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

<b>let </b><font color="Maroon" title="c1">G</font> be  non <a href="struct_0.html#V3" title="STRUCT_0:attr.3">empty</a> <a href="necklace.html#V1" title="NECKLACE:attr.1">symmetric</a> <a href="necklace.html#V3" title="NECKLACE:attr.3">irreflexive</a>  <a href="orders_2.html#L1" title="ORDERS_2:struct.1">RelStr</a> ;<br/><b>let </b><font color="Maroon" title="c2">a</font>, <font color="Maroon" title="c3">b</font>, <font color="Maroon" title="c4">c</font>, <font color="Maroon" title="c5">d</font> be   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Maroon" title="c1">G</font>;<br/><b>let </b><font color="Maroon" title="c6">Z</font> be   <a href="struct_0.html#NM2" title="STRUCT_0:NM.2">Subset</a> of <font color="Maroon" title="c1">G</font>;<br/>





<b>assume </b><b>that </b><br/><a NAME="E1:60"/><i><font color="Green" title="E36">A1</font></i>: 
<font color="Maroon" title="c6">Z</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1"><a href="domain_1.html#K9" title="DOMAIN_1:func.9">{</a><span class="default"><font color="Maroon" title="c2">a</font>,<font color="Maroon" title="c3">b</font>,<font color="Maroon" title="c4">c</font>,<font color="Maroon" title="c5">d</font></span><a href="domain_1.html#K9" title="DOMAIN_1:func.9">}</a></span>
 <b>and </b><br/><a NAME="E2:60"/><i><font color="Green" title="E37">A2</font></i>: 
<font color="Maroon" title="c2">a</font>,<font color="Maroon" title="c3">b</font>,<font color="Maroon" title="c4">c</font>,<font color="Maroon" title="c5">d</font> <a href="incproj.html#R2" title="INCPROJ:pred.2">are_mutually_different</a> 
 <b>and </b><br/><a NAME="E3:60"/><i><font color="Green" title="E38">A3</font></i>: 
<span class="p1"><a href="domain_1.html#K1" title="DOMAIN_1:func.1">[</a><span class="default"><font color="Maroon" title="c2">a</font>,<font color="Maroon" title="c3">b</font></span><a href="domain_1.html#K1" title="DOMAIN_1:func.1">]</a></span> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> the <a href="orders_2.html#U1" title="ORDERS_2:sel.1">InternalRel</a> of <font color="Maroon" title="c1">G</font>
 <b>and </b><br/><a NAME="E4:60"/><i><font color="Green" title="E39">A4</font></i>: 
<span class="p1"><a href="domain_1.html#K1" title="DOMAIN_1:func.1">[</a><span class="default"><font color="Maroon" title="c3">b</font>,<font color="Maroon" title="c4">c</font></span><a href="domain_1.html#K1" title="DOMAIN_1:func.1">]</a></span> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> the <a href="orders_2.html#U1" title="ORDERS_2:sel.1">InternalRel</a> of <font color="Maroon" title="c1">G</font>
 <b>and </b><br/><a NAME="E5:60"/><i><font color="Green" title="E40">A5</font></i>: 
<span class="p1"><a href="domain_1.html#K1" title="DOMAIN_1:func.1">[</a><span class="default"><font color="Maroon" title="c4">c</font>,<font color="Maroon" title="c5">d</font></span><a href="domain_1.html#K1" title="DOMAIN_1:func.1">]</a></span> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> the <a href="orders_2.html#U1" title="ORDERS_2:sel.1">InternalRel</a> of <font color="Maroon" title="c1">G</font>
 <b>and </b><br/><a NAME="E6:60"/><i><font color="Green" title="E41">A6</font></i>: 
not <span class="p1"><a href="domain_1.html#K1" title="DOMAIN_1:func.1">[</a><span class="default"><font color="Maroon" title="c2">a</font>,<font color="Maroon" title="c4">c</font></span><a href="domain_1.html#K1" title="DOMAIN_1:func.1">]</a></span> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> the <a href="orders_2.html#U1" title="ORDERS_2:sel.1">InternalRel</a> of <font color="Maroon" title="c1">G</font>
 <b>and </b><br/><a NAME="E7:60"/><i><font color="Green" title="E42">A7</font></i>: 
not <span class="p1"><a href="domain_1.html#K1" title="DOMAIN_1:func.1">[</a><span class="default"><font color="Maroon" title="c2">a</font>,<font color="Maroon" title="c5">d</font></span><a href="domain_1.html#K1" title="DOMAIN_1:func.1">]</a></span> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> the <a href="orders_2.html#U1" title="ORDERS_2:sel.1">InternalRel</a> of <font color="Maroon" title="c1">G</font>
 <b>and </b><br/><a NAME="E8:60"/><i><font color="Green" title="E43">A8</font></i>: 
not <span class="p1"><a href="domain_1.html#K1" title="DOMAIN_1:func.1">[</a><span class="default"><font color="Maroon" title="c3">b</font>,<font color="Maroon" title="c5">d</font></span><a href="domain_1.html#K1" title="DOMAIN_1:func.1">]</a></span> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> the <a href="orders_2.html#U1" title="ORDERS_2:sel.1">InternalRel</a> of <font color="Maroon" title="c1">G</font>
 ;<br/>

<b>set </b><font color="Maroon" title="c7">H</font> =  <a href="yellow_0.html#K5" title="YELLOW_0:func.5">subrelstr</a> <font color="Maroon" title="c6">Z</font>;<br/>
<b>set </b><font color="Maroon" title="c8">N4</font> =  <a href="necklace.html#K4" title="NECKLACE:func.4">Necklace</a> 4;<br/>
<b>set </b><font color="Maroon" title="c9">IH</font> = the <a href="orders_2.html#U1" title="ORDERS_2:sel.1">InternalRel</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="c6">Z</font></span>)</span>;<br/>
<b>set </b><font color="Maroon" title="c10">cH</font> = 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="c6">Z</font></span>)</span>;<br/>
<b>set </b><font color="Maroon" title="c11">IG</font> = the <a href="orders_2.html#U1" title="ORDERS_2:sel.1">InternalRel</a> of <font color="Maroon" title="c1">G</font>;<br/>
<b>set </b><font color="Maroon" title="c12">X</font> = <span class="p1"><a href="enumset1.html#K6" title="ENUMSET1:func.6">{</a><span class="default"><span class="p2"><a href="domain_1.html#K1" title="DOMAIN_1:func.1">[</a><span class="default"><font color="Maroon" title="c2">a</font>,<font color="Maroon" title="c2">a</font></span><a href="domain_1.html#K1" title="DOMAIN_1:func.1">]</a></span>,<span class="p2"><a href="domain_1.html#K1" title="DOMAIN_1:func.1">[</a><span class="default"><font color="Maroon" title="c2">a</font>,<font color="Maroon" title="c3">b</font></span><a href="domain_1.html#K1" title="DOMAIN_1:func.1">]</a></span>,<span class="p2"><a href="domain_1.html#K1" title="DOMAIN_1:func.1">[</a><span class="default"><font color="Maroon" title="c3">b</font>,<font color="Maroon" title="c2">a</font></span><a href="domain_1.html#K1" title="DOMAIN_1:func.1">]</a></span>,<span class="p2"><a href="domain_1.html#K1" title="DOMAIN_1:func.1">[</a><span class="default"><font color="Maroon" title="c3">b</font>,<font color="Maroon" title="c3">b</font></span><a href="domain_1.html#K1" title="DOMAIN_1:func.1">]</a></span>,<span class="p2"><a href="domain_1.html#K1" title="DOMAIN_1:func.1">[</a><span class="default"><font color="Maroon" title="c2">a</font>,<font color="Maroon" title="c4">c</font></span><a href="domain_1.html#K1" title="DOMAIN_1:func.1">]</a></span>,<span class="p2"><a href="domain_1.html#K1" title="DOMAIN_1:func.1">[</a><span class="default"><font color="Maroon" title="c2">a</font>,<font color="Maroon" title="c5">d</font></span><a href="domain_1.html#K1" title="DOMAIN_1:func.1">]</a></span>,<span class="p2"><a href="domain_1.html#K1" title="DOMAIN_1:func.1">[</a><span class="default"><font color="Maroon" title="c3">b</font>,<font color="Maroon" title="c4">c</font></span><a href="domain_1.html#K1" title="DOMAIN_1:func.1">]</a></span>,<span class="p2"><a href="domain_1.html#K1" title="DOMAIN_1:func.1">[</a><span class="default"><font color="Maroon" title="c3">b</font>,<font color="Maroon" title="c5">d</font></span><a href="domain_1.html#K1" title="DOMAIN_1:func.1">]</a></span></span><a href="enumset1.html#K6" title="ENUMSET1:func.6">}</a></span>;<br/>
<b>set </b><font color="Maroon" title="c13">Y</font> = <span class="p1"><a href="enumset1.html#K6" title="ENUMSET1:func.6">{</a><span class="default"><span class="p2"><a href="domain_1.html#K1" title="DOMAIN_1:func.1">[</a><span class="default"><font color="Maroon" title="c4">c</font>,<font color="Maroon" title="c2">a</font></span><a href="domain_1.html#K1" title="DOMAIN_1:func.1">]</a></span>,<span class="p2"><a href="domain_1.html#K1" title="DOMAIN_1:func.1">[</a><span class="default"><font color="Maroon" title="c4">c</font>,<font color="Maroon" title="c3">b</font></span><a href="domain_1.html#K1" title="DOMAIN_1:func.1">]</a></span>,<span class="p2"><a href="domain_1.html#K1" title="DOMAIN_1:func.1">[</a><span class="default"><font color="Maroon" title="c5">d</font>,<font color="Maroon" title="c2">a</font></span><a href="domain_1.html#K1" title="DOMAIN_1:func.1">]</a></span>,<span class="p2"><a href="domain_1.html#K1" title="DOMAIN_1:func.1">[</a><span class="default"><font color="Maroon" title="c5">d</font>,<font color="Maroon" title="c3">b</font></span><a href="domain_1.html#K1" title="DOMAIN_1:func.1">]</a></span>,<span class="p2"><a href="domain_1.html#K1" title="DOMAIN_1:func.1">[</a><span class="default"><font color="Maroon" title="c4">c</font>,<font color="Maroon" title="c4">c</font></span><a href="domain_1.html#K1" title="DOMAIN_1:func.1">]</a></span>,<span class="p2"><a href="domain_1.html#K1" title="DOMAIN_1:func.1">[</a><span class="default"><font color="Maroon" title="c4">c</font>,<font color="Maroon" title="c5">d</font></span><a href="domain_1.html#K1" title="DOMAIN_1:func.1">]</a></span>,<span class="p2"><a href="domain_1.html#K1" title="DOMAIN_1:func.1">[</a><span class="default"><font color="Maroon" title="c5">d</font>,<font color="Maroon" title="c4">c</font></span><a href="domain_1.html#K1" title="DOMAIN_1:func.1">]</a></span>,<span class="p2"><a href="domain_1.html#K1" title="DOMAIN_1:func.1">[</a><span class="default"><font color="Maroon" title="c5">d</font>,<font color="Maroon" title="c5">d</font></span><a href="domain_1.html#K1" title="DOMAIN_1:func.1">]</a></span></span><a href="enumset1.html#K6" title="ENUMSET1:func.6">}</a></span>;<br/>
<a NAME="E9:60"/><i><font color="Green" title="E44">A9</font></i>: 
the <a href="orders_2.html#U1" title="ORDERS_2:sel.1">InternalRel</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="c6">Z</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1"><a href="enumset1.html#K4" title="ENUMSET1:func.4">{</a><span class="default"><span class="p2"><a href="domain_1.html#K1" title="DOMAIN_1:func.1">[</a><span class="default"><font color="Maroon" title="c2">a</font>,<font color="Maroon" title="c3">b</font></span><a href="domain_1.html#K1" title="DOMAIN_1:func.1">]</a></span>,<span class="p2"><a href="domain_1.html#K1" title="DOMAIN_1:func.1">[</a><span class="default"><font color="Maroon" title="c3">b</font>,<font color="Maroon" title="c2">a</font></span><a href="domain_1.html#K1" title="DOMAIN_1:func.1">]</a></span>,<span class="p2"><a href="domain_1.html#K1" title="DOMAIN_1:func.1">[</a><span class="default"><font color="Maroon" title="c3">b</font>,<font color="Maroon" title="c4">c</font></span><a href="domain_1.html#K1" title="DOMAIN_1:func.1">]</a></span>,<span class="p2"><a href="domain_1.html#K1" title="DOMAIN_1:func.1">[</a><span class="default"><font color="Maroon" title="c4">c</font>,<font color="Maroon" title="c3">b</font></span><a href="domain_1.html#K1" title="DOMAIN_1:func.1">]</a></span>,<span class="p2"><a href="domain_1.html#K1" title="DOMAIN_1:func.1">[</a><span class="default"><font color="Maroon" title="c4">c</font>,<font color="Maroon" title="c5">d</font></span><a href="domain_1.html#K1" title="DOMAIN_1:func.1">]</a></span>,<span class="p2"><a href="domain_1.html#K1" title="DOMAIN_1:func.1">[</a><span class="default"><font color="Maroon" title="c5">d</font>,<font color="Maroon" title="c4">c</font></span><a href="domain_1.html#K1" title="DOMAIN_1:func.1">]</a></span></span><a href="enumset1.html#K4" title="ENUMSET1:func.4">}</a></span>
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="60_1"><b>proof </b></a><div class="add">

<b>thus </b><a NAME="E1:60_1"/>
the <a href="orders_2.html#U1" title="ORDERS_2:sel.1">InternalRel</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="c6">Z</font></span>)</span> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <span class="p1"><a href="enumset1.html#K4" title="ENUMSET1:func.4">{</a><span class="default"><span class="p2"><a href="domain_1.html#K1" title="DOMAIN_1:func.1">[</a><span class="default"><font color="Maroon" title="c2">a</font>,<font color="Maroon" title="c3">b</font></span><a href="domain_1.html#K1" title="DOMAIN_1:func.1">]</a></span>,<span class="p2"><a href="domain_1.html#K1" title="DOMAIN_1:func.1">[</a><span class="default"><font color="Maroon" title="c3">b</font>,<font color="Maroon" title="c2">a</font></span><a href="domain_1.html#K1" title="DOMAIN_1:func.1">]</a></span>,<span class="p2"><a href="domain_1.html#K1" title="DOMAIN_1:func.1">[</a><span class="default"><font color="Maroon" title="c3">b</font>,<font color="Maroon" title="c4">c</font></span><a href="domain_1.html#K1" title="DOMAIN_1:func.1">]</a></span>,<span class="p2"><a href="domain_1.html#K1" title="DOMAIN_1:func.1">[</a><span class="default"><font color="Maroon" title="c4">c</font>,<font color="Maroon" title="c3">b</font></span><a href="domain_1.html#K1" title="DOMAIN_1:func.1">]</a></span>,<span class="p2"><a href="domain_1.html#K1" title="DOMAIN_1:func.1">[</a><span class="default"><font color="Maroon" title="c4">c</font>,<font color="Maroon" title="c5">d</font></span><a href="domain_1.html#K1" title="DOMAIN_1:func.1">]</a></span>,<span class="p2"><a href="domain_1.html#K1" title="DOMAIN_1:func.1">[</a><span class="default"><font color="Maroon" title="c5">d</font>,<font color="Maroon" title="c4">c</font></span><a href="domain_1.html#K1" title="DOMAIN_1:func.1">]</a></span></span><a href="enumset1.html#K4" title="ENUMSET1:func.4">}</a></span>
  <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="60_1_1"><b>proof </b></a><div class="add">

<b>let </b><font color="Maroon" title="c14">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="E1:60_1_1"/>
<font color="Maroon" title="c14">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> the <a href="orders_2.html#U1" title="ORDERS_2:sel.1">InternalRel</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="c6">Z</font></span>)</span>
 ;<br/>

<a NAME="E2:60_1_1"/><b>then </b>
<font color="Maroon" title="c14">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> the <a href="orders_2.html#U1" title="ORDERS_2:sel.1">InternalRel</a> of <font color="Maroon" title="c1">G</font> <a href="wellord1.html#K2" title="WELLORD1:func.2">|_2</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="c6">Z</font></span>)</span>
 
<b>by </b><i><a class="ref" href="yellow_0.html#D14" title="YELLOW_0:def.14">YELLOW_0:def 14</a></i>;<br/>
<a NAME="E3:60_1_1"/><b>then </b><i><font color="Green" title="E45">A10</font></i>: 
<font color="Maroon" title="c14">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> the <a href="orders_2.html#U1" title="ORDERS_2:sel.1">InternalRel</a> of <font color="Maroon" title="c1">G</font> <a href="subset_1.html#K8" title="SUBSET_1:func.8">/\</a> <span class="p1"><a href="zfmisc_1.html#K2" title="ZFMISC_1:func.2">[:</a><span class="default">the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <span class="p2">(<span class="default"><a href="yellow_0.html#K5" title="YELLOW_0:func.5">subrelstr</a> <font color="Maroon" title="c6">Z</font></span>)</span>,the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <span class="p2">(<span class="default"><a href="yellow_0.html#K5" title="YELLOW_0:func.5">subrelstr</a> <font color="Maroon" title="c6">Z</font></span>)</span></span><a href="zfmisc_1.html#K2" title="ZFMISC_1:func.2">:]</a></span>
 
;<br/>
<a NAME="E4:60_1_1"/><b>then </b><i><font color="Green" title="E46">A11</font></i>: 
( <font color="Maroon" title="c14">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> the <a href="orders_2.html#U1" title="ORDERS_2:sel.1">InternalRel</a> of <font color="Maroon" title="c1">G</font> &amp; <font color="Maroon" title="c14">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <span class="p1"><a href="zfmisc_1.html#K2" title="ZFMISC_1:func.2">[:</a><span class="default">the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <span class="p2">(<span class="default"><a href="yellow_0.html#K5" title="YELLOW_0:func.5">subrelstr</a> <font color="Maroon" title="c6">Z</font></span>)</span>,the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <span class="p2">(<span class="default"><a href="yellow_0.html#K5" title="YELLOW_0:func.5">subrelstr</a> <font color="Maroon" title="c6">Z</font></span>)</span></span><a href="zfmisc_1.html#K2" title="ZFMISC_1:func.2">:]</a></span> )
 
<b>by </b><i><a class="ref" href="xboole_0.html#D3" title="XBOOLE_0:def.3">XBOOLE_0:def 3</a></i>;<br/>
<a NAME="E5:60_1_1"/>
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="c6">Z</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c6">Z</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="E6:60_1_1"/><b>then </b><i><font color="Green" title="E47">A12</font></i>: 
<font color="Maroon" title="c14">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <span class="p1"><a href="enumset1.html#K6" title="ENUMSET1:func.6">{</a><span class="default"><span class="p2"><a href="domain_1.html#K1" title="DOMAIN_1:func.1">[</a><span class="default"><font color="Maroon" title="c2">a</font>,<font color="Maroon" title="c2">a</font></span><a href="domain_1.html#K1" title="DOMAIN_1:func.1">]</a></span>,<span class="p2"><a href="domain_1.html#K1" title="DOMAIN_1:func.1">[</a><span class="default"><font color="Maroon" title="c2">a</font>,<font color="Maroon" title="c3">b</font></span><a href="domain_1.html#K1" title="DOMAIN_1:func.1">]</a></span>,<span class="p2"><a href="domain_1.html#K1" title="DOMAIN_1:func.1">[</a><span class="default"><font color="Maroon" title="c3">b</font>,<font color="Maroon" title="c2">a</font></span><a href="domain_1.html#K1" title="DOMAIN_1:func.1">]</a></span>,<span class="p2"><a href="domain_1.html#K1" title="DOMAIN_1:func.1">[</a><span class="default"><font color="Maroon" title="c3">b</font>,<font color="Maroon" title="c3">b</font></span><a href="domain_1.html#K1" title="DOMAIN_1:func.1">]</a></span>,<span class="p2"><a href="domain_1.html#K1" title="DOMAIN_1:func.1">[</a><span class="default"><font color="Maroon" title="c2">a</font>,<font color="Maroon" title="c4">c</font></span><a href="domain_1.html#K1" title="DOMAIN_1:func.1">]</a></span>,<span class="p2"><a href="domain_1.html#K1" title="DOMAIN_1:func.1">[</a><span class="default"><font color="Maroon" title="c2">a</font>,<font color="Maroon" title="c5">d</font></span><a href="domain_1.html#K1" title="DOMAIN_1:func.1">]</a></span>,<span class="p2"><a href="domain_1.html#K1" title="DOMAIN_1:func.1">[</a><span class="default"><font color="Maroon" title="c3">b</font>,<font color="Maroon" title="c4">c</font></span><a href="domain_1.html#K1" title="DOMAIN_1:func.1">]</a></span>,<span class="p2"><a href="domain_1.html#K1" title="DOMAIN_1:func.1">[</a><span class="default"><font color="Maroon" title="c3">b</font>,<font color="Maroon" title="c5">d</font></span><a href="domain_1.html#K1" title="DOMAIN_1:func.1">]</a></span></span><a href="enumset1.html#K6" title="ENUMSET1:func.6">}</a></span> <a href="xboole_0.html#K2" title="XBOOLE_0:func.2">\/</a> <span class="p1"><a href="enumset1.html#K6" title="ENUMSET1:func.6">{</a><span class="default"><span class="p2"><a href="domain_1.html#K1" title="DOMAIN_1:func.1">[</a><span class="default"><font color="Maroon" title="c4">c</font>,<font color="Maroon" title="c2">a</font></span><a href="domain_1.html#K1" title="DOMAIN_1:func.1">]</a></span>,<span class="p2"><a href="domain_1.html#K1" title="DOMAIN_1:func.1">[</a><span class="default"><font color="Maroon" title="c4">c</font>,<font color="Maroon" title="c3">b</font></span><a href="domain_1.html#K1" title="DOMAIN_1:func.1">]</a></span>,<span class="p2"><a href="domain_1.html#K1" title="DOMAIN_1:func.1">[</a><span class="default"><font color="Maroon" title="c5">d</font>,<font color="Maroon" title="c2">a</font></span><a href="domain_1.html#K1" title="DOMAIN_1:func.1">]</a></span>,<span class="p2"><a href="domain_1.html#K1" title="DOMAIN_1:func.1">[</a><span class="default"><font color="Maroon" title="c5">d</font>,<font color="Maroon" title="c3">b</font></span><a href="domain_1.html#K1" title="DOMAIN_1:func.1">]</a></span>,<span class="p2"><a href="domain_1.html#K1" title="DOMAIN_1:func.1">[</a><span class="default"><font color="Maroon" title="c4">c</font>,<font color="Maroon" title="c4">c</font></span><a href="domain_1.html#K1" title="DOMAIN_1:func.1">]</a></span>,<span class="p2"><a href="domain_1.html#K1" title="DOMAIN_1:func.1">[</a><span class="default"><font color="Maroon" title="c4">c</font>,<font color="Maroon" title="c5">d</font></span><a href="domain_1.html#K1" title="DOMAIN_1:func.1">]</a></span>,<span class="p2"><a href="domain_1.html#K1" title="DOMAIN_1:func.1">[</a><span class="default"><font color="Maroon" title="c5">d</font>,<font color="Maroon" title="c4">c</font></span><a href="domain_1.html#K1" title="DOMAIN_1:func.1">]</a></span>,<span class="p2"><a href="domain_1.html#K1" title="DOMAIN_1:func.1">[</a><span class="default"><font color="Maroon" title="c5">d</font>,<font color="Maroon" title="c5">d</font></span><a href="domain_1.html#K1" title="DOMAIN_1:func.1">]</a></span></span><a href="enumset1.html#K6" title="ENUMSET1:func.6">}</a></span>
 
<b>by </b><i><a class="txt" href="neckla_3.html#E1:60"><i><font color="Green" title="E36">A1</font></i></a>, <a class="txt" href="neckla_3.html#E4:60_1_1"><i><font color="Green" title="E46">A11</font></i></a>, <a class="ref" href="neckla_3.html#T3" target="_self" title="NECKLA_3:th.3">Th3</a></i>;<br/>
<div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="60_1_1_1"><b>per </b></a><a class="txt" onclick="hs(this)" href="javascript:()"><b>cases </b></a><span class="hide"><a NAME="E1:60_1_1_1"/>
( <font color="Maroon" title="c14">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <span class="p1"><a href="enumset1.html#K6" title="ENUMSET1:func.6">{</a><span class="default"><span class="p2"><a href="domain_1.html#K1" title="DOMAIN_1:func.1">[</a><span class="default"><font color="Maroon" title="c2">a</font>,<font color="Maroon" title="c2">a</font></span><a href="domain_1.html#K1" title="DOMAIN_1:func.1">]</a></span>,<span class="p2"><a href="domain_1.html#K1" title="DOMAIN_1:func.1">[</a><span class="default"><font color="Maroon" title="c2">a</font>,<font color="Maroon" title="c3">b</font></span><a href="domain_1.html#K1" title="DOMAIN_1:func.1">]</a></span>,<span class="p2"><a href="domain_1.html#K1" title="DOMAIN_1:func.1">[</a><span class="default"><font color="Maroon" title="c3">b</font>,<font color="Maroon" title="c2">a</font></span><a href="domain_1.html#K1" title="DOMAIN_1:func.1">]</a></span>,<span class="p2"><a href="domain_1.html#K1" title="DOMAIN_1:func.1">[</a><span class="default"><font color="Maroon" title="c3">b</font>,<font color="Maroon" title="c3">b</font></span><a href="domain_1.html#K1" title="DOMAIN_1:func.1">]</a></span>,<span class="p2"><a href="domain_1.html#K1" title="DOMAIN_1:func.1">[</a><span class="default"><font color="Maroon" title="c2">a</font>,<font color="Maroon" title="c4">c</font></span><a href="domain_1.html#K1" title="DOMAIN_1:func.1">]</a></span>,<span class="p2"><a href="domain_1.html#K1" title="DOMAIN_1:func.1">[</a><span class="default"><font color="Maroon" title="c2">a</font>,<font color="Maroon" title="c5">d</font></span><a href="domain_1.html#K1" title="DOMAIN_1:func.1">]</a></span>,<span class="p2"><a href="domain_1.html#K1" title="DOMAIN_1:func.1">[</a><span class="default"><font color="Maroon" title="c3">b</font>,<font color="Maroon" title="c4">c</font></span><a href="domain_1.html#K1" title="DOMAIN_1:func.1">]</a></span>,<span class="p2"><a href="domain_1.html#K1" title="DOMAIN_1:func.1">[</a><span class="default"><font color="Maroon" title="c3">b</font>,<font color="Maroon" title="c5">d</font></span><a href="domain_1.html#K1" title="DOMAIN_1:func.1">]</a></span></span><a href="enumset1.html#K6" title="ENUMSET1:func.6">}</a></span> or <font color="Maroon" title="c14">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <span class="p1"><a href="enumset1.html#K6" title="ENUMSET1:func.6">{</a><span class="default"><span class="p2"><a href="domain_1.html#K1" title="DOMAIN_1:func.1">[</a><span class="default"><font color="Maroon" title="c4">c</font>,<font color="Maroon" title="c2">a</font></span><a href="domain_1.html#K1" title="DOMAIN_1:func.1">]</a></span>,<span class="p2"><a href="domain_1.html#K1" title="DOMAIN_1:func.1">[</a><span class="default"><font color="Maroon" title="c4">c</font>,<font color="Maroon" title="c3">b</font></span><a href="domain_1.html#K1" title="DOMAIN_1:func.1">]</a></span>,<span class="p2"><a href="domain_1.html#K1" title="DOMAIN_1:func.1">[</a><span class="default"><font color="Maroon" title="c5">d</font>,<font color="Maroon" title="c2">a</font></span><a href="domain_1.html#K1" title="DOMAIN_1:func.1">]</a></span>,<span class="p2"><a href="domain_1.html#K1" title="DOMAIN_1:func.1">[</a><span class="default"><font color="Maroon" title="c5">d</font>,<font color="Maroon" title="c3">b</font></span><a href="domain_1.html#K1" title="DOMAIN_1:func.1">]</a></span>,<span class="p2"><a href="domain_1.html#K1" title="DOMAIN_1:func.1">[</a><span class="default"><font color="Maroon" title="c4">c</font>,<font color="Maroon" title="c4">c</font></span><a href="domain_1.html#K1" title="DOMAIN_1:func.1">]</a></span>,<span class="p2"><a href="domain_1.html#K1" title="DOMAIN_1:func.1">[</a><span class="default"><font color="Maroon" title="c4">c</font>,<font color="Maroon" title="c5">d</font></span><a href="domain_1.html#K1" title="DOMAIN_1:func.1">]</a></span>,<span class="p2"><a href="domain_1.html#K1" title="DOMAIN_1:func.1">[</a><span class="default"><font color="Maroon" title="c5">d</font>,<font color="Maroon" title="c4">c</font></span><a href="domain_1.html#K1" title="DOMAIN_1:func.1">]</a></span>,<span class="p2"><a href="domain_1.html#K1" title="DOMAIN_1:func.1">[</a><span class="default"><font color="Maroon" title="c5">d</font>,<font color="Maroon" title="c5">d</font></span><a href="domain_1.html#K1" title="DOMAIN_1:func.1">]</a></span></span><a href="enumset1.html#K6" title="ENUMSET1:func.6">}</a></span> )
 </span><b>by </b><i><a class="txt" href="neckla_3.html#E6:60_1_1"><i><font color="Green" title="E47">A12</font></i></a>, <a class="ref" href="xboole_0.html#D2" title="XBOOLE_0:def.2">XBOOLE_0:def 2</a></i>;<br/><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="60_1_1_1_1"><b>suppose </b></a><a NAME="E1:60_1_1_1_1"/><i><font color="Green" title="E48">A13</font></i>: 
<font color="Maroon" title="c14">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <span class="p1"><a href="enumset1.html#K6" title="ENUMSET1:func.6">{</a><span class="default"><span class="p2"><a href="domain_1.html#K1" title="DOMAIN_1:func.1">[</a><span class="default"><font color="Maroon" title="c2">a</font>,<font color="Maroon" title="c2">a</font></span><a href="domain_1.html#K1" title="DOMAIN_1:func.1">]</a></span>,<span class="p2"><a href="domain_1.html#K1" title="DOMAIN_1:func.1">[</a><span class="default"><font color="Maroon" title="c2">a</font>,<font color="Maroon" title="c3">b</font></span><a href="domain_1.html#K1" title="DOMAIN_1:func.1">]</a></span>,<span class="p2"><a href="domain_1.html#K1" title="DOMAIN_1:func.1">[</a><span class="default"><font color="Maroon" title="c3">b</font>,<font color="Maroon" title="c2">a</font></span><a href="domain_1.html#K1" title="DOMAIN_1:func.1">]</a></span>,<span class="p2"><a href="domain_1.html#K1" title="DOMAIN_1:func.1">[</a><span class="default"><font color="Maroon" title="c3">b</font>,<font color="Maroon" title="c3">b</font></span><a href="domain_1.html#K1" title="DOMAIN_1:func.1">]</a></span>,<span class="p2"><a href="domain_1.html#K1" title="DOMAIN_1:func.1">[</a><span class="default"><font color="Maroon" title="c2">a</font>,<font color="Maroon" title="c4">c</font></span><a href="domain_1.html#K1" title="DOMAIN_1:func.1">]</a></span>,<span class="p2"><a href="domain_1.html#K1" title="DOMAIN_1:func.1">[</a><span class="default"><font color="Maroon" title="c2">a</font>,<font color="Maroon" title="c5">d</font></span><a href="domain_1.html#K1" title="DOMAIN_1:func.1">]</a></span>,<span class="p2"><a href="domain_1.html#K1" title="DOMAIN_1:func.1">[</a><span class="default"><font color="Maroon" title="c3">b</font>,<font color="Maroon" title="c4">c</font></span><a href="domain_1.html#K1" title="DOMAIN_1:func.1">]</a></span>,<span class="p2"><a href="domain_1.html#K1" title="DOMAIN_1:func.1">[</a><span class="default"><font color="Maroon" title="c3">b</font>,<font color="Maroon" title="c5">d</font></span><a href="domain_1.html#K1" title="DOMAIN_1:func.1">]</a></span></span><a href="enumset1.html#K6" title="ENUMSET1:func.6">}</a></span>
 ;<br/><div class="add"><b>thus </b><a NAME="E2:60_1_1_1_1"/>
<font color="Maroon" title="c14">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <span class="p1"><a href="enumset1.html#K4" title="ENUMSET1:func.4">{</a><span class="default"><span class="p2"><a href="domain_1.html#K1" title="DOMAIN_1:func.1">[</a><span class="default"><font color="Maroon" title="c2">a</font>,<font color="Maroon" title="c3">b</font></span><a href="domain_1.html#K1" title="DOMAIN_1:func.1">]</a></span>,<span class="p2"><a href="domain_1.html#K1" title="DOMAIN_1:func.1">[</a><span class="default"><font color="Maroon" title="c3">b</font>,<font color="Maroon" title="c2">a</font></span><a href="domain_1.html#K1" title="DOMAIN_1:func.1">]</a></span>,<span class="p2"><a href="domain_1.html#K1" title="DOMAIN_1:func.1">[</a><span class="default"><font color="Maroon" title="c3">b</font>,<font color="Maroon" title="c4">c</font></span><a href="domain_1.html#K1" title="DOMAIN_1:func.1">]</a></span>,<span class="p2"><a href="domain_1.html#K1" title="DOMAIN_1:func.1">[</a><span class="default"><font color="Maroon" title="c4">c</font>,<font color="Maroon" title="c3">b</font></span><a href="domain_1.html#K1" title="DOMAIN_1:func.1">]</a></span>,<span class="p2"><a href="domain_1.html#K1" title="DOMAIN_1:func.1">[</a><span class="default"><font color="Maroon" title="c4">c</font>,<font color="Maroon" title="c5">d</font></span><a href="domain_1.html#K1" title="DOMAIN_1:func.1">]</a></span>,<span class="p2"><a href="domain_1.html#K1" title="DOMAIN_1:func.1">[</a><span class="default"><font color="Maroon" title="c5">d</font>,<font color="Maroon" title="c4">c</font></span><a href="domain_1.html#K1" title="DOMAIN_1:func.1">]</a></span></span><a href="enumset1.html#K4" title="ENUMSET1:func.4">}</a></span>
 <div><a class="txt" onclick="hs2(this)" href="javascript:()" title="60_1_1_1_1_1"><b>proof </b></a><div class="add">

<div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="60_1_1_1_1_1_1"><b>per </b></a><a class="txt" onclick="hs(this)" href="javascript:()"><b>cases </b></a><span class="hide"><a NAME="E1:60_1_1_1_1_1_1"/>
( <font color="Maroon" title="c14">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1"><a href="domain_1.html#K1" title="DOMAIN_1:func.1">[</a><span class="default"><font color="Maroon" title="c2">a</font>,<font color="Maroon" title="c2">a</font></span><a href="domain_1.html#K1" title="DOMAIN_1:func.1">]</a></span> or <font color="Maroon" title="c14">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1"><a href="domain_1.html#K1" title="DOMAIN_1:func.1">[</a><span class="default"><font color="Maroon" title="c2">a</font>,<font color="Maroon" title="c3">b</font></span><a href="domain_1.html#K1" title="DOMAIN_1:func.1">]</a></span> or <font color="Maroon" title="c14">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1"><a href="domain_1.html#K1" title="DOMAIN_1:func.1">[</a><span class="default"><font color="Maroon" title="c3">b</font>,<font color="Maroon" title="c2">a</font></span><a href="domain_1.html#K1" title="DOMAIN_1:func.1">]</a></span> or <font color="Maroon" title="c14">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1"><a href="domain_1.html#K1" title="DOMAIN_1:func.1">[</a><span class="default"><font color="Maroon" title="c3">b</font>,<font color="Maroon" title="c3">b</font></span><a href="domain_1.html#K1" title="DOMAIN_1:func.1">]</a></span> or <font color="Maroon" title="c14">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1"><a href="domain_1.html#K1" title="DOMAIN_1:func.1">[</a><span class="default"><font color="Maroon" title="c2">a</font>,<font color="Maroon" title="c4">c</font></span><a href="domain_1.html#K1" title="DOMAIN_1:func.1">]</a></span> or <font color="Maroon" title="c14">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1"><a href="domain_1.html#K1" title="DOMAIN_1:func.1">[</a><span class="default"><font color="Maroon" title="c2">a</font>,<font color="Maroon" title="c5">d</font></span><a href="domain_1.html#K1" title="DOMAIN_1:func.1">]</a></span> or <font color="Maroon" title="c14">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1"><a href="domain_1.html#K1" title="DOMAIN_1:func.1">[</a><span class="default"><font color="Maroon" title="c3">b</font>,<font color="Maroon" title="c4">c</font></span><a href="domain_1.html#K1" title="DOMAIN_1:func.1">]</a></span> or <font color="Maroon" title="c14">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1"><a href="domain_1.html#K1" title="DOMAIN_1:func.1">[</a><span class="default"><font color="Maroon" title="c3">b</font>,<font color="Maroon" title="c5">d</font></span><a href="domain_1.html#K1" title="DOMAIN_1:func.1">]</a></span> )
 </span><b>by </b><i><a class="txt" href="neckla_3.html#E1:60_1_1_1_1"><i><font color="Green" title="E48">A13</font></i></a>, <a class="ref" href="enumset1.html#D6" title="ENUMSET1:def.6">ENUMSET1:def 6</a></i>;<br/><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="60_1_1_1_1_1_1_1"><b>suppose </b></a><a NAME="E1:60_1_1_1_1_1_1_1"/><i><font color="Green" title="E49">A14</font></i>: 
<font color="Maroon" title="c14">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1"><a href="domain_1.html#K1" title="DOMAIN_1:func.1">[</a><span class="default"><font color="Maroon" title="c2">a</font>,<font color="Maroon" title="c2">a</font></span><a href="domain_1.html#K1" title="DOMAIN_1:func.1">]</a></span>
 ;<br/><div class="add"><a NAME="E2:60_1_1_1_1_1_1_1"/>
not <span class="p1"><a href="domain_1.html#K1" title="DOMAIN_1:func.1">[</a><span class="default"><font color="Maroon" title="c2">a</font>,<font color="Maroon" title="c2">a</font></span><a href="domain_1.html#K1" title="DOMAIN_1:func.1">]</a></span> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> the <a href="orders_2.html#U1" title="ORDERS_2:sel.1">InternalRel</a> of <font color="Maroon" title="c1">G</font>
 <b>by </b><i><a class="ref" href="necklace.html#D6" title="NECKLACE:def.6">NECKLACE:def 6</a></i>;<br/><b>hence </b><a NAME="E3:60_1_1_1_1_1_1_1"/>
<font color="Maroon" title="c14">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <span class="p1"><a href="enumset1.html#K4" title="ENUMSET1:func.4">{</a><span class="default"><span class="p2"><a href="domain_1.html#K1" title="DOMAIN_1:func.1">[</a><span class="default"><font color="Maroon" title="c2">a</font>,<font color="Maroon" title="c3">b</font></span><a href="domain_1.html#K1" title="DOMAIN_1:func.1">]</a></span>,<span class="p2"><a href="domain_1.html#K1" title="DOMAIN_1:func.1">[</a><span class="default"><font color="Maroon" title="c3">b</font>,<font color="Maroon" title="c2">a</font></span><a href="domain_1.html#K1" title="DOMAIN_1:func.1">]</a></span>,<span class="p2"><a href="domain_1.html#K1" title="DOMAIN_1:func.1">[</a><span class="default"><font color="Maroon" title="c3">b</font>,<font color="Maroon" title="c4">c</font></span><a href="domain_1.html#K1" title="DOMAIN_1:func.1">]</a></span>,<span class="p2"><a href="domain_1.html#K1" title="DOMAIN_1:func.1">[</a><span class="default"><font color="Maroon" title="c4">c</font>,<font color="Maroon" title="c3">b</font></span><a href="domain_1.html#K1" title="DOMAIN_1:func.1">]</a></span>,<span class="p2"><a href="domain_1.html#K1" title="DOMAIN_1:func.1">[</a><span class="default"><font color="Maroon" title="c4">c</font>,<font color="Maroon" title="c5">d</font></span><a href="domain_1.html#K1" title="DOMAIN_1:func.1">]</a></span>,<span class="p2"><a href="domain_1.html#K1" title="DOMAIN_1:func.1">[</a><span class="default"><font color="Maroon" title="c5">d</font>,<font color="Maroon" title="c4">c</font></span><a href="domain_1.html#K1" title="DOMAIN_1:func.1">]</a></span></span><a href="enumset1.html#K4" title="ENUMSET1:func.4">}</a></span>
 <b>by </b><i><a class="txt" href="neckla_3.html#E3:60_1_1"><i><font color="Green" title="E45">A10</font></i></a>, <a class="txt" href="neckla_3.html#E1:60_1_1_1_1_1_1_1"><i><font color="Green" title="E49">A14</font></i></a>, <a class="ref" href="xboole_0.html#D3" title="XBOOLE_0:def.3">XBOOLE_0:def 3</a></i>;<br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="60_1_1_1_1_1_1_2"><b>suppose </b></a><a NAME="E1:60_1_1_1_1_1_1_2"/>
<font color="Maroon" title="c14">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1"><a href="domain_1.html#K1" title="DOMAIN_1:func.1">[</a><span class="default"><font color="Maroon" title="c2">a</font>,<font color="Maroon" title="c3">b</font></span><a href="domain_1.html#K1" title="DOMAIN_1:func.1">]</a></span>
 ;<br/><div class="add"><b>hence </b><a NAME="E2:60_1_1_1_1_1_1_2"/>
<font color="Maroon" title="c14">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <span class="p1"><a href="enumset1.html#K4" title="ENUMSET1:func.4">{</a><span class="default"><span class="p2"><a href="domain_1.html#K1" title="DOMAIN_1:func.1">[</a><span class="default"><font color="Maroon" title="c2">a</font>,<font color="Maroon" title="c3">b</font></span><a href="domain_1.html#K1" title="DOMAIN_1:func.1">]</a></span>,<span class="p2"><a href="domain_1.html#K1" title="DOMAIN_1:func.1">[</a><span class="default"><font color="Maroon" title="c3">b</font>,<font color="Maroon" title="c2">a</font></span><a href="domain_1.html#K1" title="DOMAIN_1:func.1">]</a></span>,<span class="p2"><a href="domain_1.html#K1" title="DOMAIN_1:func.1">[</a><span class="default"><font color="Maroon" title="c3">b</font>,<font color="Maroon" title="c4">c</font></span><a href="domain_1.html#K1" title="DOMAIN_1:func.1">]</a></span>,<span class="p2"><a href="domain_1.html#K1" title="DOMAIN_1:func.1">[</a><span class="default"><font color="Maroon" title="c4">c</font>,<font color="Maroon" title="c3">b</font></span><a href="domain_1.html#K1" title="DOMAIN_1:func.1">]</a></span>,<span class="p2"><a href="domain_1.html#K1" title="DOMAIN_1:func.1">[</a><span class="default"><font color="Maroon" title="c4">c</font>,<font color="Maroon" title="c5">d</font></span><a href="domain_1.html#K1" title="DOMAIN_1:func.1">]</a></span>,<span class="p2"><a href="domain_1.html#K1" title="DOMAIN_1:func.1">[</a><span class="default"><font color="Maroon" title="c5">d</font>,<font color="Maroon" title="c4">c</font></span><a href="domain_1.html#K1" title="DOMAIN_1:func.1">]</a></span></span><a href="enumset1.html#K4" title="ENUMSET1:func.4">}</a></span>
 <b>by </b><i><a class="ref" href="enumset1.html#D4" title="ENUMSET1:def.4">ENUMSET1:def 4</a></i>;<br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="60_1_1_1_1_1_1_3"><b>suppose </b></a><a NAME="E1:60_1_1_1_1_1_1_3"/>
<font color="Maroon" title="c14">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1"><a href="domain_1.html#K1" title="DOMAIN_1:func.1">[</a><span class="default"><font color="Maroon" title="c3">b</font>,<font color="Maroon" title="c2">a</font></span><a href="domain_1.html#K1" title="DOMAIN_1:func.1">]</a></span>
 ;<br/><div class="add"><b>hence </b><a NAME="E2:60_1_1_1_1_1_1_3"/>
<font color="Maroon" title="c14">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <span class="p1"><a href="enumset1.html#K4" title="ENUMSET1:func.4">{</a><span class="default"><span class="p2"><a href="domain_1.html#K1" title="DOMAIN_1:func.1">[</a><span class="default"><font color="Maroon" title="c2">a</font>,<font color="Maroon" title="c3">b</font></span><a href="domain_1.html#K1" title="DOMAIN_1:func.1">]</a></span>,<span class="p2"><a href="domain_1.html#K1" title="DOMAIN_1:func.1">[</a><span class="default"><font color="Maroon" title="c3">b</font>,<font color="Maroon" title="c2">a</font></span><a href="domain_1.html#K1" title="DOMAIN_1:func.1">]</a></span>,<span class="p2"><a href="domain_1.html#K1" title="DOMAIN_1:func.1">[</a><span class="default"><font color="Maroon" title="c3">b</font>,<font color="Maroon" title="c4">c</font></span><a href="domain_1.html#K1" title="DOMAIN_1:func.1">]</a></span>,<span class="p2"><a href="domain_1.html#K1" title="DOMAIN_1:func.1">[</a><span class="default"><font color="Maroon" title="c4">c</font>,<font color="Maroon" title="c3">b</font></span><a href="domain_1.html#K1" title="DOMAIN_1:func.1">]</a></span>,<span class="p2"><a href="domain_1.html#K1" title="DOMAIN_1:func.1">[</a><span class="default"><font color="Maroon" title="c4">c</font>,<font color="Maroon" title="c5">d</font></span><a href="domain_1.html#K1" title="DOMAIN_1:func.1">]</a></span>,<span class="p2"><a href="domain_1.html#K1" title="DOMAIN_1:func.1">[</a><span class="default"><font color="Maroon" title="c5">d</font>,<font color="Maroon" title="c4">c</font></span><a href="domain_1.html#K1" title="DOMAIN_1:func.1">]</a></span></span><a href="enumset1.html#K4" title="ENUMSET1:func.4">}</a></span>
 <b>by </b><i><a class="ref" href="enumset1.html#D4" title="ENUMSET1:def.4">ENUMSET1:def 4</a></i>;<br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="60_1_1_1_1_1_1_4"><b>suppose </b></a><a NAME="E1:60_1_1_1_1_1_1_4"/><i><font color="Green" title="E49">A15</font></i>: 
<font color="Maroon" title="c14">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1"><a href="domain_1.html#K1" title="DOMAIN_1:func.1">[</a><span class="default"><font color="Maroon" title="c3">b</font>,<font color="Maroon" title="c3">b</font></span><a href="domain_1.html#K1" title="DOMAIN_1:func.1">]</a></span>
 ;<br/><div class="add"><a NAME="E2:60_1_1_1_1_1_1_4"/>
not <span class="p1"><a href="domain_1.html#K1" title="DOMAIN_1:func.1">[</a><span class="default"><font color="Maroon" title="c3">b</font>,<font color="Maroon" title="c3">b</font></span><a href="domain_1.html#K1" title="DOMAIN_1:func.1">]</a></span> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> the <a href="orders_2.html#U1" title="ORDERS_2:sel.1">InternalRel</a> of <font color="Maroon" title="c1">G</font>
 <b>by </b><i><a class="ref" href="necklace.html#D6" title="NECKLACE:def.6">NECKLACE:def 6</a></i>;<br/><b>hence </b><a NAME="E3:60_1_1_1_1_1_1_4"/>
<font color="Maroon" title="c14">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <span class="p1"><a href="enumset1.html#K4" title="ENUMSET1:func.4">{</a><span class="default"><span class="p2"><a href="domain_1.html#K1" title="DOMAIN_1:func.1">[</a><span class="default"><font color="Maroon" title="c2">a</font>,<font color="Maroon" title="c3">b</font></span><a href="domain_1.html#K1" title="DOMAIN_1:func.1">]</a></span>,<span class="p2"><a href="domain_1.html#K1" title="DOMAIN_1:func.1">[</a><span class="default"><font color="Maroon" title="c3">b</font>,<font color="Maroon" title="c2">a</font></span><a href="domain_1.html#K1" title="DOMAIN_1:func.1">]</a></span>,<span class="p2"><a href="domain_1.html#K1" title="DOMAIN_1:func.1">[</a><span class="default"><font color="Maroon" title="c3">b</font>,<font color="Maroon" title="c4">c</font></span><a href="domain_1.html#K1" title="DOMAIN_1:func.1">]</a></span>,<span class="p2"><a href="domain_1.html#K1" title="DOMAIN_1:func.1">[</a><span class="default"><font color="Maroon" title="c4">c</font>,<font color="Maroon" title="c3">b</font></span><a href="domain_1.html#K1" title="DOMAIN_1:func.1">]</a></span>,<span class="p2"><a href="domain_1.html#K1" title="DOMAIN_1:func.1">[</a><span class="default"><font color="Maroon" title="c4">c</font>,<font color="Maroon" title="c5">d</font></span><a href="domain_1.html#K1" title="DOMAIN_1:func.1">]</a></span>,<span class="p2"><a href="domain_1.html#K1" title="DOMAIN_1:func.1">[</a><span class="default"><font color="Maroon" title="c5">d</font>,<font color="Maroon" title="c4">c</font></span><a href="domain_1.html#K1" title="DOMAIN_1:func.1">]</a></span></span><a href="enumset1.html#K4" title="ENUMSET1:func.4">}</a></span>
 <b>by </b><i><a class="txt" href="neckla_3.html#E3:60_1_1"><i><font color="Green" title="E45">A10</font></i></a>, <a class="txt" href="neckla_3.html#E1:60_1_1_1_1_1_1_4"><i><font color="Green" title="E49">A15</font></i></a>, <a class="ref" href="xboole_0.html#D3" title="XBOOLE_0:def.3">XBOOLE_0:def 3</a></i>;<br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="60_1_1_1_1_1_1_5"><b>suppose </b></a><a NAME="E1:60_1_1_1_1_1_1_5"/>
<font color="Maroon" title="c14">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1"><a href="domain_1.html#K1" title="DOMAIN_1:func.1">[</a><span class="default"><font color="Maroon" title="c2">a</font>,<font color="Maroon" title="c4">c</font></span><a href="domain_1.html#K1" title="DOMAIN_1:func.1">]</a></span>
 ;<br/><div class="add"><b>hence </b><a NAME="E2:60_1_1_1_1_1_1_5"/>
<font color="Maroon" title="c14">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <span class="p1"><a href="enumset1.html#K4" title="ENUMSET1:func.4">{</a><span class="default"><span class="p2"><a href="domain_1.html#K1" title="DOMAIN_1:func.1">[</a><span class="default"><font color="Maroon" title="c2">a</font>,<font color="Maroon" title="c3">b</font></span><a href="domain_1.html#K1" title="DOMAIN_1:func.1">]</a></span>,<span class="p2"><a href="domain_1.html#K1" title="DOMAIN_1:func.1">[</a><span class="default"><font color="Maroon" title="c3">b</font>,<font color="Maroon" title="c2">a</font></span><a href="domain_1.html#K1" title="DOMAIN_1:func.1">]</a></span>,<span class="p2"><a href="domain_1.html#K1" title="DOMAIN_1:func.1">[</a><span class="default"><font color="Maroon" title="c3">b</font>,<font color="Maroon" title="c4">c</font></span><a href="domain_1.html#K1" title="DOMAIN_1:func.1">]</a></span>,<span class="p2"><a href="domain_1.html#K1" title="DOMAIN_1:func.1">[</a><span class="default"><font color="Maroon" title="c4">c</font>,<font color="Maroon" title="c3">b</font></span><a href="domain_1.html#K1" title="DOMAIN_1:func.1">]</a></span>,<span class="p2"><a href="domain_1.html#K1" title="DOMAIN_1:func.1">[</a><span class="default"><font color="Maroon" title="c4">c</font>,<font color="Maroon" title="c5">d</font></span><a href="domain_1.html#K1" title="DOMAIN_1:func.1">]</a></span>,<span class="p2"><a href="domain_1.html#K1" title="DOMAIN_1:func.1">[</a><span class="default"><font color="Maroon" title="c5">d</font>,<font color="Maroon" title="c4">c</font></span><a href="domain_1.html#K1" title="DOMAIN_1:func.1">]</a></span></span><a href="enumset1.html#K4" title="ENUMSET1:func.4">}</a></span>
 <b>by </b><i><a class="txt" href="neckla_3.html#E6:60"><i><font color="Green" title="E41">A6</font></i></a>, <a class="txt" href="neckla_3.html#E3:60_1_1"><i><font color="Green" title="E45">A10</font></i></a>, <a class="ref" href="xboole_0.html#D3" title="XBOOLE_0:def.3">XBOOLE_0:def 3</a></i>;<br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="60_1_1_1_1_1_1_6"><b>suppose </b></a><a NAME="E1:60_1_1_1_1_1_1_6"/>
<font color="Maroon" title="c14">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1"><a href="domain_1.html#K1" title="DOMAIN_1:func.1">[</a><span class="default"><font color="Maroon" title="c2">a</font>,<font color="Maroon" title="c5">d</font></span><a href="domain_1.html#K1" title="DOMAIN_1:func.1">]</a></span>
 ;<br/><div class="add"><b>hence </b><a NAME="E2:60_1_1_1_1_1_1_6"/>
<font color="Maroon" title="c14">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <span class="p1"><a href="enumset1.html#K4" title="ENUMSET1:func.4">{</a><span class="default"><span class="p2"><a href="domain_1.html#K1" title="DOMAIN_1:func.1">[</a><span class="default"><font color="Maroon" title="c2">a</font>,<font color="Maroon" title="c3">b</font></span><a href="domain_1.html#K1" title="DOMAIN_1:func.1">]</a></span>,<span class="p2"><a href="domain_1.html#K1" title="DOMAIN_1:func.1">[</a><span class="default"><font color="Maroon" title="c3">b</font>,<font color="Maroon" title="c2">a</font></span><a href="domain_1.html#K1" title="DOMAIN_1:func.1">]</a></span>,<span class="p2"><a href="domain_1.html#K1" title="DOMAIN_1:func.1">[</a><span class="default"><font color="Maroon" title="c3">b</font>,<font color="Maroon" title="c4">c</font></span><a href="domain_1.html#K1" title="DOMAIN_1:func.1">]</a></span>,<span class="p2"><a href="domain_1.html#K1" title="DOMAIN_1:func.1">[</a><span class="default"><font color="Maroon" title="c4">c</font>,<font color="Maroon" title="c3">b</font></span><a href="domain_1.html#K1" title="DOMAIN_1:func.1">]</a></span>,<span class="p2"><a href="domain_1.html#K1" title="DOMAIN_1:func.1">[</a><span class="default"><font color="Maroon" title="c4">c</font>,<font color="Maroon" title="c5">d</font></span><a href="domain_1.html#K1" title="DOMAIN_1:func.1">]</a></span>,<span class="p2"><a href="domain_1.html#K1" title="DOMAIN_1:func.1">[</a><span class="default"><font color="Maroon" title="c5">d</font>,<font color="Maroon" title="c4">c</font></span><a href="domain_1.html#K1" title="DOMAIN_1:func.1">]</a></span></span><a href="enumset1.html#K4" title="ENUMSET1:func.4">}</a></span>
 <b>by </b><i><a class="txt" href="neckla_3.html#E7:60"><i><font color="Green" title="E42">A7</font></i></a>, <a class="txt" href="neckla_3.html#E3:60_1_1"><i><font color="Green" title="E45">A10</font></i></a>, <a class="ref" href="xboole_0.html#D3" title="XBOOLE_0:def.3">XBOOLE_0:def 3</a></i>;<br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="60_1_1_1_1_1_1_7"><b>suppose </b></a><a NAME="E1:60_1_1_1_1_1_1_7"/>
<font color="Maroon" title="c14">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1"><a href="domain_1.html#K1" title="DOMAIN_1:func.1">[</a><span class="default"><font color="Maroon" title="c3">b</font>,<font color="Maroon" title="c4">c</font></span><a href="domain_1.html#K1" title="DOMAIN_1:func.1">]</a></span>
 ;<br/><div class="add"><b>hence </b><a NAME="E2:60_1_1_1_1_1_1_7"/>
<font color="Maroon" title="c14">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <span class="p1"><a href="enumset1.html#K4" title="ENUMSET1:func.4">{</a><span class="default"><span class="p2"><a href="domain_1.html#K1" title="DOMAIN_1:func.1">[</a><span class="default"><font color="Maroon" title="c2">a</font>,<font color="Maroon" title="c3">b</font></span><a href="domain_1.html#K1" title="DOMAIN_1:func.1">]</a></span>,<span class="p2"><a href="domain_1.html#K1" title="DOMAIN_1:func.1">[</a><span class="default"><font color="Maroon" title="c3">b</font>,<font color="Maroon" title="c2">a</font></span><a href="domain_1.html#K1" title="DOMAIN_1:func.1">]</a></span>,<span class="p2"><a href="domain_1.html#K1" title="DOMAIN_1:func.1">[</a><span class="default"><font color="Maroon" title="c3">b</font>,<font color="Maroon" title="c4">c</font></span><a href="domain_1.html#K1" title="DOMAIN_1:func.1">]</a></span>,<span class="p2"><a href="domain_1.html#K1" title="DOMAIN_1:func.1">[</a><span class="default"><font color="Maroon" title="c4">c</font>,<font color="Maroon" title="c3">b</font></span><a href="domain_1.html#K1" title="DOMAIN_1:func.1">]</a></span>,<span class="p2"><a href="domain_1.html#K1" title="DOMAIN_1:func.1">[</a><span class="default"><font color="Maroon" title="c4">c</font>,<font color="Maroon" title="c5">d</font></span><a href="domain_1.html#K1" title="DOMAIN_1:func.1">]</a></span>,<span class="p2"><a href="domain_1.html#K1" title="DOMAIN_1:func.1">[</a><span class="default"><font color="Maroon" title="c5">d</font>,<font color="Maroon" title="c4">c</font></span><a href="domain_1.html#K1" title="DOMAIN_1:func.1">]</a></span></span><a href="enumset1.html#K4" title="ENUMSET1:func.4">}</a></span>
 <b>by </b><i><a class="ref" href="enumset1.html#D4" title="ENUMSET1:def.4">ENUMSET1:def 4</a></i>;<br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="60_1_1_1_1_1_1_8"><b>suppose </b></a><a NAME="E1:60_1_1_1_1_1_1_8"/>
<font color="Maroon" title="c14">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1"><a href="domain_1.html#K1" title="DOMAIN_1:func.1">[</a><span class="default"><font color="Maroon" title="c3">b</font>,<font color="Maroon" title="c5">d</font></span><a href="domain_1.html#K1" title="DOMAIN_1:func.1">]</a></span>
 ;<br/><div class="add"><b>hence </b><a NAME="E2:60_1_1_1_1_1_1_8"/>
<font color="Maroon" title="c14">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <span class="p1"><a href="enumset1.html#K4" title="ENUMSET1:func.4">{</a><span class="default"><span class="p2"><a href="domain_1.html#K1" title="DOMAIN_1:func.1">[</a><span class="default"><font color="Maroon" title="c2">a</font>,<font color="Maroon" title="c3">b</font></span><a href="domain_1.html#K1" title="DOMAIN_1:func.1">]</a></span>,<span class="p2"><a href="domain_1.html#K1" title="DOMAIN_1:func.1">[</a><span class="default"><font color="Maroon" title="c3">b</font>,<font color="Maroon" title="c2">a</font></span><a href="domain_1.html#K1" title="DOMAIN_1:func.1">]</a></span>,<span class="p2"><a href="domain_1.html#K1" title="DOMAIN_1:func.1">[</a><span class="default"><font color="Maroon" title="c3">b</font>,<font color="Maroon" title="c4">c</font></span><a href="domain_1.html#K1" title="DOMAIN_1:func.1">]</a></span>,<span class="p2"><a href="domain_1.html#K1" title="DOMAIN_1:func.1">[</a><span class="default"><font color="Maroon" title="c4">c</font>,<font color="Maroon" title="c3">b</font></span><a href="domain_1.html#K1" title="DOMAIN_1:func.1">]</a></span>,<span class="p2"><a href="domain_1.html#K1" title="DOMAIN_1:func.1">[</a><span class="default"><font color="Maroon" title="c4">c</font>,<font color="Maroon" title="c5">d</font></span><a href="domain_1.html#K1" title="DOMAIN_1:func.1">]</a></span>,<span class="p2"><a href="domain_1.html#K1" title="DOMAIN_1:func.1">[</a><span class="default"><font color="Maroon" title="c5">d</font>,<font color="Maroon" title="c4">c</font></span><a href="domain_1.html#K1" title="DOMAIN_1:func.1">]</a></span></span><a href="enumset1.html#K4" title="ENUMSET1:func.4">}</a></span>
 <b>by </b><i><a class="txt" href="neckla_3.html#E8:60"><i><font color="Green" title="E43">A8</font></i></a>, <a class="txt" href="neckla_3.html#E3:60_1_1"><i><font color="Green" title="E45">A10</font></i></a>, <a class="ref" href="xboole_0.html#D3" title="XBOOLE_0:def.3">XBOOLE_0:def 3</a></i>;<br/></div><b>end;</b></div></div><b>end;</b></div>

</div><b>end;</b></div></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="60_1_1_1_2"><b>suppose </b></a><a NAME="E1:60_1_1_1_2"/><i><font color="Green" title="E48">A16</font></i>: 
<font color="Maroon" title="c14">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <span class="p1"><a href="enumset1.html#K6" title="ENUMSET1:func.6">{</a><span class="default"><span class="p2"><a href="domain_1.html#K1" title="DOMAIN_1:func.1">[</a><span class="default"><font color="Maroon" title="c4">c</font>,<font color="Maroon" title="c2">a</font></span><a href="domain_1.html#K1" title="DOMAIN_1:func.1">]</a></span>,<span class="p2"><a href="domain_1.html#K1" title="DOMAIN_1:func.1">[</a><span class="default"><font color="Maroon" title="c4">c</font>,<font color="Maroon" title="c3">b</font></span><a href="domain_1.html#K1" title="DOMAIN_1:func.1">]</a></span>,<span class="p2"><a href="domain_1.html#K1" title="DOMAIN_1:func.1">[</a><span class="default"><font color="Maroon" title="c5">d</font>,<font color="Maroon" title="c2">a</font></span><a href="domain_1.html#K1" title="DOMAIN_1:func.1">]</a></span>,<span class="p2"><a href="domain_1.html#K1" title="DOMAIN_1:func.1">[</a><span class="default"><font color="Maroon" title="c5">d</font>,<font color="Maroon" title="c3">b</font></span><a href="domain_1.html#K1" title="DOMAIN_1:func.1">]</a></span>,<span class="p2"><a href="domain_1.html#K1" title="DOMAIN_1:func.1">[</a><span class="default"><font color="Maroon" title="c4">c</font>,<font color="Maroon" title="c4">c</font></span><a href="domain_1.html#K1" title="DOMAIN_1:func.1">]</a></span>,<span class="p2"><a href="domain_1.html#K1" title="DOMAIN_1:func.1">[</a><span class="default"><font color="Maroon" title="c4">c</font>,<font color="Maroon" title="c5">d</font></span><a href="domain_1.html#K1" title="DOMAIN_1:func.1">]</a></span>,<span class="p2"><a href="domain_1.html#K1" title="DOMAIN_1:func.1">[</a><span class="default"><font color="Maroon" title="c5">d</font>,<font color="Maroon" title="c4">c</font></span><a href="domain_1.html#K1" title="DOMAIN_1:func.1">]</a></span>,<span class="p2"><a href="domain_1.html#K1" title="DOMAIN_1:func.1">[</a><span class="default"><font color="Maroon" title="c5">d</font>,<font color="Maroon" title="c5">d</font></span><a href="domain_1.html#K1" title="DOMAIN_1:func.1">]</a></span></span><a href="enumset1.html#K6" title="ENUMSET1:func.6">}</a></span>
 ;<br/><div class="add"><a NAME="E2:60_1_1_1_2"/><i><font color="Green" title="E49">A17</font></i>: 
the <a href="orders_2.html#U1" title="ORDERS_2:sel.1">InternalRel</a> of <font color="Maroon" title="c1">G</font> <a href="relat_2.html#R3" title="RELAT_2:pred.3">is_symmetric_in</a> the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c1">G</font>
 <b>by </b><i><a class="ref" href="necklace.html#D4" title="NECKLACE:def.4">NECKLACE:def 4</a></i>;<br/><b>thus </b><a NAME="E3:60_1_1_1_2"/>
<font color="Maroon" title="c14">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <span class="p1"><a href="enumset1.html#K4" title="ENUMSET1:func.4">{</a><span class="default"><span class="p2"><a href="domain_1.html#K1" title="DOMAIN_1:func.1">[</a><span class="default"><font color="Maroon" title="c2">a</font>,<font color="Maroon" title="c3">b</font></span><a href="domain_1.html#K1" title="DOMAIN_1:func.1">]</a></span>,<span class="p2"><a href="domain_1.html#K1" title="DOMAIN_1:func.1">[</a><span class="default"><font color="Maroon" title="c3">b</font>,<font color="Maroon" title="c2">a</font></span><a href="domain_1.html#K1" title="DOMAIN_1:func.1">]</a></span>,<span class="p2"><a href="domain_1.html#K1" title="DOMAIN_1:func.1">[</a><span class="default"><font color="Maroon" title="c3">b</font>,<font color="Maroon" title="c4">c</font></span><a href="domain_1.html#K1" title="DOMAIN_1:func.1">]</a></span>,<span class="p2"><a href="domain_1.html#K1" title="DOMAIN_1:func.1">[</a><span class="default"><font color="Maroon" title="c4">c</font>,<font color="Maroon" title="c3">b</font></span><a href="domain_1.html#K1" title="DOMAIN_1:func.1">]</a></span>,<span class="p2"><a href="domain_1.html#K1" title="DOMAIN_1:func.1">[</a><span class="default"><font color="Maroon" title="c4">c</font>,<font color="Maroon" title="c5">d</font></span><a href="domain_1.html#K1" title="DOMAIN_1:func.1">]</a></span>,<span class="p2"><a href="domain_1.html#K1" title="DOMAIN_1:func.1">[</a><span class="default"><font color="Maroon" title="c5">d</font>,<font color="Maroon" title="c4">c</font></span><a href="domain_1.html#K1" title="DOMAIN_1:func.1">]</a></span></span><a href="enumset1.html#K4" title="ENUMSET1:func.4">}</a></span>
 <div><a class="txt" onclick="hs2(this)" href="javascript:()" title="60_1_1_1_2_1"><b>proof </b></a><div class="add">

<div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="60_1_1_1_2_1_1"><b>per </b></a><a class="txt" onclick="hs(this)" href="javascript:()"><b>cases </b></a><span class="hide"><a NAME="E1:60_1_1_1_2_1_1"/>
( <font color="Maroon" title="c14">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1"><a href="domain_1.html#K1" title="DOMAIN_1:func.1">[</a><span class="default"><font color="Maroon" title="c4">c</font>,<font color="Maroon" title="c2">a</font></span><a href="domain_1.html#K1" title="DOMAIN_1:func.1">]</a></span> or <font color="Maroon" title="c14">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1"><a href="domain_1.html#K1" title="DOMAIN_1:func.1">[</a><span class="default"><font color="Maroon" title="c4">c</font>,<font color="Maroon" title="c3">b</font></span><a href="domain_1.html#K1" title="DOMAIN_1:func.1">]</a></span> or <font color="Maroon" title="c14">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1"><a href="domain_1.html#K1" title="DOMAIN_1:func.1">[</a><span class="default"><font color="Maroon" title="c5">d</font>,<font color="Maroon" title="c2">a</font></span><a href="domain_1.html#K1" title="DOMAIN_1:func.1">]</a></span> or <font color="Maroon" title="c14">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1"><a href="domain_1.html#K1" title="DOMAIN_1:func.1">[</a><span class="default"><font color="Maroon" title="c5">d</font>,<font color="Maroon" title="c3">b</font></span><a href="domain_1.html#K1" title="DOMAIN_1:func.1">]</a></span> or <font color="Maroon" title="c14">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1"><a href="domain_1.html#K1" title="DOMAIN_1:func.1">[</a><span class="default"><font color="Maroon" title="c4">c</font>,<font color="Maroon" title="c4">c</font></span><a href="domain_1.html#K1" title="DOMAIN_1:func.1">]</a></span> or <font color="Maroon" title="c14">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1"><a href="domain_1.html#K1" title="DOMAIN_1:func.1">[</a><span class="default"><font color="Maroon" title="c4">c</font>,<font color="Maroon" title="c5">d</font></span><a href="domain_1.html#K1" title="DOMAIN_1:func.1">]</a></span> or <font color="Maroon" title="c14">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1"><a href="domain_1.html#K1" title="DOMAIN_1:func.1">[</a><span class="default"><font color="Maroon" title="c5">d</font>,<font color="Maroon" title="c4">c</font></span><a href="domain_1.html#K1" title="DOMAIN_1:func.1">]</a></span> or <font color="Maroon" title="c14">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1"><a href="domain_1.html#K1" title="DOMAIN_1:func.1">[</a><span class="default"><font color="Maroon" title="c5">d</font>,<font color="Maroon" title="c5">d</font></span><a href="domain_1.html#K1" title="DOMAIN_1:func.1">]</a></span> )
 </span><b>by </b><i><a class="txt" href="neckla_3.html#E1:60_1_1_1_2"><i><font color="Green" title="E48">A16</font></i></a>, <a class="ref" href="enumset1.html#D6" title="ENUMSET1:def.6">ENUMSET1:def 6</a></i>;<br/><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="60_1_1_1_2_1_1_1"><b>suppose </b></a><a NAME="E1:60_1_1_1_2_1_1_1"/>
<font color="Maroon" title="c14">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1"><a href="domain_1.html#K1" title="DOMAIN_1:func.1">[</a><span class="default"><font color="Maroon" title="c4">c</font>,<font color="Maroon" title="c2">a</font></span><a href="domain_1.html#K1" title="DOMAIN_1:func.1">]</a></span>
 ;<br/><div class="add"><b>hence </b><a NAME="E2:60_1_1_1_2_1_1_1"/>
<font color="Maroon" title="c14">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <span class="p1"><a href="enumset1.html#K4" title="ENUMSET1:func.4">{</a><span class="default"><span class="p2"><a href="domain_1.html#K1" title="DOMAIN_1:func.1">[</a><span class="default"><font color="Maroon" title="c2">a</font>,<font color="Maroon" title="c3">b</font></span><a href="domain_1.html#K1" title="DOMAIN_1:func.1">]</a></span>,<span class="p2"><a href="domain_1.html#K1" title="DOMAIN_1:func.1">[</a><span class="default"><font color="Maroon" title="c3">b</font>,<font color="Maroon" title="c2">a</font></span><a href="domain_1.html#K1" title="DOMAIN_1:func.1">]</a></span>,<span class="p2"><a href="domain_1.html#K1" title="DOMAIN_1:func.1">[</a><span class="default"><font color="Maroon" title="c3">b</font>,<font color="Maroon" title="c4">c</font></span><a href="domain_1.html#K1" title="DOMAIN_1:func.1">]</a></span>,<span class="p2"><a href="domain_1.html#K1" title="DOMAIN_1:func.1">[</a><span class="default"><font color="Maroon" title="c4">c</font>,<font color="Maroon" title="c3">b</font></span><a href="domain_1.html#K1" title="DOMAIN_1:func.1">]</a></span>,<span class="p2"><a href="domain_1.html#K1" title="DOMAIN_1:func.1">[</a><span class="default"><font color="Maroon" title="c4">c</font>,<font color="Maroon" title="c5">d</font></span><a href="domain_1.html#K1" title="DOMAIN_1:func.1">]</a></span>,<span class="p2"><a href="domain_1.html#K1" title="DOMAIN_1:func.1">[</a><span class="default"><font color="Maroon" title="c5">d</font>,<font color="Maroon" title="c4">c</font></span><a href="domain_1.html#K1" title="DOMAIN_1:func.1">]</a></span></span><a href="enumset1.html#K4" title="ENUMSET1:func.4">}</a></span>
 <b>by </b><i><a class="txt" href="neckla_3.html#E6:60"><i><font color="Green" title="E41">A6</font></i></a>, <a class="txt" href="neckla_3.html#E4:60_1_1"><i><font color="Green" title="E46">A11</font></i></a>, <a class="txt" href="neckla_3.html#E2:60_1_1_1_2"><i><font color="Green" title="E49">A17</font></i></a>, <a class="ref" href="relat_2.html#D3" title="RELAT_2:def.3">RELAT_2:def 3</a></i>;<br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="60_1_1_1_2_1_1_2"><b>suppose </b></a><a NAME="E1:60_1_1_1_2_1_1_2"/>
<font color="Maroon" title="c14">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1"><a href="domain_1.html#K1" title="DOMAIN_1:func.1">[</a><span class="default"><font color="Maroon" title="c4">c</font>,<font color="Maroon" title="c3">b</font></span><a href="domain_1.html#K1" title="DOMAIN_1:func.1">]</a></span>
 ;<br/><div class="add"><b>hence </b><a NAME="E2:60_1_1_1_2_1_1_2"/>
<font color="Maroon" title="c14">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <span class="p1"><a href="enumset1.html#K4" title="ENUMSET1:func.4">{</a><span class="default"><span class="p2"><a href="domain_1.html#K1" title="DOMAIN_1:func.1">[</a><span class="default"><font color="Maroon" title="c2">a</font>,<font color="Maroon" title="c3">b</font></span><a href="domain_1.html#K1" title="DOMAIN_1:func.1">]</a></span>,<span class="p2"><a href="domain_1.html#K1" title="DOMAIN_1:func.1">[</a><span class="default"><font color="Maroon" title="c3">b</font>,<font color="Maroon" title="c2">a</font></span><a href="domain_1.html#K1" title="DOMAIN_1:func.1">]</a></span>,<span class="p2"><a href="domain_1.html#K1" title="DOMAIN_1:func.1">[</a><span class="default"><font color="Maroon" title="c3">b</font>,<font color="Maroon" title="c4">c</font></span><a href="domain_1.html#K1" title="DOMAIN_1:func.1">]</a></span>,<span class="p2"><a href="domain_1.html#K1" title="DOMAIN_1:func.1">[</a><span class="default"><font color="Maroon" title="c4">c</font>,<font color="Maroon" title="c3">b</font></span><a href="domain_1.html#K1" title="DOMAIN_1:func.1">]</a></span>,<span class="p2"><a href="domain_1.html#K1" title="DOMAIN_1:func.1">[</a><span class="default"><font color="Maroon" title="c4">c</font>,<font color="Maroon" title="c5">d</font></span><a href="domain_1.html#K1" title="DOMAIN_1:func.1">]</a></span>,<span class="p2"><a href="domain_1.html#K1" title="DOMAIN_1:func.1">[</a><span class="default"><font color="Maroon" title="c5">d</font>,<font color="Maroon" title="c4">c</font></span><a href="domain_1.html#K1" title="DOMAIN_1:func.1">]</a></span></span><a href="enumset1.html#K4" title="ENUMSET1:func.4">}</a></span>
 <b>by </b><i><a class="ref" href="enumset1.html#D4" title="ENUMSET1:def.4">ENUMSET1:def 4</a></i>;<br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="60_1_1_1_2_1_1_3"><b>suppose </b></a><a NAME="E1:60_1_1_1_2_1_1_3"/>
<font color="Maroon" title="c14">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1"><a href="domain_1.html#K1" title="DOMAIN_1:func.1">[</a><span class="default"><font color="Maroon" title="c5">d</font>,<font color="Maroon" title="c2">a</font></span><a href="domain_1.html#K1" title="DOMAIN_1:func.1">]</a></span>
 ;<br/><div class="add"><b>hence </b><a NAME="E2:60_1_1_1_2_1_1_3"/>
<font color="Maroon" title="c14">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <span class="p1"><a href="enumset1.html#K4" title="ENUMSET1:func.4">{</a><span class="default"><span class="p2"><a href="domain_1.html#K1" title="DOMAIN_1:func.1">[</a><span class="default"><font color="Maroon" title="c2">a</font>,<font color="Maroon" title="c3">b</font></span><a href="domain_1.html#K1" title="DOMAIN_1:func.1">]</a></span>,<span class="p2"><a href="domain_1.html#K1" title="DOMAIN_1:func.1">[</a><span class="default"><font color="Maroon" title="c3">b</font>,<font color="Maroon" title="c2">a</font></span><a href="domain_1.html#K1" title="DOMAIN_1:func.1">]</a></span>,<span class="p2"><a href="domain_1.html#K1" title="DOMAIN_1:func.1">[</a><span class="default"><font color="Maroon" title="c3">b</font>,<font color="Maroon" title="c4">c</font></span><a href="domain_1.html#K1" title="DOMAIN_1:func.1">]</a></span>,<span class="p2"><a href="domain_1.html#K1" title="DOMAIN_1:func.1">[</a><span class="default"><font color="Maroon" title="c4">c</font>,<font color="Maroon" title="c3">b</font></span><a href="domain_1.html#K1" title="DOMAIN_1:func.1">]</a></span>,<span class="p2"><a href="domain_1.html#K1" title="DOMAIN_1:func.1">[</a><span class="default"><font color="Maroon" title="c4">c</font>,<font color="Maroon" title="c5">d</font></span><a href="domain_1.html#K1" title="DOMAIN_1:func.1">]</a></span>,<span class="p2"><a href="domain_1.html#K1" title="DOMAIN_1:func.1">[</a><span class="default"><font color="Maroon" title="c5">d</font>,<font color="Maroon" title="c4">c</font></span><a href="domain_1.html#K1" title="DOMAIN_1:func.1">]</a></span></span><a href="enumset1.html#K4" title="ENUMSET1:func.4">}</a></span>
 <b>by </b><i><a class="txt" href="neckla_3.html#E7:60"><i><font color="Green" title="E42">A7</font></i></a>, <a class="txt" href="neckla_3.html#E4:60_1_1"><i><font color="Green" title="E46">A11</font></i></a>, <a class="txt" href="neckla_3.html#E2:60_1_1_1_2"><i><font color="Green" title="E49">A17</font></i></a>, <a class="ref" href="relat_2.html#D3" title="RELAT_2:def.3">RELAT_2:def 3</a></i>;<br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="60_1_1_1_2_1_1_4"><b>suppose </b></a><a NAME="E1:60_1_1_1_2_1_1_4"/>
<font color="Maroon" title="c14">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1"><a href="domain_1.html#K1" title="DOMAIN_1:func.1">[</a><span class="default"><font color="Maroon" title="c5">d</font>,<font color="Maroon" title="c3">b</font></span><a href="domain_1.html#K1" title="DOMAIN_1:func.1">]</a></span>
 ;<br/><div class="add"><b>hence </b><a NAME="E2:60_1_1_1_2_1_1_4"/>
<font color="Maroon" title="c14">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <span class="p1"><a href="enumset1.html#K4" title="ENUMSET1:func.4">{</a><span class="default"><span class="p2"><a href="domain_1.html#K1" title="DOMAIN_1:func.1">[</a><span class="default"><font color="Maroon" title="c2">a</font>,<font color="Maroon" title="c3">b</font></span><a href="domain_1.html#K1" title="DOMAIN_1:func.1">]</a></span>,<span class="p2"><a href="domain_1.html#K1" title="DOMAIN_1:func.1">[</a><span class="default"><font color="Maroon" title="c3">b</font>,<font color="Maroon" title="c2">a</font></span><a href="domain_1.html#K1" title="DOMAIN_1:func.1">]</a></span>,<span class="p2"><a href="domain_1.html#K1" title="DOMAIN_1:func.1">[</a><span class="default"><font color="Maroon" title="c3">b</font>,<font color="Maroon" title="c4">c</font></span><a href="domain_1.html#K1" title="DOMAIN_1:func.1">]</a></span>,<span class="p2"><a href="domain_1.html#K1" title="DOMAIN_1:func.1">[</a><span class="default"><font color="Maroon" title="c4">c</font>,<font color="Maroon" title="c3">b</font></span><a href="domain_1.html#K1" title="DOMAIN_1:func.1">]</a></span>,<span class="p2"><a href="domain_1.html#K1" title="DOMAIN_1:func.1">[</a><span class="default"><font color="Maroon" title="c4">c</font>,<font color="Maroon" title="c5">d</font></span><a href="domain_1.html#K1" title="DOMAIN_1:func.1">]</a></span>,<span class="p2"><a href="domain_1.html#K1" title="DOMAIN_1:func.1">[</a><span class="default"><font color="Maroon" title="c5">d</font>,<font color="Maroon" title="c4">c</font></span><a href="domain_1.html#K1" title="DOMAIN_1:func.1">]</a></span></span><a href="enumset1.html#K4" title="ENUMSET1:func.4">}</a></span>
 <b>by </b><i><a class="txt" href="neckla_3.html#E8:60"><i><font color="Green" title="E43">A8</font></i></a>, <a class="txt" href="neckla_3.html#E4:60_1_1"><i><font color="Green" title="E46">A11</font></i></a>, <a class="txt" href="neckla_3.html#E2:60_1_1_1_2"><i><font color="Green" title="E49">A17</font></i></a>, <a class="ref" href="relat_2.html#D3" title="RELAT_2:def.3">RELAT_2:def 3</a></i>;<br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="60_1_1_1_2_1_1_5"><b>suppose </b></a><a NAME="E1:60_1_1_1_2_1_1_5"/><i><font color="Green" title="E50">A18</font></i>: 
<font color="Maroon" title="c14">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1"><a href="domain_1.html#K1" title="DOMAIN_1:func.1">[</a><span class="default"><font color="Maroon" title="c4">c</font>,<font color="Maroon" title="c4">c</font></span><a href="domain_1.html#K1" title="DOMAIN_1:func.1">]</a></span>
 ;<br/><div class="add"><a NAME="E2:60_1_1_1_2_1_1_5"/>
not <span class="p1"><a href="domain_1.html#K1" title="DOMAIN_1:func.1">[</a><span class="default"><font color="Maroon" title="c4">c</font>,<font color="Maroon" title="c4">c</font></span><a href="domain_1.html#K1" title="DOMAIN_1:func.1">]</a></span> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> the <a href="orders_2.html#U1" title="ORDERS_2:sel.1">InternalRel</a> of <font color="Maroon" title="c1">G</font>
 <b>by </b><i><a class="ref" href="necklace.html#D6" title="NECKLACE:def.6">NECKLACE:def 6</a></i>;<br/><b>hence </b><a NAME="E3:60_1_1_1_2_1_1_5"/>
<font color="Maroon" title="c14">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <span class="p1"><a href="enumset1.html#K4" title="ENUMSET1:func.4">{</a><span class="default"><span class="p2"><a href="domain_1.html#K1" title="DOMAIN_1:func.1">[</a><span class="default"><font color="Maroon" title="c2">a</font>,<font color="Maroon" title="c3">b</font></span><a href="domain_1.html#K1" title="DOMAIN_1:func.1">]</a></span>,<span class="p2"><a href="domain_1.html#K1" title="DOMAIN_1:func.1">[</a><span class="default"><font color="Maroon" title="c3">b</font>,<font color="Maroon" title="c2">a</font></span><a href="domain_1.html#K1" title="DOMAIN_1:func.1">]</a></span>,<span class="p2"><a href="domain_1.html#K1" title="DOMAIN_1:func.1">[</a><span class="default"><font color="Maroon" title="c3">b</font>,<font color="Maroon" title="c4">c</font></span><a href="domain_1.html#K1" title="DOMAIN_1:func.1">]</a></span>,<span class="p2"><a href="domain_1.html#K1" title="DOMAIN_1:func.1">[</a><span class="default"><font color="Maroon" title="c4">c</font>,<font color="Maroon" title="c3">b</font></span><a href="domain_1.html#K1" title="DOMAIN_1:func.1">]</a></span>,<span class="p2"><a href="domain_1.html#K1" title="DOMAIN_1:func.1">[</a><span class="default"><font color="Maroon" title="c4">c</font>,<font color="Maroon" title="c5">d</font></span><a href="domain_1.html#K1" title="DOMAIN_1:func.1">]</a></span>,<span class="p2"><a href="domain_1.html#K1" title="DOMAIN_1:func.1">[</a><span class="default"><font color="Maroon" title="c5">d</font>,<font color="Maroon" title="c4">c</font></span><a href="domain_1.html#K1" title="DOMAIN_1:func.1">]</a></span></span><a href="enumset1.html#K4" title="ENUMSET1:func.4">}</a></span>
 <b>by </b><i><a class="txt" href="neckla_3.html#E3:60_1_1"><i><font color="Green" title="E45">A10</font></i></a>, <a class="txt" href="neckla_3.html#E1:60_1_1_1_2_1_1_5"><i><font color="Green" title="E50">A18</font></i></a>, <a class="ref" href="xboole_0.html#D3" title="XBOOLE_0:def.3">XBOOLE_0:def 3</a></i>;<br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="60_1_1_1_2_1_1_6"><b>suppose </b></a><a NAME="E1:60_1_1_1_2_1_1_6"/>
<font color="Maroon" title="c14">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1"><a href="domain_1.html#K1" title="DOMAIN_1:func.1">[</a><span class="default"><font color="Maroon" title="c4">c</font>,<font color="Maroon" title="c5">d</font></span><a href="domain_1.html#K1" title="DOMAIN_1:func.1">]</a></span>
 ;<br/><div class="add"><b>hence </b><a NAME="E2:60_1_1_1_2_1_1_6"/>
<font color="Maroon" title="c14">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <span class="p1"><a href="enumset1.html#K4" title="ENUMSET1:func.4">{</a><span class="default"><span class="p2"><a href="domain_1.html#K1" title="DOMAIN_1:func.1">[</a><span class="default"><font color="Maroon" title="c2">a</font>,<font color="Maroon" title="c3">b</font></span><a href="domain_1.html#K1" title="DOMAIN_1:func.1">]</a></span>,<span class="p2"><a href="domain_1.html#K1" title="DOMAIN_1:func.1">[</a><span class="default"><font color="Maroon" title="c3">b</font>,<font color="Maroon" title="c2">a</font></span><a href="domain_1.html#K1" title="DOMAIN_1:func.1">]</a></span>,<span class="p2"><a href="domain_1.html#K1" title="DOMAIN_1:func.1">[</a><span class="default"><font color="Maroon" title="c3">b</font>,<font color="Maroon" title="c4">c</font></span><a href="domain_1.html#K1" title="DOMAIN_1:func.1">]</a></span>,<span class="p2"><a href="domain_1.html#K1" title="DOMAIN_1:func.1">[</a><span class="default"><font color="Maroon" title="c4">c</font>,<font color="Maroon" title="c3">b</font></span><a href="domain_1.html#K1" title="DOMAIN_1:func.1">]</a></span>,<span class="p2"><a href="domain_1.html#K1" title="DOMAIN_1:func.1">[</a><span class="default"><font color="Maroon" title="c4">c</font>,<font color="Maroon" title="c5">d</font></span><a href="domain_1.html#K1" title="DOMAIN_1:func.1">]</a></span>,<span class="p2"><a href="domain_1.html#K1" title="DOMAIN_1:func.1">[</a><span class="default"><font color="Maroon" title="c5">d</font>,<font color="Maroon" title="c4">c</font></span><a href="domain_1.html#K1" title="DOMAIN_1:func.1">]</a></span></span><a href="enumset1.html#K4" title="ENUMSET1:func.4">}</a></span>
 <b>by </b><i><a class="ref" href="enumset1.html#D4" title="ENUMSET1:def.4">ENUMSET1:def 4</a></i>;<br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="60_1_1_1_2_1_1_7"><b>suppose </b></a><a NAME="E1:60_1_1_1_2_1_1_7"/>
<font color="Maroon" title="c14">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1"><a href="domain_1.html#K1" title="DOMAIN_1:func.1">[</a><span class="default"><font color="Maroon" title="c5">d</font>,<font color="Maroon" title="c4">c</font></span><a href="domain_1.html#K1" title="DOMAIN_1:func.1">]</a></span>
 ;<br/><div class="add"><b>hence </b><a NAME="E2:60_1_1_1_2_1_1_7"/>
<font color="Maroon" title="c14">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <span class="p1"><a href="enumset1.html#K4" title="ENUMSET1:func.4">{</a><span class="default"><span class="p2"><a href="domain_1.html#K1" title="DOMAIN_1:func.1">[</a><span class="default"><font color="Maroon" title="c2">a</font>,<font color="Maroon" title="c3">b</font></span><a href="domain_1.html#K1" title="DOMAIN_1:func.1">]</a></span>,<span class="p2"><a href="domain_1.html#K1" title="DOMAIN_1:func.1">[</a><span class="default"><font color="Maroon" title="c3">b</font>,<font color="Maroon" title="c2">a</font></span><a href="domain_1.html#K1" title="DOMAIN_1:func.1">]</a></span>,<span class="p2"><a href="domain_1.html#K1" title="DOMAIN_1:func.1">[</a><span class="default"><font color="Maroon" title="c3">b</font>,<font color="Maroon" title="c4">c</font></span><a href="domain_1.html#K1" title="DOMAIN_1:func.1">]</a></span>,<span class="p2"><a href="domain_1.html#K1" title="DOMAIN_1:func.1">[</a><span class="default"><font color="Maroon" title="c4">c</font>,<font color="Maroon" title="c3">b</font></span><a href="domain_1.html#K1" title="DOMAIN_1:func.1">]</a></span>,<span class="p2"><a href="domain_1.html#K1" title="DOMAIN_1:func.1">[</a><span class="default"><font color="Maroon" title="c4">c</font>,<font color="Maroon" title="c5">d</font></span><a href="domain_1.html#K1" title="DOMAIN_1:func.1">]</a></span>,<span class="p2"><a href="domain_1.html#K1" title="DOMAIN_1:func.1">[</a><span class="default"><font color="Maroon" title="c5">d</font>,<font color="Maroon" title="c4">c</font></span><a href="domain_1.html#K1" title="DOMAIN_1:func.1">]</a></span></span><a href="enumset1.html#K4" title="ENUMSET1:func.4">}</a></span>
 <b>by </b><i><a class="ref" href="enumset1.html#D4" title="ENUMSET1:def.4">ENUMSET1:def 4</a></i>;<br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="60_1_1_1_2_1_1_8"><b>suppose </b></a><a NAME="E1:60_1_1_1_2_1_1_8"/><i><font color="Green" title="E50">A19</font></i>: 
<font color="Maroon" title="c14">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1"><a href="domain_1.html#K1" title="DOMAIN_1:func.1">[</a><span class="default"><font color="Maroon" title="c5">d</font>,<font color="Maroon" title="c5">d</font></span><a href="domain_1.html#K1" title="DOMAIN_1:func.1">]</a></span>
 ;<br/><div class="add"><a NAME="E2:60_1_1_1_2_1_1_8"/>
not <span class="p1"><a href="domain_1.html#K1" title="DOMAIN_1:func.1">[</a><span class="default"><font color="Maroon" title="c5">d</font>,<font color="Maroon" title="c5">d</font></span><a href="domain_1.html#K1" title="DOMAIN_1:func.1">]</a></span> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> the <a href="orders_2.html#U1" title="ORDERS_2:sel.1">InternalRel</a> of <font color="Maroon" title="c1">G</font>
 <b>by </b><i><a class="ref" href="necklace.html#D6" title="NECKLACE:def.6">NECKLACE:def 6</a></i>;<br/><b>hence </b><a NAME="E3:60_1_1_1_2_1_1_8"/>
<font color="Maroon" title="c14">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <span class="p1"><a href="enumset1.html#K4" title="ENUMSET1:func.4">{</a><span class="default"><span class="p2"><a href="domain_1.html#K1" title="DOMAIN_1:func.1">[</a><span class="default"><font color="Maroon" title="c2">a</font>,<font color="Maroon" title="c3">b</font></span><a href="domain_1.html#K1" title="DOMAIN_1:func.1">]</a></span>,<span class="p2"><a href="domain_1.html#K1" title="DOMAIN_1:func.1">[</a><span class="default"><font color="Maroon" title="c3">b</font>,<font color="Maroon" title="c2">a</font></span><a href="domain_1.html#K1" title="DOMAIN_1:func.1">]</a></span>,<span class="p2"><a href="domain_1.html#K1" title="DOMAIN_1:func.1">[</a><span class="default"><font color="Maroon" title="c3">b</font>,<font color="Maroon" title="c4">c</font></span><a href="domain_1.html#K1" title="DOMAIN_1:func.1">]</a></span>,<span class="p2"><a href="domain_1.html#K1" title="DOMAIN_1:func.1">[</a><span class="default"><font color="Maroon" title="c4">c</font>,<font color="Maroon" title="c3">b</font></span><a href="domain_1.html#K1" title="DOMAIN_1:func.1">]</a></span>,<span class="p2"><a href="domain_1.html#K1" title="DOMAIN_1:func.1">[</a><span class="default"><font color="Maroon" title="c4">c</font>,<font color="Maroon" title="c5">d</font></span><a href="domain_1.html#K1" title="DOMAIN_1:func.1">]</a></span>,<span class="p2"><a href="domain_1.html#K1" title="DOMAIN_1:func.1">[</a><span class="default"><font color="Maroon" title="c5">d</font>,<font color="Maroon" title="c4">c</font></span><a href="domain_1.html#K1" title="DOMAIN_1:func.1">]</a></span></span><a href="enumset1.html#K4" title="ENUMSET1:func.4">}</a></span>
 <b>by </b><i><a class="txt" href="neckla_3.html#E3:60_1_1"><i><font color="Green" title="E45">A10</font></i></a>, <a class="txt" href="neckla_3.html#E1:60_1_1_1_2_1_1_8"><i><font color="Green" title="E50">A19</font></i></a>, <a class="ref" href="xboole_0.html#D3" title="XBOOLE_0:def.3">XBOOLE_0:def 3</a></i>;<br/></div><b>end;</b></div></div><b>end;</b></div>

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

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

<b>let </b><font color="Maroon" title="c14">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="E2:60_1"/><i><font color="Green" title="E45">A20</font></i>: 
<font color="Maroon" title="c14">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <span class="p1"><a href="enumset1.html#K4" title="ENUMSET1:func.4">{</a><span class="default"><span class="p2"><a href="domain_1.html#K1" title="DOMAIN_1:func.1">[</a><span class="default"><font color="Maroon" title="c2">a</font>,<font color="Maroon" title="c3">b</font></span><a href="domain_1.html#K1" title="DOMAIN_1:func.1">]</a></span>,<span class="p2"><a href="domain_1.html#K1" title="DOMAIN_1:func.1">[</a><span class="default"><font color="Maroon" title="c3">b</font>,<font color="Maroon" title="c2">a</font></span><a href="domain_1.html#K1" title="DOMAIN_1:func.1">]</a></span>,<span class="p2"><a href="domain_1.html#K1" title="DOMAIN_1:func.1">[</a><span class="default"><font color="Maroon" title="c3">b</font>,<font color="Maroon" title="c4">c</font></span><a href="domain_1.html#K1" title="DOMAIN_1:func.1">]</a></span>,<span class="p2"><a href="domain_1.html#K1" title="DOMAIN_1:func.1">[</a><span class="default"><font color="Maroon" title="c4">c</font>,<font color="Maroon" title="c3">b</font></span><a href="domain_1.html#K1" title="DOMAIN_1:func.1">]</a></span>,<span class="p2"><a href="domain_1.html#K1" title="DOMAIN_1:func.1">[</a><span class="default"><font color="Maroon" title="c4">c</font>,<font color="Maroon" title="c5">d</font></span><a href="domain_1.html#K1" title="DOMAIN_1:func.1">]</a></span>,<span class="p2"><a href="domain_1.html#K1" title="DOMAIN_1:func.1">[</a><span class="default"><font color="Maroon" title="c5">d</font>,<font color="Maroon" title="c4">c</font></span><a href="domain_1.html#K1" title="DOMAIN_1:func.1">]</a></span></span><a href="enumset1.html#K4" title="ENUMSET1:func.4">}</a></span>
 ;<br/>

<div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="60_1_2"><b>per </b></a><a class="txt" onclick="hs(this)" href="javascript:()"><b>cases </b></a><span class="hide"><a NAME="E1:60_1_2"/>
( <font color="Maroon" title="c14">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1"><a href="domain_1.html#K1" title="DOMAIN_1:func.1">[</a><span class="default"><font color="Maroon" title="c2">a</font>,<font color="Maroon" title="c3">b</font></span><a href="domain_1.html#K1" title="DOMAIN_1:func.1">]</a></span> or <font color="Maroon" title="c14">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1"><a href="domain_1.html#K1" title="DOMAIN_1:func.1">[</a><span class="default"><font color="Maroon" title="c3">b</font>,<font color="Maroon" title="c2">a</font></span><a href="domain_1.html#K1" title="DOMAIN_1:func.1">]</a></span> or <font color="Maroon" title="c14">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1"><a href="domain_1.html#K1" title="DOMAIN_1:func.1">[</a><span class="default"><font color="Maroon" title="c3">b</font>,<font color="Maroon" title="c4">c</font></span><a href="domain_1.html#K1" title="DOMAIN_1:func.1">]</a></span> or <font color="Maroon" title="c14">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1"><a href="domain_1.html#K1" title="DOMAIN_1:func.1">[</a><span class="default"><font color="Maroon" title="c4">c</font>,<font color="Maroon" title="c3">b</font></span><a href="domain_1.html#K1" title="DOMAIN_1:func.1">]</a></span> or <font color="Maroon" title="c14">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1"><a href="domain_1.html#K1" title="DOMAIN_1:func.1">[</a><span class="default"><font color="Maroon" title="c4">c</font>,<font color="Maroon" title="c5">d</font></span><a href="domain_1.html#K1" title="DOMAIN_1:func.1">]</a></span> or <font color="Maroon" title="c14">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1"><a href="domain_1.html#K1" title="DOMAIN_1:func.1">[</a><span class="default"><font color="Maroon" title="c5">d</font>,<font color="Maroon" title="c4">c</font></span><a href="domain_1.html#K1" title="DOMAIN_1:func.1">]</a></span> )
 </span><b>by </b><i><a class="txt" href="neckla_3.html#E2:60_1"><i><font color="Green" title="E45">A20</font></i></a>, <a class="ref" href="enumset1.html#D4" title="ENUMSET1:def.4">ENUMSET1:def 4</a></i>;<br/><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="60_1_2_1"><b>suppose </b></a><a NAME="E1:60_1_2_1"/><i><font color="Green" title="E46">A21</font></i>: 
<font color="Maroon" title="c14">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1"><a href="domain_1.html#K1" title="DOMAIN_1:func.1">[</a><span class="default"><font color="Maroon" title="c2">a</font>,<font color="Maroon" title="c3">b</font></span><a href="domain_1.html#K1" title="DOMAIN_1:func.1">]</a></span>
 ;<br/><div class="add"><a NAME="E2:60_1_2_1"/>
( <font color="Maroon" title="c2">a</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c6">Z</font> &amp; <font color="Maroon" title="c3">b</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c6">Z</font> )
 <b>by </b><i><a class="txt" href="neckla_3.html#E1:60"><i><font color="Green" title="E36">A1</font></i></a>, <a class="ref" href="enumset1.html#D2" title="ENUMSET1:def.2">ENUMSET1:def 2</a></i>;<br/><a NAME="E3:60_1_2_1"/><b>then </b>
( <font color="Maroon" title="c2">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 <span class="p1">(<span class="default"><a href="yellow_0.html#K5" title="YELLOW_0:func.5">subrelstr</a> <font color="Maroon" title="c6">Z</font></span>)</span> &amp; <font color="Maroon" title="c3">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 <span class="p1">(<span class="default"><a href="yellow_0.html#K5" title="YELLOW_0:func.5">subrelstr</a> <font color="Maroon" title="c6">Z</font></span>)</span> )
 <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="E4:60_1_2_1"/><b>then </b>
<span class="p1"><a href="domain_1.html#K1" title="DOMAIN_1:func.1">[</a><span class="default"><font color="Maroon" title="c2">a</font>,<font color="Maroon" title="c3">b</font></span><a href="domain_1.html#K1" title="DOMAIN_1:func.1">]</a></span> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <span class="p1"><a href="zfmisc_1.html#K2" title="ZFMISC_1:func.2">[:</a><span class="default">the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <span class="p2">(<span class="default"><a href="yellow_0.html#K5" title="YELLOW_0:func.5">subrelstr</a> <font color="Maroon" title="c6">Z</font></span>)</span>,the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <span class="p2">(<span class="default"><a href="yellow_0.html#K5" title="YELLOW_0:func.5">subrelstr</a> <font color="Maroon" title="c6">Z</font></span>)</span></span><a href="zfmisc_1.html#K2" title="ZFMISC_1:func.2">:]</a></span>
 <b>by </b><i><a class="ref" href="zfmisc_1.html#T106" title="ZFMISC_1:th.106">ZFMISC_1:106</a></i>;<br/><a NAME="E5:60_1_2_1"/><b>then </b>
<font color="Maroon" title="c14">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> the <a href="orders_2.html#U1" title="ORDERS_2:sel.1">InternalRel</a> of <font color="Maroon" title="c1">G</font> <a href="subset_1.html#K8" title="SUBSET_1:func.8">/\</a> <span class="p1"><a href="zfmisc_1.html#K2" title="ZFMISC_1:func.2">[:</a><span class="default">the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <span class="p2">(<span class="default"><a href="yellow_0.html#K5" title="YELLOW_0:func.5">subrelstr</a> <font color="Maroon" title="c6">Z</font></span>)</span>,the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <span class="p2">(<span class="default"><a href="yellow_0.html#K5" title="YELLOW_0:func.5">subrelstr</a> <font color="Maroon" title="c6">Z</font></span>)</span></span><a href="zfmisc_1.html#K2" title="ZFMISC_1:func.2">:]</a></span>
 <b>by </b><i><a class="txt" href="neckla_3.html#E3:60"><i><font color="Green" title="E38">A3</font></i></a>, <a class="txt" href="neckla_3.html#E1:60_1_2_1"><i><font color="Green" title="E46">A21</font></i></a>, <a class="ref" href="xboole_0.html#D3" title="XBOOLE_0:def.3">XBOOLE_0:def 3</a></i>;<br/><a NAME="E6:60_1_2_1"/><b>then </b>
<font color="Maroon" title="c14">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> the <a href="orders_2.html#U1" title="ORDERS_2:sel.1">InternalRel</a> of <font color="Maroon" title="c1">G</font> <a href="wellord1.html#K2" title="WELLORD1:func.2">|_2</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="c6">Z</font></span>)</span>
 ;<br/><b>hence </b><a NAME="E7:60_1_2_1"/>
<font color="Maroon" title="c14">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> the <a href="orders_2.html#U1" title="ORDERS_2:sel.1">InternalRel</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="c6">Z</font></span>)</span>
 <b>by </b><i><a class="ref" href="yellow_0.html#D14" title="YELLOW_0:def.14">YELLOW_0:def 14</a></i>;<br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="60_1_2_2"><b>suppose </b></a><a NAME="E1:60_1_2_2"/><i><font color="Green" title="E46">A22</font></i>: 
<font color="Maroon" title="c14">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1"><a href="domain_1.html#K1" title="DOMAIN_1:func.1">[</a><span class="default"><font color="Maroon" title="c3">b</font>,<font color="Maroon" title="c2">a</font></span><a href="domain_1.html#K1" title="DOMAIN_1:func.1">]</a></span>
 ;<br/><div class="add"><a NAME="E2:60_1_2_2"/>
the <a href="orders_2.html#U1" title="ORDERS_2:sel.1">InternalRel</a> of <font color="Maroon" title="c1">G</font> <a href="relat_2.html#R3" title="RELAT_2:pred.3">is_symmetric_in</a> the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c1">G</font>
 <b>by </b><i><a class="ref" href="necklace.html#D4" title="NECKLACE:def.4">NECKLACE:def 4</a></i>;<br/><a NAME="E3:60_1_2_2"/><b>then </b><i><font color="Green" title="E47">A23</font></i>: 
<span class="p1"><a href="domain_1.html#K1" title="DOMAIN_1:func.1">[</a><span class="default"><font color="Maroon" title="c3">b</font>,<font color="Maroon" title="c2">a</font></span><a href="domain_1.html#K1" title="DOMAIN_1:func.1">]</a></span> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> the <a href="orders_2.html#U1" title="ORDERS_2:sel.1">InternalRel</a> of <font color="Maroon" title="c1">G</font>
 <b>by </b><i><a class="txt" href="neckla_3.html#E3:60"><i><font color="Green" title="E38">A3</font></i></a>, <a class="ref" href="relat_2.html#D3" title="RELAT_2:def.3">RELAT_2:def 3</a></i>;<br/><a NAME="E4:60_1_2_2"/>
( <font color="Maroon" title="c3">b</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c6">Z</font> &amp; <font color="Maroon" title="c2">a</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c6">Z</font> )
 <b>by </b><i><a class="txt" href="neckla_3.html#E1:60"><i><font color="Green" title="E36">A1</font></i></a>, <a class="ref" href="enumset1.html#D2" title="ENUMSET1:def.2">ENUMSET1:def 2</a></i>;<br/><a NAME="E5:60_1_2_2"/><b>then </b>
( <font color="Maroon" title="c3">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 <span class="p1">(<span class="default"><a href="yellow_0.html#K5" title="YELLOW_0:func.5">subrelstr</a> <font color="Maroon" title="c6">Z</font></span>)</span> &amp; <font color="Maroon" title="c2">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 <span class="p1">(<span class="default"><a href="yellow_0.html#K5" title="YELLOW_0:func.5">subrelstr</a> <font color="Maroon" title="c6">Z</font></span>)</span> )
 <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="E6:60_1_2_2"/><b>then </b>
<span class="p1"><a href="domain_1.html#K1" title="DOMAIN_1:func.1">[</a><span class="default"><font color="Maroon" title="c3">b</font>,<font color="Maroon" title="c2">a</font></span><a href="domain_1.html#K1" title="DOMAIN_1:func.1">]</a></span> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <span class="p1"><a href="zfmisc_1.html#K2" title="ZFMISC_1:func.2">[:</a><span class="default">the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <span class="p2">(<span class="default"><a href="yellow_0.html#K5" title="YELLOW_0:func.5">subrelstr</a> <font color="Maroon" title="c6">Z</font></span>)</span>,the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <span class="p2">(<span class="default"><a href="yellow_0.html#K5" title="YELLOW_0:func.5">subrelstr</a> <font color="Maroon" title="c6">Z</font></span>)</span></span><a href="zfmisc_1.html#K2" title="ZFMISC_1:func.2">:]</a></span>
 <b>by </b><i><a class="ref" href="zfmisc_1.html#T106" title="ZFMISC_1:th.106">ZFMISC_1:106</a></i>;<br/><a NAME="E7:60_1_2_2"/><b>then </b>
<font color="Maroon" title="c14">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> the <a href="orders_2.html#U1" title="ORDERS_2:sel.1">InternalRel</a> of <font color="Maroon" title="c1">G</font> <a href="subset_1.html#K8" title="SUBSET_1:func.8">/\</a> <span class="p1"><a href="zfmisc_1.html#K2" title="ZFMISC_1:func.2">[:</a><span class="default">the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <span class="p2">(<span class="default"><a href="yellow_0.html#K5" title="YELLOW_0:func.5">subrelstr</a> <font color="Maroon" title="c6">Z</font></span>)</span>,the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <span class="p2">(<span class="default"><a href="yellow_0.html#K5" title="YELLOW_0:func.5">subrelstr</a> <font color="Maroon" title="c6">Z</font></span>)</span></span><a href="zfmisc_1.html#K2" title="ZFMISC_1:func.2">:]</a></span>
 <b>by </b><i><a class="txt" href="neckla_3.html#E1:60_1_2_2"><i><font color="Green" title="E46">A22</font></i></a>, <a class="txt" href="neckla_3.html#E3:60_1_2_2"><i><font color="Green" title="E47">A23</font></i></a>, <a class="ref" href="xboole_0.html#D3" title="XBOOLE_0:def.3">XBOOLE_0:def 3</a></i>;<br/><a NAME="E8:60_1_2_2"/><b>then </b>
<font color="Maroon" title="c14">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> the <a href="orders_2.html#U1" title="ORDERS_2:sel.1">InternalRel</a> of <font color="Maroon" title="c1">G</font> <a href="wellord1.html#K2" title="WELLORD1:func.2">|_2</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="c6">Z</font></span>)</span>
 ;<br/><b>hence </b><a NAME="E9:60_1_2_2"/>
<font color="Maroon" title="c14">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> the <a href="orders_2.html#U1" title="ORDERS_2:sel.1">InternalRel</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="c6">Z</font></span>)</span>
 <b>by </b><i><a class="ref" href="yellow_0.html#D14" title="YELLOW_0:def.14">YELLOW_0:def 14</a></i>;<br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="60_1_2_3"><b>suppose </b></a><a NAME="E1:60_1_2_3"/><i><font color="Green" title="E46">A24</font></i>: 
<font color="Maroon" title="c14">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1"><a href="domain_1.html#K1" title="DOMAIN_1:func.1">[</a><span class="default"><font color="Maroon" title="c3">b</font>,<font color="Maroon" title="c4">c</font></span><a href="domain_1.html#K1" title="DOMAIN_1:func.1">]</a></span>
 ;<br/><div class="add"><a NAME="E2:60_1_2_3"/>
( <font color="Maroon" title="c3">b</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c6">Z</font> &amp; <font color="Maroon" title="c4">c</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c6">Z</font> )
 <b>by </b><i><a class="txt" href="neckla_3.html#E1:60"><i><font color="Green" title="E36">A1</font></i></a>, <a class="ref" href="enumset1.html#D2" title="ENUMSET1:def.2">ENUMSET1:def 2</a></i>;<br/><a NAME="E3:60_1_2_3"/><b>then </b>
( <font color="Maroon" title="c3">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 <span class="p1">(<span class="default"><a href="yellow_0.html#K5" title="YELLOW_0:func.5">subrelstr</a> <font color="Maroon" title="c6">Z</font></span>)</span> &amp; <font color="Maroon" title="c4">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 <span class="p1">(<span class="default"><a href="yellow_0.html#K5" title="YELLOW_0:func.5">subrelstr</a> <font color="Maroon" title="c6">Z</font></span>)</span> )
 <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="E4:60_1_2_3"/><b>then </b>
<span class="p1"><a href="domain_1.html#K1" title="DOMAIN_1:func.1">[</a><span class="default"><font color="Maroon" title="c3">b</font>,<font color="Maroon" title="c4">c</font></span><a href="domain_1.html#K1" title="DOMAIN_1:func.1">]</a></span> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <span class="p1"><a href="zfmisc_1.html#K2" title="ZFMISC_1:func.2">[:</a><span class="default">the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <span class="p2">(<span class="default"><a href="yellow_0.html#K5" title="YELLOW_0:func.5">subrelstr</a> <font color="Maroon" title="c6">Z</font></span>)</span>,the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <span class="p2">(<span class="default"><a href="yellow_0.html#K5" title="YELLOW_0:func.5">subrelstr</a> <font color="Maroon" title="c6">Z</font></span>)</span></span><a href="zfmisc_1.html#K2" title="ZFMISC_1:func.2">:]</a></span>
 <b>by </b><i><a class="ref" href="zfmisc_1.html#T106" title="ZFMISC_1:th.106">ZFMISC_1:106</a></i>;<br/><a NAME="E5:60_1_2_3"/><b>then </b>
<font color="Maroon" title="c14">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> the <a href="orders_2.html#U1" title="ORDERS_2:sel.1">InternalRel</a> of <font color="Maroon" title="c1">G</font> <a href="subset_1.html#K8" title="SUBSET_1:func.8">/\</a> <span class="p1"><a href="zfmisc_1.html#K2" title="ZFMISC_1:func.2">[:</a><span class="default">the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <span class="p2">(<span class="default"><a href="yellow_0.html#K5" title="YELLOW_0:func.5">subrelstr</a> <font color="Maroon" title="c6">Z</font></span>)</span>,the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <span class="p2">(<span class="default"><a href="yellow_0.html#K5" title="YELLOW_0:func.5">subrelstr</a> <font color="Maroon" title="c6">Z</font></span>)</span></span><a href="zfmisc_1.html#K2" title="ZFMISC_1:func.2">:]</a></span>
 <b>by </b><i><a class="txt" href="neckla_3.html#E4:60"><i><font color="Green" title="E39">A4</font></i></a>, <a class="txt" href="neckla_3.html#E1:60_1_2_3"><i><font color="Green" title="E46">A24</font></i></a>, <a class="ref" href="xboole_0.html#D3" title="XBOOLE_0:def.3">XBOOLE_0:def 3</a></i>;<br/><a NAME="E6:60_1_2_3"/><b>then </b>
<font color="Maroon" title="c14">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> the <a href="orders_2.html#U1" title="ORDERS_2:sel.1">InternalRel</a> of <font color="Maroon" title="c1">G</font> <a href="wellord1.html#K2" title="WELLORD1:func.2">|_2</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="c6">Z</font></span>)</span>
 ;<br/><b>hence </b><a NAME="E7:60_1_2_3"/>
<font color="Maroon" title="c14">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> the <a href="orders_2.html#U1" title="ORDERS_2:sel.1">InternalRel</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="c6">Z</font></span>)</span>
 <b>by </b><i><a class="ref" href="yellow_0.html#D14" title="YELLOW_0:def.14">YELLOW_0:def 14</a></i>;<br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="60_1_2_4"><b>suppose </b></a><a NAME="E1:60_1_2_4"/><i><font color="Green" title="E46">A25</font></i>: 
<font color="Maroon" title="c14">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1"><a href="domain_1.html#K1" title="DOMAIN_1:func.1">[</a><span class="default"><font color="Maroon" title="c4">c</font>,<font color="Maroon" title="c3">b</font></span><a href="domain_1.html#K1" title="DOMAIN_1:func.1">]</a></span>
 ;<br/><div class="add"><a NAME="E2:60_1_2_4"/>
the <a href="orders_2.html#U1" title="ORDERS_2:sel.1">InternalRel</a> of <font color="Maroon" title="c1">G</font> <a href="relat_2.html#R3" title="RELAT_2:pred.3">is_symmetric_in</a> the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c1">G</font>
 <b>by </b><i><a class="ref" href="necklace.html#D4" title="NECKLACE:def.4">NECKLACE:def 4</a></i>;<br/><a NAME="E3:60_1_2_4"/><b>then </b><i><font color="Green" title="E47">A26</font></i>: 
<span class="p1"><a href="domain_1.html#K1" title="DOMAIN_1:func.1">[</a><span class="default"><font color="Maroon" title="c4">c</font>,<font color="Maroon" title="c3">b</font></span><a href="domain_1.html#K1" title="DOMAIN_1:func.1">]</a></span> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> the <a href="orders_2.html#U1" title="ORDERS_2:sel.1">InternalRel</a> of <font color="Maroon" title="c1">G</font>
 <b>by </b><i><a class="txt" href="neckla_3.html#E4:60"><i><font color="Green" title="E39">A4</font></i></a>, <a class="ref" href="relat_2.html#D3" title="RELAT_2:def.3">RELAT_2:def 3</a></i>;<br/><a NAME="E4:60_1_2_4"/>
( <font color="Maroon" title="c3">b</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c6">Z</font> &amp; <font color="Maroon" title="c4">c</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c6">Z</font> )
 <b>by </b><i><a class="txt" href="neckla_3.html#E1:60"><i><font color="Green" title="E36">A1</font></i></a>, <a class="ref" href="enumset1.html#D2" title="ENUMSET1:def.2">ENUMSET1:def 2</a></i>;<br/><a NAME="E5:60_1_2_4"/><b>then </b>
( <font color="Maroon" title="c3">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 <span class="p1">(<span class="default"><a href="yellow_0.html#K5" title="YELLOW_0:func.5">subrelstr</a> <font color="Maroon" title="c6">Z</font></span>)</span> &amp; <font color="Maroon" title="c4">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 <span class="p1">(<span class="default"><a href="yellow_0.html#K5" title="YELLOW_0:func.5">subrelstr</a> <font color="Maroon" title="c6">Z</font></span>)</span> )
 <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="E6:60_1_2_4"/><b>then </b>
<span class="p1"><a href="domain_1.html#K1" title="DOMAIN_1:func.1">[</a><span class="default"><font color="Maroon" title="c4">c</font>,<font color="Maroon" title="c3">b</font></span><a href="domain_1.html#K1" title="DOMAIN_1:func.1">]</a></span> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <span class="p1"><a href="zfmisc_1.html#K2" title="ZFMISC_1:func.2">[:</a><span class="default">the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <span class="p2">(<span class="default"><a href="yellow_0.html#K5" title="YELLOW_0:func.5">subrelstr</a> <font color="Maroon" title="c6">Z</font></span>)</span>,the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <span class="p2">(<span class="default"><a href="yellow_0.html#K5" title="YELLOW_0:func.5">subrelstr</a> <font color="Maroon" title="c6">Z</font></span>)</span></span><a href="zfmisc_1.html#K2" title="ZFMISC_1:func.2">:]</a></span>
 <b>by </b><i><a class="ref" href="zfmisc_1.html#T106" title="ZFMISC_1:th.106">ZFMISC_1:106</a></i>;<br/><a NAME="E7:60_1_2_4"/><b>then </b>
<font color="Maroon" title="c14">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> the <a href="orders_2.html#U1" title="ORDERS_2:sel.1">InternalRel</a> of <font color="Maroon" title="c1">G</font> <a href="subset_1.html#K8" title="SUBSET_1:func.8">/\</a> <span class="p1"><a href="zfmisc_1.html#K2" title="ZFMISC_1:func.2">[:</a><span class="default">the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <span class="p2">(<span class="default"><a href="yellow_0.html#K5" title="YELLOW_0:func.5">subrelstr</a> <font color="Maroon" title="c6">Z</font></span>)</span>,the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <span class="p2">(<span class="default"><a href="yellow_0.html#K5" title="YELLOW_0:func.5">subrelstr</a> <font color="Maroon" title="c6">Z</font></span>)</span></span><a href="zfmisc_1.html#K2" title="ZFMISC_1:func.2">:]</a></span>
 <b>by </b><i><a class="txt" href="neckla_3.html#E1:60_1_2_4"><i><font color="Green" title="E46">A25</font></i></a>, <a class="txt" href="neckla_3.html#E3:60_1_2_4"><i><font color="Green" title="E47">A26</font></i></a>, <a class="ref" href="xboole_0.html#D3" title="XBOOLE_0:def.3">XBOOLE_0:def 3</a></i>;<br/><a NAME="E8:60_1_2_4"/><b>then </b>
<font color="Maroon" title="c14">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> the <a href="orders_2.html#U1" title="ORDERS_2:sel.1">InternalRel</a> of <font color="Maroon" title="c1">G</font> <a href="wellord1.html#K2" title="WELLORD1:func.2">|_2</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="c6">Z</font></span>)</span>
 ;<br/><b>hence </b><a NAME="E9:60_1_2_4"/>
<font color="Maroon" title="c14">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> the <a href="orders_2.html#U1" title="ORDERS_2:sel.1">InternalRel</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="c6">Z</font></span>)</span>
 <b>by </b><i><a class="ref" href="yellow_0.html#D14" title="YELLOW_0:def.14">YELLOW_0:def 14</a></i>;<br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="60_1_2_5"><b>suppose </b></a><a NAME="E1:60_1_2_5"/><i><font color="Green" title="E46">A27</font></i>: 
<font color="Maroon" title="c14">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1"><a href="domain_1.html#K1" title="DOMAIN_1:func.1">[</a><span class="default"><font color="Maroon" title="c4">c</font>,<font color="Maroon" title="c5">d</font></span><a href="domain_1.html#K1" title="DOMAIN_1:func.1">]</a></span>
 ;<br/><div class="add"><a NAME="E2:60_1_2_5"/>
( <font color="Maroon" title="c4">c</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c6">Z</font> &amp; <font color="Maroon" title="c5">d</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c6">Z</font> )
 <b>by </b><i><a class="txt" href="neckla_3.html#E1:60"><i><font color="Green" title="E36">A1</font></i></a>, <a class="ref" href="enumset1.html#D2" title="ENUMSET1:def.2">ENUMSET1:def 2</a></i>;<br/><a NAME="E3:60_1_2_5"/><b>then </b>
( <font color="Maroon" title="c4">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 <span class="p1">(<span class="default"><a href="yellow_0.html#K5" title="YELLOW_0:func.5">subrelstr</a> <font color="Maroon" title="c6">Z</font></span>)</span> &amp; <font color="Maroon" title="c5">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 <span class="p1">(<span class="default"><a href="yellow_0.html#K5" title="YELLOW_0:func.5">subrelstr</a> <font color="Maroon" title="c6">Z</font></span>)</span> )
 <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="E4:60_1_2_5"/><b>then </b>
<span class="p1"><a href="domain_1.html#K1" title="DOMAIN_1:func.1">[</a><span class="default"><font color="Maroon" title="c4">c</font>,<font color="Maroon" title="c5">d</font></span><a href="domain_1.html#K1" title="DOMAIN_1:func.1">]</a></span> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <span class="p1"><a href="zfmisc_1.html#K2" title="ZFMISC_1:func.2">[:</a><span class="default">the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <span class="p2">(<span class="default"><a href="yellow_0.html#K5" title="YELLOW_0:func.5">subrelstr</a> <font color="Maroon" title="c6">Z</font></span>)</span>,the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <span class="p2">(<span class="default"><a href="yellow_0.html#K5" title="YELLOW_0:func.5">subrelstr</a> <font color="Maroon" title="c6">Z</font></span>)</span></span><a href="zfmisc_1.html#K2" title="ZFMISC_1:func.2">:]</a></span>
 <b>by </b><i><a class="ref" href="zfmisc_1.html#T106" title="ZFMISC_1:th.106">ZFMISC_1:106</a></i>;<br/><a NAME="E5:60_1_2_5"/><b>then </b>
<font color="Maroon" title="c14">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> the <a href="orders_2.html#U1" title="ORDERS_2:sel.1">InternalRel</a> of <font color="Maroon" title="c1">G</font> <a href="subset_1.html#K8" title="SUBSET_1:func.8">/\</a> <span class="p1"><a href="zfmisc_1.html#K2" title="ZFMISC_1:func.2">[:</a><span class="default">the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <span class="p2">(<span class="default"><a href="yellow_0.html#K5" title="YELLOW_0:func.5">subrelstr</a> <font color="Maroon" title="c6">Z</font></span>)</span>,the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <span class="p2">(<span class="default"><a href="yellow_0.html#K5" title="YELLOW_0:func.5">subrelstr</a> <font color="Maroon" title="c6">Z</font></span>)</span></span><a href="zfmisc_1.html#K2" title="ZFMISC_1:func.2">:]</a></span>
 <b>by </b><i><a class="txt" href="neckla_3.html#E5:60"><i><font color="Green" title="E40">A5</font></i></a>, <a class="txt" href="neckla_3.html#E1:60_1_2_5"><i><font color="Green" title="E46">A27</font></i></a>, <a class="ref" href="xboole_0.html#D3" title="XBOOLE_0:def.3">XBOOLE_0:def 3</a></i>;<br/><a NAME="E6:60_1_2_5"/><b>then </b>
<font color="Maroon" title="c14">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> the <a href="orders_2.html#U1" title="ORDERS_2:sel.1">InternalRel</a> of <font color="Maroon" title="c1">G</font> <a href="wellord1.html#K2" title="WELLORD1:func.2">|_2</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="c6">Z</font></span>)</span>
 ;<br/><b>hence </b><a NAME="E7:60_1_2_5"/>
<font color="Maroon" title="c14">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> the <a href="orders_2.html#U1" title="ORDERS_2:sel.1">InternalRel</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="c6">Z</font></span>)</span>
 <b>by </b><i><a class="ref" href="yellow_0.html#D14" title="YELLOW_0:def.14">YELLOW_0:def 14</a></i>;<br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="60_1_2_6"><b>suppose </b></a><a NAME="E1:60_1_2_6"/><i><font color="Green" title="E46">A28</font></i>: 
<font color="Maroon" title="c14">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1"><a href="domain_1.html#K1" title="DOMAIN_1:func.1">[</a><span class="default"><font color="Maroon" title="c5">d</font>,<font color="Maroon" title="c4">c</font></span><a href="domain_1.html#K1" title="DOMAIN_1:func.1">]</a></span>
 ;<br/><div class="add"><a NAME="E2:60_1_2_6"/>
the <a href="orders_2.html#U1" title="ORDERS_2:sel.1">InternalRel</a> of <font color="Maroon" title="c1">G</font> <a href="relat_2.html#R3" title="RELAT_2:pred.3">is_symmetric_in</a> the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c1">G</font>
 <b>by </b><i><a class="ref" href="necklace.html#D4" title="NECKLACE:def.4">NECKLACE:def 4</a></i>;<br/><a NAME="E3:60_1_2_6"/><b>then </b><i><font color="Green" title="E47">A29</font></i>: 
<span class="p1"><a href="domain_1.html#K1" title="DOMAIN_1:func.1">[</a><span class="default"><font color="Maroon" title="c5">d</font>,<font color="Maroon" title="c4">c</font></span><a href="domain_1.html#K1" title="DOMAIN_1:func.1">]</a></span> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> the <a href="orders_2.html#U1" title="ORDERS_2:sel.1">InternalRel</a> of <font color="Maroon" title="c1">G</font>
 <b>by </b><i><a class="txt" href="neckla_3.html#E5:60"><i><font color="Green" title="E40">A5</font></i></a>, <a class="ref" href="relat_2.html#D3" title="RELAT_2:def.3">RELAT_2:def 3</a></i>;<br/><a NAME="E4:60_1_2_6"/>
( <font color="Maroon" title="c4">c</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c6">Z</font> &amp; <font color="Maroon" title="c5">d</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c6">Z</font> )
 <b>by </b><i><a class="txt" href="neckla_3.html#E1:60"><i><font color="Green" title="E36">A1</font></i></a>, <a class="ref" href="enumset1.html#D2" title="ENUMSET1:def.2">ENUMSET1:def 2</a></i>;<br/><a NAME="E5:60_1_2_6"/><b>then </b>
( <font color="Maroon" title="c4">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 <span class="p1">(<span class="default"><a href="yellow_0.html#K5" title="YELLOW_0:func.5">subrelstr</a> <font color="Maroon" title="c6">Z</font></span>)</span> &amp; <font color="Maroon" title="c5">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 <span class="p1">(<span class="default"><a href="yellow_0.html#K5" title="YELLOW_0:func.5">subrelstr</a> <font color="Maroon" title="c6">Z</font></span>)</span> )
 <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="E6:60_1_2_6"/><b>then </b>
<span class="p1"><a href="domain_1.html#K1" title="DOMAIN_1:func.1">[</a><span class="default"><font color="Maroon" title="c5">d</font>,<font color="Maroon" title="c4">c</font></span><a href="domain_1.html#K1" title="DOMAIN_1:func.1">]</a></span> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <span class="p1"><a href="zfmisc_1.html#K2" title="ZFMISC_1:func.2">[:</a><span class="default">the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <span class="p2">(<span class="default"><a href="yellow_0.html#K5" title="YELLOW_0:func.5">subrelstr</a> <font color="Maroon" title="c6">Z</font></span>)</span>,the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <span class="p2">(<span class="default"><a href="yellow_0.html#K5" title="YELLOW_0:func.5">subrelstr</a> <font color="Maroon" title="c6">Z</font></span>)</span></span><a href="zfmisc_1.html#K2" title="ZFMISC_1:func.2">:]</a></span>
 <b>by </b><i><a class="ref" href="zfmisc_1.html#T106" title="ZFMISC_1:th.106">ZFMISC_1:106</a></i>;<br/><a NAME="E7:60_1_2_6"/><b>then </b>
<font color="Maroon" title="c14">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> the <a href="orders_2.html#U1" title="ORDERS_2:sel.1">InternalRel</a> of <font color="Maroon" title="c1">G</font> <a href="subset_1.html#K8" title="SUBSET_1:func.8">/\</a> <span class="p1"><a href="zfmisc_1.html#K2" title="ZFMISC_1:func.2">[:</a><span class="default">the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <span class="p2">(<span class="default"><a href="yellow_0.html#K5" title="YELLOW_0:func.5">subrelstr</a> <font color="Maroon" title="c6">Z</font></span>)</span>,the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <span class="p2">(<span class="default"><a href="yellow_0.html#K5" title="YELLOW_0:func.5">subrelstr</a> <font color="Maroon" title="c6">Z</font></span>)</span></span><a href="zfmisc_1.html#K2" title="ZFMISC_1:func.2">:]</a></span>
 <b>by </b><i><a class="txt" href="neckla_3.html#E1:60_1_2_6"><i><font color="Green" title="E46">A28</font></i></a>, <a class="txt" href="neckla_3.html#E3:60_1_2_6"><i><font color="Green" title="E47">A29</font></i></a>, <a class="ref" href="xboole_0.html#D3" title="XBOOLE_0:def.3">XBOOLE_0:def 3</a></i>;<br/><a NAME="E8:60_1_2_6"/><b>then </b>
<font color="Maroon" title="c14">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> the <a href="orders_2.html#U1" title="ORDERS_2:sel.1">InternalRel</a> of <font color="Maroon" title="c1">G</font> <a href="wellord1.html#K2" title="WELLORD1:func.2">|_2</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="c6">Z</font></span>)</span>
 ;<br/><b>hence </b><a NAME="E9:60_1_2_6"/>
<font color="Maroon" title="c14">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> the <a href="orders_2.html#U1" title="ORDERS_2:sel.1">InternalRel</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="c6">Z</font></span>)</span>
 <b>by </b><i><a class="ref" href="yellow_0.html#D14" title="YELLOW_0:def.14">YELLOW_0:def 14</a></i>;<br/></div><b>end;</b></div></div><b>end;</b></div>

</div><b>end;</b></div>
<a NAME="E10:60"/><i><font color="Green" title="E45">A30</font></i>: 
( <font color="Maroon" title="c2">a</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c3">b</font> &amp; <font color="Maroon" title="c2">a</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c4">c</font> &amp; <font color="Maroon" title="c2">a</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c5">d</font> &amp; <font color="Maroon" title="c3">b</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c4">c</font> &amp; <font color="Maroon" title="c3">b</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c5">d</font> &amp; <font color="Maroon" title="c4">c</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c5">d</font> )
 
<b>by </b><i><a class="txt" href="neckla_3.html#E2:60"><i><font color="Green" title="E37">A2</font></i></a>, <a class="ref" href="incproj.html#D6" title="INCPROJ:def.6">INCPROJ:def 6</a></i>;<br/>
<b>set </b><font color="Maroon" title="c14">g</font> = 0,1 <a href="funct_4.html#K5" title="FUNCT_4:func.5">--&gt;</a> <font color="Maroon" title="c2">a</font>,<font color="Maroon" title="c3">b</font>;<br/>
<b>set </b><font color="Maroon" title="c15">h</font> = 2,3 <a href="funct_4.html#K5" title="FUNCT_4:func.5">--&gt;</a> <font color="Maroon" title="c4">c</font>,<font color="Maroon" title="c5">d</font>;<br/>
<b>set </b><font color="Maroon" title="c16">f</font> = <span class="p1">(<span class="default">0,1 <a href="funct_4.html#K5" title="FUNCT_4:func.5">--&gt;</a> <font color="Maroon" title="c2">a</font>,<font color="Maroon" title="c3">b</font></span>)</span> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p1">(<span class="default">2,3 <a href="funct_4.html#K5" title="FUNCT_4:func.5">--&gt;</a> <font color="Maroon" title="c4">c</font>,<font color="Maroon" title="c5">d</font></span>)</span>;<br/>
 <a href="relat_1.html#K1" title="RELAT_1:func.1">dom</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default">0,1 <a href="funct_4.html#K5" title="FUNCT_4:func.5">--&gt;</a> <font color="Maroon" title="c2">a</font>,<font color="Maroon" title="c3">b</font></span>)</span> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p2">(<span class="default">2,3 <a href="funct_4.html#K5" title="FUNCT_4:func.5">--&gt;</a> <font color="Maroon" title="c4">c</font>,<font color="Maroon" title="c5">d</font></span>)</span></span>)</span> = 
<span class="p1">(<span class="default"><a href="relset_1.html#K4" title="RELSET_1:func.4">dom</a> <span class="p2">(<span class="default">0,1 <a href="funct_4.html#K5" title="FUNCT_4:func.5">--&gt;</a> <font color="Maroon" title="c2">a</font>,<font color="Maroon" title="c3">b</font></span>)</span></span>)</span> <a href="xboole_0.html#K2" title="XBOOLE_0:func.2">\/</a> <span class="p1">(<span class="default"><a href="relset_1.html#K4" title="RELSET_1:func.4">dom</a> <span class="p2">(<span class="default">2,3 <a href="funct_4.html#K5" title="FUNCT_4:func.5">--&gt;</a> <font color="Maroon" title="c4">c</font>,<font color="Maroon" title="c5">d</font></span>)</span></span>)</span>
<b>by </b><i><a class="ref" href="funct_4.html#D1" title="FUNCT_4:def.1">FUNCT_4:def 1</a></i>
<br/>.= 
<span class="p1"><a href="tarski.html#K2" title="TARSKI:func.2">{</a><span class="default">0,1</span><a href="tarski.html#K2" title="TARSKI:func.2">}</a></span> <a href="xboole_0.html#K2" title="XBOOLE_0:func.2">\/</a> <span class="p1">(<span class="default"><a href="relset_1.html#K4" title="RELSET_1:func.4">dom</a> <span class="p2">(<span class="default">2,3 <a href="funct_4.html#K5" title="FUNCT_4:func.5">--&gt;</a> <font color="Maroon" title="c4">c</font>,<font color="Maroon" title="c5">d</font></span>)</span></span>)</span>
<b>by </b><i><a class="ref" href="funct_4.html#T65" title="FUNCT_4:th.65">FUNCT_4:65</a></i>
<br/>.= 
<span class="p1"><a href="tarski.html#K2" title="TARSKI:func.2">{</a><span class="default">0,1</span><a href="tarski.html#K2" title="TARSKI:func.2">}</a></span> <a href="xboole_0.html#K2" title="XBOOLE_0:func.2">\/</a> <span class="p1"><a href="tarski.html#K2" title="TARSKI:func.2">{</a><span class="default">2,3</span><a href="tarski.html#K2" title="TARSKI:func.2">}</a></span>
<b>by </b><i><a class="ref" href="funct_4.html#T65" title="FUNCT_4:th.65">FUNCT_4:65</a></i>
<br/>.= 
<span class="p1"><a href="enumset1.html#K2" title="ENUMSET1:func.2">{</a><span class="default">0,1,2,3</span><a href="enumset1.html#K2" title="ENUMSET1:func.2">}</a></span>
<b>by </b><i><a class="ref" href="enumset1.html#T45" title="ENUMSET1:th.45">ENUMSET1:45</a></i>
;<br/>
<a NAME="E12:60"/><b>then </b><i><font color="Green" title="E46">A31</font></i>: 
 <a href="relat_1.html#K1" title="RELAT_1:func.1">dom</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default">0,1 <a href="funct_4.html#K5" title="FUNCT_4:func.5">--&gt;</a> <font color="Maroon" title="c2">a</font>,<font color="Maroon" title="c3">b</font></span>)</span> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p2">(<span class="default">2,3 <a href="funct_4.html#K5" title="FUNCT_4:func.5">--&gt;</a> <font color="Maroon" title="c4">c</font>,<font color="Maroon" title="c5">d</font></span>)</span></span>)</span> <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 <span class="p1">(<span class="default"><a href="necklace.html#K4" title="NECKLACE:func.4">Necklace</a> 4</span>)</span>
 
<b>by </b><i><a class="ref" href="necklace.html#T2" title="NECKLACE:th.2">NECKLACE:2</a>, <a class="ref" href="necklace.html#T21" title="NECKLACE:th.21">NECKLACE:21</a></i>;<br/>
<a NAME="E13:60"/><i><font color="Green" title="E47">A32</font></i>: 
 <a href="relat_1.html#K2" title="RELAT_1:func.2">rng</a> <span class="p1">(<span class="default">0,1 <a href="funct_4.html#K5" title="FUNCT_4:func.5">--&gt;</a> <font color="Maroon" title="c2">a</font>,<font color="Maroon" title="c3">b</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1"><a href="domain_1.html#K7" title="DOMAIN_1:func.7">{</a><span class="default"><font color="Maroon" title="c2">a</font>,<font color="Maroon" title="c3">b</font></span><a href="domain_1.html#K7" title="DOMAIN_1:func.7">}</a></span>
 
<b>by </b><i><a class="ref" href="funct_4.html#T67" title="FUNCT_4:th.67">FUNCT_4:67</a></i>;<br/>
<a NAME="E14:60"/><i><font color="Green" title="E48">A33</font></i>: 
 <a href="relat_1.html#K2" title="RELAT_1:func.2">rng</a> <span class="p1">(<span class="default">2,3 <a href="funct_4.html#K5" title="FUNCT_4:func.5">--&gt;</a> <font color="Maroon" title="c4">c</font>,<font color="Maroon" title="c5">d</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1"><a href="domain_1.html#K7" title="DOMAIN_1:func.7">{</a><span class="default"><font color="Maroon" title="c4">c</font>,<font color="Maroon" title="c5">d</font></span><a href="domain_1.html#K7" title="DOMAIN_1:func.7">}</a></span>
 
<b>by </b><i><a class="ref" href="funct_4.html#T67" title="FUNCT_4:th.67">FUNCT_4:67</a></i>;<br/>
<a NAME="E15:60"/><i><font color="Green" title="E49">A34</font></i>: 
not 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="c6">Z</font></span>)</span> is <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a>
 
<b>by </b><i><a class="txt" href="neckla_3.html#E1:60"><i><font color="Green" title="E36">A1</font></i></a>, <a class="ref" href="yellow_0.html#D15" title="YELLOW_0:def.15">YELLOW_0:def 15</a></i>;<br/>
<a NAME="E16:60"/><i><font color="Green" title="E50">A35</font></i>: 
 <a href="relset_1.html#K4" title="RELSET_1:func.4">dom</a> <span class="p1">(<span class="default">0,1 <a href="funct_4.html#K5" title="FUNCT_4:func.5">--&gt;</a> <font color="Maroon" title="c2">a</font>,<font color="Maroon" title="c3">b</font></span>)</span> <a href="xboole_0.html#R1" title="XBOOLE_0:pred.1">misses</a>  <a href="relset_1.html#K4" title="RELSET_1:func.4">dom</a> <span class="p1">(<span class="default">2,3 <a href="funct_4.html#K5" title="FUNCT_4:func.5">--&gt;</a> <font color="Maroon" title="c4">c</font>,<font color="Maroon" title="c5">d</font></span>)</span>
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="60_3"><b>proof </b></a><div class="add">

<b>assume </b><a NAME="E1:60_3"/>
not  <a href="relset_1.html#K4" title="RELSET_1:func.4">dom</a> <span class="p1">(<span class="default">0,1 <a href="funct_4.html#K5" title="FUNCT_4:func.5">--&gt;</a> <font color="Maroon" title="c2">a</font>,<font color="Maroon" title="c3">b</font></span>)</span> <a href="xboole_0.html#R1" title="XBOOLE_0:pred.1">misses</a>  <a href="relset_1.html#K4" title="RELSET_1:func.4">dom</a> <span class="p1">(<span class="default">2,3 <a href="funct_4.html#K5" title="FUNCT_4:func.5">--&gt;</a> <font color="Maroon" title="c4">c</font>,<font color="Maroon" title="c5">d</font></span>)</span>
 ;<br/>

<b>then consider </b><font color="Maroon" title="c17">x</font> being    <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a> <b> such that </b><br/><a NAME="E3:60_3"/><i><font color="Green" title="E51">A36</font></i>: 
( <font color="Maroon" title="c17">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> <span class="p1">(<span class="default">0,1 <a href="funct_4.html#K5" title="FUNCT_4:func.5">--&gt;</a> <font color="Maroon" title="c2">a</font>,<font color="Maroon" title="c3">b</font></span>)</span> &amp; <font color="Maroon" title="c17">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> <span class="p1">(<span class="default">2,3 <a href="funct_4.html#K5" title="FUNCT_4:func.5">--&gt;</a> <font color="Maroon" title="c4">c</font>,<font color="Maroon" title="c5">d</font></span>)</span> )
 <b>by </b><i><a class="ref" href="xboole_0.html#T3" title="XBOOLE_0:th.3">XBOOLE_0:3</a></i>;<br/>
<a NAME="E4:60_3"/>
( ( <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 ) &amp; ( <font color="Maroon" title="c17">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 2 or <font color="Maroon" title="c17">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 3 ) )
 
<b>by </b><i><a class="txt" href="neckla_3.html#E3:60_3"><i><font color="Green" title="E51">A36</font></i></a>, <a class="ref" href="tarski.html#D2" title="TARSKI:def.2">TARSKI:def 2</a></i>;<br/>
<b>hence </b><a NAME="E5:60_3"/>
contradiction
 ;<br/>


</div><b>end;</b></div>
<a NAME="E17:60"/><i><font color="Green" title="E51">A37</font></i>: 
 <a href="relat_1.html#K2" title="RELAT_1:func.2">rng</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default">0,1 <a href="funct_4.html#K5" title="FUNCT_4:func.5">--&gt;</a> <font color="Maroon" title="c2">a</font>,<font color="Maroon" title="c3">b</font></span>)</span> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p2">(<span class="default">2,3 <a href="funct_4.html#K5" title="FUNCT_4:func.5">--&gt;</a> <font color="Maroon" title="c4">c</font>,<font color="Maroon" title="c5">d</font></span>)</span></span>)</span> <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 <span class="p1">(<span class="default"><a href="yellow_0.html#K5" title="YELLOW_0:func.5">subrelstr</a> <font color="Maroon" title="c6">Z</font></span>)</span>
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="60_4"><b>proof </b></a><div class="add">

<a NAME="E1:60_4"/>
 <a href="relat_1.html#K2" title="RELAT_1:func.2">rng</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default">0,1 <a href="funct_4.html#K5" title="FUNCT_4:func.5">--&gt;</a> <font color="Maroon" title="c2">a</font>,<font color="Maroon" title="c3">b</font></span>)</span> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p2">(<span class="default">2,3 <a href="funct_4.html#K5" title="FUNCT_4:func.5">--&gt;</a> <font color="Maroon" title="c4">c</font>,<font color="Maroon" title="c5">d</font></span>)</span></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="relat_1.html#K2" title="RELAT_1:func.2">rng</a> <span class="p2">(<span class="default">0,1 <a href="funct_4.html#K5" title="FUNCT_4:func.5">--&gt;</a> <font color="Maroon" title="c2">a</font>,<font color="Maroon" title="c3">b</font></span>)</span></span>)</span> <a href="xboole_0.html#K2" title="XBOOLE_0:func.2">\/</a> <span class="p1">(<span class="default"><a href="relat_1.html#K2" title="RELAT_1:func.2">rng</a> <span class="p2">(<span class="default">2,3 <a href="funct_4.html#K5" title="FUNCT_4:func.5">--&gt;</a> <font color="Maroon" title="c4">c</font>,<font color="Maroon" title="c5">d</font></span>)</span></span>)</span>
 
<b>by </b><i><a class="txt" href="neckla_3.html#E16:60"><i><font color="Green" title="E50">A35</font></i></a>, <a class="ref" href="necklace.html#T7" title="NECKLACE:th.7">NECKLACE:7</a></i>;<br/>
<a NAME="E2:60_4"/><b>then </b>
 <a href="relat_1.html#K2" title="RELAT_1:func.2">rng</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default">0,1 <a href="funct_4.html#K5" title="FUNCT_4:func.5">--&gt;</a> <font color="Maroon" title="c2">a</font>,<font color="Maroon" title="c3">b</font></span>)</span> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p2">(<span class="default">2,3 <a href="funct_4.html#K5" title="FUNCT_4:func.5">--&gt;</a> <font color="Maroon" title="c4">c</font>,<font color="Maroon" title="c5">d</font></span>)</span></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1"><a href="domain_1.html#K9" title="DOMAIN_1:func.9">{</a><span class="default"><font color="Maroon" title="c2">a</font>,<font color="Maroon" title="c3">b</font>,<font color="Maroon" title="c4">c</font>,<font color="Maroon" title="c5">d</font></span><a href="domain_1.html#K9" title="DOMAIN_1:func.9">}</a></span>
 
<b>by </b><i><a class="txt" href="neckla_3.html#E13:60"><i><font color="Green" title="E47">A32</font></i></a>, <a class="txt" href="neckla_3.html#E14:60"><i><font color="Green" title="E48">A33</font></i></a>, <a class="ref" href="enumset1.html#T45" title="ENUMSET1:th.45">ENUMSET1:45</a></i>;<br/>
<b>hence </b><a NAME="E3:60_4"/>
 <a href="relat_1.html#K2" title="RELAT_1:func.2">rng</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default">0,1 <a href="funct_4.html#K5" title="FUNCT_4:func.5">--&gt;</a> <font color="Maroon" title="c2">a</font>,<font color="Maroon" title="c3">b</font></span>)</span> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p2">(<span class="default">2,3 <a href="funct_4.html#K5" title="FUNCT_4:func.5">--&gt;</a> <font color="Maroon" title="c4">c</font>,<font color="Maroon" title="c5">d</font></span>)</span></span>)</span> <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 <span class="p1">(<span class="default"><a href="yellow_0.html#K5" title="YELLOW_0:func.5">subrelstr</a> <font color="Maroon" title="c6">Z</font></span>)</span>
 <b>by </b><i><a class="txt" href="neckla_3.html#E1:60"><i><font color="Green" title="E36">A1</font></i></a>, <a class="ref" href="yellow_0.html#D15" title="YELLOW_0:def.15">YELLOW_0:def 15</a></i>;<br/>


</div><b>end;</b></div>
<b>then reconsider </b><font color="Maroon" title="c17">f</font> = <span class="p1">(<span class="default">0,1 <a href="funct_4.html#K5" title="FUNCT_4:func.5">--&gt;</a> <font color="Maroon" title="c2">a</font>,<font color="Maroon" title="c3">b</font></span>)</span> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p1">(<span class="default">2,3 <a href="funct_4.html#K5" title="FUNCT_4:func.5">--&gt;</a> <font color="Maroon" title="c4">c</font>,<font color="Maroon" title="c5">d</font></span>)</span> as   <a href="struct_0.html#NM6" title="STRUCT_0:NM.6">Function</a> of <span class="p1">(<span class="default"><a href="necklace.html#K4" title="NECKLACE:func.4">Necklace</a> 4</span>)</span>,<span class="p1">(<span class="default"><a href="yellow_0.html#K5" title="YELLOW_0:func.5">subrelstr</a> <font color="Maroon" title="c6">Z</font></span>)</span> <b>by </b><i><a class="txt" href="neckla_3.html#E12:60"><i><font color="Green" title="E46">A31</font></i></a>, <a class="txt" href="neckla_3.html#E15:60"><i><font color="Green" title="E49">A34</font></i></a>, <a class="ref" href="funct_2.html#D1" title="FUNCT_2:def.1">FUNCT_2:def 1</a>, <a class="ref" href="relset_1.html#T11" title="RELSET_1:th.11">RELSET_1:11</a></i>;<br/>
<a NAME="E19:60"/><i><font color="Green" title="E52">A38</font></i>: 
0,1 <a href="funct_4.html#K5" title="FUNCT_4:func.5">--&gt;</a> <font color="Maroon" title="c2">a</font>,<font color="Maroon" title="c3">b</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="60_5"><b>proof </b></a><div class="add">

<a NAME="E1:60_5"/><i><font color="Green" title="E53">A39</font></i>: 
0,1 <a href="funct_4.html#K5" title="FUNCT_4:func.5">--&gt;</a> <font color="Maroon" title="c2">a</font>,<font color="Maroon" title="c3">b</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><span class="p2"><a href="tarski.html#K1" title="TARSKI:func.1">{</a><span class="default">0</span><a href="tarski.html#K1" title="TARSKI:func.1">}</a></span> <a href="funcop_1.html#K2" title="FUNCOP_1:func.2">--&gt;</a> <font color="Maroon" title="c2">a</font></span>)</span> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p1">(<span class="default"><span class="p2"><a href="tarski.html#K1" title="TARSKI:func.1">{</a><span class="default">1</span><a href="tarski.html#K1" title="TARSKI:func.1">}</a></span> <a href="funcop_1.html#K2" title="FUNCOP_1:func.2">--&gt;</a> <font color="Maroon" title="c3">b</font></span>)</span>
 
<b>by </b><i><a class="ref" href="funct_4.html#D4" title="FUNCT_4:def.4">FUNCT_4:def 4</a></i>;<br/>
<a NAME="E2:60_5"/>
 <a href="relat_1.html#K2" title="RELAT_1:func.2">rng</a> <span class="p1">(<span class="default">0 <a href="cqc_lang.html#K3" title="CQC_LANG:func.3">.--&gt;</a> <font color="Maroon" title="c2">a</font></span>)</span> <a href="xboole_0.html#R1" title="XBOOLE_0:pred.1">misses</a>  <a href="relat_1.html#K2" title="RELAT_1:func.2">rng</a> <span class="p1">(<span class="default">1 <a href="cqc_lang.html#K3" title="CQC_LANG:func.3">.--&gt;</a> <font color="Maroon" title="c3">b</font></span>)</span>
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="60_5_1"><b>proof </b></a><div class="add">

<b>assume </b><a NAME="E1:60_5_1"/>
 <a href="relat_1.html#K2" title="RELAT_1:func.2">rng</a> <span class="p1">(<span class="default">0 <a href="cqc_lang.html#K3" title="CQC_LANG:func.3">.--&gt;</a> <font color="Maroon" title="c2">a</font></span>)</span> <a href="xboole_0.html#NR5" title="XBOOLE_0:NR.5">meets</a>  <a href="relat_1.html#K2" title="RELAT_1:func.2">rng</a> <span class="p1">(<span class="default">1 <a href="cqc_lang.html#K3" title="CQC_LANG:func.3">.--&gt;</a> <font color="Maroon" title="c3">b</font></span>)</span>
 ;<br/>

<b>then consider </b><font color="Maroon" title="c18">x</font> being    <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a> <b> such that </b><br/><a NAME="E3:60_5_1"/><i><font color="Green" title="E54">A40</font></i>: 
( <font color="Maroon" title="c18">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="relat_1.html#K2" title="RELAT_1:func.2">rng</a> <span class="p1">(<span class="default">0 <a href="cqc_lang.html#K3" title="CQC_LANG:func.3">.--&gt;</a> <font color="Maroon" title="c2">a</font></span>)</span> &amp; <font color="Maroon" title="c18">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="relat_1.html#K2" title="RELAT_1:func.2">rng</a> <span class="p1">(<span class="default">1 <a href="cqc_lang.html#K3" title="CQC_LANG:func.3">.--&gt;</a> <font color="Maroon" title="c3">b</font></span>)</span> )
 <b>by </b><i><a class="ref" href="xboole_0.html#T3" title="XBOOLE_0:th.3">XBOOLE_0:3</a></i>;<br/>
<a NAME="E4:60_5_1"/><i><font color="Green" title="E55">A41</font></i>: 
 <a href="relat_1.html#K2" title="RELAT_1:func.2">rng</a> <span class="p1">(<span class="default">0 <a href="cqc_lang.html#K3" title="CQC_LANG:func.3">.--&gt;</a> <font color="Maroon" title="c2">a</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1"><a href="domain_1.html#K6" title="DOMAIN_1:func.6">{</a><span class="default"><font color="Maroon" title="c2">a</font></span><a href="domain_1.html#K6" title="DOMAIN_1:func.6">}</a></span>
 
<b>by </b><i><a class="ref" href="cqc_lang.html#T5" title="CQC_LANG:th.5">CQC_LANG:5</a></i>;<br/>
<a NAME="E5:60_5_1"/><i><font color="Green" title="E56">A42</font></i>: 
 <a href="relat_1.html#K2" title="RELAT_1:func.2">rng</a> <span class="p1">(<span class="default">1 <a href="cqc_lang.html#K3" title="CQC_LANG:func.3">.--&gt;</a> <font color="Maroon" title="c3">b</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1"><a href="domain_1.html#K6" title="DOMAIN_1:func.6">{</a><span class="default"><font color="Maroon" title="c3">b</font></span><a href="domain_1.html#K6" title="DOMAIN_1:func.6">}</a></span>
 
<b>by </b><i><a class="ref" href="cqc_lang.html#T5" title="CQC_LANG:th.5">CQC_LANG:5</a></i>;<br/>
<a NAME="E6:60_5_1"/>
<font color="Maroon" title="c18">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c2">a</font>
 
<b>by </b><i><a class="txt" href="neckla_3.html#E3:60_5_1"><i><font color="Green" title="E54">A40</font></i></a>, <a class="txt" href="neckla_3.html#E4:60_5_1"><i><font color="Green" title="E55">A41</font></i></a>, <a class="ref" href="tarski.html#D1" title="TARSKI:def.1">TARSKI:def 1</a></i>;<br/>
<b>hence </b><a NAME="E7:60_5_1"/>
contradiction
 <b>by </b><i><a class="txt" href="neckla_3.html#E10:60"><i><font color="Green" title="E45">A30</font></i></a>, <a class="txt" href="neckla_3.html#E3:60_5_1"><i><font color="Green" title="E54">A40</font></i></a>, <a class="txt" href="neckla_3.html#E5:60_5_1"><i><font color="Green" title="E56">A42</font></i></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="E3:60_5"/>
0,1 <a href="funct_4.html#K5" title="FUNCT_4:func.5">--&gt;</a> <font color="Maroon" title="c2">a</font>,<font color="Maroon" title="c3">b</font> is <a href="funct_1.html#V2" title="FUNCT_1:attr.2">one-to-one</a>
 <b>by </b><i><a class="txt" href="neckla_3.html#E1:60_5"><i><font color="Green" title="E53">A39</font></i></a>, <a class="ref" href="knaster.html#T1" title="KNASTER:th.1">KNASTER:1</a></i>;<br/>


</div><b>end;</b></div>
<a NAME="E20:60"/><i><font color="Green" title="E53">A43</font></i>: 
2,3 <a href="funct_4.html#K5" title="FUNCT_4:func.5">--&gt;</a> <font color="Maroon" title="c4">c</font>,<font color="Maroon" title="c5">d</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="60_6"><b>proof </b></a><div class="add">

<a NAME="E1:60_6"/><i><font color="Green" title="E54">A44</font></i>: 
2,3 <a href="funct_4.html#K5" title="FUNCT_4:func.5">--&gt;</a> <font color="Maroon" title="c4">c</font>,<font color="Maroon" title="c5">d</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><span class="p2"><a href="tarski.html#K1" title="TARSKI:func.1">{</a><span class="default">2</span><a href="tarski.html#K1" title="TARSKI:func.1">}</a></span> <a href="funcop_1.html#K2" title="FUNCOP_1:func.2">--&gt;</a> <font color="Maroon" title="c4">c</font></span>)</span> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p1">(<span class="default"><span class="p2"><a href="tarski.html#K1" title="TARSKI:func.1">{</a><span class="default">3</span><a href="tarski.html#K1" title="TARSKI:func.1">}</a></span> <a href="funcop_1.html#K2" title="FUNCOP_1:func.2">--&gt;</a> <font color="Maroon" title="c5">d</font></span>)</span>
 
<b>by </b><i><a class="ref" href="funct_4.html#D4" title="FUNCT_4:def.4">FUNCT_4:def 4</a></i>;<br/>
<a NAME="E2:60_6"/>
 <a href="relat_1.html#K2" title="RELAT_1:func.2">rng</a> <span class="p1">(<span class="default">2 <a href="cqc_lang.html#K3" title="CQC_LANG:func.3">.--&gt;</a> <font color="Maroon" title="c4">c</font></span>)</span> <a href="xboole_0.html#R1" title="XBOOLE_0:pred.1">misses</a>  <a href="relat_1.html#K2" title="RELAT_1:func.2">rng</a> <span class="p1">(<span class="default">3 <a href="cqc_lang.html#K3" title="CQC_LANG:func.3">.--&gt;</a> <font color="Maroon" title="c5">d</font></span>)</span>
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="60_6_1"><b>proof </b></a><div class="add">

<b>assume </b><a NAME="E1:60_6_1"/>
 <a href="relat_1.html#K2" title="RELAT_1:func.2">rng</a> <span class="p1">(<span class="default">2 <a href="cqc_lang.html#K3" title="CQC_LANG:func.3">.--&gt;</a> <font color="Maroon" title="c4">c</font></span>)</span> <a href="xboole_0.html#NR5" title="XBOOLE_0:NR.5">meets</a>  <a href="relat_1.html#K2" title="RELAT_1:func.2">rng</a> <span class="p1">(<span class="default">3 <a href="cqc_lang.html#K3" title="CQC_LANG:func.3">.--&gt;</a> <font color="Maroon" title="c5">d</font></span>)</span>
 ;<br/>

<b>then consider </b><font color="Maroon" title="c18">x</font> being    <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a> <b> such that </b><br/><a NAME="E3:60_6_1"/><i><font color="Green" title="E55">A45</font></i>: 
( <font color="Maroon" title="c18">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="relat_1.html#K2" title="RELAT_1:func.2">rng</a> <span class="p1">(<span class="default">2 <a href="cqc_lang.html#K3" title="CQC_LANG:func.3">.--&gt;</a> <font color="Maroon" title="c4">c</font></span>)</span> &amp; <font color="Maroon" title="c18">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="relat_1.html#K2" title="RELAT_1:func.2">rng</a> <span class="p1">(<span class="default">3 <a href="cqc_lang.html#K3" title="CQC_LANG:func.3">.--&gt;</a> <font color="Maroon" title="c5">d</font></span>)</span> )
 <b>by </b><i><a class="ref" href="xboole_0.html#T3" title="XBOOLE_0:th.3">XBOOLE_0:3</a></i>;<br/>
<a NAME="E4:60_6_1"/><i><font color="Green" title="E56">A46</font></i>: 
 <a href="relat_1.html#K2" title="RELAT_1:func.2">rng</a> <span class="p1">(<span class="default">2 <a href="cqc_lang.html#K3" title="CQC_LANG:func.3">.--&gt;</a> <font color="Maroon" title="c4">c</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1"><a href="domain_1.html#K6" title="DOMAIN_1:func.6">{</a><span class="default"><font color="Maroon" title="c4">c</font></span><a href="domain_1.html#K6" title="DOMAIN_1:func.6">}</a></span>
 
<b>by </b><i><a class="ref" href="cqc_lang.html#T5" title="CQC_LANG:th.5">CQC_LANG:5</a></i>;<br/>
<a NAME="E5:60_6_1"/><i><font color="Green" title="E57">A47</font></i>: 
 <a href="relat_1.html#K2" title="RELAT_1:func.2">rng</a> <span class="p1">(<span class="default">3 <a href="cqc_lang.html#K3" title="CQC_LANG:func.3">.--&gt;</a> <font color="Maroon" title="c5">d</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1"><a href="domain_1.html#K6" title="DOMAIN_1:func.6">{</a><span class="default"><font color="Maroon" title="c5">d</font></span><a href="domain_1.html#K6" title="DOMAIN_1:func.6">}</a></span>
 
<b>by </b><i><a class="ref" href="cqc_lang.html#T5" title="CQC_LANG:th.5">CQC_LANG:5</a></i>;<br/>
<a NAME="E6:60_6_1"/>
<font color="Maroon" title="c18">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c4">c</font>
 
<b>by </b><i><a class="txt" href="neckla_3.html#E3:60_6_1"><i><font color="Green" title="E55">A45</font></i></a>, <a class="txt" href="neckla_3.html#E4:60_6_1"><i><font color="Green" title="E56">A46</font></i></a>, <a class="ref" href="tarski.html#D1" title="TARSKI:def.1">TARSKI:def 1</a></i>;<br/>
<b>hence </b><a NAME="E7:60_6_1"/>
contradiction
 <b>by </b><i><a class="txt" href="neckla_3.html#E10:60"><i><font color="Green" title="E45">A30</font></i></a>, <a class="txt" href="neckla_3.html#E3:60_6_1"><i><font color="Green" title="E55">A45</font></i></a>, <a class="txt" href="neckla_3.html#E5:60_6_1"><i><font color="Green" title="E57">A47</font></i></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="E3:60_6"/>
2,3 <a href="funct_4.html#K5" title="FUNCT_4:func.5">--&gt;</a> <font color="Maroon" title="c4">c</font>,<font color="Maroon" title="c5">d</font> is <a href="funct_1.html#V2" title="FUNCT_1:attr.2">one-to-one</a>
 <b>by </b><i><a class="txt" href="neckla_3.html#E1:60_6"><i><font color="Green" title="E54">A44</font></i></a>, <a class="ref" href="knaster.html#T1" title="KNASTER:th.1">KNASTER:1</a></i>;<br/>


</div><b>end;</b></div>
<a NAME="E21:60"/><i><font color="Green" title="E54">A48</font></i>: 
 <a href="relat_1.html#K2" title="RELAT_1:func.2">rng</a> <span class="p1">(<span class="default">0,1 <a href="funct_4.html#K5" title="FUNCT_4:func.5">--&gt;</a> <font color="Maroon" title="c2">a</font>,<font color="Maroon" title="c3">b</font></span>)</span> <a href="xboole_0.html#R1" title="XBOOLE_0:pred.1">misses</a>  <a href="relat_1.html#K2" title="RELAT_1:func.2">rng</a> <span class="p1">(<span class="default">2,3 <a href="funct_4.html#K5" title="FUNCT_4:func.5">--&gt;</a> <font color="Maroon" title="c4">c</font>,<font color="Maroon" title="c5">d</font></span>)</span>
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="60_7"><b>proof </b></a><div class="add">

<b>assume </b><a NAME="E1:60_7"/>
not  <a href="relat_1.html#K2" title="RELAT_1:func.2">rng</a> <span class="p1">(<span class="default">0,1 <a href="funct_4.html#K5" title="FUNCT_4:func.5">--&gt;</a> <font color="Maroon" title="c2">a</font>,<font color="Maroon" title="c3">b</font></span>)</span> <a href="xboole_0.html#R1" title="XBOOLE_0:pred.1">misses</a>  <a href="relat_1.html#K2" title="RELAT_1:func.2">rng</a> <span class="p1">(<span class="default">2,3 <a href="funct_4.html#K5" title="FUNCT_4:func.5">--&gt;</a> <font color="Maroon" title="c4">c</font>,<font color="Maroon" title="c5">d</font></span>)</span>
 ;<br/>

<b>then consider </b><font color="Maroon" title="c18">x</font> being    <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a> <b> such that </b><br/><a NAME="E3:60_7"/><i><font color="Green" title="E55">A49</font></i>: 
( <font color="Maroon" title="c18">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="relat_1.html#K2" title="RELAT_1:func.2">rng</a> <span class="p1">(<span class="default">0,1 <a href="funct_4.html#K5" title="FUNCT_4:func.5">--&gt;</a> <font color="Maroon" title="c2">a</font>,<font color="Maroon" title="c3">b</font></span>)</span> &amp; <font color="Maroon" title="c18">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="relat_1.html#K2" title="RELAT_1:func.2">rng</a> <span class="p1">(<span class="default">2,3 <a href="funct_4.html#K5" title="FUNCT_4:func.5">--&gt;</a> <font color="Maroon" title="c4">c</font>,<font color="Maroon" title="c5">d</font></span>)</span> )
 <b>by </b><i><a class="ref" href="xboole_0.html#T3" title="XBOOLE_0:th.3">XBOOLE_0:3</a></i>;<br/>
<a NAME="E4:60_7"/>
( ( <font color="Maroon" title="c18">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c2">a</font> or <font color="Maroon" title="c18">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c3">b</font> ) &amp; ( <font color="Maroon" title="c18">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c4">c</font> or <font color="Maroon" title="c18">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c5">d</font> ) )
 
<b>by </b><i><a class="txt" href="neckla_3.html#E13:60"><i><font color="Green" title="E47">A32</font></i></a>, <a class="txt" href="neckla_3.html#E14:60"><i><font color="Green" title="E48">A33</font></i></a>, <a class="txt" href="neckla_3.html#E3:60_7"><i><font color="Green" title="E55">A49</font></i></a>, <a class="ref" href="tarski.html#D2" title="TARSKI:def.2">TARSKI:def 2</a></i>;<br/>
<b>hence </b><a NAME="E5:60_7"/>
contradiction
 <b>by </b><i><a class="txt" href="neckla_3.html#E2:60"><i><font color="Green" title="E37">A2</font></i></a>, <a class="ref" href="incproj.html#D6" title="INCPROJ:def.6">INCPROJ:def 6</a></i>;<br/>


</div><b>end;</b></div>
<a NAME="E22:60"/><b>then </b><i><font color="Green" title="E55">A50</font></i>: 
<font color="Maroon" title="c17">f</font> is <a href="funct_1.html#V2" title="FUNCT_1:attr.2">one-to-one</a>
 
<b>by </b><i><a class="txt" href="neckla_3.html#E19:60"><i><font color="Green" title="E52">A38</font></i></a>, <a class="txt" href="neckla_3.html#E20:60"><i><font color="Green" title="E53">A43</font></i></a>, <a class="ref" href="knaster.html#T1" title="KNASTER:th.1">KNASTER:1</a></i>;<br/>
<a NAME="E23:60"/>
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 <span class="p1">(<span class="default"><a href="necklace.html#K4" title="NECKLACE:func.4">Necklace</a> 4</span>)</span> holds <br/> ( <span class="p1"><a href="domain_1.html#K1" title="DOMAIN_1:func.1">[</a><span class="default"><font color="Olive" title="b1">x</font>,<font color="Olive" title="b2">y</font></span><a href="domain_1.html#K1" title="DOMAIN_1:func.1">]</a></span> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> the <a href="orders_2.html#U1" title="ORDERS_2:sel.1">InternalRel</a> of <span class="p1">(<span class="default"><a href="necklace.html#K4" title="NECKLACE:func.4">Necklace</a> 4</span>)</span> iff <span class="p1"><a href="tarski.html#K4" title="TARSKI:func.4">[</a><span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c17">f</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Olive" title="b1">x</font></span>)</span>,<span class="p2">(<span class="default"><font color="Maroon" title="c17">f</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Olive" title="b2">y</font></span>)</span></span><a href="tarski.html#K4" title="TARSKI:func.4">]</a></span> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> the <a href="orders_2.html#U1" title="ORDERS_2:sel.1">InternalRel</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="c6">Z</font></span>)</span> )
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="60_8"><b>proof </b></a><div class="add">

<b>let </b><font color="Maroon" title="c18">x</font>, <font color="Maroon" title="c19">y</font> be   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <span class="p1">(<span class="default"><a href="necklace.html#K4" title="NECKLACE:func.4">Necklace</a> 4</span>)</span>;<br/>

<b>thus </b><a NAME="E1:60_8"/>
( <span class="p1"><a href="domain_1.html#K1" title="DOMAIN_1:func.1">[</a><span class="default"><font color="Maroon" title="c18">x</font>,<font color="Maroon" title="c19">y</font></span><a href="domain_1.html#K1" title="DOMAIN_1:func.1">]</a></span> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> the <a href="orders_2.html#U1" title="ORDERS_2:sel.1">InternalRel</a> of <span class="p1">(<span class="default"><a href="necklace.html#K4" title="NECKLACE:func.4">Necklace</a> 4</span>)</span> implies <span class="p1"><a href="tarski.html#K4" title="TARSKI:func.4">[</a><span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c17">f</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c18">x</font></span>)</span>,<span class="p2">(<span class="default"><font color="Maroon" title="c17">f</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c19">y</font></span>)</span></span><a href="tarski.html#K4" title="TARSKI:func.4">]</a></span> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> the <a href="orders_2.html#U1" title="ORDERS_2:sel.1">InternalRel</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="c6">Z</font></span>)</span> )
 <div><a class="txt" onclick="hs2(this)" href="javascript:()" title="60_8_1"><b>proof </b></a><div class="add">

<b>assume </b><a NAME="E1:60_8_1"/><i><font color="Green" title="E56">A51</font></i>: 
<span class="p1"><a href="domain_1.html#K1" title="DOMAIN_1:func.1">[</a><span class="default"><font color="Maroon" title="c18">x</font>,<font color="Maroon" title="c19">y</font></span><a href="domain_1.html#K1" title="DOMAIN_1:func.1">]</a></span> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> the <a href="orders_2.html#U1" title="ORDERS_2:sel.1">InternalRel</a> of <span class="p1">(<span class="default"><a href="necklace.html#K4" title="NECKLACE:func.4">Necklace</a> 4</span>)</span>
 ;<br/>

<div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="60_8_1_1"><b>per </b></a><a class="txt" onclick="hs(this)" href="javascript:()"><b>cases </b></a><span class="hide"><a NAME="E1:60_8_1_1"/>
( <span class="p1"><a href="domain_1.html#K1" title="DOMAIN_1:func.1">[</a><span class="default"><font color="Maroon" title="c18">x</font>,<font color="Maroon" title="c19">y</font></span><a href="domain_1.html#K1" title="DOMAIN_1:func.1">]</a></span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1"><a href="tarski.html#K4" title="TARSKI:func.4">[</a><span class="default">0,1</span><a href="tarski.html#K4" title="TARSKI:func.4">]</a></span> or <span class="p1"><a href="domain_1.html#K1" title="DOMAIN_1:func.1">[</a><span class="default"><font color="Maroon" title="c18">x</font>,<font color="Maroon" title="c19">y</font></span><a href="domain_1.html#K1" title="DOMAIN_1:func.1">]</a></span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1"><a href="tarski.html#K4" title="TARSKI:func.4">[</a><span class="default">1,0</span><a href="tarski.html#K4" title="TARSKI:func.4">]</a></span> or <span class="p1"><a href="domain_1.html#K1" title="DOMAIN_1:func.1">[</a><span class="default"><font color="Maroon" title="c18">x</font>,<font color="Maroon" title="c19">y</font></span><a href="domain_1.html#K1" title="DOMAIN_1:func.1">]</a></span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1"><a href="tarski.html#K4" title="TARSKI:func.4">[</a><span class="default">1,2</span><a href="tarski.html#K4" title="TARSKI:func.4">]</a></span> or <span class="p1"><a href="domain_1.html#K1" title="DOMAIN_1:func.1">[</a><span class="default"><font color="Maroon" title="c18">x</font>,<font color="Maroon" title="c19">y</font></span><a href="domain_1.html#K1" title="DOMAIN_1:func.1">]</a></span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1"><a href="tarski.html#K4" title="TARSKI:func.4">[</a><span class="default">2,1</span><a href="tarski.html#K4" title="TARSKI:func.4">]</a></span> or <span class="p1"><a href="domain_1.html#K1" title="DOMAIN_1:func.1">[</a><span class="default"><font color="Maroon" title="c18">x</font>,<font color="Maroon" title="c19">y</font></span><a href="domain_1.html#K1" title="DOMAIN_1:func.1">]</a></span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1"><a href="tarski.html#K4" title="TARSKI:func.4">[</a><span class="default">2,3</span><a href="tarski.html#K4" title="TARSKI:func.4">]</a></span> or <span class="p1"><a href="domain_1.html#K1" title="DOMAIN_1:func.1">[</a><span class="default"><font color="Maroon" title="c18">x</font>,<font color="Maroon" title="c19">y</font></span><a href="domain_1.html#K1" title="DOMAIN_1:func.1">]</a></span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1"><a href="tarski.html#K4" title="TARSKI:func.4">[</a><span class="default">3,2</span><a href="tarski.html#K4" title="TARSKI:func.4">]</a></span> )
 </span><b>by </b><i><a class="txt" href="neckla_3.html#E1:60_8_1"><i><font color="Green" title="E56">A51</font></i></a>, <a class="ref" href="enumset1.html#D4" title="ENUMSET1:def.4">ENUMSET1:def 4</a>, <a class="ref" href="neckla_2.html#T2" title="NECKLA_2:th.2">NECKLA_2:2</a></i>;<br/><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="60_8_1_1_1"><b>suppose </b></a><a NAME="E1:60_8_1_1_1"/>
<span class="p1"><a href="domain_1.html#K1" title="DOMAIN_1:func.1">[</a><span class="default"><font color="Maroon" title="c18">x</font>,<font color="Maroon" title="c19">y</font></span><a href="domain_1.html#K1" title="DOMAIN_1:func.1">]</a></span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1"><a href="tarski.html#K4" title="TARSKI:func.4">[</a><span class="default">0,1</span><a href="tarski.html#K4" title="TARSKI:func.4">]</a></span>
 ;<br/><div class="add"><a NAME="E2:60_8_1_1_1"/><b>then </b><i><font color="Green" title="E57">A52</font></i>: 
( <font color="Maroon" title="c18">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 0 &amp; <font color="Maroon" title="c19">y</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 1 )
 <b>by </b><i><a class="ref" href="zfmisc_1.html#T33" title="ZFMISC_1:th.33">ZFMISC_1:33</a></i>;<br/><a NAME="E3:60_8_1_1_1"/><b>then </b>
( <font color="Maroon" title="c18">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <span class="p1"><a href="tarski.html#K2" title="TARSKI:func.2">{</a><span class="default">0,1</span><a href="tarski.html#K2" title="TARSKI:func.2">}</a></span> &amp; <font color="Maroon" title="c19">y</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <span class="p1"><a href="tarski.html#K2" title="TARSKI:func.2">{</a><span class="default">0,1</span><a href="tarski.html#K2" title="TARSKI:func.2">}</a></span> )
 <b>by </b><i><a class="ref" href="tarski.html#D2" title="TARSKI:def.2">TARSKI:def 2</a></i>;<br/><a NAME="E4:60_8_1_1_1"/><b>then </b><i><font color="Green" title="E58">A53</font></i>: 
( <font color="Maroon" title="c18">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> <span class="p1">(<span class="default">0,1 <a href="funct_4.html#K5" title="FUNCT_4:func.5">--&gt;</a> <font color="Maroon" title="c2">a</font>,<font color="Maroon" title="c3">b</font></span>)</span> &amp; <font color="Maroon" title="c19">y</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> <span class="p1">(<span class="default">0,1 <a href="funct_4.html#K5" title="FUNCT_4:func.5">--&gt;</a> <font color="Maroon" title="c2">a</font>,<font color="Maroon" title="c3">b</font></span>)</span> )
 <b>by </b><i><a class="ref" href="funct_4.html#T65" title="FUNCT_4:th.65">FUNCT_4:65</a></i>;<br/><b>then </b><i><font color="Green" title="E59">A54</font></i>: <font color="Maroon" title="c17">f</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c18">x</font> = 
<span class="p1">(<span class="default">0,1 <a href="funct_4.html#K5" title="FUNCT_4:func.5">--&gt;</a> <font color="Maroon" title="c2">a</font>,<font color="Maroon" title="c3">b</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> 0
<b>by </b><i><a class="txt" href="neckla_3.html#E16:60"><i><font color="Green" title="E50">A35</font></i></a>, <a class="txt" href="neckla_3.html#E2:60_8_1_1_1"><i><font color="Green" title="E57">A52</font></i></a>, <a class="ref" href="funct_4.html#T17" title="FUNCT_4:th.17">FUNCT_4:17</a></i>
<br/>.= 
<font color="Maroon" title="c2">a</font>
<b>by </b><i><a class="ref" href="funct_4.html#T66" title="FUNCT_4:th.66">FUNCT_4:66</a></i>
;<br/><font color="Maroon" title="c17">f</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c19">y</font> = 
<span class="p1">(<span class="default">0,1 <a href="funct_4.html#K5" title="FUNCT_4:func.5">--&gt;</a> <font color="Maroon" title="c2">a</font>,<font color="Maroon" title="c3">b</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> 1
<b>by </b><i><a class="txt" href="neckla_3.html#E16:60"><i><font color="Green" title="E50">A35</font></i></a>, <a class="txt" href="neckla_3.html#E2:60_8_1_1_1"><i><font color="Green" title="E57">A52</font></i></a>, <a class="txt" href="neckla_3.html#E4:60_8_1_1_1"><i><font color="Green" title="E58">A53</font></i></a>, <a class="ref" href="funct_4.html#T17" title="FUNCT_4:th.17">FUNCT_4:17</a></i>
<br/>.= 
<font color="Maroon" title="c3">b</font>
<b>by </b><i><a class="ref" href="funct_4.html#T66" title="FUNCT_4:th.66">FUNCT_4:66</a></i>
;<br/><b>hence </b><a NAME="E7:60_8_1_1_1"/>
<span class="p1"><a href="tarski.html#K4" title="TARSKI:func.4">[</a><span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c17">f</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c18">x</font></span>)</span>,<span class="p2">(<span class="default"><font color="Maroon" title="c17">f</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c19">y</font></span>)</span></span><a href="tarski.html#K4" title="TARSKI:func.4">]</a></span> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> the <a href="orders_2.html#U1" title="ORDERS_2:sel.1">InternalRel</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="c6">Z</font></span>)</span>
 <b>by </b><i><a class="txt" href="neckla_3.html#E9:60"><i><font color="Green" title="E44">A9</font></i></a>, <a class="txt" href="neckla_3.html#E5:60_8_1_1_1"><i><font color="Green" title="E59">A54</font></i></a>, <a class="ref" href="enumset1.html#D4" title="ENUMSET1:def.4">ENUMSET1:def 4</a></i>;<br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="60_8_1_1_2"><b>suppose </b></a><a NAME="E1:60_8_1_1_2"/>
<span class="p1"><a href="domain_1.html#K1" title="DOMAIN_1:func.1">[</a><span class="default"><font color="Maroon" title="c18">x</font>,<font color="Maroon" title="c19">y</font></span><a href="domain_1.html#K1" title="DOMAIN_1:func.1">]</a></span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1"><a href="tarski.html#K4" title="TARSKI:func.4">[</a><span class="default">1,0</span><a href="tarski.html#K4" title="TARSKI:func.4">]</a></span>
 ;<br/><div class="add"><a NAME="E2:60_8_1_1_2"/><b>then </b><i><font color="Green" title="E57">A55</font></i>: 
( <font color="Maroon" title="c18">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 1 &amp; <font color="Maroon" title="c19">y</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 0 )
 <b>by </b><i><a class="ref" href="zfmisc_1.html#T33" title="ZFMISC_1:th.33">ZFMISC_1:33</a></i>;<br/><a NAME="E3:60_8_1_1_2"/><b>then </b>
( <font color="Maroon" title="c18">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <span class="p1"><a href="tarski.html#K2" title="TARSKI:func.2">{</a><span class="default">0,1</span><a href="tarski.html#K2" title="TARSKI:func.2">}</a></span> &amp; <font color="Maroon" title="c19">y</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <span class="p1"><a href="tarski.html#K2" title="TARSKI:func.2">{</a><span class="default">0,1</span><a href="tarski.html#K2" title="TARSKI:func.2">}</a></span> )
 <b>by </b><i><a class="ref" href="tarski.html#D2" title="TARSKI:def.2">TARSKI:def 2</a></i>;<br/><a NAME="E4:60_8_1_1_2"/><b>then </b><i><font color="Green" title="E58">A56</font></i>: 
( <font color="Maroon" title="c18">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> <span class="p1">(<span class="default">0,1 <a href="funct_4.html#K5" title="FUNCT_4:func.5">--&gt;</a> <font color="Maroon" title="c2">a</font>,<font color="Maroon" title="c3">b</font></span>)</span> &amp; <font color="Maroon" title="c19">y</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> <span class="p1">(<span class="default">0,1 <a href="funct_4.html#K5" title="FUNCT_4:func.5">--&gt;</a> <font color="Maroon" title="c2">a</font>,<font color="Maroon" title="c3">b</font></span>)</span> )
 <b>by </b><i><a class="ref" href="funct_4.html#T65" title="FUNCT_4:th.65">FUNCT_4:65</a></i>;<br/><b>then </b><i><font color="Green" title="E59">A57</font></i>: <font color="Maroon" title="c17">f</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c18">x</font> = 
<span class="p1">(<span class="default">0,1 <a href="funct_4.html#K5" title="FUNCT_4:func.5">--&gt;</a> <font color="Maroon" title="c2">a</font>,<font color="Maroon" title="c3">b</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> 1
<b>by </b><i><a class="txt" href="neckla_3.html#E16:60"><i><font color="Green" title="E50">A35</font></i></a>, <a class="txt" href="neckla_3.html#E2:60_8_1_1_2"><i><font color="Green" title="E57">A55</font></i></a>, <a class="ref" href="funct_4.html#T17" title="FUNCT_4:th.17">FUNCT_4:17</a></i>
<br/>.= 
<font color="Maroon" title="c3">b</font>
<b>by </b><i><a class="ref" href="funct_4.html#T66" title="FUNCT_4:th.66">FUNCT_4:66</a></i>
;<br/><font color="Maroon" title="c17">f</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c19">y</font> = 
<span class="p1">(<span class="default">0,1 <a href="funct_4.html#K5" title="FUNCT_4:func.5">--&gt;</a> <font color="Maroon" title="c2">a</font>,<font color="Maroon" title="c3">b</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> 0
<b>by </b><i><a class="txt" href="neckla_3.html#E16:60"><i><font color="Green" title="E50">A35</font></i></a>, <a class="txt" href="neckla_3.html#E2:60_8_1_1_2"><i><font color="Green" title="E57">A55</font></i></a>, <a class="txt" href="neckla_3.html#E4:60_8_1_1_2"><i><font color="Green" title="E58">A56</font></i></a>, <a class="ref" href="funct_4.html#T17" title="FUNCT_4:th.17">FUNCT_4:17</a></i>
<br/>.= 
<font color="Maroon" title="c2">a</font>
<b>by </b><i><a class="ref" href="funct_4.html#T66" title="FUNCT_4:th.66">FUNCT_4:66</a></i>
;<br/><b>hence </b><a NAME="E7:60_8_1_1_2"/>
<span class="p1"><a href="tarski.html#K4" title="TARSKI:func.4">[</a><span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c17">f</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c18">x</font></span>)</span>,<span class="p2">(<span class="default"><font color="Maroon" title="c17">f</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c19">y</font></span>)</span></span><a href="tarski.html#K4" title="TARSKI:func.4">]</a></span> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> the <a href="orders_2.html#U1" title="ORDERS_2:sel.1">InternalRel</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="c6">Z</font></span>)</span>
 <b>by </b><i><a class="txt" href="neckla_3.html#E9:60"><i><font color="Green" title="E44">A9</font></i></a>, <a class="txt" href="neckla_3.html#E5:60_8_1_1_2"><i><font color="Green" title="E59">A57</font></i></a>, <a class="ref" href="enumset1.html#D4" title="ENUMSET1:def.4">ENUMSET1:def 4</a></i>;<br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="60_8_1_1_3"><b>suppose </b></a><a NAME="E1:60_8_1_1_3"/>
<span class="p1"><a href="domain_1.html#K1" title="DOMAIN_1:func.1">[</a><span class="default"><font color="Maroon" title="c18">x</font>,<font color="Maroon" title="c19">y</font></span><a href="domain_1.html#K1" title="DOMAIN_1:func.1">]</a></span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1"><a href="tarski.html#K4" title="TARSKI:func.4">[</a><span class="default">1,2</span><a href="tarski.html#K4" title="TARSKI:func.4">]</a></span>
 ;<br/><div class="add"><a NAME="E2:60_8_1_1_3"/><b>then </b><i><font color="Green" title="E57">A58</font></i>: 
( <font color="Maroon" title="c18">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 1 &amp; <font color="Maroon" title="c19">y</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 2 )
 <b>by </b><i><a class="ref" href="zfmisc_1.html#T33" title="ZFMISC_1:th.33">ZFMISC_1:33</a></i>;<br/><a NAME="E3:60_8_1_1_3"/><b>then </b>
( <font color="Maroon" title="c18">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <span class="p1"><a href="tarski.html#K2" title="TARSKI:func.2">{</a><span class="default">0,1</span><a href="tarski.html#K2" title="TARSKI:func.2">}</a></span> &amp; <font color="Maroon" title="c19">y</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <span class="p1"><a href="tarski.html#K2" title="TARSKI:func.2">{</a><span class="default">2,3</span><a href="tarski.html#K2" title="TARSKI:func.2">}</a></span> )
 <b>by </b><i><a class="ref" href="tarski.html#D2" title="TARSKI:def.2">TARSKI:def 2</a></i>;<br/><a NAME="E4:60_8_1_1_3"/><b>then </b><i><font color="Green" title="E58">A59</font></i>: 
( <font color="Maroon" title="c18">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> <span class="p1">(<span class="default">0,1 <a href="funct_4.html#K5" title="FUNCT_4:func.5">--&gt;</a> <font color="Maroon" title="c2">a</font>,<font color="Maroon" title="c3">b</font></span>)</span> &amp; <font color="Maroon" title="c19">y</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> <span class="p1">(<span class="default">2,3 <a href="funct_4.html#K5" title="FUNCT_4:func.5">--&gt;</a> <font color="Maroon" title="c4">c</font>,<font color="Maroon" title="c5">d</font></span>)</span> )
 <b>by </b><i><a class="ref" href="funct_4.html#T65" title="FUNCT_4:th.65">FUNCT_4:65</a></i>;<br/><b>then </b><i><font color="Green" title="E59">A60</font></i>: <font color="Maroon" title="c17">f</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c18">x</font> = 
<span class="p1">(<span class="default">0,1 <a href="funct_4.html#K5" title="FUNCT_4:func.5">--&gt;</a> <font color="Maroon" title="c2">a</font>,<font color="Maroon" title="c3">b</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> 1
<b>by </b><i><a class="txt" href="neckla_3.html#E16:60"><i><font color="Green" title="E50">A35</font></i></a>, <a class="txt" href="neckla_3.html#E2:60_8_1_1_3"><i><font color="Green" title="E57">A58</font></i></a>, <a class="ref" href="funct_4.html#T17" title="FUNCT_4:th.17">FUNCT_4:17</a></i>
<br/>.= 
<font color="Maroon" title="c3">b</font>
<b>by </b><i><a class="ref" href="funct_4.html#T66" title="FUNCT_4:th.66">FUNCT_4:66</a></i>
;<br/><a NAME="E6:60_8_1_1_3"/>
<span class="p1">(<span class="default">0,1 <a href="funct_4.html#K5" title="FUNCT_4:func.5">--&gt;</a> <font color="Maroon" title="c2">a</font>,<font color="Maroon" title="c3">b</font></span>)</span> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p1">(<span class="default">2,3 <a href="funct_4.html#K5" title="FUNCT_4:func.5">--&gt;</a> <font color="Maroon" title="c4">c</font>,<font color="Maroon" title="c5">d</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default">2,3 <a href="funct_4.html#K5" title="FUNCT_4:func.5">--&gt;</a> <font color="Maroon" title="c4">c</font>,<font color="Maroon" title="c5">d</font></span>)</span> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p1">(<span class="default">0,1 <a href="funct_4.html#K5" title="FUNCT_4:func.5">--&gt;</a> <font color="Maroon" title="c2">a</font>,<font color="Maroon" title="c3">b</font></span>)</span>
 <b>by </b><i><a class="txt" href="neckla_3.html#E16:60"><i><font color="Green" title="E50">A35</font></i></a>, <a class="ref" href="funct_4.html#T36" title="FUNCT_4:th.36">FUNCT_4:36</a></i>;<br/><b>then </b><font color="Maroon" title="c17">f</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c19">y</font> = 
<span class="p1">(<span class="default">2,3 <a href="funct_4.html#K5" title="FUNCT_4:func.5">--&gt;</a> <font color="Maroon" title="c4">c</font>,<font color="Maroon" title="c5">d</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> 2
<b>by </b><i><a class="txt" href="neckla_3.html#E16:60"><i><font color="Green" title="E50">A35</font></i></a>, <a class="txt" href="neckla_3.html#E2:60_8_1_1_3"><i><font color="Green" title="E57">A58</font></i></a>, <a class="txt" href="neckla_3.html#E4:60_8_1_1_3"><i><font color="Green" title="E58">A59</font></i></a>, <a class="ref" href="funct_4.html#T17" title="FUNCT_4:th.17">FUNCT_4:17</a></i>
<br/>.= 
<font color="Maroon" title="c4">c</font>
<b>by </b><i><a class="ref" href="funct_4.html#T66" title="FUNCT_4:th.66">FUNCT_4:66</a></i>
;<br/><b>hence </b><a NAME="E8:60_8_1_1_3"/>
<span class="p1"><a href="tarski.html#K4" title="TARSKI:func.4">[</a><span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c17">f</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c18">x</font></span>)</span>,<span class="p2">(<span class="default"><font color="Maroon" title="c17">f</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c19">y</font></span>)</span></span><a href="tarski.html#K4" title="TARSKI:func.4">]</a></span> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> the <a href="orders_2.html#U1" title="ORDERS_2:sel.1">InternalRel</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="c6">Z</font></span>)</span>
 <b>by </b><i><a class="txt" href="neckla_3.html#E9:60"><i><font color="Green" title="E44">A9</font></i></a>, <a class="txt" href="neckla_3.html#E5:60_8_1_1_3"><i><font color="Green" title="E59">A60</font></i></a>, <a class="ref" href="enumset1.html#D4" title="ENUMSET1:def.4">ENUMSET1:def 4</a></i>;<br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="60_8_1_1_4"><b>suppose </b></a><a NAME="E1:60_8_1_1_4"/>
<span class="p1"><a href="domain_1.html#K1" title="DOMAIN_1:func.1">[</a><span class="default"><font color="Maroon" title="c18">x</font>,<font color="Maroon" title="c19">y</font></span><a href="domain_1.html#K1" title="DOMAIN_1:func.1">]</a></span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1"><a href="tarski.html#K4" title="TARSKI:func.4">[</a><span class="default">2,1</span><a href="tarski.html#K4" title="TARSKI:func.4">]</a></span>
 ;<br/><div class="add"><a NAME="E2:60_8_1_1_4"/><b>then </b><i><font color="Green" title="E57">A61</font></i>: 
( <font color="Maroon" title="c18">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 2 &amp; <font color="Maroon" title="c19">y</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 1 )
 <b>by </b><i><a class="ref" href="zfmisc_1.html#T33" title="ZFMISC_1:th.33">ZFMISC_1:33</a></i>;<br/><a NAME="E3:60_8_1_1_4"/><b>then </b>
( <font color="Maroon" title="c18">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <span class="p1"><a href="tarski.html#K2" title="TARSKI:func.2">{</a><span class="default">2,3</span><a href="tarski.html#K2" title="TARSKI:func.2">}</a></span> &amp; <font color="Maroon" title="c19">y</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <span class="p1"><a href="tarski.html#K2" title="TARSKI:func.2">{</a><span class="default">0,1</span><a href="tarski.html#K2" title="TARSKI:func.2">}</a></span> )
 <b>by </b><i><a class="ref" href="tarski.html#D2" title="TARSKI:def.2">TARSKI:def 2</a></i>;<br/><a NAME="E4:60_8_1_1_4"/><b>then </b><i><font color="Green" title="E58">A62</font></i>: 
( <font color="Maroon" title="c18">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> <span class="p1">(<span class="default">2,3 <a href="funct_4.html#K5" title="FUNCT_4:func.5">--&gt;</a> <font color="Maroon" title="c4">c</font>,<font color="Maroon" title="c5">d</font></span>)</span> &amp; <font color="Maroon" title="c19">y</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> <span class="p1">(<span class="default">0,1 <a href="funct_4.html#K5" title="FUNCT_4:func.5">--&gt;</a> <font color="Maroon" title="c2">a</font>,<font color="Maroon" title="c3">b</font></span>)</span> )
 <b>by </b><i><a class="ref" href="funct_4.html#T65" title="FUNCT_4:th.65">FUNCT_4:65</a></i>;<br/><b>then </b><i><font color="Green" title="E59">A63</font></i>: <font color="Maroon" title="c17">f</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c19">y</font> = 
<span class="p1">(<span class="default">0,1 <a href="funct_4.html#K5" title="FUNCT_4:func.5">--&gt;</a> <font color="Maroon" title="c2">a</font>,<font color="Maroon" title="c3">b</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> 1
<b>by </b><i><a class="txt" href="neckla_3.html#E16:60"><i><font color="Green" title="E50">A35</font></i></a>, <a class="txt" href="neckla_3.html#E2:60_8_1_1_4"><i><font color="Green" title="E57">A61</font></i></a>, <a class="ref" href="funct_4.html#T17" title="FUNCT_4:th.17">FUNCT_4:17</a></i>
<br/>.= 
<font color="Maroon" title="c3">b</font>
<b>by </b><i><a class="ref" href="funct_4.html#T66" title="FUNCT_4:th.66">FUNCT_4:66</a></i>
;<br/><a NAME="E6:60_8_1_1_4"/>
<span class="p1">(<span class="default">0,1 <a href="funct_4.html#K5" title="FUNCT_4:func.5">--&gt;</a> <font color="Maroon" title="c2">a</font>,<font color="Maroon" title="c3">b</font></span>)</span> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p1">(<span class="default">2,3 <a href="funct_4.html#K5" title="FUNCT_4:func.5">--&gt;</a> <font color="Maroon" title="c4">c</font>,<font color="Maroon" title="c5">d</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default">2,3 <a href="funct_4.html#K5" title="FUNCT_4:func.5">--&gt;</a> <font color="Maroon" title="c4">c</font>,<font color="Maroon" title="c5">d</font></span>)</span> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p1">(<span class="default">0,1 <a href="funct_4.html#K5" title="FUNCT_4:func.5">--&gt;</a> <font color="Maroon" title="c2">a</font>,<font color="Maroon" title="c3">b</font></span>)</span>
 <b>by </b><i><a class="txt" href="neckla_3.html#E16:60"><i><font color="Green" title="E50">A35</font></i></a>, <a class="ref" href="funct_4.html#T36" title="FUNCT_4:th.36">FUNCT_4:36</a></i>;<br/><b>then </b><font color="Maroon" title="c17">f</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c18">x</font> = 
<span class="p1">(<span class="default">2,3 <a href="funct_4.html#K5" title="FUNCT_4:func.5">--&gt;</a> <font color="Maroon" title="c4">c</font>,<font color="Maroon" title="c5">d</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> 2
<b>by </b><i><a class="txt" href="neckla_3.html#E16:60"><i><font color="Green" title="E50">A35</font></i></a>, <a class="txt" href="neckla_3.html#E2:60_8_1_1_4"><i><font color="Green" title="E57">A61</font></i></a>, <a class="txt" href="neckla_3.html#E4:60_8_1_1_4"><i><font color="Green" title="E58">A62</font></i></a>, <a class="ref" href="funct_4.html#T17" title="FUNCT_4:th.17">FUNCT_4:17</a></i>
<br/>.= 
<font color="Maroon" title="c4">c</font>
<b>by </b><i><a class="ref" href="funct_4.html#T66" title="FUNCT_4:th.66">FUNCT_4:66</a></i>
;<br/><b>hence </b><a NAME="E8:60_8_1_1_4"/>
<span class="p1"><a href="tarski.html#K4" title="TARSKI:func.4">[</a><span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c17">f</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c18">x</font></span>)</span>,<span class="p2">(<span class="default"><font color="Maroon" title="c17">f</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c19">y</font></span>)</span></span><a href="tarski.html#K4" title="TARSKI:func.4">]</a></span> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> the <a href="orders_2.html#U1" title="ORDERS_2:sel.1">InternalRel</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="c6">Z</font></span>)</span>
 <b>by </b><i><a class="txt" href="neckla_3.html#E9:60"><i><font color="Green" title="E44">A9</font></i></a>, <a class="txt" href="neckla_3.html#E5:60_8_1_1_4"><i><font color="Green" title="E59">A63</font></i></a>, <a class="ref" href="enumset1.html#D4" title="ENUMSET1:def.4">ENUMSET1:def 4</a></i>;<br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="60_8_1_1_5"><b>suppose </b></a><a NAME="E1:60_8_1_1_5"/>
<span class="p1"><a href="domain_1.html#K1" title="DOMAIN_1:func.1">[</a><span class="default"><font color="Maroon" title="c18">x</font>,<font color="Maroon" title="c19">y</font></span><a href="domain_1.html#K1" title="DOMAIN_1:func.1">]</a></span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1"><a href="tarski.html#K4" title="TARSKI:func.4">[</a><span class="default">2,3</span><a href="tarski.html#K4" title="TARSKI:func.4">]</a></span>
 ;<br/><div class="add"><a NAME="E2:60_8_1_1_5"/><b>then </b><i><font color="Green" title="E57">A64</font></i>: 
( <font color="Maroon" title="c18">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 2 &amp; <font color="Maroon" title="c19">y</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 3 )
 <b>by </b><i><a class="ref" href="zfmisc_1.html#T33" title="ZFMISC_1:th.33">ZFMISC_1:33</a></i>;<br/><a NAME="E3:60_8_1_1_5"/><b>then </b>
( <font color="Maroon" title="c18">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <span class="p1"><a href="tarski.html#K2" title="TARSKI:func.2">{</a><span class="default">2,3</span><a href="tarski.html#K2" title="TARSKI:func.2">}</a></span> &amp; <font color="Maroon" title="c19">y</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <span class="p1"><a href="tarski.html#K2" title="TARSKI:func.2">{</a><span class="default">2,3</span><a href="tarski.html#K2" title="TARSKI:func.2">}</a></span> )
 <b>by </b><i><a class="ref" href="tarski.html#D2" title="TARSKI:def.2">TARSKI:def 2</a></i>;<br/><a NAME="E4:60_8_1_1_5"/><b>then </b><i><font color="Green" title="E58">A65</font></i>: 
( <font color="Maroon" title="c18">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> <span class="p1">(<span class="default">2,3 <a href="funct_4.html#K5" title="FUNCT_4:func.5">--&gt;</a> <font color="Maroon" title="c4">c</font>,<font color="Maroon" title="c5">d</font></span>)</span> &amp; <font color="Maroon" title="c19">y</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> <span class="p1">(<span class="default">2,3 <a href="funct_4.html#K5" title="FUNCT_4:func.5">--&gt;</a> <font color="Maroon" title="c4">c</font>,<font color="Maroon" title="c5">d</font></span>)</span> )
 <b>by </b><i><a class="ref" href="funct_4.html#T65" title="FUNCT_4:th.65">FUNCT_4:65</a></i>;<br/><a NAME="E5:60_8_1_1_5"/><i><font color="Green" title="E59">A66</font></i>: 
<span class="p1">(<span class="default">0,1 <a href="funct_4.html#K5" title="FUNCT_4:func.5">--&gt;</a> <font color="Maroon" title="c2">a</font>,<font color="Maroon" title="c3">b</font></span>)</span> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p1">(<span class="default">2,3 <a href="funct_4.html#K5" title="FUNCT_4:func.5">--&gt;</a> <font color="Maroon" title="c4">c</font>,<font color="Maroon" title="c5">d</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default">2,3 <a href="funct_4.html#K5" title="FUNCT_4:func.5">--&gt;</a> <font color="Maroon" title="c4">c</font>,<font color="Maroon" title="c5">d</font></span>)</span> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p1">(<span class="default">0,1 <a href="funct_4.html#K5" title="FUNCT_4:func.5">--&gt;</a> <font color="Maroon" title="c2">a</font>,<font color="Maroon" title="c3">b</font></span>)</span>
 <b>by </b><i><a class="txt" href="neckla_3.html#E16:60"><i><font color="Green" title="E50">A35</font></i></a>, <a class="ref" href="funct_4.html#T36" title="FUNCT_4:th.36">FUNCT_4:36</a></i>;<br/><b>then </b><i><font color="Green" title="E60">A67</font></i>: <font color="Maroon" title="c17">f</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c18">x</font> = 
<span class="p1">(<span class="default">2,3 <a href="funct_4.html#K5" title="FUNCT_4:func.5">--&gt;</a> <font color="Maroon" title="c4">c</font>,<font color="Maroon" title="c5">d</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> 2
<b>by </b><i><a class="txt" href="neckla_3.html#E16:60"><i><font color="Green" title="E50">A35</font></i></a>, <a class="txt" href="neckla_3.html#E2:60_8_1_1_5"><i><font color="Green" title="E57">A64</font></i></a>, <a class="txt" href="neckla_3.html#E4:60_8_1_1_5"><i><font color="Green" title="E58">A65</font></i></a>, <a class="ref" href="funct_4.html#T17" title="FUNCT_4:th.17">FUNCT_4:17</a></i>
<br/>.= 
<font color="Maroon" title="c4">c</font>
<b>by </b><i><a class="ref" href="funct_4.html#T66" title="FUNCT_4:th.66">FUNCT_4:66</a></i>
;<br/><font color="Maroon" title="c17">f</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c19">y</font> = 
<span class="p1">(<span class="default">2,3 <a href="funct_4.html#K5" title="FUNCT_4:func.5">--&gt;</a> <font color="Maroon" title="c4">c</font>,<font color="Maroon" title="c5">d</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> 3
<b>by </b><i><a class="txt" href="neckla_3.html#E16:60"><i><font color="Green" title="E50">A35</font></i></a>, <a class="txt" href="neckla_3.html#E2:60_8_1_1_5"><i><font color="Green" title="E57">A64</font></i></a>, <a class="txt" href="neckla_3.html#E4:60_8_1_1_5"><i><font color="Green" title="E58">A65</font></i></a>, <a class="txt" href="neckla_3.html#E5:60_8_1_1_5"><i><font color="Green" title="E59">A66</font></i></a>, <a class="ref" href="funct_4.html#T17" title="FUNCT_4:th.17">FUNCT_4:17</a></i>
<br/>.= 
<font color="Maroon" title="c5">d</font>
<b>by </b><i><a class="ref" href="funct_4.html#T66" title="FUNCT_4:th.66">FUNCT_4:66</a></i>
;<br/><b>hence </b><a NAME="E8:60_8_1_1_5"/>
<span class="p1"><a href="tarski.html#K4" title="TARSKI:func.4">[</a><span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c17">f</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c18">x</font></span>)</span>,<span class="p2">(<span class="default"><font color="Maroon" title="c17">f</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c19">y</font></span>)</span></span><a href="tarski.html#K4" title="TARSKI:func.4">]</a></span> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> the <a href="orders_2.html#U1" title="ORDERS_2:sel.1">InternalRel</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="c6">Z</font></span>)</span>
 <b>by </b><i><a class="txt" href="neckla_3.html#E9:60"><i><font color="Green" title="E44">A9</font></i></a>, <a class="txt" href="neckla_3.html#E6:60_8_1_1_5"><i><font color="Green" title="E60">A67</font></i></a>, <a class="ref" href="enumset1.html#D4" title="ENUMSET1:def.4">ENUMSET1:def 4</a></i>;<br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="60_8_1_1_6"><b>suppose </b></a><a NAME="E1:60_8_1_1_6"/>
<span class="p1"><a href="domain_1.html#K1" title="DOMAIN_1:func.1">[</a><span class="default"><font color="Maroon" title="c18">x</font>,<font color="Maroon" title="c19">y</font></span><a href="domain_1.html#K1" title="DOMAIN_1:func.1">]</a></span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1"><a href="tarski.html#K4" title="TARSKI:func.4">[</a><span class="default">3,2</span><a href="tarski.html#K4" title="TARSKI:func.4">]</a></span>
 ;<br/><div class="add"><a NAME="E2:60_8_1_1_6"/><b>then </b><i><font color="Green" title="E57">A68</font></i>: 
( <font color="Maroon" title="c18">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 3 &amp; <font color="Maroon" title="c19">y</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 2 )
 <b>by </b><i><a class="ref" href="zfmisc_1.html#T33" title="ZFMISC_1:th.33">ZFMISC_1:33</a></i>;<br/><a NAME="E3:60_8_1_1_6"/><b>then </b>
( <font color="Maroon" title="c18">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <span class="p1"><a href="tarski.html#K2" title="TARSKI:func.2">{</a><span class="default">3,2</span><a href="tarski.html#K2" title="TARSKI:func.2">}</a></span> &amp; <font color="Maroon" title="c19">y</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <span class="p1"><a href="tarski.html#K2" title="TARSKI:func.2">{</a><span class="default">3,2</span><a href="tarski.html#K2" title="TARSKI:func.2">}</a></span> )
 <b>by </b><i><a class="ref" href="tarski.html#D2" title="TARSKI:def.2">TARSKI:def 2</a></i>;<br/><a NAME="E4:60_8_1_1_6"/><b>then </b><i><font color="Green" title="E58">A69</font></i>: 
( <font color="Maroon" title="c18">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> <span class="p1">(<span class="default">2,3 <a href="funct_4.html#K5" title="FUNCT_4:func.5">--&gt;</a> <font color="Maroon" title="c4">c</font>,<font color="Maroon" title="c5">d</font></span>)</span> &amp; <font color="Maroon" title="c19">y</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> <span class="p1">(<span class="default">2,3 <a href="funct_4.html#K5" title="FUNCT_4:func.5">--&gt;</a> <font color="Maroon" title="c4">c</font>,<font color="Maroon" title="c5">d</font></span>)</span> )
 <b>by </b><i><a class="ref" href="funct_4.html#T65" title="FUNCT_4:th.65">FUNCT_4:65</a></i>;<br/><a NAME="E5:60_8_1_1_6"/><i><font color="Green" title="E59">A70</font></i>: 
<span class="p1">(<span class="default">0,1 <a href="funct_4.html#K5" title="FUNCT_4:func.5">--&gt;</a> <font color="Maroon" title="c2">a</font>,<font color="Maroon" title="c3">b</font></span>)</span> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p1">(<span class="default">2,3 <a href="funct_4.html#K5" title="FUNCT_4:func.5">--&gt;</a> <font color="Maroon" title="c4">c</font>,<font color="Maroon" title="c5">d</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default">2,3 <a href="funct_4.html#K5" title="FUNCT_4:func.5">--&gt;</a> <font color="Maroon" title="c4">c</font>,<font color="Maroon" title="c5">d</font></span>)</span> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p1">(<span class="default">0,1 <a href="funct_4.html#K5" title="FUNCT_4:func.5">--&gt;</a> <font color="Maroon" title="c2">a</font>,<font color="Maroon" title="c3">b</font></span>)</span>
 <b>by </b><i><a class="txt" href="neckla_3.html#E16:60"><i><font color="Green" title="E50">A35</font></i></a>, <a class="ref" href="funct_4.html#T36" title="FUNCT_4:th.36">FUNCT_4:36</a></i>;<br/><b>then </b><i><font color="Green" title="E60">A71</font></i>: <font color="Maroon" title="c17">f</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c18">x</font> = 
<span class="p1">(<span class="default">2,3 <a href="funct_4.html#K5" title="FUNCT_4:func.5">--&gt;</a> <font color="Maroon" title="c4">c</font>,<font color="Maroon" title="c5">d</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> 3
<b>by </b><i><a class="txt" href="neckla_3.html#E16:60"><i><font color="Green" title="E50">A35</font></i></a>, <a class="txt" href="neckla_3.html#E2:60_8_1_1_6"><i><font color="Green" title="E57">A68</font></i></a>, <a class="txt" href="neckla_3.html#E4:60_8_1_1_6"><i><font color="Green" title="E58">A69</font></i></a>, <a class="ref" href="funct_4.html#T17" title="FUNCT_4:th.17">FUNCT_4:17</a></i>
<br/>.= 
<font color="Maroon" title="c5">d</font>
<b>by </b><i><a class="ref" href="funct_4.html#T66" title="FUNCT_4:th.66">FUNCT_4:66</a></i>
;<br/><font color="Maroon" title="c17">f</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c19">y</font> = 
<span class="p1">(<span class="default">2,3 <a href="funct_4.html#K5" title="FUNCT_4:func.5">--&gt;</a> <font color="Maroon" title="c4">c</font>,<font color="Maroon" title="c5">d</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> 2
<b>by </b><i><a class="txt" href="neckla_3.html#E16:60"><i><font color="Green" title="E50">A35</font></i></a>, <a class="txt" href="neckla_3.html#E2:60_8_1_1_6"><i><font color="Green" title="E57">A68</font></i></a>, <a class="txt" href="neckla_3.html#E4:60_8_1_1_6"><i><font color="Green" title="E58">A69</font></i></a>, <a class="txt" href="neckla_3.html#E5:60_8_1_1_6"><i><font color="Green" title="E59">A70</font></i></a>, <a class="ref" href="funct_4.html#T17" title="FUNCT_4:th.17">FUNCT_4:17</a></i>
<br/>.= 
<font color="Maroon" title="c4">c</font>
<b>by </b><i><a class="ref" href="funct_4.html#T66" title="FUNCT_4:th.66">FUNCT_4:66</a></i>
;<br/><b>hence </b><a NAME="E8:60_8_1_1_6"/>
<span class="p1"><a href="tarski.html#K4" title="TARSKI:func.4">[</a><span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c17">f</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c18">x</font></span>)</span>,<span class="p2">(<span class="default"><font color="Maroon" title="c17">f</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c19">y</font></span>)</span></span><a href="tarski.html#K4" title="TARSKI:func.4">]</a></span> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> the <a href="orders_2.html#U1" title="ORDERS_2:sel.1">InternalRel</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="c6">Z</font></span>)</span>
 <b>by </b><i><a class="txt" href="neckla_3.html#E9:60"><i><font color="Green" title="E44">A9</font></i></a>, <a class="txt" href="neckla_3.html#E6:60_8_1_1_6"><i><font color="Green" title="E60">A71</font></i></a>, <a class="ref" href="enumset1.html#D4" title="ENUMSET1:def.4">ENUMSET1:def 4</a></i>;<br/></div><b>end;</b></div></div><b>end;</b></div>

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

<b>thus </b><a NAME="E2:60_8"/>
( <span class="p1"><a href="tarski.html#K4" title="TARSKI:func.4">[</a><span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c17">f</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c18">x</font></span>)</span>,<span class="p2">(<span class="default"><font color="Maroon" title="c17">f</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c19">y</font></span>)</span></span><a href="tarski.html#K4" title="TARSKI:func.4">]</a></span> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> the <a href="orders_2.html#U1" title="ORDERS_2:sel.1">InternalRel</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="c6">Z</font></span>)</span> implies <span class="p1"><a href="domain_1.html#K1" title="DOMAIN_1:func.1">[</a><span class="default"><font color="Maroon" title="c18">x</font>,<font color="Maroon" title="c19">y</font></span><a href="domain_1.html#K1" title="DOMAIN_1:func.1">]</a></span> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> the <a href="orders_2.html#U1" title="ORDERS_2:sel.1">InternalRel</a> of <span class="p1">(<span class="default"><a href="necklace.html#K4" title="NECKLACE:func.4">Necklace</a> 4</span>)</span> )
 <div><a class="txt" onclick="hs2(this)" href="javascript:()" title="60_8_2"><b>proof </b></a><div class="add">

<b>assume </b><a NAME="E1:60_8_2"/><i><font color="Green" title="E56">A72</font></i>: 
<span class="p1"><a href="tarski.html#K4" title="TARSKI:func.4">[</a><span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c17">f</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c18">x</font></span>)</span>,<span class="p2">(<span class="default"><font color="Maroon" title="c17">f</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c19">y</font></span>)</span></span><a href="tarski.html#K4" title="TARSKI:func.4">]</a></span> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> the <a href="orders_2.html#U1" title="ORDERS_2:sel.1">InternalRel</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="c6">Z</font></span>)</span>
 ;<br/>

<a NAME="E2:60_8_2"/><i><font color="Green" title="E57">A73</font></i>: 
(  <a href="relset_1.html#K4" title="RELSET_1:func.4">dom</a> <span class="p1">(<span class="default">0,1 <a href="funct_4.html#K5" title="FUNCT_4:func.5">--&gt;</a> <font color="Maroon" title="c2">a</font>,<font color="Maroon" title="c3">b</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1"><a href="tarski.html#K2" title="TARSKI:func.2">{</a><span class="default">0,1</span><a href="tarski.html#K2" title="TARSKI:func.2">}</a></span> &amp;  <a href="relat_1.html#K2" title="RELAT_1:func.2">rng</a> <span class="p1">(<span class="default">0,1 <a href="funct_4.html#K5" title="FUNCT_4:func.5">--&gt;</a> <font color="Maroon" title="c2">a</font>,<font color="Maroon" title="c3">b</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1"><a href="domain_1.html#K7" title="DOMAIN_1:func.7">{</a><span class="default"><font color="Maroon" title="c2">a</font>,<font color="Maroon" title="c3">b</font></span><a href="domain_1.html#K7" title="DOMAIN_1:func.7">}</a></span> )
 
<b>by </b><i><a class="ref" href="funct_4.html#T65" title="FUNCT_4:th.65">FUNCT_4:65</a>, <a class="ref" href="funct_4.html#T67" title="FUNCT_4:th.67">FUNCT_4:67</a></i>;<br/>
<b>then reconsider </b><font color="Maroon" title="c20">g</font> = 0,1 <a href="funct_4.html#K5" title="FUNCT_4:func.5">--&gt;</a> <font color="Maroon" title="c2">a</font>,<font color="Maroon" title="c3">b</font> as   <a href="funct_2.html#NM1" title="FUNCT_2:NM.1">Function</a> of <span class="p1"><a href="tarski.html#K2" title="TARSKI:func.2">{</a><span class="default">0,1</span><a href="tarski.html#K2" title="TARSKI:func.2">}</a></span>,<span class="p1"><a href="domain_1.html#K7" title="DOMAIN_1:func.7">{</a><span class="default"><font color="Maroon" title="c2">a</font>,<font color="Maroon" title="c3">b</font></span><a href="domain_1.html#K7" title="DOMAIN_1:func.7">}</a></span> <b>by </b><i><a class="ref" href="funct_2.html#D1" title="FUNCT_2:def.1">FUNCT_2:def 1</a>, <a class="ref" href="relset_1.html#T11" title="RELSET_1:th.11">RELSET_1:11</a></i>;<br/>
<b>reconsider </b><font color="Maroon" title="c21">G</font> = <font color="Maroon" title="c20">g</font> <a href="funct_1.html#K2" title="FUNCT_1:func.2">"</a>  as   <a href="funct_2.html#NM1" title="FUNCT_2:NM.1">Function</a> of <span class="p1"><a href="domain_1.html#K7" title="DOMAIN_1:func.7">{</a><span class="default"><font color="Maroon" title="c2">a</font>,<font color="Maroon" title="c3">b</font></span><a href="domain_1.html#K7" title="DOMAIN_1:func.7">}</a></span>,<span class="p1"><a href="tarski.html#K2" title="TARSKI:func.2">{</a><span class="default">0,1</span><a href="tarski.html#K2" title="TARSKI:func.2">}</a></span> <b>by </b><i><a class="txt" href="neckla_3.html#E13:60"><i><font color="Green" title="E47">A32</font></i></a>, <a class="txt" href="neckla_3.html#E19:60"><i><font color="Green" title="E52">A38</font></i></a>, <a class="ref" href="funct_2.html#T31" title="FUNCT_2:th.31">FUNCT_2:31</a></i>;<br/>
<a NAME="E5:60_8_2"/><i><font color="Green" title="E58">A74</font></i>: 
(  <a href="relset_1.html#K4" title="RELSET_1:func.4">dom</a> <span class="p1">(<span class="default">2,3 <a href="funct_4.html#K5" title="FUNCT_4:func.5">--&gt;</a> <font color="Maroon" title="c4">c</font>,<font color="Maroon" title="c5">d</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1"><a href="tarski.html#K2" title="TARSKI:func.2">{</a><span class="default">2,3</span><a href="tarski.html#K2" title="TARSKI:func.2">}</a></span> &amp;  <a href="relat_1.html#K2" title="RELAT_1:func.2">rng</a> <span class="p1">(<span class="default">2,3 <a href="funct_4.html#K5" title="FUNCT_4:func.5">--&gt;</a> <font color="Maroon" title="c4">c</font>,<font color="Maroon" title="c5">d</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1"><a href="domain_1.html#K7" title="DOMAIN_1:func.7">{</a><span class="default"><font color="Maroon" title="c4">c</font>,<font color="Maroon" title="c5">d</font></span><a href="domain_1.html#K7" title="DOMAIN_1:func.7">}</a></span> )
 
<b>by </b><i><a class="ref" href="funct_4.html#T65" title="FUNCT_4:th.65">FUNCT_4:65</a>, <a class="ref" href="funct_4.html#T67" title="FUNCT_4:th.67">FUNCT_4:67</a></i>;<br/>
<b>then reconsider </b><font color="Maroon" title="c22">h</font> = 2,3 <a href="funct_4.html#K5" title="FUNCT_4:func.5">--&gt;</a> <font color="Maroon" title="c4">c</font>,<font color="Maroon" title="c5">d</font> as   <a href="funct_2.html#NM1" title="FUNCT_2:NM.1">Function</a> of <span class="p1"><a href="tarski.html#K2" title="TARSKI:func.2">{</a><span class="default">2,3</span><a href="tarski.html#K2" title="TARSKI:func.2">}</a></span>,<span class="p1"><a href="domain_1.html#K7" title="DOMAIN_1:func.7">{</a><span class="default"><font color="Maroon" title="c4">c</font>,<font color="Maroon" title="c5">d</font></span><a href="domain_1.html#K7" title="DOMAIN_1:func.7">}</a></span> <b>by </b><i><a class="ref" href="funct_2.html#D1" title="FUNCT_2:def.1">FUNCT_2:def 1</a>, <a class="ref" href="relset_1.html#T11" title="RELSET_1:th.11">RELSET_1:11</a></i>;<br/>
<b>reconsider </b><font color="Maroon" title="c23">Hh</font> = <font color="Maroon" title="c22">h</font> <a href="funct_1.html#K2" title="FUNCT_1:func.2">"</a>  as   <a href="funct_2.html#NM1" title="FUNCT_2:NM.1">Function</a> of <span class="p1"><a href="domain_1.html#K7" title="DOMAIN_1:func.7">{</a><span class="default"><font color="Maroon" title="c4">c</font>,<font color="Maroon" title="c5">d</font></span><a href="domain_1.html#K7" title="DOMAIN_1:func.7">}</a></span>,<span class="p1"><a href="tarski.html#K2" title="TARSKI:func.2">{</a><span class="default">2,3</span><a href="tarski.html#K2" title="TARSKI:func.2">}</a></span> <b>by </b><i><a class="txt" href="neckla_3.html#E14:60"><i><font color="Green" title="E48">A33</font></i></a>, <a class="txt" href="neckla_3.html#E20:60"><i><font color="Green" title="E53">A43</font></i></a>, <a class="ref" href="funct_2.html#T31" title="FUNCT_2:th.31">FUNCT_2:31</a></i>;<br/>
<b>reconsider </b><font color="Maroon" title="c24">F</font> = <font color="Maroon" title="c17">f</font> <a href="funct_1.html#K2" title="FUNCT_1:func.2">"</a>  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 <span class="p1">(<span class="default"><a href="yellow_0.html#K5" title="YELLOW_0:func.5">subrelstr</a> <font color="Maroon" title="c6">Z</font></span>)</span>,the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <span class="p1">(<span class="default"><a href="necklace.html#K4" title="NECKLACE:func.4">Necklace</a> 4</span>)</span> <b>by </b><i><a class="txt" href="neckla_3.html#E17:60"><i><font color="Green" title="E51">A37</font></i></a>, <a class="txt" href="neckla_3.html#E22:60"><i><font color="Green" title="E55">A50</font></i></a>, <a class="ref" href="funct_2.html#T31" title="FUNCT_2:th.31">FUNCT_2:31</a></i>;<br/>
<a NAME="E9:60_8_2"/><i><font color="Green" title="E59">A75</font></i>: 
(  <a href="relset_1.html#K4" title="RELSET_1:func.4">dom</a> <font color="Maroon" title="c21">G</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1"><a href="domain_1.html#K7" title="DOMAIN_1:func.7">{</a><span class="default"><font color="Maroon" title="c2">a</font>,<font color="Maroon" title="c3">b</font></span><a href="domain_1.html#K7" title="DOMAIN_1:func.7">}</a></span> &amp;  <a href="relat_1.html#K2" title="RELAT_1:func.2">rng</a> <font color="Maroon" title="c21">G</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1"><a href="tarski.html#K2" title="TARSKI:func.2">{</a><span class="default">0,1</span><a href="tarski.html#K2" title="TARSKI:func.2">}</a></span> )
 
<b>by </b><i><a class="txt" href="neckla_3.html#E19:60"><i><font color="Green" title="E52">A38</font></i></a>, <a class="txt" href="neckla_3.html#E2:60_8_2"><i><font color="Green" title="E57">A73</font></i></a>, <a class="ref" href="funct_1.html#T55" title="FUNCT_1:th.55">FUNCT_1:55</a></i>;<br/>
<a NAME="E10:60_8_2"/><i><font color="Green" title="E60">A76</font></i>: 
(  <a href="relset_1.html#K4" title="RELSET_1:func.4">dom</a> <font color="Maroon" title="c23">Hh</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1"><a href="domain_1.html#K7" title="DOMAIN_1:func.7">{</a><span class="default"><font color="Maroon" title="c4">c</font>,<font color="Maroon" title="c5">d</font></span><a href="domain_1.html#K7" title="DOMAIN_1:func.7">}</a></span> &amp;  <a href="relat_1.html#K2" title="RELAT_1:func.2">rng</a> <font color="Maroon" title="c23">Hh</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1"><a href="tarski.html#K2" title="TARSKI:func.2">{</a><span class="default">2,3</span><a href="tarski.html#K2" title="TARSKI:func.2">}</a></span> )
 
<b>by </b><i><a class="txt" href="neckla_3.html#E20:60"><i><font color="Green" title="E53">A43</font></i></a>, <a class="txt" href="neckla_3.html#E5:60_8_2"><i><font color="Green" title="E58">A74</font></i></a>, <a class="ref" href="funct_1.html#T55" title="FUNCT_1:th.55">FUNCT_1:55</a></i>;<br/>
<a NAME="E11:60_8_2"/><b>then </b>
<font color="Maroon" title="c21">G</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <font color="Maroon" title="c23">Hh</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c23">Hh</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <font color="Maroon" title="c21">G</font>
 
<b>by </b><i><a class="txt" href="neckla_3.html#E13:60"><i><font color="Green" title="E47">A32</font></i></a>, <a class="txt" href="neckla_3.html#E14:60"><i><font color="Green" title="E48">A33</font></i></a>, <a class="txt" href="neckla_3.html#E21:60"><i><font color="Green" title="E54">A48</font></i></a>, <a class="txt" href="neckla_3.html#E9:60_8_2"><i><font color="Green" title="E59">A75</font></i></a>, <a class="ref" href="funct_4.html#T36" title="FUNCT_4:th.36">FUNCT_4:36</a></i>;<br/>
<a NAME="E12:60_8_2"/><b>then </b><i><font color="Green" title="E61">A77</font></i>: 
( <font color="Maroon" title="c24">F</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c21">G</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <font color="Maroon" title="c23">Hh</font> &amp; <font color="Maroon" title="c24">F</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c23">Hh</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <font color="Maroon" title="c21">G</font> )
 
<b>by </b><i><a class="txt" href="neckla_3.html#E16:60"><i><font color="Green" title="E50">A35</font></i></a>, <a class="txt" href="neckla_3.html#E19:60"><i><font color="Green" title="E52">A38</font></i></a>, <a class="txt" href="neckla_3.html#E20:60"><i><font color="Green" title="E53">A43</font></i></a>, <a class="txt" href="neckla_3.html#E21:60"><i><font color="Green" title="E54">A48</font></i></a>, <a class="ref" href="necklace.html#T8" title="NECKLACE:th.8">NECKLACE:8</a></i>;<br/>
<a NAME="E13:60_8_2"/><i><font color="Green" title="E62">A78</font></i>: 
( <font color="Maroon" title="c21">G</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c2">a</font>,<font color="Maroon" title="c3">b</font> <a href="funct_4.html#K4" title="FUNCT_4:func.4">--&gt;</a> 0,1 &amp; <font color="Maroon" title="c23">Hh</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c4">c</font>,<font color="Maroon" title="c5">d</font> <a href="funct_4.html#K4" title="FUNCT_4:func.4">--&gt;</a> 2,3 )
 
<b>by </b><i><a class="txt" href="neckla_3.html#E10:60"><i><font color="Green" title="E45">A30</font></i></a>, <a class="ref" href="necklace.html#T11" title="NECKLACE:th.11">NECKLACE:11</a></i>;<br/>
<div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="60_8_2_1"><b>per </b></a><a class="txt" onclick="hs(this)" href="javascript:()"><b>cases </b></a><span class="hide"><a NAME="E1:60_8_2_1"/>
( <span class="p1"><a href="tarski.html#K4" title="TARSKI:func.4">[</a><span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c17">f</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c18">x</font></span>)</span>,<span class="p2">(<span class="default"><font color="Maroon" title="c17">f</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c19">y</font></span>)</span></span><a href="tarski.html#K4" title="TARSKI:func.4">]</a></span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1"><a href="domain_1.html#K1" title="DOMAIN_1:func.1">[</a><span class="default"><font color="Maroon" title="c2">a</font>,<font color="Maroon" title="c3">b</font></span><a href="domain_1.html#K1" title="DOMAIN_1:func.1">]</a></span> or <span class="p1"><a href="tarski.html#K4" title="TARSKI:func.4">[</a><span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c17">f</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c18">x</font></span>)</span>,<span class="p2">(<span class="default"><font color="Maroon" title="c17">f</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c19">y</font></span>)</span></span><a href="tarski.html#K4" title="TARSKI:func.4">]</a></span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1"><a href="domain_1.html#K1" title="DOMAIN_1:func.1">[</a><span class="default"><font color="Maroon" title="c3">b</font>,<font color="Maroon" title="c2">a</font></span><a href="domain_1.html#K1" title="DOMAIN_1:func.1">]</a></span> or <span class="p1"><a href="tarski.html#K4" title="TARSKI:func.4">[</a><span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c17">f</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c18">x</font></span>)</span>,<span class="p2">(<span class="default"><font color="Maroon" title="c17">f</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c19">y</font></span>)</span></span><a href="tarski.html#K4" title="TARSKI:func.4">]</a></span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1"><a href="domain_1.html#K1" title="DOMAIN_1:func.1">[</a><span class="default"><font color="Maroon" title="c3">b</font>,<font color="Maroon" title="c4">c</font></span><a href="domain_1.html#K1" title="DOMAIN_1:func.1">]</a></span> or <span class="p1"><a href="tarski.html#K4" title="TARSKI:func.4">[</a><span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c17">f</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c18">x</font></span>)</span>,<span class="p2">(<span class="default"><font color="Maroon" title="c17">f</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c19">y</font></span>)</span></span><a href="tarski.html#K4" title="TARSKI:func.4">]</a></span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1"><a href="domain_1.html#K1" title="DOMAIN_1:func.1">[</a><span class="default"><font color="Maroon" title="c4">c</font>,<font color="Maroon" title="c3">b</font></span><a href="domain_1.html#K1" title="DOMAIN_1:func.1">]</a></span> or <span class="p1"><a href="tarski.html#K4" title="TARSKI:func.4">[</a><span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c17">f</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c18">x</font></span>)</span>,<span class="p2">(<span class="default"><font color="Maroon" title="c17">f</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c19">y</font></span>)</span></span><a href="tarski.html#K4" title="TARSKI:func.4">]</a></span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1"><a href="domain_1.html#K1" title="DOMAIN_1:func.1">[</a><span class="default"><font color="Maroon" title="c4">c</font>,<font color="Maroon" title="c5">d</font></span><a href="domain_1.html#K1" title="DOMAIN_1:func.1">]</a></span> or <span class="p1"><a href="tarski.html#K4" title="TARSKI:func.4">[</a><span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c17">f</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c18">x</font></span>)</span>,<span class="p2">(<span class="default"><font color="Maroon" title="c17">f</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c19">y</font></span>)</span></span><a href="tarski.html#K4" title="TARSKI:func.4">]</a></span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1"><a href="domain_1.html#K1" title="DOMAIN_1:func.1">[</a><span class="default"><font color="Maroon" title="c5">d</font>,<font color="Maroon" title="c4">c</font></span><a href="domain_1.html#K1" title="DOMAIN_1:func.1">]</a></span> )
 </span><b>by </b><i><a class="txt" href="neckla_3.html#E9:60"><i><font color="Green" title="E44">A9</font></i></a>, <a class="txt" href="neckla_3.html#E1:60_8_2"><i><font color="Green" title="E56">A72</font></i></a>, <a class="ref" href="enumset1.html#D4" title="ENUMSET1:def.4">ENUMSET1:def 4</a></i>;<br/><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="60_8_2_1_1"><b>suppose </b></a><a NAME="E1:60_8_2_1_1"/>
<span class="p1"><a href="tarski.html#K4" title="TARSKI:func.4">[</a><span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c17">f</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c18">x</font></span>)</span>,<span class="p2">(<span class="default"><font color="Maroon" title="c17">f</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c19">y</font></span>)</span></span><a href="tarski.html#K4" title="TARSKI:func.4">]</a></span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1"><a href="domain_1.html#K1" title="DOMAIN_1:func.1">[</a><span class="default"><font color="Maroon" title="c2">a</font>,<font color="Maroon" title="c3">b</font></span><a href="domain_1.html#K1" title="DOMAIN_1:func.1">]</a></span>
 ;<br/><div class="add"><a NAME="E2:60_8_2_1_1"/><b>then </b><i><font color="Green" title="E63">A79</font></i>: 
( <font color="Maroon" title="c17">f</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c18">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c2">a</font> &amp; <font color="Maroon" title="c17">f</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c19">y</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c3">b</font> )
 <b>by </b><i><a class="ref" href="zfmisc_1.html#T33" title="ZFMISC_1:th.33">ZFMISC_1:33</a></i>;<br/><a NAME="E3:60_8_2_1_1"/><b>then </b><i><font color="Green" title="E64">A80</font></i>: 
( <font color="Maroon" title="c17">f</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c18">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <span class="p1"><a href="domain_1.html#K7" title="DOMAIN_1:func.7">{</a><span class="default"><font color="Maroon" title="c2">a</font>,<font color="Maroon" title="c3">b</font></span><a href="domain_1.html#K7" title="DOMAIN_1:func.7">}</a></span> &amp; <font color="Maroon" title="c17">f</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c19">y</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <span class="p1"><a href="domain_1.html#K7" title="DOMAIN_1:func.7">{</a><span class="default"><font color="Maroon" title="c2">a</font>,<font color="Maroon" title="c3">b</font></span><a href="domain_1.html#K7" title="DOMAIN_1:func.7">}</a></span> )
 <b>by </b><i><a class="ref" href="tarski.html#D2" title="TARSKI:def.2">TARSKI:def 2</a></i>;<br/><a NAME="E4:60_8_2_1_1"/><i><font color="Green" title="E65">A81</font></i>: 
( <font color="Maroon" title="c17">f</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c18">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="c21">G</font> &amp; <font color="Maroon" title="c17">f</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c19">y</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="c21">G</font> )
 <b>by </b><i><a class="txt" href="neckla_3.html#E9:60_8_2"><i><font color="Green" title="E59">A75</font></i></a>, <a class="txt" href="neckla_3.html#E2:60_8_2_1_1"><i><font color="Green" title="E63">A79</font></i></a>, <a class="ref" href="tarski.html#D2" title="TARSKI:def.2">TARSKI:def 2</a></i>;<br/><font color="Maroon" title="c24">F</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p1">(<span class="default"><font color="Maroon" title="c17">f</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c18">x</font></span>)</span> = 
<font color="Maroon" title="c21">G</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c2">a</font>
<b>by </b><i><a class="txt" href="neckla_3.html#E13:60"><i><font color="Green" title="E47">A32</font></i></a>, <a class="txt" href="neckla_3.html#E14:60"><i><font color="Green" title="E48">A33</font></i></a>, <a class="txt" href="neckla_3.html#E21:60"><i><font color="Green" title="E54">A48</font></i></a>, <a class="txt" href="neckla_3.html#E9:60_8_2"><i><font color="Green" title="E59">A75</font></i></a>, <a class="txt" href="neckla_3.html#E10:60_8_2"><i><font color="Green" title="E60">A76</font></i></a>, <a class="txt" href="neckla_3.html#E12:60_8_2"><i><font color="Green" title="E61">A77</font></i></a>, <a class="txt" href="neckla_3.html#E2:60_8_2_1_1"><i><font color="Green" title="E63">A79</font></i></a>, <a class="txt" href="neckla_3.html#E3:60_8_2_1_1"><i><font color="Green" title="E64">A80</font></i></a>, <a class="ref" href="funct_4.html#T17" title="FUNCT_4:th.17">FUNCT_4:17</a></i>
<br/>.= 
0
<b>by </b><i><a class="txt" href="neckla_3.html#E10:60"><i><font color="Green" title="E45">A30</font></i></a>, <a class="txt" href="neckla_3.html#E13:60_8_2"><i><font color="Green" title="E62">A78</font></i></a>, <a class="ref" href="funct_4.html#T66" title="FUNCT_4:th.66">FUNCT_4:66</a></i>
;<br/><a NAME="E6:60_8_2_1_1"/><b>then </b><i><font color="Green" title="E66">A82</font></i>: 
<font color="Maroon" title="c18">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 0
 <b>by </b><i><a class="txt" href="neckla_3.html#E15:60"><i><font color="Green" title="E49">A34</font></i></a>, <a class="txt" href="neckla_3.html#E22:60"><i><font color="Green" title="E55">A50</font></i></a>, <a class="ref" href="funct_2.html#T32" title="FUNCT_2:th.32">FUNCT_2:32</a></i>;<br/><i><font color="Green" title="E67">A83</font></i>: <font color="Maroon" title="c24">F</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p1">(<span class="default"><font color="Maroon" title="c17">f</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c19">y</font></span>)</span> = 
<font color="Maroon" title="c21">G</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c3">b</font>
<b>by </b><i><a class="txt" href="neckla_3.html#E13:60"><i><font color="Green" title="E47">A32</font></i></a>, <a class="txt" href="neckla_3.html#E14:60"><i><font color="Green" title="E48">A33</font></i></a>, <a class="txt" href="neckla_3.html#E21:60"><i><font color="Green" title="E54">A48</font></i></a>, <a class="txt" href="neckla_3.html#E9:60_8_2"><i><font color="Green" title="E59">A75</font></i></a>, <a class="txt" href="neckla_3.html#E10:60_8_2"><i><font color="Green" title="E60">A76</font></i></a>, <a class="txt" href="neckla_3.html#E12:60_8_2"><i><font color="Green" title="E61">A77</font></i></a>, <a class="txt" href="neckla_3.html#E2:60_8_2_1_1"><i><font color="Green" title="E63">A79</font></i></a>, <a class="txt" href="neckla_3.html#E4:60_8_2_1_1"><i><font color="Green" title="E65">A81</font></i></a>, <a class="ref" href="funct_4.html#T17" title="FUNCT_4:th.17">FUNCT_4:17</a></i>
<br/>.= 
1
<b>by </b><i><a class="txt" href="neckla_3.html#E10:60"><i><font color="Green" title="E45">A30</font></i></a>, <a class="txt" href="neckla_3.html#E13:60_8_2"><i><font color="Green" title="E62">A78</font></i></a>, <a class="ref" href="funct_4.html#T66" title="FUNCT_4:th.66">FUNCT_4:66</a></i>
;<br/><a NAME="E8:60_8_2_1_1"/>
<font color="Maroon" title="c24">F</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p1">(<span class="default"><font color="Maroon" title="c17">f</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c19">y</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c19">y</font>
 <b>by </b><i><a class="txt" href="neckla_3.html#E15:60"><i><font color="Green" title="E49">A34</font></i></a>, <a class="txt" href="neckla_3.html#E22:60"><i><font color="Green" title="E55">A50</font></i></a>, <a class="ref" href="funct_2.html#T32" title="FUNCT_2:th.32">FUNCT_2:32</a></i>;<br/><b>hence </b><a NAME="E9:60_8_2_1_1"/>
<span class="p1"><a href="domain_1.html#K1" title="DOMAIN_1:func.1">[</a><span class="default"><font color="Maroon" title="c18">x</font>,<font color="Maroon" title="c19">y</font></span><a href="domain_1.html#K1" title="DOMAIN_1:func.1">]</a></span> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> the <a href="orders_2.html#U1" title="ORDERS_2:sel.1">InternalRel</a> of <span class="p1">(<span class="default"><a href="necklace.html#K4" title="NECKLACE:func.4">Necklace</a> 4</span>)</span>
 <b>by </b><i><a class="txt" href="neckla_3.html#E6:60_8_2_1_1"><i><font color="Green" title="E66">A82</font></i></a>, <a class="txt" href="neckla_3.html#E7:60_8_2_1_1"><i><font color="Green" title="E67">A83</font></i></a>, <a class="ref" href="enumset1.html#D4" title="ENUMSET1:def.4">ENUMSET1:def 4</a>, <a class="ref" href="neckla_2.html#T2" title="NECKLA_2:th.2">NECKLA_2:2</a></i>;<br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="60_8_2_1_2"><b>suppose </b></a><a NAME="E1:60_8_2_1_2"/>
<span class="p1"><a href="tarski.html#K4" title="TARSKI:func.4">[</a><span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c17">f</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c18">x</font></span>)</span>,<span class="p2">(<span class="default"><font color="Maroon" title="c17">f</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c19">y</font></span>)</span></span><a href="tarski.html#K4" title="TARSKI:func.4">]</a></span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1"><a href="domain_1.html#K1" title="DOMAIN_1:func.1">[</a><span class="default"><font color="Maroon" title="c3">b</font>,<font color="Maroon" title="c2">a</font></span><a href="domain_1.html#K1" title="DOMAIN_1:func.1">]</a></span>
 ;<br/><div class="add"><a NAME="E2:60_8_2_1_2"/><b>then </b><i><font color="Green" title="E63">A84</font></i>: 
( <font color="Maroon" title="c17">f</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c18">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c3">b</font> &amp; <font color="Maroon" title="c17">f</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c19">y</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c2">a</font> )
 <b>by </b><i><a class="ref" href="zfmisc_1.html#T33" title="ZFMISC_1:th.33">ZFMISC_1:33</a></i>;<br/><a NAME="E3:60_8_2_1_2"/><b>then </b><i><font color="Green" title="E64">A85</font></i>: 
( <font color="Maroon" title="c17">f</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c18">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <span class="p1"><a href="domain_1.html#K7" title="DOMAIN_1:func.7">{</a><span class="default"><font color="Maroon" title="c2">a</font>,<font color="Maroon" title="c3">b</font></span><a href="domain_1.html#K7" title="DOMAIN_1:func.7">}</a></span> &amp; <font color="Maroon" title="c17">f</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c19">y</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <span class="p1"><a href="domain_1.html#K7" title="DOMAIN_1:func.7">{</a><span class="default"><font color="Maroon" title="c2">a</font>,<font color="Maroon" title="c3">b</font></span><a href="domain_1.html#K7" title="DOMAIN_1:func.7">}</a></span> )
 <b>by </b><i><a class="ref" href="tarski.html#D2" title="TARSKI:def.2">TARSKI:def 2</a></i>;<br/><a NAME="E4:60_8_2_1_2"/><i><font color="Green" title="E65">A86</font></i>: 
( <font color="Maroon" title="c17">f</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c18">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="c21">G</font> &amp; <font color="Maroon" title="c17">f</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c19">y</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="c21">G</font> )
 <b>by </b><i><a class="txt" href="neckla_3.html#E9:60_8_2"><i><font color="Green" title="E59">A75</font></i></a>, <a class="txt" href="neckla_3.html#E2:60_8_2_1_2"><i><font color="Green" title="E63">A84</font></i></a>, <a class="ref" href="tarski.html#D2" title="TARSKI:def.2">TARSKI:def 2</a></i>;<br/><font color="Maroon" title="c24">F</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p1">(<span class="default"><font color="Maroon" title="c17">f</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c19">y</font></span>)</span> = 
<font color="Maroon" title="c21">G</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c2">a</font>
<b>by </b><i><a class="txt" href="neckla_3.html#E13:60"><i><font color="Green" title="E47">A32</font></i></a>, <a class="txt" href="neckla_3.html#E14:60"><i><font color="Green" title="E48">A33</font></i></a>, <a class="txt" href="neckla_3.html#E21:60"><i><font color="Green" title="E54">A48</font></i></a>, <a class="txt" href="neckla_3.html#E9:60_8_2"><i><font color="Green" title="E59">A75</font></i></a>, <a class="txt" href="neckla_3.html#E10:60_8_2"><i><font color="Green" title="E60">A76</font></i></a>, <a class="txt" href="neckla_3.html#E12:60_8_2"><i><font color="Green" title="E61">A77</font></i></a>, <a class="txt" href="neckla_3.html#E2:60_8_2_1_2"><i><font color="Green" title="E63">A84</font></i></a>, <a class="txt" href="neckla_3.html#E3:60_8_2_1_2"><i><font color="Green" title="E64">A85</font></i></a>, <a class="ref" href="funct_4.html#T17" title="FUNCT_4:th.17">FUNCT_4:17</a></i>
<br/>.= 
0
<b>by </b><i><a class="txt" href="neckla_3.html#E10:60"><i><font color="Green" title="E45">A30</font></i></a>, <a class="txt" href="neckla_3.html#E13:60_8_2"><i><font color="Green" title="E62">A78</font></i></a>, <a class="ref" href="funct_4.html#T66" title="FUNCT_4:th.66">FUNCT_4:66</a></i>
;<br/><a NAME="E6:60_8_2_1_2"/><b>then </b><i><font color="Green" title="E66">A87</font></i>: 
<font color="Maroon" title="c19">y</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 0
 <b>by </b><i><a class="txt" href="neckla_3.html#E15:60"><i><font color="Green" title="E49">A34</font></i></a>, <a class="txt" href="neckla_3.html#E22:60"><i><font color="Green" title="E55">A50</font></i></a>, <a class="ref" href="funct_2.html#T32" title="FUNCT_2:th.32">FUNCT_2:32</a></i>;<br/><i><font color="Green" title="E67">A88</font></i>: <font color="Maroon" title="c24">F</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p1">(<span class="default"><font color="Maroon" title="c17">f</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c18">x</font></span>)</span> = 
<font color="Maroon" title="c21">G</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c3">b</font>
<b>by </b><i><a class="txt" href="neckla_3.html#E13:60"><i><font color="Green" title="E47">A32</font></i></a>, <a class="txt" href="neckla_3.html#E14:60"><i><font color="Green" title="E48">A33</font></i></a>, <a class="txt" href="neckla_3.html#E21:60"><i><font color="Green" title="E54">A48</font></i></a>, <a class="txt" href="neckla_3.html#E9:60_8_2"><i><font color="Green" title="E59">A75</font></i></a>, <a class="txt" href="neckla_3.html#E10:60_8_2"><i><font color="Green" title="E60">A76</font></i></a>, <a class="txt" href="neckla_3.html#E12:60_8_2"><i><font color="Green" title="E61">A77</font></i></a>, <a class="txt" href="neckla_3.html#E2:60_8_2_1_2"><i><font color="Green" title="E63">A84</font></i></a>, <a class="txt" href="neckla_3.html#E4:60_8_2_1_2"><i><font color="Green" title="E65">A86</font></i></a>, <a class="ref" href="funct_4.html#T17" title="FUNCT_4:th.17">FUNCT_4:17</a></i>
<br/>.= 
1
<b>by </b><i><a class="txt" href="neckla_3.html#E10:60"><i><font color="Green" title="E45">A30</font></i></a>, <a class="txt" href="neckla_3.html#E13:60_8_2"><i><font color="Green" title="E62">A78</font></i></a>, <a class="ref" href="funct_4.html#T66" title="FUNCT_4:th.66">FUNCT_4:66</a></i>
;<br/><a NAME="E8:60_8_2_1_2"/>
<font color="Maroon" title="c24">F</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p1">(<span class="default"><font color="Maroon" title="c17">f</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c18">x</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c18">x</font>
 <b>by </b><i><a class="txt" href="neckla_3.html#E15:60"><i><font color="Green" title="E49">A34</font></i></a>, <a class="txt" href="neckla_3.html#E22:60"><i><font color="Green" title="E55">A50</font></i></a>, <a class="ref" href="funct_2.html#T32" title="FUNCT_2:th.32">FUNCT_2:32</a></i>;<br/><b>hence </b><a NAME="E9:60_8_2_1_2"/>
<span class="p1"><a href="domain_1.html#K1" title="DOMAIN_1:func.1">[</a><span class="default"><font color="Maroon" title="c18">x</font>,<font color="Maroon" title="c19">y</font></span><a href="domain_1.html#K1" title="DOMAIN_1:func.1">]</a></span> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> the <a href="orders_2.html#U1" title="ORDERS_2:sel.1">InternalRel</a> of <span class="p1">(<span class="default"><a href="necklace.html#K4" title="NECKLACE:func.4">Necklace</a> 4</span>)</span>
 <b>by </b><i><a class="txt" href="neckla_3.html#E6:60_8_2_1_2"><i><font color="Green" title="E66">A87</font></i></a>, <a class="txt" href="neckla_3.html#E7:60_8_2_1_2"><i><font color="Green" title="E67">A88</font></i></a>, <a class="ref" href="enumset1.html#D4" title="ENUMSET1:def.4">ENUMSET1:def 4</a>, <a class="ref" href="neckla_2.html#T2" title="NECKLA_2:th.2">NECKLA_2:2</a></i>;<br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="60_8_2_1_3"><b>suppose </b></a><a NAME="E1:60_8_2_1_3"/>
<span class="p1"><a href="tarski.html#K4" title="TARSKI:func.4">[</a><span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c17">f</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c18">x</font></span>)</span>,<span class="p2">(<span class="default"><font color="Maroon" title="c17">f</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c19">y</font></span>)</span></span><a href="tarski.html#K4" title="TARSKI:func.4">]</a></span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1"><a href="domain_1.html#K1" title="DOMAIN_1:func.1">[</a><span class="default"><font color="Maroon" title="c3">b</font>,<font color="Maroon" title="c4">c</font></span><a href="domain_1.html#K1" title="DOMAIN_1:func.1">]</a></span>
 ;<br/><div class="add"><a NAME="E2:60_8_2_1_3"/><b>then </b><i><font color="Green" title="E63">A89</font></i>: 
( <font color="Maroon" title="c17">f</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c18">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c3">b</font> &amp; <font color="Maroon" title="c17">f</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c19">y</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c4">c</font> )
 <b>by </b><i><a class="ref" href="zfmisc_1.html#T33" title="ZFMISC_1:th.33">ZFMISC_1:33</a></i>;<br/><a NAME="E3:60_8_2_1_3"/><b>then </b><i><font color="Green" title="E64">A90</font></i>: 
( <font color="Maroon" title="c17">f</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c18">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="c21">G</font> &amp; <font color="Maroon" title="c17">f</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c19">y</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="c23">Hh</font> )
 <b>by </b><i><a class="txt" href="neckla_3.html#E9:60_8_2"><i><font color="Green" title="E59">A75</font></i></a>, <a class="txt" href="neckla_3.html#E10:60_8_2"><i><font color="Green" title="E60">A76</font></i></a>, <a class="ref" href="tarski.html#D2" title="TARSKI:def.2">TARSKI:def 2</a></i>;<br/><b>then </b><font color="Maroon" title="c24">F</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p1">(<span class="default"><font color="Maroon" title="c17">f</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c18">x</font></span>)</span> = 
<font color="Maroon" title="c21">G</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c3">b</font>
<b>by </b><i><a class="txt" href="neckla_3.html#E13:60"><i><font color="Green" title="E47">A32</font></i></a>, <a class="txt" href="neckla_3.html#E14:60"><i><font color="Green" title="E48">A33</font></i></a>, <a class="txt" href="neckla_3.html#E21:60"><i><font color="Green" title="E54">A48</font></i></a>, <a class="txt" href="neckla_3.html#E9:60_8_2"><i><font color="Green" title="E59">A75</font></i></a>, <a class="txt" href="neckla_3.html#E10:60_8_2"><i><font color="Green" title="E60">A76</font></i></a>, <a class="txt" href="neckla_3.html#E12:60_8_2"><i><font color="Green" title="E61">A77</font></i></a>, <a class="txt" href="neckla_3.html#E2:60_8_2_1_3"><i><font color="Green" title="E63">A89</font></i></a>, <a class="ref" href="funct_4.html#T17" title="FUNCT_4:th.17">FUNCT_4:17</a></i>
<br/>.= 
1
<b>by </b><i><a class="txt" href="neckla_3.html#E10:60"><i><font color="Green" title="E45">A30</font></i></a>, <a class="txt" href="neckla_3.html#E13:60_8_2"><i><font color="Green" title="E62">A78</font></i></a>, <a class="ref" href="funct_4.html#T66" title="FUNCT_4:th.66">FUNCT_4:66</a></i>
;<br/><a NAME="E5:60_8_2_1_3"/><b>then </b><i><font color="Green" title="E65">A91</font></i>: 
<font color="Maroon" title="c18">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 1
 <b>by </b><i><a class="txt" href="neckla_3.html#E15:60"><i><font color="Green" title="E49">A34</font></i></a>, <a class="txt" href="neckla_3.html#E22:60"><i><font color="Green" title="E55">A50</font></i></a>, <a class="ref" href="funct_2.html#T32" title="FUNCT_2:th.32">FUNCT_2:32</a></i>;<br/><i><font color="Green" title="E66">A92</font></i>: <font color="Maroon" title="c24">F</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p1">(<span class="default"><font color="Maroon" title="c17">f</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c19">y</font></span>)</span> = 
<font color="Maroon" title="c23">Hh</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c4">c</font>
<b>by </b><i><a class="txt" href="neckla_3.html#E13:60"><i><font color="Green" title="E47">A32</font></i></a>, <a class="txt" href="neckla_3.html#E14:60"><i><font color="Green" title="E48">A33</font></i></a>, <a class="txt" href="neckla_3.html#E21:60"><i><font color="Green" title="E54">A48</font></i></a>, <a class="txt" href="neckla_3.html#E9:60_8_2"><i><font color="Green" title="E59">A75</font></i></a>, <a class="txt" href="neckla_3.html#E10:60_8_2"><i><font color="Green" title="E60">A76</font></i></a>, <a class="txt" href="neckla_3.html#E12:60_8_2"><i><font color="Green" title="E61">A77</font></i></a>, <a class="txt" href="neckla_3.html#E2:60_8_2_1_3"><i><font color="Green" title="E63">A89</font></i></a>, <a class="txt" href="neckla_3.html#E3:60_8_2_1_3"><i><font color="Green" title="E64">A90</font></i></a>, <a class="ref" href="funct_4.html#T17" title="FUNCT_4:th.17">FUNCT_4:17</a></i>
<br/>.= 
2
<b>by </b><i><a class="txt" href="neckla_3.html#E10:60"><i><font color="Green" title="E45">A30</font></i></a>, <a class="txt" href="neckla_3.html#E13:60_8_2"><i><font color="Green" title="E62">A78</font></i></a>, <a class="ref" href="funct_4.html#T66" title="FUNCT_4:th.66">FUNCT_4:66</a></i>
;<br/><a NAME="E7:60_8_2_1_3"/>
<font color="Maroon" title="c24">F</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p1">(<span class="default"><font color="Maroon" title="c17">f</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c19">y</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c19">y</font>
 <b>by </b><i><a class="txt" href="neckla_3.html#E15:60"><i><font color="Green" title="E49">A34</font></i></a>, <a class="txt" href="neckla_3.html#E22:60"><i><font color="Green" title="E55">A50</font></i></a>, <a class="ref" href="funct_2.html#T32" title="FUNCT_2:th.32">FUNCT_2:32</a></i>;<br/><b>hence </b><a NAME="E8:60_8_2_1_3"/>
<span class="p1"><a href="domain_1.html#K1" title="DOMAIN_1:func.1">[</a><span class="default"><font color="Maroon" title="c18">x</font>,<font color="Maroon" title="c19">y</font></span><a href="domain_1.html#K1" title="DOMAIN_1:func.1">]</a></span> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> the <a href="orders_2.html#U1" title="ORDERS_2:sel.1">InternalRel</a> of <span class="p1">(<span class="default"><a href="necklace.html#K4" title="NECKLACE:func.4">Necklace</a> 4</span>)</span>
 <b>by </b><i><a class="txt" href="neckla_3.html#E5:60_8_2_1_3"><i><font color="Green" title="E65">A91</font></i></a>, <a class="txt" href="neckla_3.html#E6:60_8_2_1_3"><i><font color="Green" title="E66">A92</font></i></a>, <a class="ref" href="enumset1.html#D4" title="ENUMSET1:def.4">ENUMSET1:def 4</a>, <a class="ref" href="neckla_2.html#T2" title="NECKLA_2:th.2">NECKLA_2:2</a></i>;<br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="60_8_2_1_4"><b>suppose </b></a><a NAME="E1:60_8_2_1_4"/>
<span class="p1"><a href="tarski.html#K4" title="TARSKI:func.4">[</a><span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c17">f</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c18">x</font></span>)</span>,<span class="p2">(<span class="default"><font color="Maroon" title="c17">f</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c19">y</font></span>)</span></span><a href="tarski.html#K4" title="TARSKI:func.4">]</a></span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1"><a href="domain_1.html#K1" title="DOMAIN_1:func.1">[</a><span class="default"><font color="Maroon" title="c4">c</font>,<font color="Maroon" title="c3">b</font></span><a href="domain_1.html#K1" title="DOMAIN_1:func.1">]</a></span>
 ;<br/><div class="add"><a NAME="E2:60_8_2_1_4"/><b>then </b><i><font color="Green" title="E63">A93</font></i>: 
( <font color="Maroon" title="c17">f</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c18">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c4">c</font> &amp; <font color="Maroon" title="c17">f</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c19">y</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c3">b</font> )
 <b>by </b><i><a class="ref" href="zfmisc_1.html#T33" title="ZFMISC_1:th.33">ZFMISC_1:33</a></i>;<br/><a NAME="E3:60_8_2_1_4"/><b>then </b><i><font color="Green" title="E64">A94</font></i>: 
( <font color="Maroon" title="c17">f</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c18">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="c23">Hh</font> &amp; <font color="Maroon" title="c17">f</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c19">y</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="c21">G</font> )
 <b>by </b><i><a class="txt" href="neckla_3.html#E9:60_8_2"><i><font color="Green" title="E59">A75</font></i></a>, <a class="txt" href="neckla_3.html#E10:60_8_2"><i><font color="Green" title="E60">A76</font></i></a>, <a class="ref" href="tarski.html#D2" title="TARSKI:def.2">TARSKI:def 2</a></i>;<br/><b>then </b><font color="Maroon" title="c24">F</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p1">(<span class="default"><font color="Maroon" title="c17">f</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c19">y</font></span>)</span> = 
<font color="Maroon" title="c21">G</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c3">b</font>
<b>by </b><i><a class="txt" href="neckla_3.html#E13:60"><i><font color="Green" title="E47">A32</font></i></a>, <a class="txt" href="neckla_3.html#E14:60"><i><font color="Green" title="E48">A33</font></i></a>, <a class="txt" href="neckla_3.html#E21:60"><i><font color="Green" title="E54">A48</font></i></a>, <a class="txt" href="neckla_3.html#E9:60_8_2"><i><font color="Green" title="E59">A75</font></i></a>, <a class="txt" href="neckla_3.html#E10:60_8_2"><i><font color="Green" title="E60">A76</font></i></a>, <a class="txt" href="neckla_3.html#E12:60_8_2"><i><font color="Green" title="E61">A77</font></i></a>, <a class="txt" href="neckla_3.html#E2:60_8_2_1_4"><i><font color="Green" title="E63">A93</font></i></a>, <a class="ref" href="funct_4.html#T17" title="FUNCT_4:th.17">FUNCT_4:17</a></i>
<br/>.= 
1
<b>by </b><i><a class="txt" href="neckla_3.html#E10:60"><i><font color="Green" title="E45">A30</font></i></a>, <a class="txt" href="neckla_3.html#E13:60_8_2"><i><font color="Green" title="E62">A78</font></i></a>, <a class="ref" href="funct_4.html#T66" title="FUNCT_4:th.66">FUNCT_4:66</a></i>
;<br/><a NAME="E5:60_8_2_1_4"/><b>then </b><i><font color="Green" title="E65">A95</font></i>: 
<font color="Maroon" title="c19">y</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 1
 <b>by </b><i><a class="txt" href="neckla_3.html#E15:60"><i><font color="Green" title="E49">A34</font></i></a>, <a class="txt" href="neckla_3.html#E22:60"><i><font color="Green" title="E55">A50</font></i></a>, <a class="ref" href="funct_2.html#T32" title="FUNCT_2:th.32">FUNCT_2:32</a></i>;<br/><i><font color="Green" title="E66">A96</font></i>: <font color="Maroon" title="c24">F</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p1">(<span class="default"><font color="Maroon" title="c17">f</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c18">x</font></span>)</span> = 
<font color="Maroon" title="c23">Hh</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c4">c</font>
<b>by </b><i><a class="txt" href="neckla_3.html#E13:60"><i><font color="Green" title="E47">A32</font></i></a>, <a class="txt" href="neckla_3.html#E14:60"><i><font color="Green" title="E48">A33</font></i></a>, <a class="txt" href="neckla_3.html#E21:60"><i><font color="Green" title="E54">A48</font></i></a>, <a class="txt" href="neckla_3.html#E9:60_8_2"><i><font color="Green" title="E59">A75</font></i></a>, <a class="txt" href="neckla_3.html#E10:60_8_2"><i><font color="Green" title="E60">A76</font></i></a>, <a class="txt" href="neckla_3.html#E12:60_8_2"><i><font color="Green" title="E61">A77</font></i></a>, <a class="txt" href="neckla_3.html#E2:60_8_2_1_4"><i><font color="Green" title="E63">A93</font></i></a>, <a class="txt" href="neckla_3.html#E3:60_8_2_1_4"><i><font color="Green" title="E64">A94</font></i></a>, <a class="ref" href="funct_4.html#T17" title="FUNCT_4:th.17">FUNCT_4:17</a></i>
<br/>.= 
2
<b>by </b><i><a class="txt" href="neckla_3.html#E10:60"><i><font color="Green" title="E45">A30</font></i></a>, <a class="txt" href="neckla_3.html#E13:60_8_2"><i><font color="Green" title="E62">A78</font></i></a>, <a class="ref" href="funct_4.html#T66" title="FUNCT_4:th.66">FUNCT_4:66</a></i>
;<br/><a NAME="E7:60_8_2_1_4"/>
<font color="Maroon" title="c24">F</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p1">(<span class="default"><font color="Maroon" title="c17">f</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c18">x</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c18">x</font>
 <b>by </b><i><a class="txt" href="neckla_3.html#E15:60"><i><font color="Green" title="E49">A34</font></i></a>, <a class="txt" href="neckla_3.html#E22:60"><i><font color="Green" title="E55">A50</font></i></a>, <a class="ref" href="funct_2.html#T32" title="FUNCT_2:th.32">FUNCT_2:32</a></i>;<br/><b>hence </b><a NAME="E8:60_8_2_1_4"/>
<span class="p1"><a href="domain_1.html#K1" title="DOMAIN_1:func.1">[</a><span class="default"><font color="Maroon" title="c18">x</font>,<font color="Maroon" title="c19">y</font></span><a href="domain_1.html#K1" title="DOMAIN_1:func.1">]</a></span> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> the <a href="orders_2.html#U1" title="ORDERS_2:sel.1">InternalRel</a> of <span class="p1">(<span class="default"><a href="necklace.html#K4" title="NECKLACE:func.4">Necklace</a> 4</span>)</span>
 <b>by </b><i><a class="txt" href="neckla_3.html#E5:60_8_2_1_4"><i><font color="Green" title="E65">A95</font></i></a>, <a class="txt" href="neckla_3.html#E6:60_8_2_1_4"><i><font color="Green" title="E66">A96</font></i></a>, <a class="ref" href="enumset1.html#D4" title="ENUMSET1:def.4">ENUMSET1:def 4</a>, <a class="ref" href="neckla_2.html#T2" title="NECKLA_2:th.2">NECKLA_2:2</a></i>;<br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="60_8_2_1_5"><b>suppose </b></a><a NAME="E1:60_8_2_1_5"/>
<span class="p1"><a href="tarski.html#K4" title="TARSKI:func.4">[</a><span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c17">f</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c18">x</font></span>)</span>,<span class="p2">(<span class="default"><font color="Maroon" title="c17">f</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c19">y</font></span>)</span></span><a href="tarski.html#K4" title="TARSKI:func.4">]</a></span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1"><a href="domain_1.html#K1" title="DOMAIN_1:func.1">[</a><span class="default"><font color="Maroon" title="c4">c</font>,<font color="Maroon" title="c5">d</font></span><a href="domain_1.html#K1" title="DOMAIN_1:func.1">]</a></span>
 ;<br/><div class="add"><a NAME="E2:60_8_2_1_5"/><b>then </b><i><font color="Green" title="E63">A97</font></i>: 
( <font color="Maroon" title="c17">f</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c18">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c4">c</font> &amp; <font color="Maroon" title="c17">f</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c19">y</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c5">d</font> )
 <b>by </b><i><a class="ref" href="zfmisc_1.html#T33" title="ZFMISC_1:th.33">ZFMISC_1:33</a></i>;<br/><a NAME="E3:60_8_2_1_5"/><b>then </b><i><font color="Green" title="E64">A98</font></i>: 
( <font color="Maroon" title="c17">f</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c18">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <span class="p1"><a href="domain_1.html#K7" title="DOMAIN_1:func.7">{</a><span class="default"><font color="Maroon" title="c4">c</font>,<font color="Maroon" title="c5">d</font></span><a href="domain_1.html#K7" title="DOMAIN_1:func.7">}</a></span> &amp; <font color="Maroon" title="c17">f</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c19">y</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <span class="p1"><a href="domain_1.html#K7" title="DOMAIN_1:func.7">{</a><span class="default"><font color="Maroon" title="c4">c</font>,<font color="Maroon" title="c5">d</font></span><a href="domain_1.html#K7" title="DOMAIN_1:func.7">}</a></span> )
 <b>by </b><i><a class="ref" href="tarski.html#D2" title="TARSKI:def.2">TARSKI:def 2</a></i>;<br/><a NAME="E4:60_8_2_1_5"/><i><font color="Green" title="E65">A99</font></i>: 
( <font color="Maroon" title="c17">f</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c18">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="c23">Hh</font> &amp; <font color="Maroon" title="c17">f</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c19">y</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="c23">Hh</font> )
 <b>by </b><i><a class="txt" href="neckla_3.html#E10:60_8_2"><i><font color="Green" title="E60">A76</font></i></a>, <a class="txt" href="neckla_3.html#E2:60_8_2_1_5"><i><font color="Green" title="E63">A97</font></i></a>, <a class="ref" href="tarski.html#D2" title="TARSKI:def.2">TARSKI:def 2</a></i>;<br/><font color="Maroon" title="c24">F</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p1">(<span class="default"><font color="Maroon" title="c17">f</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c18">x</font></span>)</span> = 
<font color="Maroon" title="c23">Hh</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c4">c</font>
<b>by </b><i><a class="txt" href="neckla_3.html#E13:60"><i><font color="Green" title="E47">A32</font></i></a>, <a class="txt" href="neckla_3.html#E14:60"><i><font color="Green" title="E48">A33</font></i></a>, <a class="txt" href="neckla_3.html#E21:60"><i><font color="Green" title="E54">A48</font></i></a>, <a class="txt" href="neckla_3.html#E9:60_8_2"><i><font color="Green" title="E59">A75</font></i></a>, <a class="txt" href="neckla_3.html#E10:60_8_2"><i><font color="Green" title="E60">A76</font></i></a>, <a class="txt" href="neckla_3.html#E12:60_8_2"><i><font color="Green" title="E61">A77</font></i></a>, <a class="txt" href="neckla_3.html#E2:60_8_2_1_5"><i><font color="Green" title="E63">A97</font></i></a>, <a class="txt" href="neckla_3.html#E3:60_8_2_1_5"><i><font color="Green" title="E64">A98</font></i></a>, <a class="ref" href="funct_4.html#T17" title="FUNCT_4:th.17">FUNCT_4:17</a></i>
<br/>.= 
2
<b>by </b><i><a class="txt" href="neckla_3.html#E10:60"><i><font color="Green" title="E45">A30</font></i></a>, <a class="txt" href="neckla_3.html#E13:60_8_2"><i><font color="Green" title="E62">A78</font></i></a>, <a class="ref" href="funct_4.html#T66" title="FUNCT_4:th.66">FUNCT_4:66</a></i>
;<br/><a NAME="E6:60_8_2_1_5"/><b>then </b><i><font color="Green" title="E66">A100</font></i>: 
<font color="Maroon" title="c18">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 2
 <b>by </b><i><a class="txt" href="neckla_3.html#E15:60"><i><font color="Green" title="E49">A34</font></i></a>, <a class="txt" href="neckla_3.html#E22:60"><i><font color="Green" title="E55">A50</font></i></a>, <a class="ref" href="funct_2.html#T32" title="FUNCT_2:th.32">FUNCT_2:32</a></i>;<br/><i><font color="Green" title="E67">A101</font></i>: <font color="Maroon" title="c24">F</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p1">(<span class="default"><font color="Maroon" title="c17">f</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c19">y</font></span>)</span> = 
<font color="Maroon" title="c23">Hh</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c5">d</font>
<b>by </b><i><a class="txt" href="neckla_3.html#E13:60"><i><font color="Green" title="E47">A32</font></i></a>, <a class="txt" href="neckla_3.html#E14:60"><i><font color="Green" title="E48">A33</font></i></a>, <a class="txt" href="neckla_3.html#E21:60"><i><font color="Green" title="E54">A48</font></i></a>, <a class="txt" href="neckla_3.html#E9:60_8_2"><i><font color="Green" title="E59">A75</font></i></a>, <a class="txt" href="neckla_3.html#E10:60_8_2"><i><font color="Green" title="E60">A76</font></i></a>, <a class="txt" href="neckla_3.html#E12:60_8_2"><i><font color="Green" title="E61">A77</font></i></a>, <a class="txt" href="neckla_3.html#E2:60_8_2_1_5"><i><font color="Green" title="E63">A97</font></i></a>, <a class="txt" href="neckla_3.html#E4:60_8_2_1_5"><i><font color="Green" title="E65">A99</font></i></a>, <a class="ref" href="funct_4.html#T17" title="FUNCT_4:th.17">FUNCT_4:17</a></i>
<br/>.= 
3
<b>by </b><i><a class="txt" href="neckla_3.html#E10:60"><i><font color="Green" title="E45">A30</font></i></a>, <a class="txt" href="neckla_3.html#E13:60_8_2"><i><font color="Green" title="E62">A78</font></i></a>, <a class="ref" href="funct_4.html#T66" title="FUNCT_4:th.66">FUNCT_4:66</a></i>
;<br/><a NAME="E8:60_8_2_1_5"/>
<font color="Maroon" title="c24">F</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p1">(<span class="default"><font color="Maroon" title="c17">f</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c19">y</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c19">y</font>
 <b>by </b><i><a class="txt" href="neckla_3.html#E15:60"><i><font color="Green" title="E49">A34</font></i></a>, <a class="txt" href="neckla_3.html#E22:60"><i><font color="Green" title="E55">A50</font></i></a>, <a class="ref" href="funct_2.html#T32" title="FUNCT_2:th.32">FUNCT_2:32</a></i>;<br/><b>hence </b><a NAME="E9:60_8_2_1_5"/>
<span class="p1"><a href="domain_1.html#K1" title="DOMAIN_1:func.1">[</a><span class="default"><font color="Maroon" title="c18">x</font>,<font color="Maroon" title="c19">y</font></span><a href="domain_1.html#K1" title="DOMAIN_1:func.1">]</a></span> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> the <a href="orders_2.html#U1" title="ORDERS_2:sel.1">InternalRel</a> of <span class="p1">(<span class="default"><a href="necklace.html#K4" title="NECKLACE:func.4">Necklace</a> 4</span>)</span>
 <b>by </b><i><a class="txt" href="neckla_3.html#E6:60_8_2_1_5"><i><font color="Green" title="E66">A100</font></i></a>, <a class="txt" href="neckla_3.html#E7:60_8_2_1_5"><i><font color="Green" title="E67">A101</font></i></a>, <a class="ref" href="enumset1.html#D4" title="ENUMSET1:def.4">ENUMSET1:def 4</a>, <a class="ref" href="neckla_2.html#T2" title="NECKLA_2:th.2">NECKLA_2:2</a></i>;<br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="60_8_2_1_6"><b>suppose </b></a><a NAME="E1:60_8_2_1_6"/>
<span class="p1"><a href="tarski.html#K4" title="TARSKI:func.4">[</a><span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c17">f</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c18">x</font></span>)</span>,<span class="p2">(<span class="default"><font color="Maroon" title="c17">f</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c19">y</font></span>)</span></span><a href="tarski.html#K4" title="TARSKI:func.4">]</a></span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1"><a href="domain_1.html#K1" title="DOMAIN_1:func.1">[</a><span class="default"><font color="Maroon" title="c5">d</font>,<font color="Maroon" title="c4">c</font></span><a href="domain_1.html#K1" title="DOMAIN_1:func.1">]</a></span>
 ;<br/><div class="add"><a NAME="E2:60_8_2_1_6"/><b>then </b><i><font color="Green" title="E63">A102</font></i>: 
( <font color="Maroon" title="c17">f</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c18">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c5">d</font> &amp; <font color="Maroon" title="c17">f</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c19">y</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c4">c</font> )
 <b>by </b><i><a class="ref" href="zfmisc_1.html#T33" title="ZFMISC_1:th.33">ZFMISC_1:33</a></i>;<br/><a NAME="E3:60_8_2_1_6"/><b>then </b><i><font color="Green" title="E64">A103</font></i>: 
( <font color="Maroon" title="c17">f</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c18">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <span class="p1"><a href="domain_1.html#K7" title="DOMAIN_1:func.7">{</a><span class="default"><font color="Maroon" title="c4">c</font>,<font color="Maroon" title="c5">d</font></span><a href="domain_1.html#K7" title="DOMAIN_1:func.7">}</a></span> &amp; <font color="Maroon" title="c17">f</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c19">y</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <span class="p1"><a href="domain_1.html#K7" title="DOMAIN_1:func.7">{</a><span class="default"><font color="Maroon" title="c4">c</font>,<font color="Maroon" title="c5">d</font></span><a href="domain_1.html#K7" title="DOMAIN_1:func.7">}</a></span> )
 <b>by </b><i><a class="ref" href="tarski.html#D2" title="TARSKI:def.2">TARSKI:def 2</a></i>;<br/><a NAME="E4:60_8_2_1_6"/><i><font color="Green" title="E65">A104</font></i>: 
( <font color="Maroon" title="c17">f</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c18">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="c23">Hh</font> &amp; <font color="Maroon" title="c17">f</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c19">y</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="c23">Hh</font> )
 <b>by </b><i><a class="txt" href="neckla_3.html#E10:60_8_2"><i><font color="Green" title="E60">A76</font></i></a>, <a class="txt" href="neckla_3.html#E2:60_8_2_1_6"><i><font color="Green" title="E63">A102</font></i></a>, <a class="ref" href="tarski.html#D2" title="TARSKI:def.2">TARSKI:def 2</a></i>;<br/><font color="Maroon" title="c24">F</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p1">(<span class="default"><font color="Maroon" title="c17">f</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c19">y</font></span>)</span> = 
<font color="Maroon" title="c23">Hh</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c4">c</font>
<b>by </b><i><a class="txt" href="neckla_3.html#E13:60"><i><font color="Green" title="E47">A32</font></i></a>, <a class="txt" href="neckla_3.html#E14:60"><i><font color="Green" title="E48">A33</font></i></a>, <a class="txt" href="neckla_3.html#E21:60"><i><font color="Green" title="E54">A48</font></i></a>, <a class="txt" href="neckla_3.html#E9:60_8_2"><i><font color="Green" title="E59">A75</font></i></a>, <a class="txt" href="neckla_3.html#E10:60_8_2"><i><font color="Green" title="E60">A76</font></i></a>, <a class="txt" href="neckla_3.html#E12:60_8_2"><i><font color="Green" title="E61">A77</font></i></a>, <a class="txt" href="neckla_3.html#E2:60_8_2_1_6"><i><font color="Green" title="E63">A102</font></i></a>, <a class="txt" href="neckla_3.html#E3:60_8_2_1_6"><i><font color="Green" title="E64">A103</font></i></a>, <a class="ref" href="funct_4.html#T17" title="FUNCT_4:th.17">FUNCT_4:17</a></i>
<br/>.= 
2
<b>by </b><i><a class="txt" href="neckla_3.html#E10:60"><i><font color="Green" title="E45">A30</font></i></a>, <a class="txt" href="neckla_3.html#E13:60_8_2"><i><font color="Green" title="E62">A78</font></i></a>, <a class="ref" href="funct_4.html#T66" title="FUNCT_4:th.66">FUNCT_4:66</a></i>
;<br/><a NAME="E6:60_8_2_1_6"/><b>then </b><i><font color="Green" title="E66">A105</font></i>: 
<font color="Maroon" title="c19">y</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 2
 <b>by </b><i><a class="txt" href="neckla_3.html#E15:60"><i><font color="Green" title="E49">A34</font></i></a>, <a class="txt" href="neckla_3.html#E22:60"><i><font color="Green" title="E55">A50</font></i></a>, <a class="ref" href="funct_2.html#T32" title="FUNCT_2:th.32">FUNCT_2:32</a></i>;<br/><i><font color="Green" title="E67">A106</font></i>: <font color="Maroon" title="c24">F</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p1">(<span class="default"><font color="Maroon" title="c17">f</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c18">x</font></span>)</span> = 
<font color="Maroon" title="c23">Hh</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c5">d</font>
<b>by </b><i><a class="txt" href="neckla_3.html#E13:60"><i><font color="Green" title="E47">A32</font></i></a>, <a class="txt" href="neckla_3.html#E14:60"><i><font color="Green" title="E48">A33</font></i></a>, <a class="txt" href="neckla_3.html#E21:60"><i><font color="Green" title="E54">A48</font></i></a>, <a class="txt" href="neckla_3.html#E9:60_8_2"><i><font color="Green" title="E59">A75</font></i></a>, <a class="txt" href="neckla_3.html#E10:60_8_2"><i><font color="Green" title="E60">A76</font></i></a>, <a class="txt" href="neckla_3.html#E12:60_8_2"><i><font color="Green" title="E61">A77</font></i></a>, <a class="txt" href="neckla_3.html#E2:60_8_2_1_6"><i><font color="Green" title="E63">A102</font></i></a>, <a class="txt" href="neckla_3.html#E4:60_8_2_1_6"><i><font color="Green" title="E65">A104</font></i></a>, <a class="ref" href="funct_4.html#T17" title="FUNCT_4:th.17">FUNCT_4:17</a></i>
<br/>.= 
3
<b>by </b><i><a class="txt" href="neckla_3.html#E10:60"><i><font color="Green" title="E45">A30</font></i></a>, <a class="txt" href="neckla_3.html#E13:60_8_2"><i><font color="Green" title="E62">A78</font></i></a>, <a class="ref" href="funct_4.html#T66" title="FUNCT_4:th.66">FUNCT_4:66</a></i>
;<br/><a NAME="E8:60_8_2_1_6"/>
<font color="Maroon" title="c24">F</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p1">(<span class="default"><font color="Maroon" title="c17">f</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c18">x</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c18">x</font>
 <b>by </b><i><a class="txt" href="neckla_3.html#E15:60"><i><font color="Green" title="E49">A34</font></i></a>, <a class="txt" href="neckla_3.html#E22:60"><i><font color="Green" title="E55">A50</font></i></a>, <a class="ref" href="funct_2.html#T32" title="FUNCT_2:th.32">FUNCT_2:32</a></i>;<br/><b>hence </b><a NAME="E9:60_8_2_1_6"/>
<span class="p1"><a href="domain_1.html#K1" title="DOMAIN_1:func.1">[</a><span class="default"><font color="Maroon" title="c18">x</font>,<font color="Maroon" title="c19">y</font></span><a href="domain_1.html#K1" title="DOMAIN_1:func.1">]</a></span> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> the <a href="orders_2.html#U1" title="ORDERS_2:sel.1">InternalRel</a> of <span class="p1">(<span class="default"><a href="necklace.html#K4" title="NECKLACE:func.4">Necklace</a> 4</span>)</span>
 <b>by </b><i><a class="txt" href="neckla_3.html#E6:60_8_2_1_6"><i><font color="Green" title="E66">A105</font></i></a>, <a class="txt" href="neckla_3.html#E7:60_8_2_1_6"><i><font color="Green" title="E67">A106</font></i></a>, <a class="ref" href="enumset1.html#D4" title="ENUMSET1:def.4">ENUMSET1:def 4</a>, <a class="ref" href="neckla_2.html#T2" title="NECKLA_2:th.2">NECKLA_2:2</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="E24:60"/>
 <a href="yellow_0.html#K5" title="YELLOW_0:func.5">subrelstr</a> <font color="Maroon" title="c6">Z</font> <a href="necklace.html#R1" title="NECKLACE:pred.1">embeds</a>  <a href="necklace.html#K4" title="NECKLACE:func.4">Necklace</a> 4
 <b>by </b><i><a class="txt" href="neckla_3.html#E22:60"><i><font color="Green" title="E55">A50</font></i></a>, <a class="ref" href="necklace.html#D2" title="NECKLACE:def.2">NECKLACE:def 2</a></i>;<br/>


</div>
