NAME="E2:15_2_3_9_2_1"/><b>then </b>
<font color="Maroon" title="c21">X</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 1
 
<b>by </b><i><a class="ref" href="yellow11.html#T2" target="_self" title="YELLOW11:th.2">Th2</a>, <a class="ref" href="tarski.html#D1" title="TARSKI:def.1">TARSKI:def 1</a></i>;<br/>
<b>hence </b><a NAME="E3:15_2_3_9_2_1"/>
<font color="Maroon" title="c21">X</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c16">t</font>
 <b>by </b><i><a class="ref" href="yellow11.html#T1" target="_self" title="YELLOW11:th.1">Th1</a>, <a class="ref" href="enumset1.html#D1" title="ENUMSET1:def.1">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" title="c18">f</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c19">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c3">a</font> &amp; <font color="Maroon" title="c18">f</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c20">y</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c3">a</font> ) or ( <font color="Maroon" title="c18">f</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c19">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c3">a</font> &amp; <font color="Maroon" title="c18">f</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c20">y</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c4">b</font> ) or ( <font color="Maroon" title="c18">f</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c19">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c3">a</font> &amp; <font color="Maroon" title="c18">f</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c20">y</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c5">c</font> ) or ( <font color="Maroon" title="c18">f</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c19">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c3">a</font> &amp; <font color="Maroon" title="c18">f</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c20">y</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c6">d</font> ) or ( <font color="Maroon" title="c18">f</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c19">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c3">a</font> &amp; <font color="Maroon" title="c18">f</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c20">y</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c7">e</font> ) or ( <font color="Maroon" title="c18">f</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c19">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c4">b</font> &amp; <font color="Maroon" title="c18">f</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c20">y</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c3">a</font> ) or ( <font color="Maroon" title="c18">f</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c19">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c4">b</font> &amp; <font color="Maroon" title="c18">f</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c20">y</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c4">b</font> ) or ( <font color="Maroon" title="c18">f</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c19">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c4">b</font> &amp; <font color="Maroon" title="c18">f</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c20">y</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c5">c</font> ) or ( <font color="Maroon" title="c18">f</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c19">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c4">b</font> &amp; <font color="Maroon" title="c18">f</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c20">y</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c6">d</font> ) or ( <font color="Maroon" title="c18">f</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c19">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c4">b</font> &amp; <font color="Maroon" title="c18">f</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c20">y</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c7">e</font> ) or ( <font color="Maroon" title="c18">f</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c19">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c5">c</font> &amp; <font color="Maroon" title="c18">f</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c20">y</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c3">a</font> ) or ( <font color="Maroon" title="c18">f</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c19">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c5">c</font> &amp; <font color="Maroon" title="c18">f</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c20">y</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c4">b</font> ) or ( <font color="Maroon" title="c18">f</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c19">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c5">c</font> &amp; <font color="Maroon" title="c18">f</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c20">y</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c5">c</font> ) or ( <font color="Maroon" title="c18">f</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c19">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c5">c</font> &amp; <font color="Maroon" title="c18">f</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c20">y</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c6">d</font> ) or ( <font color="Maroon" title="c18">f</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c19">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c5">c</font> &amp; <font color="Maroon" title="c18">f</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c20">y</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c7">e</font> ) or ( <font color="Maroon" title="c18">f</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c19">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c6">d</font> &amp; <font color="Maroon" title="c18">f</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c20">y</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c3">a</font> ) or ( <font color="Maroon" title="c18">f</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c19">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c6">d</font> &amp; <font color="Maroon" title="c18">f</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c20">y</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c4">b</font> ) or ( <font color="Maroon" title="c18">f</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c19">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c6">d</font> &amp; <font color="Maroon" title="c18">f</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c20">y</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c5">c</font> ) or ( <font color="Maroon" title="c18">f</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c19">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c6">d</font> &amp; <font color="Maroon" title="c18">f</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c20">y</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c6">d</font> ) or ( <font color="Maroon" title="c18">f</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c19">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c6">d</font> &amp; <font color="Maroon" title="c18">f</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c20">y</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c7">e</font> ) or ( <font color="Maroon" title="c18">f</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c19">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c7">e</font> &amp; <font color="Maroon" title="c18">f</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c20">y</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c3">a</font> ) or ( <font color="Maroon" title="c18">f</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c19">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c7">e</font> &amp; <font color="Maroon" title="c18">f</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c20">y</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c4">b</font> ) or ( <font color="Maroon" title="c18">f</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c19">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c7">e</font> &amp; <font color="Maroon" title="c18">f</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c20">y</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c5">c</font> ) or ( <font color="Maroon" title="c18">f</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c19">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c7">e</font> &amp; <font color="Maroon" title="c18">f</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c20">y</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c6">d</font> ) or ( <font color="Maroon" title="c18">f</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c19">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c7">e</font> &amp; <font color="Maroon" title="c18">f</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c20">y</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c7">e</font> ) )
 </span><b>by </b><i><a class="txt" href="yellow11.html#E2:15_2_3_9_2"><i><font color="Green" title="E27">A120</font></i></a>, <a class="ref" href="enumset1.html#D3" title="ENUMSET1:def.3">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" title="c18">f</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c19">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c3">a</font> &amp; <font color="Maroon" title="c18">f</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c20">y</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c3">a</font> )
 ;<br/><div class="add"><b>hence </b><a NAME="E2:15_2_3_9_2_2_1"/>
<font color="Maroon" title="c19">x</font> <a href="orders_2.html#R3" title="ORDERS_2:pred.3">&lt;=</a> <font color="Maroon" title="c20">y</font>
 <b>by </b><i><a class="txt" href="yellow11.html#E15:15_2_3"><i><font color="Green" title="E23">A91</font></i></a>, <a class="ref" href="waybel_1.html#D1" title="WAYBEL_1:def.1">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" title="E29">A122</font></i>: 
( <font color="Maroon" title="c18">f</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c19">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c3">a</font> &amp; <font color="Maroon" title="c18">f</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c20">y</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c4">b</font> )
 ;<br/><div class="add"><a NAME="E2:15_2_3_9_2_2_2"/>
( <font color="Maroon" title="c18">f</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c12">z</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c3">a</font> &amp; <font color="Maroon" title="c18">f</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c13">j</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c4">b</font> )
 <b>by </b><i><a class="txt" href="yellow11.html#E13:15_2_3"><i><font color="Green" title="E22">A90</font></i></a></i>;<br/><a NAME="E3:15_2_3_9_2_2_2"/><b>then </b>
( <font color="Maroon" title="c12">z</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c19">x</font> &amp; <font color="Maroon" title="c13">j</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c20">y</font> )
 <b>by </b><i><a class="txt" href="yellow11.html#E15:15_2_3"><i><font color="Green" title="E23">A91</font></i></a>, <a class="txt" href="yellow11.html#E1:15_2_3_9_2_2_2"><i><font color="Green" title="E29">A122</font></i></a>, <a class="ref" href="waybel_1.html#D1" title="WAYBEL_1:def.1">WAYBEL_1:def 1</a></i>;<br/><a NAME="E4:15_2_3_9_2_2_2"/><b>then </b>
<font color="Maroon" title="c19">x</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <font color="Maroon" title="c20">y</font>
 <b>by </b><i><a class="ref" href="xboole_1.html#T2" title="XBOOLE_1:th.2">XBOOLE_1:2</a></i>;<br/><b>hence </b><a NAME="E5:15_2_3_9_2_2_2"/>
<font color="Maroon" title="c19">x</font> <a href="orders_2.html#R3" title="ORDERS_2:pred.3">&lt;=</a> <font color="Maroon" title="c20">y</font>
 <b>by </b><i><a class="ref" href="yellow_1.html#T3" title="YELLOW_1:th.3">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" title="E29">A123</font></i>: 
( <font color="Maroon" title="c18">f</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c19">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c3">a</font> &amp; <font color="Maroon" title="c18">f</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c20">y</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c5">c</font> )
 ;<br/><div class="add"><a NAME="E2:15_2_3_9_2_2_3"/>
( <font color="Maroon" title="c18">f</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c12">z</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c3">a</font> &amp; <font color="Maroon" title="c18">f</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c14">dj</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c5">c</font> )
 <b>by </b><i><a class="txt" href="yellow11.html#E13:15_2_3"><i><font color="Green" title="E22">A90</font></i></a></i>;<br/><a NAME="E3:15_2_3_9_2_2_3"/><b>then </b>
( <font color="Maroon" title="c12">z</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c19">x</font> &amp; <font color="Maroon" title="c14">dj</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c20">y</font> )
 <b>by </b><i><a class="txt" href="yellow11.html#E15:15_2_3"><i><font color="Green" title="E23">A91</font></i></a>, <a class="txt" href="yellow11.html#E1:15_2_3_9_2_2_3"><i><font color="Green" title="E29">A123</font></i></a>, <a class="ref" href="waybel_1.html#D1" title="WAYBEL_1:def.1">WAYBEL_1:def 1</a></i>;<br/><a NAME="E4:15_2_3_9_2_2_3"/><b>then </b>
<font color="Maroon" title="c19">x</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <font color="Maroon" title="c20">y</font>
 <b>by </b><i><a class="ref" href="xboole_1.html#T2" title="XBOOLE_1:th.2">XBOOLE_1:2</a></i>;<br/><b>hence </b><a NAME="E5:15_2_3_9_2_2_3"/>
<font color="Maroon" title="c19">x</font> <a href="orders_2.html#R3" title="ORDERS_2:pred.3">&lt;=</a> <font color="Maroon" title="c20">y</font>
 <b>by </b><i><a class="ref" href="yellow_1.html#T3" title="YELLOW_1:th.3">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" title="E29">A124</font></i>: 
( <font color="Maroon" title="c18">f</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c19">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c3">a</font> &amp; <font color="Maroon" title="c18">f</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c20">y</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c6">d</font> )
 ;<br/><div class="add"><a NAME="E2:15_2_3_9_2_2_4"/>
( <font color="Maroon" title="c18">f</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c12">z</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c3">a</font> &amp; <font color="Maroon" title="c18">f</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c15">td</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c6">d</font> )
 <b>by </b><i><a class="txt" href="yellow11.html#E13:15_2_3"><i><font color="Green" title="E22">A90</font></i></a></i>;<br/><a NAME="E3:15_2_3_9_2_2_4"/><b>then </b>
( <font color="Maroon" title="c12">z</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c19">x</font> &amp; <font color="Maroon" title="c15">td</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c20">y</font> )
 <b>by </b><i><a class="txt" href="yellow11.html#E15:15_2_3"><i><font color="Green" title="E23">A91</font></i></a>, <a class="txt" href="yellow11.html#E1:15_2_3_9_2_2_4"><i><font color="Green" title="E29">A124</font></i></a>, <a class="ref" href="waybel_1.html#D1" title="WAYBEL_1:def.1">WAYBEL_1:def 1</a></i>;<br/><a NAME="E4:15_2_3_9_2_2_4"/><b>then </b>
<font color="Maroon" title="c19">x</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <font color="Maroon" title="c20">y</font>
 <b>by </b><i><a class="ref" href="xboole_1.html#T2" title="XBOOLE_1:th.2">XBOOLE_1:2</a></i>;<br/><b>hence </b><a NAME="E5:15_2_3_9_2_2_4"/>
<font color="Maroon" title="c19">x</font> <a href="orders_2.html#R3" title="ORDERS_2:pred.3">&lt;=</a> <font color="Maroon" title="c20">y</font>
 <b>by </b><i><a class="ref" href="yellow_1.html#T3" title="YELLOW_1:th.3">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" title="E29">A125</font></i>: 
( <font color="Maroon" title="c18">f</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c19">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c3">a</font> &amp; <font color="Maroon" title="c18">f</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c20">y</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c7">e</font> )
 ;<br/><div class="add"><a NAME="E2:15_2_3_9_2_2_5"/>
( <font color="Maroon" title="c18">f</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c12">z</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c3">a</font> &amp; <font color="Maroon" title="c18">f</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c16">t</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c7">e</font> )
 <b>by </b><i><a class="txt" href="yellow11.html#E13:15_2_3"><i><font color="Green" title="E22">A90</font></i></a></i>;<br/><a NAME="E3:15_2_3_9_2_2_5"/><b>then </b>
( <font color="Maroon" title="c12">z</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c19">x</font> &amp; <font color="Maroon" title="c16">t</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c20">y</font> )
 <b>by </b><i><a class="txt" href="yellow11.html#E15:15_2_3"><i><font color="Green" title="E23">A91</font></i></a>, <a class="txt" href="yellow11.html#E1:15_2_3_9_2_2_5"><i><font color="Green" title="E29">A125</font></i></a>, <a class="ref" href="waybel_1.html#D1" title="WAYBEL_1:def.1">WAYBEL_1:def 1</a></i>;<br/><a NAME="E4:15_2_3_9_2_2_5"/><b>then </b>
<font color="Maroon" title="c19">x</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <font color="Maroon" title="c20">y</font>
 <b>by </b><i><a class="ref" href="xboole_1.html#T2" title="XBOOLE_1:th.2">XBOOLE_1:2</a></i>;<br/><b>hence </b><a NAME="E5:15_2_3_9_2_2_5"/>
<font color="Maroon" title="c19">x</font> <a href="orders_2.html#R3" title="ORDERS_2:pred.3">&lt;=</a> <font color="Maroon" title="c20">y</font>
 <b>by </b><i><a class="ref" href="yellow_1.html#T3" title="YELLOW_1:th.3">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" title="c18">f</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c19">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c4">b</font> &amp; <font color="Maroon" title="c18">f</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c20">y</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c3">a</font> )
 ;<br/><div class="add"><a NAME="E2:15_2_3_9_2_2_6"/><b>then </b>
<font color="Maroon" title="c4">b</font> <a href="orders_2.html#R3" title="ORDERS_2:pred.3">&lt;=</a> <font color="Maroon" title="c3">a</font>
 <b>by </b><i><a class="txt" href="yellow11.html#E1:15_2_3_9_2"><i><font color="Green" title="E26">A119</font></i></a>, <a class="ref" href="yellow_0.html#T60" title="YELLOW_0:th.60">YELLOW_0:60</a></i>;<br/><b>hence </b><a NAME="E3:15_2_3_9_2_2_6"/>
<font color="Maroon" title="c19">x</font> <a href="orders_2.html#R3" title="ORDERS_2:pred.3">&lt;=</a> <font color="Maroon" title="c20">y</font>
 <b>by </b><i><a class="txt" href="yellow11.html#E2:15_2"><i><font color="Green" title="E13">A56</font></i></a>, <a class="ref" href="yellow_0.html#T25" title="YELLOW_0:th.25">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" title="c18">f</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c19">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c4">b</font> &amp; <font color="Maroon" title="c18">f</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c20">y</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c4">b</font> )
 ;<br/><div class="add"><b>hence </b><a NAME="E2:15_2_3_9_2_2_7"/>
<font color="Maroon" title="c19">x</font> <a href="orders_2.html#R3" title="ORDERS_2:pred.3">&lt;=</a> <font color="Maroon" title="c20">y</font>
 <b>by </b><i><a class="txt" href="yellow11.html#E15:15_2_3"><i><font color="Green" title="E23">A91</font></i></a>, <a class="ref" href="waybel_1.html#D1" title="WAYBEL_1:def.1">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" title="c18">f</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c19">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c4">b</font> &amp; <font color="Maroon" title="c18">f</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c20">y</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c5">c</font> )
 ;<br/><div class="add"><a NAME="E2:15_2_3_9_2_2_8"/><b>then </b>
<font color="Maroon" title="c4">b</font> <a href="orders_2.html#R3" title="ORDERS_2:pred.3">&lt;=</a> <font color="Maroon" title="c5">c</font>
 <b>by </b><i><a class="txt" href="yellow11.html#E1:15_2_3_9_2"><i><font color="Green" title="E26">A119</font></i></a>, <a class="ref" href="yellow_0.html#T60" title="YELLOW_0:th.60">YELLOW_0:60</a></i>;<br/><b>hence </b><a NAME="E3:15_2_3_9_2_2_8"/>
<font color="Maroon" title="c19">x</font> <a href="orders_2.html#R3" title="ORDERS_2:pred.3">&lt;=</a> <font color="Maroon" title="c20">y</font>
 <b>by </b><i><a class="txt" href="yellow11.html#E2:15_2"><i><font color="Green" title="E13">A56</font></i></a>, <a class="ref" href="yellow_0.html#T25" title="YELLOW_0:th.25">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" title="c18">f</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c19">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c4">b</font> &amp; <font color="Maroon" title="c18">f</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c20">y</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c6">d</font> )
 ;<br/><div class="add"><a NAME="E2:15_2_3_9_2_2_9"/><b>then </b>
<font color="Maroon" title="c4">b</font> <a href="orders_2.html#R3" title="ORDERS_2:pred.3">&lt;=</a> <font color="Maroon" title="c6">d</font>
 <b>by </b><i><a class="txt" href="yellow11.html#E1:15_2_3_9_2"><i><font color="Green" title="E26">A119</font></i></a>, <a class="ref" href="yellow_0.html#T60" title="YELLOW_0:th.60">YELLOW_0:60</a></i>;<br/><b>hence </b><a NAME="E3:15_2_3_9_2_2_9"/>
<font color="Maroon" title="c19">x</font> <a href="orders_2.html#R3" title="ORDERS_2:pred.3">&lt;=</a> <font color="Maroon" title="c20">y</font>
 <b>by </b><i><a class="txt" href="yellow11.html#E2:15_2"><i><font color="Green" title="E13">A56</font></i></a>, <a class="ref" href="yellow_0.html#T25" title="YELLOW_0:th.25">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" title="E29">A126</font></i>: 
( <font color="Maroon" title="c18">f</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c19">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c4">b</font> &amp; <font color="Maroon" title="c18">f</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c20">y</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c7">e</font> )
 ;<br/><div class="add"><a NAME="E2:15_2_3_9_2_2_10"/>
( <font color="Maroon" title="c18">f</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c13">j</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c4">b</font> &amp; <font color="Maroon" title="c18">f</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c16">t</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c7">e</font> )
 <b>by </b><i><a class="txt" href="yellow11.html#E13:15_2_3"><i><font color="Green" title="E22">A90</font></i></a></i>;<br/><a NAME="E3:15_2_3_9_2_2_10"/><b>then </b>
( <font color="Maroon" title="c13">j</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c19">x</font> &amp; <font color="Maroon" title="c16">t</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c20">y</font> )
 <b>by </b><i><a class="txt" href="yellow11.html#E15:15_2_3"><i><font color="Green" title="E23">A91</font></i></a>, <a class="txt" href="yellow11.html#E1:15_2_3_9_2_2_10"><i><font color="Green" title="E29">A126</font></i></a>, <a class="ref" href="waybel_1.html#D1" title="WAYBEL_1:def.1">WAYBEL_1:def 1</a></i>;<br/><a NAME="E4:15_2_3_9_2_2_10"/><b>then </b>
<font color="Maroon" title="c19">x</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <font color="Maroon" title="c20">y</font>
 <b>by </b><i><a class="ref" href="card_1.html#T56" title="CARD_1:th.56">CARD_1:56</a></i>;<br/><b>hence </b><a NAME="E5:15_2_3_9_2_2_10"/>
<font color="Maroon" title="c19">x</font> <a href="orders_2.html#R3" title="ORDERS_2:pred.3">&lt;=</a> <font color="Maroon" title="c20">y</font>
 <b>by </b><i><a class="ref" href="yellow_1.html#T3" title="YELLOW_1:th.3">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" title="c18">f</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c19">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c5">c</font> &amp; <font color="Maroon" title="c18">f</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c20">y</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c3">a</font> )
 ;<br/><div class="add"><a NAME="E2:15_2_3_9_2_2_11"/><b>then </b>
<font color="Maroon" title="c5">c</font> <a href="orders_2.html#R3" title="ORDERS_2:pred.3">&lt;=</a> <font color="Maroon" title="c3">a</font>
 <b>by </b><i><a class="txt" href="yellow11.html#E1:15_2_3_9_2"><i><font color="Green" title="E26">A119</font></i></a>, <a class="ref" href="yellow_0.html#T60" title="YELLOW_0:th.60">YELLOW_0:60</a></i>;<br/><b>hence </b><a NAME="E3:15_2_3_9_2_2_11"/>
<font color="Maroon" title="c19">x</font> <a href="orders_2.html#R3" title="ORDERS_2:pred.3">&lt;=</a> <font color="Maroon" title="c20">y</font>
 <b>by </b><i><a class="txt" href="yellow11.html#E2:15_2"><i><font color="Green" title="E13">A56</font></i></a>, <a class="ref" href="yellow_0.html#T25" title="YELLOW_0:th.25">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" title="c18">f</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c19">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c5">c</font> &amp; <font color="Maroon" title="c18">f</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c20">y</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c4">b</font> )
 ;<br/><div class="add"><a NAME="E2:15_2_3_9_2_2_12"/><b>then </b>
<font color="Maroon" title="c5">c</font> <a href="orders_2.html#R3" title="ORDERS_2:pred.3">&lt;=</a> <font color="Maroon" title="c4">b</font>
 <b>by </b><i><a class="txt" href="yellow11.html#E1:15_2_3_9_2"><i><font color="Green" title="E26">A119</font></i></a>, <a class="ref" href="yellow_0.html#T60" title="YELLOW_0:th.60">YELLOW_0:60</a></i>;<br/><b>hence </b><a NAME="E3:15_2_3_9_2_2_12"/>
<font color="Maroon" title="c19">x</font> <a href="orders_2.html#R3" title="ORDERS_2:pred.3">&lt;=</a> <font color="Maroon" title="c20">y</font>
 <b>by </b><i><a class="txt" href="yellow11.html#E2:15_2"><i><font color="Green" title="E13">A56</font></i></a>, <a class="ref" href="yellow_0.html#T25" title="YELLOW_0:th.25">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" title="c18">f</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c19">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c5">c</font> &amp; <font color="Maroon" title="c18">f</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c20">y</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c5">c</font> )
 ;<br/><div class="add"><b>hence </b><a NAME="E2:15_2_3_9_2_2_13"/>
<font color="Maroon" title="c19">x</font> <a href="orders_2.html#R3" title="ORDERS_2:pred.3">&lt;=</a> <font color="Maroon" title="c20">y</font>
 <b>by </b><i><a class="txt" href="yellow11.html#E15:15_2_3"><i><font color="Green" title="E23">A91</font></i></a>, <a class="ref" href="waybel_1.html#D1" title="WAYBEL_1:def.1">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" title="c18">f</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c19">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c5">c</font> &amp; <font color="Maroon" title="c18">f</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c20">y</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c6">d</font> )
 ;<br/><div class="add"><a NAME="E2:15_2_3_9_2_2_14"/><b>then </b>
<font color="Maroon" title="c5">c</font> <a href="orders_2.html#R3" title="ORDERS_2:pred.3">&lt;=</a> <font color="Maroon" title="c6">d</font>
 <b>by </b><i><a class="txt" href="yellow11.html#E1:15_2_3_9_2"><i><font color="Green" title="E26">A119</font></i></a>, <a class="ref" href="yellow_0.html#T60" title="YELLOW_0:th.60">YELLOW_0:60</a></i>;<br/><b>hence </b><a NAME="E3:15_2_3_9_2_2_14"/>
<font color="Maroon" title="c19">x</font> <a href="orders_2.html#R3" title="ORDERS_2:pred.3">&lt;=</a> <font color="Maroon" title="c20">y</font>
 <b>by </b><i><a class="txt" href="yellow11.html#E2:15_2"><i><font color="Green" title="E13">A56</font></i></a>, <a class="ref" href="yellow_0.html#T25" title="YELLOW_0:th.25">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" title="E29">A127</font></i>: 
( <font color="Maroon" title="c18">f</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c19">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c5">c</font> &amp; <font color="Maroon" title="c18">f</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c20">y</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c7">e</font> )
 ;<br/><div class="add"><a NAME="E2:15_2_3_9_2_2_15"/>
( <font color="Maroon" title="c18">f</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c14">dj</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c5">c</font> &amp; <font color="Maroon" title="c18">f</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c16">t</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c7">e</font> )
 <b>by </b><i><a class="txt" href="yellow11.html#E13:15_2_3"><i><font color="Green" title="E22">A90</font></i></a></i>;<br/><a NAME="E3:15_2_3_9_2_2_15"/><b>then </b>
( <font color="Maroon" title="c14">dj</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c19">x</font> &amp; <font color="Maroon" title="c16">t</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c20">y</font> )
 <b>by </b><i><a class="txt" href="yellow11.html#E15:15_2_3"><i><font color="Green" title="E23">A91</font></i></a>, <a class="txt" href="yellow11.html#E1:15_2_3_9_2_2_15"><i><font color="Green" title="E29">A127</font></i></a>, <a class="ref" href="waybel_1.html#D1" title="WAYBEL_1:def.1">WAYBEL_1:def 1</a></i>;<br/><b>hence </b><a NAME="E4:15_2_3_9_2_2_15"/>
<font color="Maroon" title="c19">x</font> <a href="orders_2.html#R3" title="ORDERS_2:pred.3">&lt;=</a> <font color="Maroon" title="c20">y</font>
 <b>by </b><i><a class="txt" href="yellow11.html#E3:15_2_3_9_2"><i><font color="Green" title="E28">A121</font></i></a>, <a class="ref" href="yellow_1.html#T3" title="YELLOW_1:th.3">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" title="c18">f</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c19">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c6">d</font> &amp; <font color="Maroon" title="c18">f</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c20">y</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c3">a</font> )
 ;<br/><div class="add"><a NAME="E2:15_2_3_9_2_2_16"/><b>then </b>
( <font color="Maroon" title="c6">d</font> <a href="orders_2.html#R3" title="ORDERS_2:pred.3">&lt;=</a> <font color="Maroon" title="c3">a</font> &amp; <font color="Maroon" title="c3">a</font> <a href="orders_2.html#R3" title="ORDERS_2:pred.3">&lt;=</a> <font color="Maroon" title="c4">b</font> )
 <b>by </b><i><a class="txt" href="yellow11.html#E2:15_2"><i><font color="Green" title="E13">A56</font></i></a>, <a class="txt" href="yellow11.html#E1:15_2_3_9_2"><i><font color="Green" title="E26">A119</font></i></a>, <a class="ref" href="yellow_0.html#T25" title="YELLOW_0:th.25">YELLOW_0:25</a>, <a class="ref" href="yellow_0.html#T60" title="YELLOW_0:th.60">YELLOW_0:60</a></i>;<br/><b>hence </b><a NAME="E3:15_2_3_9_2_2_16"/>
<font color="Maroon" title="c19">x</font> <a href="orders_2.html#R3" title="ORDERS_2:pred.3">&lt;=</a> <font color="Maroon" title="c20">y</font>
 <b>by </b><i><a class="txt" href="yellow11.html#E2:15_2"><i><font color="Green" title="E13">A56</font></i></a>, <a class="ref" href="yellow_0.html#T25" title="YELLOW_0:th.25">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" title="c18">f</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c19">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c6">d</font> &amp; <font color="Maroon" title="c18">f</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c20">y</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c4">b</font> )
 ;<br/><div class="add"><a NAME="E2:15_2_3_9_2_2_17"/><b>then </b>
<font color="Maroon" title="c6">d</font> <a href="orders_2.html#R3" title="ORDERS_2:pred.3">&lt;=</a> <font color="Maroon" title="c4">b</font>
 <b>by </b><i><a class="txt" href="yellow11.html#E1:15_2_3_9_2"><i><font color="Green" title="E26">A119</font></i></a>, <a class="ref" href="yellow_0.html#T60" title="YELLOW_0:th.60">YELLOW_0:60</a></i>;<br/><b>hence </b><a NAME="E3:15_2_3_9_2_2_17"/>
<font color="Maroon" title="c19">x</font> <a href="orders_2.html#R3" title="ORDERS_2:pred.3">&lt;=</a> <font color="Maroon" title="c20">y</font>
 <b>by </b><i><a class="txt" href="yellow11.html#E2:15_2"><i><font color="Green" title="E13">A56</font></i></a>, <a class="ref" href="yellow_0.html#T25" title="YELLOW_0:th.25">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" title="c18">f</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c19">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c6">d</font> &amp; <font color="Maroon" title="c18">f</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c20">y</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c5">c</font> )
 ;<br/><div class="add"><a NAME="E2:15_2_3_9_2_2_18"/><b>then </b>
<font color="Maroon" title="c6">d</font> <a href="orders_2.html#R3" title="ORDERS_2:pred.3">&lt;=</a> <font color="Maroon" title="c5">c</font>
 <b>by </b><i><a class="txt" href="yellow11.html#E1:15_2_3_9_2"><i><font color="Green" title="E26">A119</font></i></a>, <a class="ref" href="yellow_0.html#T60" title="YELLOW_0:th.60">YELLOW_0:60</a></i>;<br/><b>hence </b><a NAME="E3:15_2_3_9_2_2_18"/>
<font color="Maroon" title="c19">x</font> <a href="orders_2.html#R3" title="ORDERS_2:pred.3">&lt;=</a> <font color="Maroon" title="c20">y</font>
 <b>by </b><i><a class="txt" href="yellow11.html#E2:15_2"><i><font color="Green" title="E13">A56</font></i></a>, <a class="ref" href="yellow_0.html#T25" title="YELLOW_0:th.25">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" title="c18">f</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c19">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c6">d</font> &amp; <font color="Maroon" title="c18">f</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c20">y</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c6">d</font> )
 ;<br/><div class="add"><b>hence </b><a NAME="E2:15_2_3_9_2_2_19"/>
<font color="Maroon" title="c19">x</font> <a href="orders_2.html#R3" title="ORDERS_2:pred.3">&lt;=</a> <font color="Maroon" title="c20">y</font>
 <b>by </b><i><a class="txt" href="yellow11.html#E15:15_2_3"><i><font color="Green" title="E23">A91</font></i></a>, <a class="ref" href="waybel_1.html#D1" title="WAYBEL_1:def.1">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" title="E29">A128</font></i>: 
( <font color="Maroon" title="c18">f</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c19">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c6">d</font> &amp; <font color="Maroon" title="c18">f</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c20">y</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c7">e</font> )
 ;<br/><div class="add"><a NAME="E2:15_2_3_9_2_2_20"/>
( <font color="Maroon" title="c18">f</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c15">td</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c6">d</font> &amp; <font color="Maroon" title="c18">f</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c16">t</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c7">e</font> )
 <b>by </b><i><a class="txt" href="yellow11.html#E13:15_2_3"><i><font color="Green" title="E22">A90</font></i></a></i>;<br/><a NAME="E3:15_2_3_9_2_2_20"/><b>then </b>
( <font color="Maroon" title="c15">td</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c19">x</font> &amp; <font color="Maroon" title="c16">t</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c20">y</font> )
 <b>by </b><i><a class="txt" href="yellow11.html#E15:15_2_3"><i><font color="Green" title="E23">A91</font></i></a>, <a class="txt" href="yellow11.html#E1:15_2_3_9_2_2_20"><i><font color="Green" title="E29">A128</font></i></a>, <a class="ref" href="waybel_1.html#D1" title="WAYBEL_1:def.1">WAYBEL_1:def 1</a></i>;<br/><b>hence </b><a NAME="E4:15_2_3_9_2_2_20"/>
<font color="Maroon" title="c19">x</font> <a href="orders_2.html#R3" title="ORDERS_2:pred.3">&lt;=</a> <font color="Maroon" title="c20">y</font>
 <b>by </b><i><a class="ref" href="yellow_1.html#T3" title="YELLOW_1:th.3">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" title="c18">f</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c19">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c7">e</font> &amp; <font color="Maroon" title="c18">f</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c20">y</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c3">a</font> )
 ;<br/><div class="add"><a NAME="E2:15_2_3_9_2_2_21"/><b>then </b>
( <font color="Maroon" title="c7">e</font> <a href="orders_2.html#R3" title="ORDERS_2:pred.3">&lt;=</a> <font color="Maroon" title="c3">a</font> &amp; <font color="Maroon" title="c3">a</font> <a href="orders_2.html#R3" title="ORDERS_2:pred.3">&lt;=</a> <font color="Maroon" title="c4">b</font> )
 <b>by </b><i><a class="txt" href="yellow11.html#E2:15_2"><i><font color="Green" title="E13">A56</font></i></a>, <a class="txt" href="yellow11.html#E1:15_2_3_9_2"><i><font color="Green" title="E26">A119</font></i></a>, <a class="ref" href="yellow_0.html#T25" title="YELLOW_0:th.25">YELLOW_0:25</a>, <a class="ref" href="yellow_0.html#T60" title="YELLOW_0:th.60">YELLOW_0:60</a></i>;<br/><a NAME="E3:15_2_3_9_2_2_21"/><b>then </b>
<font color="Maroon" title="c7">e</font> <a href="orders_2.html#R3" title="ORDERS_2:pred.3">&lt;=</a> <font color="Maroon" title="c4">b</font>
 <b>by </b><i><a class="ref" href="orders_2.html#T26" title="ORDERS_2:th.26">ORDERS_2:26</a></i>;<br/><b>hence </b><a NAME="E4:15_2_3_9_2_2_21"/>
<font color="Maroon" title="c19">x</font> <a href="orders_2.html#R3" title="ORDERS_2:pred.3">&lt;=</a> <font color="Maroon" title="c20">y</font>
 <b>by </b><i><a class="txt" href="yellow11.html#E2:15_2"><i><font color="Green" title="E13">A56</font></i></a>, <a class="ref" href="yellow_0.html#T25" title="YELLOW_0:th.25">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" title="c18">f</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c19">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c7">e</font> &amp; <font color="Maroon" title="c18">f</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c20">y</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c4">b</font> )
 ;<br/><div class="add"><a NAME="E2:15_2_3_9_2_2_22"/><b>then </b>
<font color="Maroon" title="c7">e</font> <a href="orders_2.html#R3" title="ORDERS_2:pred.3">&lt;=</a> <font color="Maroon" title="c4">b</font>
 <b>by </b><i><a class="txt" href="yellow11.html#E1:15_2_3_9_2"><i><font color="Green" title="E26">A119</font></i></a>, <a class="ref" href="yellow_0.html#T60" title="YELLOW_0:th.60">YELLOW_0:60</a></i>;<br/><b>hence </b><a NAME="E3:15_2_3_9_2_2_22"/>
<font color="Maroon" title="c19">x</font> <a href="orders_2.html#R3" title="ORDERS_2:pred.3">&lt;=</a> <font color="Maroon" title="c20">y</font>
 <b>by </b><i><a class="txt" href="yellow11.html#E2:15_2"><i><font color="Green" title="E13">A56</font></i></a>, <a class="ref" href="yellow_0.html#T25" title="YELLOW_0:th.25">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" title="c18">f</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c19">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c7">e</font> &amp; <font color="Maroon" title="c18">f</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c20">y</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c5">c</font> )
 ;<br/><div class="add"><a NAME="E2:15_2_3_9_2_2_23"/><b>then </b>
<font color="Maroon" title="c7">e</font> <a href="orders_2.html#R3" title="ORDERS_2:pred.3">&lt;=</a> <font color="Maroon" title="c5">c</font>
 <b>by </b><i><a class="txt" href="yellow11.html#E1:15_2_3_9_2"><i><font color="Green" title="E26">A119</font></i></a>, <a class="ref" href="yellow_0.html#T60" title="YELLOW_0:th.60">YELLOW_0:60</a></i>;<br/><b>hence </b><a NAME="E3:15_2_3_9_2_2_23"/>
<font color="Maroon" title="c19">x</font> <a href="orders_2.html#R3" title="ORDERS_2:pred.3">&lt;=</a> <font color="Maroon" title="c20">y</font>
 <b>by </b><i><a class="txt" href="yellow11.html#E2:15_2"><i><font color="Green" title="E13">A56</font></i></a>, <a class="ref" href="yellow_0.html#T25" title="YELLOW_0:th.25">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" title="c18">f</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c19">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c7">e</font> &amp; <font color="Maroon" title="c18">f</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c20">y</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c6">d</font> )
 ;<br/><div class="add"><a NAME="E2:15_2_3_9_2_2_24"/><b>then </b>
<font color="Maroon" title="c7">e</font> <a href="orders_2.html#R3" title="ORDERS_2:pred.3">&lt;=</a> <font color="Maroon" title="c6">d</font>
 <b>by </b><i><a class="txt" href="yellow11.html#E1:15_2_3_9_2"><i><font color="Green" title="E26">A119</font></i></a>, <a class="ref" href="yellow_0.html#T60" title="YELLOW_0:th.60">YELLOW_0:60</a></i>;<br/><b>hence </b><a NAME="E3:15_2_3_9_2_2_24"/>
<font color="Maroon" title="c19">x</font> <a href="orders_2.html#R3" title="ORDERS_2:pred.3">&lt;=</a> <font color="Maroon" title="c20">y</font>
 <b>by </b><i><a class="txt" href="yellow11.html#E2:15_2"><i><font color="Green" title="E13">A56</font></i></a>, <a class="ref" href="yellow_0.html#T25" title="YELLOW_0:th.25">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" title="c18">f</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c19">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c7">e</font> &amp; <font color="Maroon" title="c18">f</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c20">y</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c7">e</font> )
 ;<br/><div class="add"><b>hence </b><a NAME="E2:15_2_3_9_2_2_25"/>
<font color="Maroon" title="c19">x</font> <a href="orders_2.html#R3" title="ORDERS_2:pred.3">&lt;=</a> <font color="Maroon" title="c20">y</font>
 <b>by </b><i><a class="txt" href="yellow11.html#E15:15_2_3"><i><font color="Green" title="E23">A91</font></i></a>, <a class="ref" href="waybel_1.html#D1" title="WAYBEL_1:def.1">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" title="c18">f</font> is <a href="waybel_0.html#V23" title="WAYBEL_0:attr.23">isomorphic</a>
 <b>by </b><i><a class="txt" href="yellow11.html#E4:15_2"><i><font color="Green" title="E14">A57</font></i></a>, <a class="txt" href="yellow11.html#E15:15_2_3"><i><font color="Green" title="E23">A91</font></i></a>, <a class="txt" href="yellow11.html#E17:15_2_3"><i><font color="Green" title="E25">A94</font></i></a>, <a class="ref" href="waybel_0.html#T66" title="WAYBEL_0:th.66">WAYBEL_0:66</a></i>;<br/>


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


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


</div>
