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

<b>defpred </b><font color="Maroon">S<sub>1</sub></font>[  <a href="nat_1.html#NM1">Nat</a>] means for <font color="Olive">b<sub>1</sub></font> being <a href="group_1.html#V6">finite</a>  <a href="orders_4.html#M1" target="_self">Chain</a>  st  <a href="card_1.html#K1">Card</a> the <a href="struct_0.html#U1">carrier</a> of <font color="Olive">b<sub>1</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">a<sub>1</sub></font> holds <br/><font color="Olive">b<sub>1</sub></font>, <a href="yellow_1.html#K2">InclPoset</a> <font color="Maroon">a<sub>1</sub></font> <a href="waybel_1.html#R5">are_isomorphic</a> ;<br/>
<a NAME="E1:17"/><i><font color="Green">E9</font></i>: 
<font color="Maroon">S<sub>1</sub></font>[0]
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="17_1"><b>proof </b></a><div class="add">

<b>let </b><font color="Maroon">c<sub>1</sub></font> be  <a href="group_1.html#V6">finite</a>  <a href="orders_4.html#M1" target="_self">Chain</a> ;<br/>

<b>assume </b><a NAME="E1:17_1"/>
 <a href="card_1.html#K1">Card</a> the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">c<sub>1</sub></font> <a href="hidden.html#R1">=</a> 0
 ;<br/>

<a NAME="E2:17_1"/><b>then </b><i><font color="Green">E10</font></i>: 
the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">c<sub>1</sub></font> <a href="hidden.html#R1">=</a>  <a href="xboole_0.html#K1">{}</a> 
 
<b>by </b><i><a class="ref" href="card_2.html#T59">CARD_2:59</a></i>;<br/>
<b>consider </b><font color="Maroon">c<sub>2</sub></font> being   <a href="struct_0.html#NM7">Function</a> of <font color="Maroon">c<sub>1</sub></font>,<span class="p1">(<span class="default"><a href="yellow_1.html#K2">InclPoset</a> 0</span>)</span>;<br/>
<b>take </b>
<font color="Maroon">c<sub>2</sub></font>
; <i><font color="Red">:: according to </font></i><a class="ref" href="waybel_1.html#D8">WAYBEL_1:def 8</a><br/>

<a NAME="E4:17_1"/>
the <a href="struct_0.html#U1">carrier</a> of <span class="p1">(<span class="default"><a href="yellow_1.html#K2">InclPoset</a> 0</span>)</span> <a href="hidden.html#R1">=</a> 0
 
<b>by </b><i><a class="ref" href="yellow_1.html#T1">YELLOW_1:1</a></i>;<br/>
<a NAME="E5:17_1"/><b>then </b>
( <font color="Maroon">c<sub>1</sub></font> is <a href="struct_0.html#V3">empty</a> &amp;  <a href="yellow_1.html#K2">InclPoset</a> 0 is <a href="struct_0.html#V3">empty</a> )
 
<b>by </b><i><a class="txt" href="orders_4.html#E2:17_1"><i><font color="Green">E10</font></i></a>, <a class="ref" href="struct_0.html#D1">STRUCT_0:def 1</a></i>;<br/>
<b>hence </b><a NAME="E6:17_1"/>
<font color="Maroon">c<sub>2</sub></font> is <a href="waybel_0.html#V23">isomorphic</a>
 <b>by </b><i><a class="ref" href="waybel_0.html#D38">WAYBEL_0:def 38</a></i>;<br/>


</div><b>end;</b></div>
<a NAME="E2:17"/><i><font color="Green">E10</font></i>: 
for <font color="Olive">b<sub>1</sub></font> being  <a href="nat_1.html#NM1">Nat</a> st <font color="Maroon">S<sub>1</sub></font>[<font color="Olive">b<sub>1</sub></font>] holds <br/><font color="Maroon">S<sub>1</sub></font>[<font color="Olive">b<sub>1</sub></font> <a href="nat_1.html#K1">+</a> 1]
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="17_2"><b>proof </b></a><div class="add">

<b>let </b><font color="Maroon">c<sub>1</sub></font> be   <a href="nat_1.html#NM1">Nat</a>;<br/>

<b>assume </b><a NAME="E1:17_2"/><i><font color="Green">E11</font></i>: 
for <font color="Olive">b<sub>1</sub></font> being <a href="group_1.html#V6">finite</a>  <a href="orders_4.html#M1" target="_self">Chain</a>  st  <a href="card_1.html#K1">Card</a> the <a href="struct_0.html#U1">carrier</a> of <font color="Olive">b<sub>1</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>1</sub></font> holds <br/><font color="Olive">b<sub>1</sub></font>, <a href="yellow_1.html#K2">InclPoset</a> <font color="Maroon">c<sub>1</sub></font> <a href="waybel_1.html#R5">are_isomorphic</a> 
 ;<br/>

<b>let </b><font color="Maroon">c<sub>2</sub></font> be  <a href="group_1.html#V6">finite</a>  <a href="orders_4.html#M1" target="_self">Chain</a> ;<br/>

<b>assume </b><a NAME="E2:17_2"/><i><font color="Green">E12</font></i>: 
 <a href="card_1.html#K4">card</a> the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">c<sub>2</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>1</sub></font> <a href="nat_1.html#K1">+</a> 1
 ;<br/>

<a NAME="E3:17_2"/>
<font color="Maroon">c<sub>1</sub></font> <a href="xxreal_0.html#NR2" target="_self">&gt;=</a> 0
 
<b>by </b><i><a class="ref" href="nat_1.html#T18">NAT_1:18</a></i>;<br/>
<a NAME="E4:17_2"/><b>then </b>
<font color="Maroon">c<sub>1</sub></font> <a href="nat_1.html#K1">+</a> 1 <a href="xxreal_0.html#NR2" target="_self">&gt;=</a> 0 <a href="nat_1.html#K1">+</a> 1
 
<b>by </b><i><a class="ref" href="xreal_1.html#T8">XREAL_1:8</a></i>;<br/>
<a NAME="E5:17_2"/><b>then </b><i><font color="Green">E13</font></i>: 
( <font color="Maroon">c<sub>1</sub></font> <a href="xxreal_0.html#NR2" target="_self">&gt;=</a> 1 or <font color="Maroon">c<sub>1</sub></font> <a href="nat_1.html#K1">+</a> 1 <a href="hidden.html#R1">=</a> 1 )
 
<b>by </b><i><a class="ref" href="nat_1.html#T26">NAT_1:26</a></i>;<br/>
<a NAME="E6:17_2"/>
the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">c<sub>2</sub></font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a>  <a href="xboole_0.html#K1">{}</a> 
 
<b>by </b><i><a class="txt" href="orders_4.html#E2:17_2"><i><font color="Green">E12</font></i></a>, <a class="ref" href="card_4.html#T17">CARD_4:17</a></i>;<br/>
<b>then reconsider </b><font color="Maroon">c<sub>3</sub></font> = <font color="Maroon">c<sub>2</sub></font> as  non <a href="struct_0.html#V3">empty</a> <a href="group_1.html#V6">finite</a>  <a href="orders_4.html#M1" target="_self">Chain</a>  <b>by </b><i><a class="ref" href="struct_0.html#D1">STRUCT_0:def 1</a></i>;<br/>
<b>set </b><font color="Maroon">c<sub>4</sub></font> =  <a href="yellow_0.html#K4">Top</a> <font color="Maroon">c<sub>3</sub></font>;<br/>
<div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="17_2_1"><b>per </b></a><a class="txt" onclick="hs(this)" href="javascript:()"><b>cases </b></a><span class="hide"><a NAME="E1:17_2_1"/>
( <font color="Maroon">c<sub>1</sub></font> <a href="nat_1.html#K1">+</a> 1 <a href="hidden.html#R1">=</a> 1 or <font color="Maroon">c<sub>1</sub></font> <a href="nat_1.html#K1">+</a> 1 <a href="xxreal_0.html#NR4" target="_self">&gt;</a> 1 )
 </span><b>by </b><i><a class="txt" href="orders_4.html#E5:17_2"><i><font color="Green">E13</font></i></a>, <a class="ref" href="nat_1.html#T38">NAT_1:38</a></i>;<br/><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="17_2_1_1"><b>suppose </b></a><a NAME="E1:17_2_1_1"/><i><font color="Green">E14</font></i>: 
<font color="Maroon">c<sub>1</sub></font> <a href="nat_1.html#K1">+</a> 1 <a href="hidden.html#R1">=</a> 1
 ;<br/><div class="add"><b>then consider </b><font color="Maroon">c<sub>5</sub></font> being    <a href="hidden.html#M1">set</a> <b> such that </b><br/><a NAME="E3:17_2_1_1"/><i><font color="Green">E15</font></i>: 
the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">c<sub>3</sub></font> <a href="hidden.html#R1">=</a> <span class="p1"><a href="tarski.html#K1">{</a><span class="default"><font color="Maroon">c<sub>5</sub></font></span><a href="tarski.html#K1">}</a></span>
 <b>by </b><i><a class="txt" href="orders_4.html#E2:17_2"><i><font color="Green">E12</font></i></a>, <a class="ref" href="card_2.html#T60">CARD_2:60</a></i>;<br/><a NAME="E4:17_2_1_1"/>
<font color="Maroon">c<sub>3</sub></font>, <a href="yellow_1.html#K2">InclPoset</a> 1 <a href="waybel_1.html#R5">are_isomorphic</a> 
 <div><a class="txt" onclick="hs2(this)" href="javascript:()" title="17_2_1_1_1"><b>proof </b></a><div class="add">

<b>set </b><font color="Maroon">c<sub>6</sub></font> = the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">c<sub>3</sub></font> <a href="pboole.html#K9">--&gt;</a> 0;<br/>
<a NAME="E1:17_2_1_1_1"/><i><font color="Green">E16</font></i>: 
 <a href="relat_1.html#K2">rng</a> <span class="p1">(<span class="default">the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">c<sub>3</sub></font> <a href="pboole.html#K9">--&gt;</a> 0</span>)</span> <a href="hidden.html#R1">=</a> <span class="p1"><a href="domain_1.html#K6">{</a><span class="default">0</span><a href="domain_1.html#K6">}</a></span>
 
<b>by </b><i><a class="ref" href="funcop_1.html#T14">FUNCOP_1:14</a></i>;<br/>
<a NAME="E2:17_2_1_1_1"/><i><font color="Green">E17</font></i>: 
<span class="p1"><a href="domain_1.html#K6">{</a><span class="default">0</span><a href="domain_1.html#K6">}</a></span> <a href="hidden.html#R1">=</a> the <a href="struct_0.html#U1">carrier</a> of <span class="p1">(<span class="default"><a href="yellow_1.html#K2">InclPoset</a> 1</span>)</span>
 
<b>by </b><i><a class="ref" href="card_5.html#T1">CARD_5:1</a>, <a class="ref" href="yellow_1.html#T1">YELLOW_1:1</a></i>;<br/>
<b>reconsider </b><font color="Maroon">c<sub>7</sub></font> = the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">c<sub>3</sub></font> <a href="pboole.html#K9">--&gt;</a> 0 as   <a href="struct_0.html#NM7">Function</a> of <font color="Maroon">c<sub>3</sub></font>,<span class="p1">(<span class="default"><a href="yellow_1.html#K2">InclPoset</a> 1</span>)</span> <b>by </b><i><a class="txt" href="orders_4.html#E2:17_2_1_1_1"><i><font color="Green">E17</font></i></a></i>;<br/>
<a NAME="E4:17_2_1_1_1"/>
<font color="Maroon">c<sub>7</sub></font> is <a href="waybel_0.html#V23">isomorphic</a>
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="17_2_1_1_1_1"><b>proof </b></a><div class="add">

<a NAME="E1:17_2_1_1_1_1"/><i><font color="Green">E18</font></i>: 
<font color="Maroon">c<sub>7</sub></font> is <a href="funct_1.html#V2">one-to-one</a>
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="17_2_1_1_1_1_1"><b>proof </b></a><div class="add">

<b>let </b><font color="Maroon">c<sub>8</sub></font>, <font color="Maroon">c<sub>9</sub></font> be   <a href="struct_0.html#NM1">Element</a> of <font color="Maroon">c<sub>3</sub></font>; <i><font color="Red">:: according to </font></i><a class="ref" href="waybel_1.html#D1">WAYBEL_1:def 1</a><br/>

<b>assume </b><a NAME="E1:17_2_1_1_1_1_1"/>
<font color="Maroon">c<sub>7</sub></font> <a href="funct_2.html#K3">.</a> <font color="Maroon">c<sub>8</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>7</sub></font> <a href="funct_2.html#K3">.</a> <font color="Maroon">c<sub>9</sub></font>
 ;<br/>

<a NAME="E2:17_2_1_1_1_1_1"/>
( <font color="Maroon">c<sub>8</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>5</sub></font> &amp; <font color="Maroon">c<sub>9</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>5</sub></font> )
 
<b>by </b><i><a class="txt" href="orders_4.html#E3:17_2_1_1"><i><font color="Green">E15</font></i></a>, <a class="ref" href="tarski.html#D1">TARSKI:def 1</a></i>;<br/>
<b>hence </b><a NAME="E3:17_2_1_1_1_1_1"/>
<font color="Maroon">c<sub>8</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>9</sub></font>
 ;<br/>


</div><b>end;</b></div>
<a NAME="E2:17_2_1_1_1_1"/>
for <font color="Olive">b<sub>1</sub></font>, <font color="Olive">b<sub>2</sub></font> being  <a href="struct_0.html#NM1">Element</a> of <font color="Maroon">c<sub>3</sub></font> holds <br/>( <font color="Olive">b<sub>1</sub></font> <a href="orders_2.html#R3">&lt;=</a> <font color="Olive">b<sub>2</sub></font> iff <font color="Maroon">c<sub>7</sub></font> <a href="funct_2.html#K3">.</a> <font color="Olive">b<sub>1</sub></font> <a href="orders_2.html#R3">&lt;=</a> <font color="Maroon">c<sub>7</sub></font> <a href="funct_2.html#K3">.</a> <font color="Olive">b<sub>2</sub></font> )
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="17_2_1_1_1_1_2"><b>proof </b></a><div class="add">

<b>let </b><font color="Maroon">c<sub>8</sub></font>, <font color="Maroon">c<sub>9</sub></font> be   <a href="struct_0.html#NM1">Element</a> of <font color="Maroon">c<sub>3</sub></font>;<br/>

<div><b>hereby </b>
<div class="add"><b>assume </b><a NAME="E1:17_2_1_1_1_1_2_1"/>
<font color="Maroon">c<sub>8</sub></font> <a href="orders_2.html#R3">&lt;=</a> <font color="Maroon">c<sub>9</sub></font>
 ;<br/><a NAME="E2:17_2_1_1_1_1_2_1"/>
( <font color="Maroon">c<sub>7</sub></font> <a href="funct_2.html#K3">.</a> <font color="Maroon">c<sub>8</sub></font> <a href="hidden.html#R1">=</a> 0 &amp; <font color="Maroon">c<sub>7</sub></font> <a href="funct_2.html#K3">.</a> <font color="Maroon">c<sub>9</sub></font> <a href="hidden.html#R1">=</a> 0 )
 <b>by </b><i><a class="ref" href="funcop_1.html#T13">FUNCOP_1:13</a></i>;<br/><b>hence </b><a NAME="E3:17_2_1_1_1_1_2_1"/>
<font color="Maroon">c<sub>7</sub></font> <a href="funct_2.html#K3">.</a> <font color="Maroon">c<sub>8</sub></font> <a href="orders_2.html#R3">&lt;=</a> <font color="Maroon">c<sub>7</sub></font> <a href="funct_2.html#K3">.</a> <font color="Maroon">c<sub>9</sub></font>
 ;<br/></div>
<b>end;</b></div>

<b>assume </b><a NAME="E2:17_2_1_1_1_1_2"/>
<font color="Maroon">c<sub>7</sub></font> <a href="funct_2.html#K3">.</a> <font color="Maroon">c<sub>8</sub></font> <a href="orders_2.html#R3">&lt;=</a> <font color="Maroon">c<sub>7</sub></font> <a href="funct_2.html#K3">.</a> <font color="Maroon">c<sub>9</sub></font>
 ;<br/>

<a NAME="E3:17_2_1_1_1_1_2"/>
<font color="Maroon">c<sub>8</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>5</sub></font>
 
<b>by </b><i><a class="txt" href="orders_4.html#E3:17_2_1_1"><i><font color="Green">E15</font></i></a>, <a class="ref" href="tarski.html#D1">TARSKI:def 1</a></i>;<br/>
<b>hence </b><a NAME="E4:17_2_1_1_1_1_2"/>
<font color="Maroon">c<sub>8</sub></font> <a href="orders_2.html#R3">&lt;=</a> <font color="Maroon">c<sub>9</sub></font>
 <b>by </b><i><a class="txt" href="orders_4.html#E3:17_2_1_1"><i><font color="Green">E15</font></i></a>, <a class="ref" href="tarski.html#D1">TARSKI:def 1</a></i>;<br/>


</div><b>end;</b></div>
<b>hence </b><a NAME="E3:17_2_1_1_1_1"/>
<font color="Maroon">c<sub>7</sub></font> is <a href="waybel_0.html#V23">isomorphic</a>
 <b>by </b><i><a class="txt" href="orders_4.html#E1:17_2_1_1_1"><i><font color="Green">E16</font></i></a>, <a class="txt" href="orders_4.html#E2:17_2_1_1_1"><i><font color="Green">E17</font></i></a>, <a class="txt" href="orders_4.html#E1:17_2_1_1_1_1"><i><font color="Green">E18</font></i></a>, <a class="ref" href="waybel_0.html#T66">WAYBEL_0:66</a></i>;<br/>


</div><b>end;</b></div>
<b>hence </b><a NAME="E5:17_2_1_1_1"/>
<font color="Maroon">c<sub>3</sub></font>, <a href="yellow_1.html#K2">InclPoset</a> 1 <a href="waybel_1.html#R5">are_isomorphic</a> 
 <b>by </b><i><a class="ref" href="waybel_1.html#D8">WAYBEL_1:def 8</a></i>;<br/>


</div><b>end;</b></div><b>hence </b><a NAME="E5:17_2_1_1"/>
<font color="Maroon">c<sub>2</sub></font>, <a href="yellow_1.html#K2">InclPoset</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="nat_1.html#K1">+</a> 1</span>)</span> <a href="waybel_1.html#R5">are_isomorphic</a> 
 <b>by </b><i><a class="txt" href="orders_4.html#E1:17_2_1_1"><i><font color="Green">E14</font></i></a></i>;<br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="17_2_1_2"><b>suppose </b></a><a NAME="E1:17_2_1_2"/>
<font color="Maroon">c<sub>1</sub></font> <a href="nat_1.html#K1">+</a> 1 <a href="xxreal_0.html#NR4" target="_self">&gt;</a> 1
 ;<br/><div class="add"><a NAME="E2:17_2_1_2"/><b>then </b><i><font color="Green">E14</font></i>: 
<span class="p1">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="nat_1.html#K1">+</a> 1</span>)</span> <a href="xcmplx_0.html#K6">-</a> 1 <a href="xxreal_0.html#NR4" target="_self">&gt;</a> 1 <a href="xcmplx_0.html#K6">-</a> 1
 <b>by </b><i><a class="ref" href="xreal_1.html#T11">XREAL_1:11</a></i>;<br/><i><font color="Green">E15</font></i>:  <a href="card_1.html#K4">card</a> <span class="p1">(<span class="default">the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">c<sub>3</sub></font> <a href="xboole_0.html#K4">\</a> <span class="p2"><a href="domain_1.html#K6">{</a><span class="default"><span class="p3">(<span class="default"><a href="yellow_0.html#K4">Top</a> <font color="Maroon">c<sub>3</sub></font></span>)</span></span><a href="domain_1.html#K6">}</a></span></span>)</span> = 
<span class="p1">(<span class="default"><a href="card_1.html#K4">card</a> the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">c<sub>3</sub></font></span>)</span> <a href="xcmplx_0.html#K6">-</a> <span class="p1">(<span class="default"><a href="card_1.html#K4">card</a> <span class="p2"><a href="domain_1.html#K6">{</a><span class="default"><span class="p3">(<span class="default"><a href="yellow_0.html#K4">Top</a> <font color="Maroon">c<sub>3</sub></font></span>)</span></span><a href="domain_1.html#K6">}</a></span></span>)</span>
<b>by </b><i><a class="ref" href="card_2.html#T63">CARD_2:63</a></i>
<br/>.= 
<span class="p1">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="nat_1.html#K1">+</a> 1</span>)</span> <a href="xcmplx_0.html#K6">-</a> 1
<b>by </b><i><a class="txt" href="orders_4.html#E2:17_2"><i><font color="Green">E12</font></i></a>, <a class="ref" href="card_1.html#T79">CARD_1:79</a></i>
<br/>.= 
<font color="Maroon">c<sub>1</sub></font>

;<br/><b>then reconsider </b><font color="Maroon">c<sub>5</sub></font> = the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">c<sub>3</sub></font> <a href="xboole_0.html#K4">\</a> <span class="p1"><a href="domain_1.html#K6">{</a><span class="default"><span class="p2">(<span class="default"><a href="yellow_0.html#K4">Top</a> <font color="Maroon">c<sub>3</sub></font></span>)</span></span><a href="domain_1.html#K6">}</a></span> as  non <a href="xboole_0.html#V1">empty</a> <a href="struct_0.html#NM2">Subset</a> of <font color="Maroon">c<sub>3</sub></font> <b>by </b><i><a class="txt" href="orders_4.html#E2:17_2_1_2"><i><font color="Green">E14</font></i></a>, <a class="ref" href="card_4.html#T17">CARD_4:17</a>, <a class="ref" href="xboole_1.html#T36">XBOOLE_1:36</a></i>;<br/><b>reconsider </b><font color="Maroon">c<sub>6</sub></font> =  <a href="yellow_0.html#K5">subrelstr</a> <font color="Maroon">c<sub>5</sub></font> as  <a href="group_1.html#V6">finite</a>  <a href="orders_4.html#M1" target="_self">Chain</a>  <b>by </b><i><a class="ref" href="orders_4.html#D1" target="_self">Def1</a></i>;<br/><a NAME="E6:17_2_1_2"/>
 <a href="card_1.html#K4">card</a> the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">c<sub>6</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>1</sub></font>
 <b>by </b><i><a class="txt" href="orders_4.html#E3:17_2_1_2"><i><font color="Green">E15</font></i></a>, <a class="ref" href="yellow_0.html#D15">YELLOW_0:def 15</a></i>;<br/><a NAME="E7:17_2_1_2"/><b>then </b>
<font color="Maroon">c<sub>6</sub></font>, <a href="yellow_1.html#K2">InclPoset</a> <font color="Maroon">c<sub>1</sub></font> <a href="waybel_1.html#R5">are_isomorphic</a> 
 <b>by </b><i><a class="txt" href="orders_4.html#E1:17_2"><i><font color="Green">E11</font></i></a></i>;<br/><b>then consider </b><font color="Maroon">c<sub>7</sub></font> being   <a href="struct_0.html#NM7">Function</a> of <font color="Maroon">c<sub>6</sub></font>,<span class="p1">(<span class="default"><a href="yellow_1.html#K2">InclPoset</a> <font color="Maroon">c<sub>1</sub></font></span>)</span><b> such that </b><br/><a NAME="E9:17_2_1_2"/><i><font color="Green">E16</font></i>: 
<font color="Maroon">c<sub>7</sub></font> is <a href="waybel_0.html#V23">isomorphic</a>
 <b>by </b><i><a class="ref" href="waybel_1.html#D8">WAYBEL_1:def 8</a></i>;<br/><a NAME="E10:17_2_1_2"/><i><font color="Green">E17</font></i>: 
the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">c<sub>6</sub></font> <a href="hidden.html#R1">=</a> the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">c<sub>3</sub></font> <a href="xboole_0.html#K4">\</a> <span class="p1"><a href="domain_1.html#K6">{</a><span class="default"><span class="p2">(<span class="default"><a href="yellow_0.html#K4">Top</a> <font color="Maroon">c<sub>3</sub></font></span>)</span></span><a href="domain_1.html#K6">}</a></span>
 <b>by </b><i><a class="ref" href="yellow_0.html#D15">YELLOW_0:def 15</a></i>;<br/><a NAME="E11:17_2_1_2"/>
<font color="Maroon">c<sub>1</sub></font> <a href="xxreal_0.html#R1">&lt;=</a> <font color="Maroon">c<sub>1</sub></font> <a href="nat_1.html#K1">+</a> 1
 <b>by </b><i><a class="ref" href="nat_1.html#T29">NAT_1:29</a></i>;<br/><a NAME="E12:17_2_1_2"/><b>then </b>
<font color="Maroon">c<sub>1</sub></font> <a href="ordinal1.html#R1">c=</a> <font color="Maroon">c<sub>1</sub></font> <a href="nat_1.html#K1">+</a> 1
 <b>by </b><i><a class="ref" href="card_1.html#T56">CARD_1:56</a></i>;<br/><a NAME="E13:17_2_1_2"/><b>then </b><i><font color="Green">E18</font></i>: 
<font color="Maroon">c<sub>1</sub></font> <a href="tarski.html#R1">c=</a> the <a href="struct_0.html#U1">carrier</a> of <span class="p1">(<span class="default"><a href="yellow_1.html#K2">InclPoset</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span>
 <b>by </b><i><a class="ref" href="yellow_1.html#T1">YELLOW_1:1</a></i>;<br/><a NAME="E14:17_2_1_2"/><i><font color="Green">E19</font></i>: 
the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">c<sub>6</sub></font>,<span class="p1"><a href="domain_1.html#K6">{</a><span class="default"><span class="p2">(<span class="default"><a href="yellow_0.html#K4">Top</a> <font color="Maroon">c<sub>3</sub></font></span>)</span></span><a href="domain_1.html#K6">}</a></span> <a href="orders_4.html#R1" target="_self">form_upper_lower_partition_of</a> <font color="Maroon">c<sub>3</sub></font>
 <b>by </b><i><a class="txt" href="orders_4.html#E10:17_2_1_2"><i><font color="Green">E17</font></i></a>, <a class="ref" href="orders_4.html#T3" target="_self">Th3</a></i>;<br/><a NAME="E15:17_2_1_2"/><i><font color="Green">E20</font></i>: 
the <a href="struct_0.html#U1">carrier</a> of <span class="p1">(<span class="default"><a href="yellow_1.html#K2">InclPoset</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>1</sub></font>
 <b>by </b><i><a class="ref" href="yellow_1.html#T1">YELLOW_1:1</a></i>;<br/><i><font color="Green">E21</font></i>: <font color="Maroon">c<sub>1</sub></font> <a href="nat_1.html#K1">+</a> 1 = 
 <a href="ordinal1.html#K1">succ</a> <font color="Maroon">c<sub>1</sub></font>
<b>by </b><i><a class="ref" href="card_1.html#T52">CARD_1:52</a></i>
<br/>.= 
<font color="Maroon">c<sub>1</sub></font> <a href="xboole_0.html#K2">\/</a> <span class="p1"><a href="domain_1.html#K6">{</a><span class="default"><font color="Maroon">c<sub>1</sub></font></span><a href="domain_1.html#K6">}</a></span>
<b>by </b><i><a class="ref" href="ordinal1.html#D1">ORDINAL1:def 1</a></i>
;<br/><a NAME="E17:17_2_1_2"/><b>then </b><i><font color="Green">E22</font></i>: 
the <a href="struct_0.html#U1">carrier</a> of <span class="p1">(<span class="default"><a href="yellow_1.html#K2">InclPoset</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="xboole_0.html#K2">\/</a> <span class="p1"><a href="domain_1.html#K6">{</a><span class="default"><font color="Maroon">c<sub>1</sub></font></span><a href="domain_1.html#K6">}</a></span> <a href="hidden.html#R1">=</a> the <a href="struct_0.html#U1">carrier</a> of <span class="p1">(<span class="default"><a href="yellow_1.html#K2">InclPoset</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span>
 <b>by </b><i><a class="txt" href="orders_4.html#E15:17_2_1_2"><i><font color="Green">E20</font></i></a>, <a class="ref" href="yellow_1.html#T1">YELLOW_1:1</a></i>;<br/><a NAME="E18:17_2_1_2"/>
for <font color="Olive">b<sub>1</sub></font>, <font color="Olive">b<sub>2</sub></font> being  <a href="struct_0.html#NM1">Element</a> of <span class="p1">(<span class="default"><a href="yellow_1.html#K2">InclPoset</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> st <font color="Olive">b<sub>1</sub></font> <a href="hidden.html#R2">in</a> the <a href="struct_0.html#U1">carrier</a> of <span class="p1">(<span class="default"><a href="yellow_1.html#K2">InclPoset</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> &amp; <font color="Olive">b<sub>2</sub></font> <a href="hidden.html#R2">in</a> <span class="p1"><a href="domain_1.html#K6">{</a><span class="default"><font color="Maroon">c<sub>1</sub></font></span><a href="domain_1.html#K6">}</a></span> holds <br/><font color="Olive">b<sub>1</sub></font> <a href="orders_2.html#R2">&lt;</a> <font color="Olive">b<sub>2</sub></font>
 <div><a class="txt" onclick="hs2(this)" href="javascript:()" title="17_2_1_2_3"><b>proof </b></a><div class="add">

<b>let </b><font color="Maroon">c<sub>8</sub></font>, <font color="Maroon">c<sub>9</sub></font> be   <a href="struct_0.html#NM1">Element</a> of <span class="p1">(<span class="default"><a href="yellow_1.html#K2">InclPoset</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span>;<br/>

<b>assume </b><a NAME="E1:17_2_1_2_3"/>
( <font color="Maroon">c<sub>8</sub></font> <a href="hidden.html#R2">in</a> the <a href="struct_0.html#U1">carrier</a> of <span class="p1">(<span class="default"><a href="yellow_1.html#K2">InclPoset</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> &amp; <font color="Maroon">c<sub>9</sub></font> <a href="hidden.html#R2">in</a> <span class="p1"><a href="domain_1.html#K6">{</a><span class="default"><font color="Maroon">c<sub>1</sub></font></span><a href="domain_1.html#K6">}</a></span> )
 ;<br/>

<a NAME="E2:17_2_1_2_3"/><b>then </b><i><font color="Green">E23</font></i>: 
( <font color="Maroon">c<sub>8</sub></font> <a href="hidden.html#R2">in</a> <font color="Maroon">c<sub>1</sub></font> &amp; <font color="Maroon">c<sub>9</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>1</sub></font> )
 
<b>by </b><i><a class="ref" href="tarski.html#D1">TARSKI:def 1</a>, <a class="ref" href="yellow_1.html#T1">YELLOW_1:1</a></i>;<br/>
<a NAME="E3:17_2_1_2_3"/><b>then </b>
( <font color="Maroon">c<sub>8</sub></font> <a href="hidden.html#R2">in</a> <span class="p1">{<span class="default"> <font color="Olive">b<sub>1</sub></font> where B is   <a href="nat_1.html#NM1">Nat</a> : <font color="Olive">b<sub>1</sub></font> <a href="xxreal_0.html#NR3" target="_self">&lt;</a> <font color="Maroon">c<sub>1</sub></font> </span>}</span>  &amp; <font color="Maroon">c<sub>9</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>1</sub></font> )
 
<b>by </b><i><a class="ref" href="axioms.html#T30">AXIOMS:30</a></i>;<br/>
<b>then consider </b><font color="Maroon">c<sub>10</sub></font> being   <a href="nat_1.html#NM1">Nat</a><b> such that </b><br/><a NAME="E5:17_2_1_2_3"/><i><font color="Green">E24</font></i>: 
( <font color="Maroon">c<sub>10</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>8</sub></font> &amp; <font color="Maroon">c<sub>10</sub></font> <a href="xxreal_0.html#NR3" target="_self">&lt;</a> <font color="Maroon">c<sub>1</sub></font> )
 ;<br/>
<a NAME="E6:17_2_1_2_3"/>
<font color="Maroon">c<sub>8</sub></font> <a href="tarski.html#R1">c=</a> <font color="Maroon">c<sub>9</sub></font>
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="17_2_1_2_3_1"><b>proof </b></a><div class="add">

<b>assume </b><a NAME="E1:17_2_1_2_3_1"/>
not <font color="Maroon">c<sub>8</sub></font> <a href="tarski.html#R1">c=</a> <font color="Maroon">c<sub>9</sub></font>
 ;<br/>

<b>then consider </b><font color="Maroon">c<sub>11</sub></font> being    <a href="hidden.html#M1">set</a> <b> such that </b><br/><a NAME="E3:17_2_1_2_3_1"/><i><font color="Green">E25</font></i>: 
( <font color="Maroon">c<sub>11</sub></font> <a href="hidden.html#R2">in</a> <font color="Maroon">c<sub>8</sub></font> &amp; not <font color="Maroon">c<sub>11</sub></font> <a href="hidden.html#R2">in</a> <font color="Maroon">c<sub>9</sub></font> )
 <b>by </b><i><a class="ref" href="tarski.html#D3">TARSKI:def 3</a></i>;<br/>
<a NAME="E4:17_2_1_2_3_1"/>
<font color="Maroon">c<sub>11</sub></font> <a href="hidden.html#R2">in</a> <span class="p1">{<span class="default"> <font color="Olive">b<sub>1</sub></font> where B is   <a href="nat_1.html#NM1">Nat</a> : <font color="Olive">b<sub>1</sub></font> <a href="xxreal_0.html#NR3" target="_self">&lt;</a> <font color="Maroon">c<sub>10</sub></font> </span>}</span> 
 
<b>by </b><i><a class="txt" href="orders_4.html#E5:17_2_1_2_3"><i><font color="Green">E24</font></i></a>, <a class="txt" href="orders_4.html#E3:17_2_1_2_3_1"><i><font color="Green">E25</font></i></a>, <a class="ref" href="axioms.html#T30">AXIOMS:30</a></i>;<br/>
<b>then consider </b><font color="Maroon">c<sub>12</sub></font> being   <a href="nat_1.html#NM1">Nat</a><b> such that </b><br/><a NAME="E6:17_2_1_2_3_1"/><i><font color="Green">E26</font></i>: 
( <font color="Maroon">c<sub>12</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>11</sub></font> &amp; <font color="Maroon">c<sub>12</sub></font> <a href="xxreal_0.html#NR3" target="_self">&lt;</a> <font color="Maroon">c<sub>10</sub></font> )
 ;<br/>
<a NAME="E7:17_2_1_2_3_1"/>
<font color="Maroon">c<sub>12</sub></font> <a href="xxreal_0.html#NR3" target="_self">&lt;</a> <font color="Maroon">c<sub>1</sub></font>
 
<b>by </b><i><a class="txt" href="orders_4.html#E5:17_2_1_2_3"><i><font color="Green">E24</font></i></a>, <a class="txt" href="orders_4.html#E6:17_2_1_2_3_1"><i><font color="Green">E26</font></i></a>, <a class="ref" href="xxreal_0.html#T2">XXREAL_0:2</a></i>;<br/>
<a NAME="E8:17_2_1_2_3_1"/><b>then </b>
<font color="Maroon">c<sub>12</sub></font> <a href="hidden.html#R2">in</a> <span class="p1">{<span class="default"> <font color="Olive">b<sub>1</sub></font> where B is   <a href="nat_1.html#NM1">Nat</a> : <font color="Olive">b<sub>1</sub></font> <a href="xxreal_0.html#NR3" target="_self">&lt;</a> <font color="Maroon">c<sub>1</sub></font> </span>}</span> 
 
;<br/>
<b>hence </b><a NAME="E9:17_2_1_2_3_1"/>
contradiction
 <b>by </b><i><a class="txt" href="orders_4.html#E2:17_2_1_2_3"><i><font color="Green">E23</font></i></a>, <a class="txt" href="orders_4.html#E3:17_2_1_2_3_1"><i><font color="Green">E25</font></i></a>, <a class="txt" href="orders_4.html#E6:17_2_1_2_3_1"><i><font color="Green">E26</font></i></a>, <a class="ref" href="axioms.html#T30">AXIOMS:30</a></i>;<br/>


</div><b>end;</b></div>
<a NAME="E7:17_2_1_2_3"/><b>then </b><i><font color="Green">E25</font></i>: 
<font color="Maroon">c<sub>8</sub></font> <a href="orders_2.html#R3">&lt;=</a> <font color="Maroon">c<sub>9</sub></font>
 
<b>by </b><i><a class="ref" href="yellow_1.html#T3">YELLOW_1:3</a></i>;<br/>
<a NAME="E8:17_2_1_2_3"/>
<font color="Maroon">c<sub>8</sub></font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> <font color="Maroon">c<sub>9</sub></font>
 
<b>by </b><i><a class="txt" href="orders_4.html#E2:17_2_1_2_3"><i><font color="Green">E23</font></i></a></i>;<br/>
<b>hence </b><a NAME="E9:17_2_1_2_3"/>
<font color="Maroon">c<sub>8</sub></font> <a href="orders_2.html#R2">&lt;</a> <font color="Maroon">c<sub>9</sub></font>
 <b>by </b><i><a class="txt" href="orders_4.html#E7:17_2_1_2_3"><i><font color="Green">E25</font></i></a>, <a class="ref" href="orders_2.html#D10">ORDERS_2:def 10</a></i>;<br/>


</div><b>end;</b></div><a NAME="E19:17_2_1_2"/><b>then </b><i><font color="Green">E23</font></i>: 
the <a href="struct_0.html#U1">carrier</a> of <span class="p1">(<span class="default"><a href="yellow_1.html#K2">InclPoset</a> <font color="Maroon">c<sub>1</sub></font></span>)</span>,<span class="p1"><a href="domain_1.html#K6">{</a><span class="default"><font color="Maroon">c<sub>1</sub></font></span><a href="domain_1.html#K6">}</a></span> <a href="orders_4.html#R1" target="_self">form_upper_lower_partition_of</a>  <a href="yellow_1.html#K2">InclPoset</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="nat_1.html#K1">+</a> 1</span>)</span>
 <b>by </b><i><a class="txt" href="orders_4.html#E17:17_2_1_2"><i><font color="Green">E22</font></i></a>, <a class="ref" href="orders_4.html#D3" target="_self">Def3</a></i>;<br/><b>set </b><font color="Maroon">c<sub>8</sub></font> =  <a href="yellow_1.html#K2">InclPoset</a> <span class="p1"><a href="domain_1.html#K6">{</a><span class="default"><span class="p2">(<span class="default"><a href="yellow_0.html#K4">Top</a> <font color="Maroon">c<sub>3</sub></font></span>)</span></span><a href="domain_1.html#K6">}</a></span>;<br/><a NAME="E20:17_2_1_2"/>
<span class="p1"><a href="domain_1.html#K6">{</a><span class="default"><span class="p2">(<span class="default"><a href="yellow_0.html#K4">Top</a> <font color="Maroon">c<sub>3</sub></font></span>)</span></span><a href="domain_1.html#K6">}</a></span> <a href="tarski.html#R1">c=</a> <span class="p1"><a href="domain_1.html#K6">{</a><span class="default"><span class="p2">(<span class="default"><a href="yellow_0.html#K4">Top</a> <font color="Maroon">c<sub>3</sub></font></span>)</span></span><a href="domain_1.html#K6">}</a></span>
 ;<br/><b>then reconsider </b><font color="Maroon">c<sub>9</sub></font> = <span class="p1"><a href="domain_1.html#K6">{</a><span class="default"><span class="p2">(<span class="default"><a href="yellow_0.html#K4">Top</a> <font color="Maroon">c<sub>3</sub></font></span>)</span></span><a href="domain_1.html#K6">}</a></span> as  non <a href="xboole_0.html#V1">empty</a> <a href="struct_0.html#NM2">Subset</a> of <span class="p1">(<span class="default"><a href="yellow_1.html#K2">InclPoset</a> <span class="p2"><a href="domain_1.html#K6">{</a><span class="default"><span class="p3">(<span class="default"><a href="yellow_0.html#K4">Top</a> <font color="Maroon">c<sub>3</sub></font></span>)</span></span><a href="domain_1.html#K6">}</a></span></span>)</span> <b>by </b><i><a class="ref" href="yellow_1.html#T1">YELLOW_1:1</a></i>;<br/><a NAME="E22:17_2_1_2"/>
<span class="p1"><a href="domain_1.html#K6">{</a><span class="default"><font color="Maroon">c<sub>1</sub></font></span><a href="domain_1.html#K6">}</a></span> <a href="tarski.html#R1">c=</a> <font color="Maroon">c<sub>1</sub></font> <a href="nat_1.html#K1">+</a> 1
 <b>by </b><i><a class="txt" href="orders_4.html#E16:17_2_1_2"><i><font color="Green">E21</font></i></a>, <a class="ref" href="xboole_1.html#T7">XBOOLE_1:7</a></i>;<br/><b>then reconsider </b><font color="Maroon">c<sub>10</sub></font> = <span class="p1"><a href="domain_1.html#K6">{</a><span class="default"><font color="Maroon">c<sub>1</sub></font></span><a href="domain_1.html#K6">}</a></span> as  non <a href="xboole_0.html#V1">empty</a> <a href="struct_0.html#NM2">Subset</a> of <span class="p1">(<span class="default"><a href="yellow_1.html#K2">InclPoset</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> <b>by </b><i><a class="ref" href="yellow_1.html#T1">YELLOW_1:1</a></i>;<br/><b>set </b><font color="Maroon">c<sub>11</sub></font> =  <a href="yellow_0.html#K5">subrelstr</a> <font color="Maroon">c<sub>9</sub></font>;<br/><b>set </b><font color="Maroon">c<sub>12</sub></font> =  <a href="yellow_0.html#K5">subrelstr</a> <font color="Maroon">c<sub>10</sub></font>;<br/><a NAME="E24:17_2_1_2"/><i><font color="Green">E24</font></i>: 
the <a href="struct_0.html#U1">carrier</a> of <span class="p1">(<span class="default"><a href="yellow_0.html#K5">subrelstr</a> <font color="Maroon">c<sub>9</sub></font></span>)</span> <a href="hidden.html#R1">=</a> <span class="p1"><a href="domain_1.html#K6">{</a><span class="default"><span class="p2">(<span class="default"><a href="yellow_0.html#K4">Top</a> <font color="Maroon">c<sub>3</sub></font></span>)</span></span><a href="domain_1.html#K6">}</a></span>
 <b>by </b><i><a class="ref" href="yellow_0.html#D15">YELLOW_0:def 15</a></i>;<br/><b>set </b><font color="Maroon">c<sub>13</sub></font> = the <a href="struct_0.html#U1">carrier</a> of <span class="p1">(<span class="default"><a href="yellow_0.html#K5">subrelstr</a> <font color="Maroon">c<sub>9</sub></font></span>)</span> <a href="pboole.html#K9">--&gt;</a> <font color="Maroon">c<sub>1</sub></font>;<br/><a NAME="E25:17_2_1_2"/><i><font color="Green">E25</font></i>: 
 <a href="relat_1.html#K1">dom</a> <span class="p1">(<span class="default">the <a href="struct_0.html#U1">carrier</a> of <span class="p2">(<span class="default"><a href="yellow_0.html#K5">subrelstr</a> <font color="Maroon">c<sub>9</sub></font></span>)</span> <a href="pboole.html#K9">--&gt;</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="hidden.html#R1">=</a> the <a href="struct_0.html#U1">carrier</a> of <span class="p1">(<span class="default"><a href="yellow_0.html#K5">subrelstr</a> <font color="Maroon">c<sub>9</sub></font></span>)</span>
 <b>by </b><i><a class="ref" href="funcop_1.html#T19">FUNCOP_1:19</a></i>;<br/><b>then reconsider </b><font color="Maroon">c<sub>14</sub></font> = the <a href="struct_0.html#U1">carrier</a> of <span class="p1">(<span class="default"><a href="yellow_0.html#K5">subrelstr</a> <font color="Maroon">c<sub>9</sub></font></span>)</span> <a href="pboole.html#K9">--&gt;</a> <font color="Maroon">c<sub>1</sub></font> as    <a href="pboole.html#M1">ManySortedSet</a> of the <a href="struct_0.html#U1">carrier</a> of <span class="p1">(<span class="default"><a href="yellow_0.html#K5">subrelstr</a> <font color="Maroon">c<sub>9</sub></font></span>)</span> <b>by </b><i><a class="ref" href="pboole.html#D3">PBOOLE:def 3</a></i>;<br/><a NAME="E27:17_2_1_2"/><i><font color="Green">E26</font></i>: 
for <font color="Olive">b<sub>1</sub></font> being  <a href="struct_0.html#NM1">Element</a> of <span class="p1">(<span class="default"><a href="yellow_0.html#K5">subrelstr</a> <font color="Maroon">c<sub>9</sub></font></span>)</span> holds <font color="Maroon">c<sub>14</sub></font> <a href="funct_1.html#K1">.</a> <font color="Olive">b<sub>1</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>1</sub></font>
 <b>by </b><i><a class="ref" href="funcop_1.html#T13">FUNCOP_1:13</a></i>;<br/><a NAME="E28:17_2_1_2"/>
 <a href="relat_1.html#K2">rng</a> <font color="Maroon">c<sub>14</sub></font> <a href="tarski.html#R1">c=</a> <span class="p1"><a href="domain_1.html#K6">{</a><span class="default"><font color="Maroon">c<sub>1</sub></font></span><a href="domain_1.html#K6">}</a></span>
 <b>by </b><i><a class="ref" href="funcop_1.html#T19">FUNCOP_1:19</a></i>;<br/><a NAME="E29:17_2_1_2"/><b>then </b><i><font color="Green">E27</font></i>: 
 <a href="relat_1.html#K2">rng</a> <font color="Maroon">c<sub>14</sub></font> <a href="tarski.html#R1">c=</a> the <a href="struct_0.html#U1">carrier</a> of <span class="p1">(<span class="default"><a href="yellow_0.html#K5">subrelstr</a> <font color="Maroon">c<sub>10</sub></font></span>)</span>
 <b>by </b><i><a class="ref" href="yellow_0.html#D15">YELLOW_0:def 15</a></i>;<br/><a NAME="E30:17_2_1_2"/>
for <font color="Olive">b<sub>1</sub></font> being   <a href="hidden.html#M1">set</a>  st <font color="Olive">b<sub>1</sub></font> <a href="hidden.html#R2">in</a> the <a href="struct_0.html#U1">carrier</a> of <span class="p1">(<span class="default"><a href="yellow_0.html#K5">subrelstr</a> <font color="Maroon">c<sub>9</sub></font></span>)</span> holds <br/><font color="Maroon">c<sub>14</sub></font> <a href="funct_1.html#K1">.</a> <font color="Olive">b<sub>1</sub></font> <a href="hidden.html#R2">in</a> the <a href="struct_0.html#U1">carrier</a> of <span class="p1">(<span class="default"><a href="yellow_0.html#K5">subrelstr</a> <font color="Maroon">c<sub>10</sub></font></span>)</span>
 <div><a class="txt" onclick="hs2(this)" href="javascript:()" title="17_2_1_2_4"><b>proof </b></a><div class="add">

<b>let </b><font color="Maroon">c<sub>15</sub></font> be    <a href="hidden.html#M1">set</a> ;<br/>

<b>assume </b><a NAME="E1:17_2_1_2_4"/>
<font color="Maroon">c<sub>15</sub></font> <a href="hidden.html#R2">in</a> the <a href="struct_0.html#U1">carrier</a> of <span class="p1">(<span class="default"><a href="yellow_0.html#K5">subrelstr</a> <font color="Maroon">c<sub>9</sub></font></span>)</span>
 ;<br/>

<a NAME="E2:17_2_1_2_4"/><b>then </b>
<font color="Maroon">c<sub>14</sub></font> <a href="funct_1.html#K1">.</a> <font color="Maroon">c<sub>15</sub></font> <a href="hidden.html#R2">in</a>  <a href="relat_1.html#K2">rng</a> <font color="Maroon">c<sub>14</sub></font>
 
<b>by </b><i><a class="txt" href="orders_4.html#E25:17_2_1_2"><i><font color="Green">E25</font></i></a>, <a class="ref" href="funct_1.html#D5">FUNCT_1:def 5</a></i>;<br/>
<b>hence </b><a NAME="E3:17_2_1_2_4"/>
<font color="Maroon">c<sub>14</sub></font> <a href="funct_1.html#K1">.</a> <font color="Maroon">c<sub>15</sub></font> <a href="hidden.html#R2">in</a> the <a href="struct_0.html#U1">carrier</a> of <span class="p1">(<span class="default"><a href="yellow_0.html#K5">subrelstr</a> <font color="Maroon">c<sub>10</sub></font></span>)</span>
 <b>by </b><i><a class="txt" href="orders_4.html#E29:17_2_1_2"><i><font color="Green">E27</font></i></a></i>;<br/>


</div><b>end;</b></div><a NAME="E31:17_2_1_2"/><b>then </b><i><font color="Green">E28</font></i>: 
( the <a href="struct_0.html#U1">carrier</a> of <span class="p1">(<span class="default"><a href="yellow_0.html#K5">subrelstr</a> <font color="Maroon">c<sub>10</sub></font></span>)</span> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>10</sub></font> &amp; the <a href="struct_0.html#U1">carrier</a> of <span class="p1">(<span class="default"><a href="yellow_0.html#K5">subrelstr</a> <span class="p2"><a href="domain_1.html#K6">{</a><span class="default"><span class="p3">(<span class="default"><a href="yellow_0.html#K4">Top</a> <font color="Maroon">c<sub>3</sub></font></span>)</span></span><a href="domain_1.html#K6">}</a></span></span>)</span> <a href="hidden.html#R1">=</a> <span class="p1"><a href="domain_1.html#K6">{</a><span class="default"><span class="p2">(<span class="default"><a href="yellow_0.html#K4">Top</a> <font color="Maroon">c<sub>3</sub></font></span>)</span></span><a href="domain_1.html#K6">}</a></span> &amp; <font color="Maroon">c<sub>14</sub></font> is   <a href="funct_2.html#NM1">Function</a> of the <a href="struct_0.html#U1">carrier</a> of <span class="p1">(<span class="default"><a href="yellow_0.html#K5">subrelstr</a> <font color="Maroon">c<sub>9</sub></font></span>)</span>,the <a href="struct_0.html#U1">carrier</a> of <span class="p1">(<span class="default"><a href="yellow_0.html#K5">subrelstr</a> <font color="Maroon">c<sub>10</sub></font></span>)</span> )
 <b>by </b><i><a class="txt" href="orders_4.html#E25:17_2_1_2"><i><font color="Green">E25</font></i></a>, <a class="ref" href="funct_2.html#T5">FUNCT_2:5</a>, <a class="ref" href="yellow_0.html#D15">YELLOW_0:def 15</a></i>;<br/><b>then reconsider </b><font color="Maroon">c<sub>15</sub></font> = <font color="Maroon">c<sub>14</sub></font> as   <a href="struct_0.html#NM7">Function</a> of <span class="p1">(<span class="default"><a href="yellow_0.html#K5">subrelstr</a> <span class="p2"><a href="domain_1.html#K6">{</a><span class="default"><span class="p3">(<span class="default"><a href="yellow_0.html#K4">Top</a> <font color="Maroon">c<sub>3</sub></font></span>)</span></span><a href="domain_1.html#K6">}</a></span></span>)</span>,<span class="p1">(<span class="default"><a href="yellow_0.html#K5">subrelstr</a> <font color="Maroon">c<sub>10</sub></font></span>)</span> <b>by </b><i><a class="txt" href="orders_4.html#E24:17_2_1_2"><i><font color="Green">E24</font></i></a></i>;<br/><a NAME="E33:17_2_1_2"/><i><font color="Green">E29</font></i>: 
<font color="Maroon">c<sub>15</sub></font> is <a href="funct_1.html#V2">one-to-one</a>
 <b>by </b><i><a class="txt" href="orders_4.html#E31:17_2_1_2"><i><font color="Green">E28</font></i></a>, <a class="ref" href="partfun1.html#T70">PARTFUN1:70</a></i>;<br/><a NAME="E34:17_2_1_2"/>
<font color="Maroon">c<sub>15</sub></font> <a href="funct_1.html#K1">.</a> <span class="p1">(<span class="default"><a href="yellow_0.html#K4">Top</a> <font color="Maroon">c<sub>3</sub></font></span>)</span> <a href="hidden.html#R2">in</a> <font color="Maroon">c<sub>10</sub></font>
 <b>by </b><i><a class="txt" href="orders_4.html#E31:17_2_1_2"><i><font color="Green">E28</font></i></a>, <a class="ref" href="funct_2.html#T61">FUNCT_2:61</a></i>;<br/><a NAME="E35:17_2_1_2"/><b>then </b>
<font color="Maroon">c<sub>15</sub></font> <a href="funct_1.html#K1">.</a> <span class="p1">(<span class="default"><a href="yellow_0.html#K4">Top</a> <font color="Maroon">c<sub>3</sub></font></span>)</span> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>1</sub></font>
 <b>by </b><i><a class="ref" href="tarski.html#D1">TARSKI:def 1</a></i>;<br/><a NAME="E36:17_2_1_2"/><b>then </b><i><font color="Green">E30</font></i>: 
 <a href="relat_1.html#K2">rng</a> <font color="Maroon">c<sub>15</sub></font> <a href="hidden.html#R1">=</a> the <a href="struct_0.html#U1">carrier</a> of <span class="p1">(<span class="default"><a href="yellow_0.html#K5">subrelstr</a> <font color="Maroon">c<sub>10</sub></font></span>)</span>
 <b>by </b><i><a class="txt" href="orders_4.html#E31:17_2_1_2"><i><font color="Green">E28</font></i></a>, <a class="ref" href="funct_2.html#T62">FUNCT_2:62</a></i>;<br/><a NAME="E37:17_2_1_2"/><i><font color="Green">E31</font></i>: 
<font color="Maroon">c<sub>15</sub></font> is <a href="waybel_0.html#V23">isomorphic</a>
 <div><a class="txt" onclick="hs2(this)" href="javascript:()" title="17_2_1_2_5"><b>proof </b></a><div class="add">

<a NAME="E1:17_2_1_2_5"/>
for <font color="Olive">b<sub>1</sub></font>, <font color="Olive">b<sub>2</sub></font> being  <a href="struct_0.html#NM1">Element</a> of <span class="p1">(<span class="default"><a href="yellow_0.html#K5">subrelstr</a> <span class="p2"><a href="domain_1.html#K6">{</a><span class="default"><span class="p3">(<span class="default"><a href="yellow_0.html#K4">Top</a> <font color="Maroon">c<sub>3</sub></font></span>)</span></span><a href="domain_1.html#K6">}</a></span></span>)</span> holds <br/>( <font color="Olive">b<sub>1</sub></font> <a href="orders_2.html#R3">&lt;=</a> <font color="Olive">b<sub>2</sub></font> iff <font color="Maroon">c<sub>15</sub></font> <a href="funct_2.html#K3">.</a> <font color="Olive">b<sub>1</sub></font> <a href="orders_2.html#R3">&lt;=</a> <font color="Maroon">c<sub>15</sub></font> <a href="funct_2.html#K3">.</a> <font color="Olive">b<sub>2</sub></font> )
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="17_2_1_2_5_1"><b>proof </b></a><div class="add">

<b>let </b><font color="Maroon">c<sub>16</sub></font>, <font color="Maroon">c<sub>17</sub></font> be   <a href="struct_0.html#NM1">Element</a> of <span class="p1">(<span class="default"><a href="yellow_0.html#K5">subrelstr</a> <span class="p2"><a href="domain_1.html#K6">{</a><span class="default"><span class="p3">(<span class="default"><a href="yellow_0.html#K4">Top</a> <font color="Maroon">c<sub>3</sub></font></span>)</span></span><a href="domain_1.html#K6">}</a></span></span>)</span>;<br/>

<a NAME="E1:17_2_1_2_5_1"/>
<font color="Maroon">c<sub>16</sub></font> <a href="hidden.html#R2">in</a> the <a href="struct_0.html#U1">carrier</a> of <span class="p1">(<span class="default"><a href="yellow_0.html#K5">subrelstr</a> <span class="p2"><a href="domain_1.html#K6">{</a><span class="default"><span class="p3">(<span class="default"><a href="yellow_0.html#K4">Top</a> <font color="Maroon">c<sub>3</sub></font></span>)</span></span><a href="domain_1.html#K6">}</a></span></span>)</span>
 
;<br/>
<a NAME="E2:17_2_1_2_5_1"/><b>then </b><i><font color="Green">E32</font></i>: 
<font color="Maroon">c<sub>16</sub></font> <a href="hidden.html#R2">in</a> <span class="p1"><a href="domain_1.html#K6">{</a><span class="default"><span class="p2">(<span class="default"><a href="yellow_0.html#K4">Top</a> <font color="Maroon">c<sub>3</sub></font></span>)</span></span><a href="domain_1.html#K6">}</a></span>
 
<b>by </b><i><a class="ref" href="yellow_0.html#D15">YELLOW_0:def 15</a></i>;<br/>
<b>reconsider </b><font color="Maroon">c<sub>18</sub></font> = <font color="Maroon">c<sub>16</sub></font> as   <a href="struct_0.html#NM1">Element</a> of <span class="p1">(<span class="default"><a href="yellow_0.html#K5">subrelstr</a> <font color="Maroon">c<sub>9</sub></font></span>)</span> <b>by </b><i><a class="txt" href="orders_4.html#E24:17_2_1_2"><i><font color="Green">E24</font></i></a>, <a class="ref" href="yellow_0.html#D15">YELLOW_0:def 15</a></i>;<br/>
<a NAME="E4:17_2_1_2_5_1"/>
<font color="Maroon">c<sub>17</sub></font> <a href="hidden.html#R2">in</a> the <a href="struct_0.html#U1">carrier</a> of <span class="p1">(<span class="default"><a href="yellow_0.html#K5">subrelstr</a> <span class="p2"><a href="domain_1.html#K6">{</a><span class="default"><span class="p3">(<span class="default"><a href="yellow_0.html#K4">Top</a> <font color="Maroon">c<sub>3</sub></font></span>)</span></span><a href="domain_1.html#K6">}</a></span></span>)</span>
 
;<br/>
<a NAME="E5:17_2_1_2_5_1"/><b>then </b><i><font color="Green">E33</font></i>: 
<font color="Maroon">c<sub>17</sub></font> <a href="hidden.html#R2">in</a> <span class="p1"><a href="domain_1.html#K6">{</a><span class="default"><span class="p2">(<span class="default"><a href="yellow_0.html#K4">Top</a> <font color="Maroon">c<sub>3</sub></font></span>)</span></span><a href="domain_1.html#K6">}</a></span>
 
<b>by </b><i><a class="ref" href="yellow_0.html#D15">YELLOW_0:def 15</a></i>;<br/>
<b>reconsider </b><font color="Maroon">c<sub>19</sub></font> = <font color="Maroon">c<sub>17</sub></font> as   <a href="struct_0.html#NM1">Element</a> of <span class="p1">(<span class="default"><a href="yellow_0.html#K5">subrelstr</a> <font color="Maroon">c<sub>9</sub></font></span>)</span> <b>by </b><i><a class="txt" href="orders_4.html#E24:17_2_1_2"><i><font color="Green">E24</font></i></a>, <a class="ref" href="yellow_0.html#D15">YELLOW_0:def 15</a></i>;<br/>
<div><b>hereby </b>
<div class="add"><b>assume </b><a NAME="E1:17_2_1_2_5_1_1"/>
<font color="Maroon">c<sub>16</sub></font> <a href="orders_2.html#R3">&lt;=</a> <font color="Maroon">c<sub>17</sub></font>
 ;<br/><a NAME="E2:17_2_1_2_5_1_1"/><i><font color="Green">E34</font></i>: 
<font color="Maroon">c<sub>15</sub></font> <a href="funct_1.html#K1">.</a> <font color="Maroon">c<sub>18</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>1</sub></font>
 <b>by </b><i><a class="txt" href="orders_4.html#E27:17_2_1_2"><i><font color="Green">E26</font></i></a></i>;<br/><a NAME="E3:17_2_1_2_5_1_1"/>
<font color="Maroon">c<sub>15</sub></font> <a href="funct_1.html#K1">.</a> <font color="Maroon">c<sub>19</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>1</sub></font>
 <b>by </b><i><a class="txt" href="orders_4.html#E27:17_2_1_2"><i><font color="Green">E26</font></i></a></i>;<br/><b>hence </b><a NAME="E4:17_2_1_2_5_1_1"/>
<font color="Maroon">c<sub>15</sub></font> <a href="funct_2.html#K3">.</a> <font color="Maroon">c<sub>16</sub></font> <a href="orders_2.html#R3">&lt;=</a> <font color="Maroon">c<sub>15</sub></font> <a href="funct_2.html#K3">.</a> <font color="Maroon">c<sub>17</sub></font>
 <b>by </b><i><a class="txt" href="orders_4.html#E2:17_2_1_2_5_1_1"><i><font color="Green">E34</font></i></a></i>;<br/></div>
<b>end;</b></div>

<b>assume </b><a NAME="E8:17_2_1_2_5_1"/>
<font color="Maroon">c<sub>15</sub></font> <a href="funct_2.html#K3">.</a> <font color="Maroon">c<sub>16</sub></font> <a href="orders_2.html#R3">&lt;=</a> <font color="Maroon">c<sub>15</sub></font> <a href="funct_2.html#K3">.</a> <font color="Maroon">c<sub>17</sub></font>
 ;<br/>

<a NAME="E9:17_2_1_2_5_1"/>
<font color="Maroon">c<sub>16</sub></font> <a href="hidden.html#R1">=</a>  <a href="yellow_0.html#K4">Top</a> <font color="Maroon">c<sub>3</sub></font>
 
<b>by </b><i><a class="txt" href="orders_4.html#E2:17_2_1_2_5_1"><i><font color="Green">E32</font></i></a>, <a class="ref" href="tarski.html#D1">TARSKI:def 1</a></i>;<br/>
<b>hence </b><a NAME="E10:17_2_1_2_5_1"/>
<font color="Maroon">c<sub>16</sub></font> <a href="orders_2.html#R3">&lt;=</a> <font color="Maroon">c<sub>17</sub></font>
 <b>by </b><i><a class="txt" href="orders_4.html#E5:17_2_1_2_5_1"><i><font color="Green">E33</font></i></a>, <a class="ref" href="tarski.html#D1">TARSKI:def 1</a></i>;<br/>


</div><b>end;</b></div>
<b>hence </b><a NAME="E2:17_2_1_2_5"/>
<font color="Maroon">c<sub>15</sub></font> is <a href="waybel_0.html#V23">isomorphic</a>
 <b>by </b><i><a class="txt" href="orders_4.html#E33:17_2_1_2"><i><font color="Green">E29</font></i></a>, <a class="txt" href="orders_4.html#E36:17_2_1_2"><i><font color="Green">E30</font></i></a>, <a class="ref" href="waybel_0.html#T66">WAYBEL_0:66</a></i>;<br/>


</div><b>end;</b></div><b>reconsider </b><font color="Maroon">c<sub>16</sub></font> = the <a href="struct_0.html#U1">carrier</a> of <span class="p1">(<span class="default"><a href="yellow_1.html#K2">InclPoset</a> <font color="Maroon">c<sub>1</sub></font></span>)</span>, <font color="Maroon">c<sub>17</sub></font> = <font color="Maroon">c<sub>10</sub></font> as   <a href="struct_0.html#NM2">Subset</a> of <span class="p1">(<span class="default"><a href="yellow_1.html#K2">InclPoset</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> <b>by </b><i><a class="txt" href="orders_4.html#E13:17_2_1_2"><i><font color="Green">E18</font></i></a>, <a class="ref" href="yellow_1.html#T1">YELLOW_1:1</a></i>;<br/><a NAME="E39:17_2_1_2"/>
<font color="Maroon">c<sub>1</sub></font> <a href="xxreal_0.html#R1">&lt;=</a> <font color="Maroon">c<sub>1</sub></font> <a href="nat_1.html#K1">+</a> 1
 <b>by </b><i><a class="ref" href="nat_1.html#T29">NAT_1:29</a></i>;<br/><a NAME="E40:17_2_1_2"/><b>then </b>
( <font color="Maroon">c<sub>16</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>1</sub></font> &amp;  <a href="yellow_1.html#K2">InclPoset</a> <font color="Maroon">c<sub>1</sub></font> is  <a href="yellow_0.html#V4">full</a>  <a href="yellow_0.html#M1">SubRelStr</a> of  <a href="yellow_1.html#K2">InclPoset</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="nat_1.html#K1">+</a> 1</span>)</span> )
 <b>by </b><i><a class="ref" href="orders_4.html#T1" target="_self">Th1</a>, <a class="ref" href="yellow_1.html#T1">YELLOW_1:1</a></i>;<br/><a NAME="E41:17_2_1_2"/><b>then </b>
(  <a href="yellow_1.html#K2">InclPoset</a> <font color="Maroon">c<sub>1</sub></font> <a href="hidden.html#R1">=</a>  <a href="yellow_0.html#K5">subrelstr</a> <font color="Maroon">c<sub>16</sub></font> &amp; the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">c<sub>6</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>5</sub></font> &amp; <font color="Maroon">c<sub>15</sub></font> is   <a href="struct_0.html#NM7">Function</a> of <span class="p1">(<span class="default"><a href="yellow_0.html#K5">subrelstr</a> <span class="p2"><a href="domain_1.html#K6">{</a><span class="default"><span class="p3">(<span class="default"><a href="yellow_0.html#K4">Top</a> <font color="Maroon">c<sub>3</sub></font></span>)</span></span><a href="domain_1.html#K6">}</a></span></span>)</span>,<span class="p1">(<span class="default"><a href="yellow_0.html#K5">subrelstr</a> <font color="Maroon">c<sub>17</sub></font></span>)</span> )
 <b>by </b><i><a class="ref" href="yellow_0.html#D15">YELLOW_0:def 15</a></i>;<br/><b>then consider </b><font color="Maroon">c<sub>18</sub></font> being   <a href="struct_0.html#NM7">Function</a> of <font color="Maroon">c<sub>3</sub></font>,<span class="p1">(<span class="default"><a href="yellow_1.html#K2">InclPoset</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span><b> such that </b><br/><a NAME="E43:17_2_1_2"/><i><font color="Green">E32</font></i>: 
( <font color="Maroon">c<sub>18</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>7</sub></font> <a href="funct_4.html#K1">+*</a> <font color="Maroon">c<sub>15</sub></font> &amp; <font color="Maroon">c<sub>18</sub></font> is <a href="waybel_0.html#V23">isomorphic</a> )
 <b>by </b><i><a class="txt" href="orders_4.html#E9:17_2_1_2"><i><font color="Green">E16</font></i></a>, <a class="txt" href="orders_4.html#E14:17_2_1_2"><i><font color="Green">E19</font></i></a>, <a class="txt" href="orders_4.html#E19:17_2_1_2"><i><font color="Green">E23</font></i></a>, <a class="txt" href="orders_4.html#E37:17_2_1_2"><i><font color="Green">E31</font></i></a>, <a class="ref" href="orders_4.html#T5" target="_self">Th5</a></i>;<br/><b>thus </b><a NAME="E44:17_2_1_2"/>
<font color="Maroon">c<sub>2</sub></font>, <a href="yellow_1.html#K2">InclPoset</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="nat_1.html#K1">+</a> 1</span>)</span> <a href="waybel_1.html#R5">are_isomorphic</a> 
 <b>by </b><i><a class="txt" href="orders_4.html#E43:17_2_1_2"><i><font color="Green">E32</font></i></a>, <a class="ref" href="waybel_1.html#D8">WAYBEL_1:def 8</a></i>;<br/></div><b>end;</b></div></div><b>end;</b></div>

</div><b>end;</b></div>
<a NAME="E3:17"/>
for <font color="Olive">b<sub>1</sub></font> being  <a href="nat_1.html#NM1">Nat</a> holds <font color="Maroon">S<sub>1</sub></font>[<font color="Olive">b<sub>1</sub></font>]
 
<b>from </b><i><a class="ref" href="nat_1.html#S1">NAT_1:sch 1</a>(<a class="txt" href="orders_4.html#E1:17"><i><font color="Green">E9</font></i></a>, <a class="txt" href="orders_4.html#E2:17"><i><font color="Green">E10</font></i></a>);<br/></i>
<b>hence </b><a NAME="E4:17"/>
for <font color="Olive">b<sub>1</sub></font> being <a href="group_1.html#V6">finite</a>  <a href="orders_4.html#M1" target="_self">Chain</a> <br/>for <font color="Olive">b<sub>2</sub></font> being  <a href="nat_1.html#NM1">Nat</a> st  <a href="card_1.html#K1">Card</a> the <a href="struct_0.html#U1">carrier</a> of <font color="Olive">b<sub>1</sub></font> <a href="hidden.html#R1">=</a> <font color="Olive">b<sub>2</sub></font> holds <br/><font color="Olive">b<sub>1</sub></font>, <a href="yellow_1.html#K2">InclPoset</a> <font color="Olive">b<sub>2</sub></font> <a href="waybel_1.html#R5">are_isomorphic</a> 
 ;<br/>


</div>
