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

<b>let </b><font color="Maroon" title="c1">A</font> be  non <a href="struct_0.html#V2" title="STRUCT_0:attr.2">empty</a> <a href="orders_2.html#NM1" title="ORDERS_2:NM.1">Poset</a>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> for <font color="Olive" title="b1">f</font> being   <a href="orders_1.html#M1" title="ORDERS_1:mode.1">Choice_Function</a> of  <a href="orders_1.html#K1" title="ORDERS_1:func.1">BOOL</a> the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c1">A</font><br/> for <font color="Olive" title="b2">fC1</font>, <font color="Olive" title="b3">fC2</font> being   <a href="orders_2.html#M2" title="ORDERS_2:mode.2">Chain</a> of <font color="Olive" title="b1">f</font>  st <font color="Olive" title="b2">fC1</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Olive" title="b3">fC2</font> holds <br/>( <font color="Olive" title="b2">fC1</font> is    <a href="orders_2.html#M1" title="ORDERS_2:mode.1">Initial_Segm</a> of <font color="Olive" title="b3">fC2</font> iff <font color="Olive" title="b3">fC2</font> is  not    <a href="orders_2.html#M1" title="ORDERS_2:mode.1">Initial_Segm</a> of <font color="Olive" title="b2">fC1</font> )</span><br/><b>let </b><font color="Maroon" title="c2">f</font> be    <a href="orders_1.html#M1" title="ORDERS_1:mode.1">Choice_Function</a> of  <a href="orders_1.html#K1" title="ORDERS_1:func.1">BOOL</a> the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c1">A</font>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> for <font color="Olive" title="b1">fC1</font>, <font color="Olive" title="b2">fC2</font> being   <a href="orders_2.html#M2" title="ORDERS_2:mode.2">Chain</a> of <font color="Maroon" title="c2">f</font>  st <font color="Olive" title="b1">fC1</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Olive" title="b2">fC2</font> holds <br/>( <font color="Olive" title="b1">fC1</font> is    <a href="orders_2.html#M1" title="ORDERS_2:mode.1">Initial_Segm</a> of <font color="Olive" title="b2">fC2</font> iff <font color="Olive" title="b2">fC2</font> is  not    <a href="orders_2.html#M1" title="ORDERS_2:mode.1">Initial_Segm</a> of <font color="Olive" title="b1">fC1</font> )</span><br/><b>let </b><font color="Maroon" title="c3">fC1</font>, <font color="Maroon" title="c4">fC2</font> be    <a href="orders_2.html#M2" title="ORDERS_2:mode.2">Chain</a> of <font color="Maroon" title="c2">f</font>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> ( <font color="Maroon" title="c3">fC1</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c4">fC2</font> implies ( <font color="Maroon" title="c3">fC1</font> is    <a href="orders_2.html#M1" title="ORDERS_2:mode.1">Initial_Segm</a> of <font color="Maroon" title="c4">fC2</font> iff <font color="Maroon" title="c4">fC2</font> is  not    <a href="orders_2.html#M1" title="ORDERS_2:mode.1">Initial_Segm</a> of <font color="Maroon" title="c3">fC1</font> ) )</span><br/>







<b>assume </b><a NAME="E1:67"/><i><font color="Green" title="E41">A1</font></i>: 
<font color="Maroon" title="c3">fC1</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c4">fC2</font>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> ( <font color="Maroon" title="c3">fC1</font> is    <a href="orders_2.html#M1" title="ORDERS_2:mode.1">Initial_Segm</a> of <font color="Maroon" title="c4">fC2</font> iff <font color="Maroon" title="c4">fC2</font> is  not    <a href="orders_2.html#M1" title="ORDERS_2:mode.1">Initial_Segm</a> of <font color="Maroon" title="c3">fC1</font> )</span><br/>

<b>set </b><font color="Maroon" title="c5">N</font> = <span class="p1">{<span class="default"> <font color="Olive" title="b1">a</font> where <font color="Olive" title="b1">a</font> is   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Maroon" title="c1">A</font> : ( <font color="Olive" title="b1">a</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c3">fC1</font> <a href="subset_1.html#K9" title="SUBSET_1:func.9">/\</a> <font color="Maroon" title="c4">fC2</font> &amp;  <a href="orders_2.html#K3" title="ORDERS_2:func.3">InitSegm</a> <font color="Maroon" title="c3">fC1</font>,<font color="Olive" title="b1">a</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="orders_2.html#K3" title="ORDERS_2:func.3">InitSegm</a> <font color="Maroon" title="c4">fC2</font>,<font color="Olive" title="b1">a</font> ) </span>}</span> ;<br/>
<a NAME="E2:67"/><i><font color="Green" title="E42">A2</font></i>: 
<span class="p1">{<span class="default"> <font color="Olive" title="b1">a</font> where <font color="Olive" title="b1">a</font> is   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Maroon" title="c1">A</font> : ( <font color="Olive" title="b1">a</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c3">fC1</font> <a href="subset_1.html#K9" title="SUBSET_1:func.9">/\</a> <font color="Maroon" title="c4">fC2</font> &amp;  <a href="orders_2.html#K3" title="ORDERS_2:func.3">InitSegm</a> <font color="Maroon" title="c3">fC1</font>,<font color="Olive" title="b1">a</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="orders_2.html#K3" title="ORDERS_2:func.3">InitSegm</a> <font color="Maroon" title="c4">fC2</font>,<font color="Olive" title="b1">a</font> ) </span>}</span>  <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <font color="Maroon" title="c3">fC1</font>
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="67_1"><b>proof </b></a><div class="add">

<b>let </b><font color="Maroon" title="c6">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> <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> (  not <font color="Maroon" title="c6">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <span class="p1">{<span class="default"> <font color="Olive" title="b1">a</font> where <font color="Olive" title="b1">a</font> is   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Maroon" title="c1">A</font> : ( <font color="Olive" title="b1">a</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c3">fC1</font> <a href="subset_1.html#K9" title="SUBSET_1:func.9">/\</a> <font color="Maroon" title="c4">fC2</font> &amp;  <a href="orders_2.html#K3" title="ORDERS_2:func.3">InitSegm</a> <font color="Maroon" title="c3">fC1</font>,<font color="Olive" title="b1">a</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="orders_2.html#K3" title="ORDERS_2:func.3">InitSegm</a> <font color="Maroon" title="c4">fC2</font>,<font color="Olive" title="b1">a</font> ) </span>}</span>  or <font color="Maroon" title="c6">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c3">fC1</font> )</span><br/>

<b>assume </b><a NAME="E1:67_1"/>
<font color="Maroon" title="c6">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <span class="p1">{<span class="default"> <font color="Olive" title="b1">a</font> where <font color="Olive" title="b1">a</font> is   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Maroon" title="c1">A</font> : ( <font color="Olive" title="b1">a</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c3">fC1</font> <a href="subset_1.html#K9" title="SUBSET_1:func.9">/\</a> <font color="Maroon" title="c4">fC2</font> &amp;  <a href="orders_2.html#K3" title="ORDERS_2:func.3">InitSegm</a> <font color="Maroon" title="c3">fC1</font>,<font color="Olive" title="b1">a</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="orders_2.html#K3" title="ORDERS_2:func.3">InitSegm</a> <font color="Maroon" title="c4">fC2</font>,<font color="Olive" title="b1">a</font> ) </span>}</span> 
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> <font color="Maroon" title="c6">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c3">fC1</font></span><br/>

<a NAME="E2:67_1"/><b>then </b>
 ex <font color="Olive" title="b1">a</font> being  <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Maroon" title="c1">A</font> st <br/>( <font color="Olive" title="b1">a</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c6">x</font> &amp; <font color="Olive" title="b1">a</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c3">fC1</font> <a href="subset_1.html#K9" title="SUBSET_1:func.9">/\</a> <font color="Maroon" title="c4">fC2</font> &amp;  <a href="orders_2.html#K3" title="ORDERS_2:func.3">InitSegm</a> <font color="Maroon" title="c3">fC1</font>,<font color="Olive" title="b1">a</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="orders_2.html#K3" title="ORDERS_2:func.3">InitSegm</a> <font color="Maroon" title="c4">fC2</font>,<font color="Olive" title="b1">a</font> )
 
;<br/>
<b>hence </b><a NAME="E3:67_1"/>
<font color="Maroon" title="c6">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c3">fC1</font>
 <b>by </b><i><a class="ref" href="xboole_0.html#D4" title="XBOOLE_0:def.4">XBOOLE_0:def 4</a></i>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> verum</span><br/>


</div><b>end;</b></div>
<b>then reconsider </b><font color="Maroon" title="c6">N</font> = <span class="p1">{<span class="default"> <font color="Olive" title="b1">a</font> where <font color="Olive" title="b1">a</font> is   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Maroon" title="c1">A</font> : ( <font color="Olive" title="b1">a</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c3">fC1</font> <a href="subset_1.html#K9" title="SUBSET_1:func.9">/\</a> <font color="Maroon" title="c4">fC2</font> &amp;  <a href="orders_2.html#K3" title="ORDERS_2:func.3">InitSegm</a> <font color="Maroon" title="c3">fC1</font>,<font color="Olive" title="b1">a</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="orders_2.html#K3" title="ORDERS_2:func.3">InitSegm</a> <font color="Maroon" title="c4">fC2</font>,<font color="Olive" title="b1">a</font> ) </span>}</span>  as   <a href="struct_0.html#NM2" title="STRUCT_0:NM.2">Subset</a> of <font color="Maroon" title="c1">A</font> <b>by </b><i><a class="ref" href="xboole_1.html#T1" title="XBOOLE_1:th.1">XBOOLE_1:1</a></i>;<br/>
<a NAME="E4:67"/><i><font color="Green" title="E43">A3</font></i>: 
the <a href="orders_2.html#U1" title="ORDERS_2:sel.1">InternalRel</a> of <font color="Maroon" title="c1">A</font> <a href="wellord1.html#R2" title="WELLORD1:pred.2">well_orders</a> <font color="Maroon" title="c3">fC1</font>
 
<b>by </b><i><a class="ref" href="orders_2.html#D16" target="_self" title="ORDERS_2:def.16">Def16</a></i>;<br/>
<div><i><font color="Green" title="E44">A4</font></i>: <a class="txt" onclick="hs2(this)" href="javascript:()" title="67_2"><b>now </b></a><div class="add"><b>let </b><font color="Maroon" title="c7">a1</font>, <font color="Maroon" title="c8">a2</font> be   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Maroon" title="c1">A</font>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> ( <font color="Maroon" title="c8">a2</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c6">N</font> &amp; <font color="Maroon" title="c7">a1</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c3">fC1</font> &amp; <font color="Maroon" title="c7">a1</font> <a href="orders_2.html#R2" title="ORDERS_2:pred.2">&lt;</a> <font color="Maroon" title="c8">a2</font> implies <font color="Maroon" title="c7">a1</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c6">N</font> )</span><br/><b>assume </b><b>that </b><br/><a NAME="E1:67_2"/><i><font color="Green" title="E45">A5</font></i>: 
<font color="Maroon" title="c8">a2</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c6">N</font>
 <b>and </b><br/><a NAME="E2:67_2"/><i><font color="Green" title="E46">A6</font></i>: 
<font color="Maroon" title="c7">a1</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c3">fC1</font>
 <b>and </b><br/><a NAME="E3:67_2"/><i><font color="Green" title="E47">A7</font></i>: 
<font color="Maroon" title="c7">a1</font> <a href="orders_2.html#R2" title="ORDERS_2:pred.2">&lt;</a> <font color="Maroon" title="c8">a2</font>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> <font color="Maroon" title="c7">a1</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c6">N</font></span><br/><a NAME="E4:67_2"/><i><font color="Green" title="E48">A8</font></i>: 
 ex <font color="Olive" title="b1">a</font> being  <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Maroon" title="c1">A</font> st <br/>( <font color="Olive" title="b1">a</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c8">a2</font> &amp; <font color="Olive" title="b1">a</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c3">fC1</font> <a href="subset_1.html#K9" title="SUBSET_1:func.9">/\</a> <font color="Maroon" title="c4">fC2</font> &amp;  <a href="orders_2.html#K3" title="ORDERS_2:func.3">InitSegm</a> <font color="Maroon" title="c3">fC1</font>,<font color="Olive" title="b1">a</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="orders_2.html#K3" title="ORDERS_2:func.3">InitSegm</a> <font color="Maroon" title="c4">fC2</font>,<font color="Olive" title="b1">a</font> )
 <b>by </b><i><a class="txt" href="#E1:67_2"><i><font color="Green" title="E45">A5</font></i></a></i>;<br/><a NAME="E5:67_2"/><b>then </b>
<font color="Maroon" title="c7">a1</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="orders_2.html#K3" title="ORDERS_2:func.3">InitSegm</a> <font color="Maroon" title="c4">fC2</font>,<font color="Maroon" title="c8">a2</font>
 <b>by </b><i><a class="txt" href="#E2:67_2"><i><font color="Green" title="E46">A6</font></i></a>, <a class="txt" href="#E3:67_2"><i><font color="Green" title="E47">A7</font></i></a>, <a class="ref" href="orders_2.html#T57" target="_self" title="ORDERS_2:th.57">Th57</a></i>;<br/><a NAME="E6:67_2"/><b>then </b>
<font color="Maroon" title="c7">a1</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c4">fC2</font>
 <b>by </b><i><a class="ref" href="xboole_0.html#D4" title="XBOOLE_0:def.4">XBOOLE_0:def 4</a></i>;<br/><a NAME="E7:67_2"/><b>then </b><i><font color="Green" title="E49">A9</font></i>: 
<font color="Maroon" title="c7">a1</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c3">fC1</font> <a href="subset_1.html#K9" title="SUBSET_1:func.9">/\</a> <font color="Maroon" title="c4">fC2</font>
 <b>by </b><i><a class="txt" href="#E2:67_2"><i><font color="Green" title="E46">A6</font></i></a>, <a class="ref" href="xboole_0.html#D4" title="XBOOLE_0:def.4">XBOOLE_0:def 4</a></i>;<br/><a NAME="E8:67_2"/>
 <a href="orders_2.html#K3" title="ORDERS_2:func.3">InitSegm</a> <font color="Maroon" title="c3">fC1</font>,<font color="Maroon" title="c7">a1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="orders_2.html#K3" title="ORDERS_2:func.3">InitSegm</a> <font color="Maroon" title="c4">fC2</font>,<font color="Maroon" title="c7">a1</font>
 <div><a class="txt" onclick="hs2(this)" href="javascript:()" title="67_2_1"><b>proof </b></a><div class="add">

<b>thus </b><a NAME="E1:67_2_1"/>
 <a href="orders_2.html#K3" title="ORDERS_2:func.3">InitSegm</a> <font color="Maroon" title="c3">fC1</font>,<font color="Maroon" title="c7">a1</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a>  <a href="orders_2.html#K3" title="ORDERS_2:func.3">InitSegm</a> <font color="Maroon" title="c4">fC2</font>,<font color="Maroon" title="c7">a1</font>
  <i><font color="Red">:: according to </font></i><a class="ref" href="xboole_0.html#D10" title="XBOOLE_0:def.10">XBOOLE_0:def 10</a> <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide">  <a href="orders_2.html#K3" title="ORDERS_2:func.3">InitSegm</a> <font color="Maroon" title="c4">fC2</font>,<font color="Maroon" title="c7">a1</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a>  <a href="orders_2.html#K3" title="ORDERS_2:func.3">InitSegm</a> <font color="Maroon" title="c3">fC1</font>,<font color="Maroon" title="c7">a1</font></span><div><a class="txt" onclick="hs2(this)" href="javascript:()" title="67_2_1_1"><b>proof </b></a><div class="add">

<b>let </b><font color="Maroon" title="c9">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> <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> (  not <font color="Maroon" title="c9">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="orders_2.html#K3" title="ORDERS_2:func.3">InitSegm</a> <font color="Maroon" title="c3">fC1</font>,<font color="Maroon" title="c7">a1</font> or <font color="Maroon" title="c9">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="orders_2.html#K3" title="ORDERS_2:func.3">InitSegm</a> <font color="Maroon" title="c4">fC2</font>,<font color="Maroon" title="c7">a1</font> )</span><br/>

<b>assume </b><a NAME="E1:67_2_1_1"/><i><font color="Green" title="E50">A10</font></i>: 
<font color="Maroon" title="c9">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="orders_2.html#K3" title="ORDERS_2:func.3">InitSegm</a> <font color="Maroon" title="c3">fC1</font>,<font color="Maroon" title="c7">a1</font>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> <font color="Maroon" title="c9">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="orders_2.html#K3" title="ORDERS_2:func.3">InitSegm</a> <font color="Maroon" title="c4">fC2</font>,<font color="Maroon" title="c7">a1</font></span><br/>

<b>then reconsider </b><font color="Maroon" title="c10">b</font> = <font color="Maroon" title="c9">x</font> as   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Maroon" title="c1">A</font> ;<br/>
<a NAME="E3:67_2_1_1"/><i><font color="Green" title="E51">A11</font></i>: 
<font color="Maroon" title="c10">b</font> <a href="orders_2.html#R2" title="ORDERS_2:pred.2">&lt;</a> <font color="Maroon" title="c7">a1</font>
 
<b>by </b><i><a class="txt" href="#E1:67_2_1_1"><i><font color="Green" title="E50">A10</font></i></a>, <a class="ref" href="orders_2.html#T57" target="_self" title="ORDERS_2:th.57">Th57</a></i>;<br/>
<a NAME="E4:67_2_1_1"/><b>then </b>
( <font color="Maroon" title="c10">b</font> <a href="orders_2.html#R2" title="ORDERS_2:pred.2">&lt;</a> <font color="Maroon" title="c8">a2</font> &amp; <font color="Maroon" title="c10">b</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c3">fC1</font> )
 
<b>by </b><i><a class="txt" href="#E3:67_2"><i><font color="Green" title="E47">A7</font></i></a>, <a class="txt" href="#E1:67_2_1_1"><i><font color="Green" title="E50">A10</font></i></a>, <a class="ref" href="orders_2.html#T29" target="_self" title="ORDERS_2:th.29">Th29</a>, <a class="ref" href="orders_2.html#T57" target="_self" title="ORDERS_2:th.57">Th57</a></i>;<br/>
<a NAME="E5:67_2_1_1"/><b>then </b>
<font color="Maroon" title="c10">b</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="orders_2.html#K3" title="ORDERS_2:func.3">InitSegm</a> <font color="Maroon" title="c3">fC1</font>,<font color="Maroon" title="c8">a2</font>
 
<b>by </b><i><a class="ref" href="orders_2.html#T57" target="_self" title="ORDERS_2:th.57">Th57</a></i>;<br/>
<a NAME="E6:67_2_1_1"/><b>then </b>
<font color="Maroon" title="c10">b</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c4">fC2</font>
 
<b>by </b><i><a class="txt" href="#E4:67_2"><i><font color="Green" title="E48">A8</font></i></a>, <a class="ref" href="orders_2.html#T57" target="_self" title="ORDERS_2:th.57">Th57</a></i>;<br/>
<b>hence </b><a NAME="E7:67_2_1_1"/>
<font color="Maroon" title="c9">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="orders_2.html#K3" title="ORDERS_2:func.3">InitSegm</a> <font color="Maroon" title="c4">fC2</font>,<font color="Maroon" title="c7">a1</font>
 <b>by </b><i><a class="txt" href="#E3:67_2_1_1"><i><font color="Green" title="E51">A11</font></i></a>, <a class="ref" href="orders_2.html#T57" target="_self" title="ORDERS_2:th.57">Th57</a></i>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> verum</span><br/>


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

<b>let </b><font color="Maroon" title="c9">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> <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> (  not <font color="Maroon" title="c9">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="orders_2.html#K3" title="ORDERS_2:func.3">InitSegm</a> <font color="Maroon" title="c4">fC2</font>,<font color="Maroon" title="c7">a1</font> or <font color="Maroon" title="c9">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="orders_2.html#K3" title="ORDERS_2:func.3">InitSegm</a> <font color="Maroon" title="c3">fC1</font>,<font color="Maroon" title="c7">a1</font> )</span><br/>

<b>assume </b><a NAME="E2:67_2_1"/><i><font color="Green" title="E50">A12</font></i>: 
<font color="Maroon" title="c9">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="orders_2.html#K3" title="ORDERS_2:func.3">InitSegm</a> <font color="Maroon" title="c4">fC2</font>,<font color="Maroon" title="c7">a1</font>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> <font color="Maroon" title="c9">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="orders_2.html#K3" title="ORDERS_2:func.3">InitSegm</a> <font color="Maroon" title="c3">fC1</font>,<font color="Maroon" title="c7">a1</font></span><br/>

<b>then reconsider </b><font color="Maroon" title="c10">b</font> = <font color="Maroon" title="c9">x</font> as   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Maroon" title="c1">A</font> ;<br/>
<a NAME="E4:67_2_1"/><i><font color="Green" title="E51">A13</font></i>: 
<font color="Maroon" title="c10">b</font> <a href="orders_2.html#R2" title="ORDERS_2:pred.2">&lt;</a> <font color="Maroon" title="c7">a1</font>
 
<b>by </b><i><a class="txt" href="#E2:67_2_1"><i><font color="Green" title="E50">A12</font></i></a>, <a class="ref" href="orders_2.html#T57" target="_self" title="ORDERS_2:th.57">Th57</a></i>;<br/>
<a NAME="E5:67_2_1"/><b>then </b>
( <font color="Maroon" title="c10">b</font> <a href="orders_2.html#R2" title="ORDERS_2:pred.2">&lt;</a> <font color="Maroon" title="c8">a2</font> &amp; <font color="Maroon" title="c10">b</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c4">fC2</font> )
 
<b>by </b><i><a class="txt" href="#E3:67_2"><i><font color="Green" title="E47">A7</font></i></a>, <a class="txt" href="#E2:67_2_1"><i><font color="Green" title="E50">A12</font></i></a>, <a class="ref" href="orders_2.html#T29" target="_self" title="ORDERS_2:th.29">Th29</a>, <a class="ref" href="orders_2.html#T57" target="_self" title="ORDERS_2:th.57">Th57</a></i>;<br/>
<a NAME="E6:67_2_1"/><b>then </b>
<font color="Maroon" title="c10">b</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="orders_2.html#K3" title="ORDERS_2:func.3">InitSegm</a> <font color="Maroon" title="c4">fC2</font>,<font color="Maroon" title="c8">a2</font>
 
<b>by </b><i><a class="ref" href="orders_2.html#T57" target="_self" title="ORDERS_2:th.57">Th57</a></i>;<br/>
<a NAME="E7:67_2_1"/><b>then </b>
<font color="Maroon" title="c10">b</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c3">fC1</font>
 
<b>by </b><i><a class="txt" href="#E4:67_2"><i><font color="Green" title="E48">A8</font></i></a>, <a class="ref" href="orders_2.html#T57" target="_self" title="ORDERS_2:th.57">Th57</a></i>;<br/>
<b>hence </b><a NAME="E8:67_2_1"/>
<font color="Maroon" title="c9">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="orders_2.html#K3" title="ORDERS_2:func.3">InitSegm</a> <font color="Maroon" title="c3">fC1</font>,<font color="Maroon" title="c7">a1</font>
 <b>by </b><i><a class="txt" href="#E4:67_2_1"><i><font color="Green" title="E51">A13</font></i></a>, <a class="ref" href="orders_2.html#T57" target="_self" title="ORDERS_2:th.57">Th57</a></i>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> verum</span><br/>


</div><b>end;</b></div><b>hence </b><a NAME="E9:67_2"/>
<font color="Maroon" title="c7">a1</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c6">N</font>
 <b>by </b><i><a class="txt" href="#E7:67_2"><i><font color="Green" title="E49">A9</font></i></a></i>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> verum</span><br/></div><b>end;</b></div>
<a NAME="E6:67"/><i><font color="Green" title="E45">A14</font></i>: 
the <a href="orders_2.html#U1" title="ORDERS_2:sel.1">InternalRel</a> of <font color="Maroon" title="c1">A</font> <a href="wellord1.html#R2" title="WELLORD1:pred.2">well_orders</a> <font color="Maroon" title="c4">fC2</font>
 
<b>by </b><i><a class="ref" href="orders_2.html#D16" target="_self" title="ORDERS_2:def.16">Def16</a></i>;<br/>
<a NAME="E7:67"/><i><font color="Green" title="E46">A15</font></i>: 
<font color="Maroon" title="c6">N</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <font color="Maroon" title="c4">fC2</font>
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="67_3"><b>proof </b></a><div class="add">

<b>let </b><font color="Maroon" title="c7">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> <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> (  not <font color="Maroon" title="c7">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c6">N</font> or <font color="Maroon" title="c7">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c4">fC2</font> )</span><br/>

<b>assume </b><a NAME="E1:67_3"/>
<font color="Maroon" title="c7">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c6">N</font>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> <font color="Maroon" title="c7">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c4">fC2</font></span><br/>

<a NAME="E2:67_3"/><b>then </b>
 ex <font color="Olive" title="b1">a</font> being  <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Maroon" title="c1">A</font> st <br/>( <font color="Olive" title="b1">a</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c7">x</font> &amp; <font color="Olive" title="b1">a</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c3">fC1</font> <a href="subset_1.html#K9" title="SUBSET_1:func.9">/\</a> <font color="Maroon" title="c4">fC2</font> &amp;  <a href="orders_2.html#K3" title="ORDERS_2:func.3">InitSegm</a> <font color="Maroon" title="c3">fC1</font>,<font color="Olive" title="b1">a</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="orders_2.html#K3" title="ORDERS_2:func.3">InitSegm</a> <font color="Maroon" title="c4">fC2</font>,<font color="Olive" title="b1">a</font> )
 
;<br/>
<b>hence </b><a NAME="E3:67_3"/>
<font color="Maroon" title="c7">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c4">fC2</font>
 <b>by </b><i><a class="ref" href="xboole_0.html#D4" title="XBOOLE_0:def.4">XBOOLE_0:def 4</a></i>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> verum</span><br/>


</div><b>end;</b></div>
<div><i><font color="Green" title="E47">A16</font></i>: <a class="txt" onclick="hs2(this)" href="javascript:()" title="67_4"><b>now </b></a><div class="add"><b>let </b><font color="Maroon" title="c7">a1</font>, <font color="Maroon" title="c8">a2</font> be   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Maroon" title="c1">A</font>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> ( <font color="Maroon" title="c8">a2</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c6">N</font> &amp; <font color="Maroon" title="c7">a1</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c4">fC2</font> &amp; <font color="Maroon" title="c7">a1</font> <a href="orders_2.html#R2" title="ORDERS_2:pred.2">&lt;</a> <font color="Maroon" title="c8">a2</font> implies <font color="Maroon" title="c7">a1</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c6">N</font> )</span><br/><b>assume </b><b>that </b><br/><a NAME="E1:67_4"/><i><font color="Green" title="E48">A17</font></i>: 
<font color="Maroon" title="c8">a2</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c6">N</font>
 <b>and </b><br/><a NAME="E2:67_4"/><i><font color="Green" title="E49">A18</font></i>: 
<font color="Maroon" title="c7">a1</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c4">fC2</font>
 <b>and </b><br/><a NAME="E3:67_4"/><i><font color="Green" title="E50">A19</font></i>: 
<font color="Maroon" title="c7">a1</font> <a href="orders_2.html#R2" title="ORDERS_2:pred.2">&lt;</a> <font color="Maroon" title="c8">a2</font>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> <font color="Maroon" title="c7">a1</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c6">N</font></span><br/><a NAME="E4:67_4"/><i><font color="Green" title="E51">A20</font></i>: 
 ex <font color="Olive" title="b1">a</font> being  <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Maroon" title="c1">A</font> st <br/>( <font color="Olive" title="b1">a</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c8">a2</font> &amp; <font color="Olive" title="b1">a</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c3">fC1</font> <a href="subset_1.html#K9" title="SUBSET_1:func.9">/\</a> <font color="Maroon" title="c4">fC2</font> &amp;  <a href="orders_2.html#K3" title="ORDERS_2:func.3">InitSegm</a> <font color="Maroon" title="c3">fC1</font>,<font color="Olive" title="b1">a</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="orders_2.html#K3" title="ORDERS_2:func.3">InitSegm</a> <font color="Maroon" title="c4">fC2</font>,<font color="Olive" title="b1">a</font> )
 <b>by </b><i><a class="txt" href="#E1:67_4"><i><font color="Green" title="E48">A17</font></i></a></i>;<br/><a NAME="E5:67_4"/><b>then </b>
<font color="Maroon" title="c7">a1</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="orders_2.html#K3" title="ORDERS_2:func.3">InitSegm</a> <font color="Maroon" title="c3">fC1</font>,<font color="Maroon" title="c8">a2</font>
 <b>by </b><i><a class="txt" href="#E2:67_4"><i><font color="Green" title="E49">A18</font></i></a>, <a class="txt" href="#E3:67_4"><i><font color="Green" title="E50">A19</font></i></a>, <a class="ref" href="orders_2.html#T57" target="_self" title="ORDERS_2:th.57">Th57</a></i>;<br/><a NAME="E6:67_4"/><b>then </b>
<font color="Maroon" title="c7">a1</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c3">fC1</font>
 <b>by </b><i><a class="ref" href="xboole_0.html#D4" title="XBOOLE_0:def.4">XBOOLE_0:def 4</a></i>;<br/><a NAME="E7:67_4"/><b>then </b><i><font color="Green" title="E52">A21</font></i>: 
<font color="Maroon" title="c7">a1</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c3">fC1</font> <a href="subset_1.html#K9" title="SUBSET_1:func.9">/\</a> <font color="Maroon" title="c4">fC2</font>
 <b>by </b><i><a class="txt" href="#E2:67_4"><i><font color="Green" title="E49">A18</font></i></a>, <a class="ref" href="xboole_0.html#D4" title="XBOOLE_0:def.4">XBOOLE_0:def 4</a></i>;<br/><a NAME="E8:67_4"/>
 <a href="orders_2.html#K3" title="ORDERS_2:func.3">InitSegm</a> <font color="Maroon" title="c3">fC1</font>,<font color="Maroon" title="c7">a1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="orders_2.html#K3" title="ORDERS_2:func.3">InitSegm</a> <font color="Maroon" title="c4">fC2</font>,<font color="Maroon" title="c7">a1</font>
 <div><a class="txt" onclick="hs2(this)" href="javascript:()" title="67_4_1"><b>proof </b></a><div class="add">

<b>thus </b><a NAME="E1:67_4_1"/>
 <a href="orders_2.html#K3" title="ORDERS_2:func.3">InitSegm</a> <font color="Maroon" title="c3">fC1</font>,<font color="Maroon" title="c7">a1</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a>  <a href="orders_2.html#K3" title="ORDERS_2:func.3">InitSegm</a> <font color="Maroon" title="c4">fC2</font>,<font color="Maroon" title="c7">a1</font>
  <i><font color="Red">:: according to </font></i><a class="ref" href="xboole_0.html#D10" title="XBOOLE_0:def.10">XBOOLE_0:def 10</a> <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide">  <a href="orders_2.html#K3" title="ORDERS_2:func.3">InitSegm</a> <font color="Maroon" title="c4">fC2</font>,<font color="Maroon" title="c7">a1</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a>  <a href="orders_2.html#K3" title="ORDERS_2:func.3">InitSegm</a> <font color="Maroon" title="c3">fC1</font>,<font color="Maroon" title="c7">a1</font></span><div><a class="txt" onclick="hs2(this)" href="javascript:()" title="67_4_1_1"><b>proof </b></a><div class="add">

<b>let </b><font color="Maroon" title="c9">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> <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> (  not <font color="Maroon" title="c9">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="orders_2.html#K3" title="ORDERS_2:func.3">InitSegm</a> <font color="Maroon" title="c3">fC1</font>,<font color="Maroon" title="c7">a1</font> or <font color="Maroon" title="c9">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="orders_2.html#K3" title="ORDERS_2:func.3">InitSegm</a> <font color="Maroon" title="c4">fC2</font>,<font color="Maroon" title="c7">a1</font> )</span><br/>

<b>assume </b><a NAME="E1:67_4_1_1"/><i><font color="Green" title="E53">A22</font></i>: 
<font color="Maroon" title="c9">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="orders_2.html#K3" title="ORDERS_2:func.3">InitSegm</a> <font color="Maroon" title="c3">fC1</font>,<font color="Maroon" title="c7">a1</font>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> <font color="Maroon" title="c9">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="orders_2.html#K3" title="ORDERS_2:func.3">InitSegm</a> <font color="Maroon" title="c4">fC2</font>,<font color="Maroon" title="c7">a1</font></span><br/>

<b>then reconsider </b><font color="Maroon" title="c10">b</font> = <font color="Maroon" title="c9">x</font> as   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Maroon" title="c1">A</font> ;<br/>
<a NAME="E3:67_4_1_1"/><i><font color="Green" title="E54">A23</font></i>: 
<font color="Maroon" title="c10">b</font> <a href="orders_2.html#R2" title="ORDERS_2:pred.2">&lt;</a> <font color="Maroon" title="c7">a1</font>
 
<b>by </b><i><a class="txt" href="#E1:67_4_1_1"><i><font color="Green" title="E53">A22</font></i></a>, <a class="ref" href="orders_2.html#T57" target="_self" title="ORDERS_2:th.57">Th57</a></i>;<br/>
<a NAME="E4:67_4_1_1"/><b>then </b>
( <font color="Maroon" title="c10">b</font> <a href="orders_2.html#R2" title="ORDERS_2:pred.2">&lt;</a> <font color="Maroon" title="c8">a2</font> &amp; <font color="Maroon" title="c10">b</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c3">fC1</font> )
 
<b>by </b><i><a class="txt" href="#E3:67_4"><i><font color="Green" title="E50">A19</font></i></a>, <a class="txt" href="#E1:67_4_1_1"><i><font color="Green" title="E53">A22</font></i></a>, <a class="ref" href="orders_2.html#T29" target="_self" title="ORDERS_2:th.29">Th29</a>, <a class="ref" href="orders_2.html#T57" target="_self" title="ORDERS_2:th.57">Th57</a></i>;<br/>
<a NAME="E5:67_4_1_1"/><b>then </b>
<font color="Maroon" title="c10">b</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="orders_2.html#K3" title="ORDERS_2:func.3">InitSegm</a> <font color="Maroon" title="c3">fC1</font>,<font color="Maroon" title="c8">a2</font>
 
<b>by </b><i><a class="ref" href="orders_2.html#T57" target="_self" title="ORDERS_2:th.57">Th57</a></i>;<br/>
<a NAME="E6:67_4_1_1"/><b>then </b>
<font color="Maroon" title="c10">b</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c4">fC2</font>
 
<b>by </b><i><a class="txt" href="#E4:67_4"><i><font color="Green" title="E51">A20</font></i></a>, <a class="ref" href="orders_2.html#T57" target="_self" title="ORDERS_2:th.57">Th57</a></i>;<br/>
<b>hence </b><a NAME="E7:67_4_1_1"/>
<font color="Maroon" title="c9">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="orders_2.html#K3" title="ORDERS_2:func.3">InitSegm</a> <font color="Maroon" title="c4">fC2</font>,<font color="Maroon" title="c7">a1</font>
 <b>by </b><i><a class="txt" href="#E3:67_4_1_1"><i><font color="Green" title="E54">A23</font></i></a>, <a class="ref" href="orders_2.html#T57" target="_self" title="ORDERS_2:th.57">Th57</a></i>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> verum</span><br/>


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

<b>let </b><font color="Maroon" title="c9">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> <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> (  not <font color="Maroon" title="c9">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="orders_2.html#K3" title="ORDERS_2:func.3">InitSegm</a> <font color="Maroon" title="c4">fC2</font>,<font color="Maroon" title="c7">a1</font> or <font color="Maroon" title="c9">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="orders_2.html#K3" title="ORDERS_2:func.3">InitSegm</a> <font color="Maroon" title="c3">fC1</font>,<font color="Maroon" title="c7">a1</font> )</span><br/>

<b>assume </b><a NAME="E2:67_4_1"/><i><font color="Green" title="E53">A24</font></i>: 
<font color="Maroon" title="c9">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="orders_2.html#K3" title="ORDERS_2:func.3">InitSegm</a> <font color="Maroon" title="c4">fC2</font>,<font color="Maroon" title="c7">a1</font>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> <font color="Maroon" title="c9">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="orders_2.html#K3" title="ORDERS_2:func.3">InitSegm</a> <font color="Maroon" title="c3">fC1</font>,<font color="Maroon" title="c7">a1</font></span><br/>

<b>then reconsider </b><font color="Maroon" title="c10">b</font> = <font color="Maroon" title="c9">x</font> as   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Maroon" title="c1">A</font> ;<br/>
<a NAME="E4:67_4_1"/><i><font color="Green" title="E54">A25</font></i>: 
<font color="Maroon" title="c10">b</font> <a href="orders_2.html#R2" title="ORDERS_2:pred.2">&lt;</a> <font color="Maroon" title="c7">a1</font>
 
<b>by </b><i><a class="txt" href="#E2:67_4_1"><i><font color="Green" title="E53">A24</font></i></a>, <a class="ref" href="orders_2.html#T57" target="_self" title="ORDERS_2:th.57">Th57</a></i>;<br/>
<a NAME="E5:67_4_1"/><b>then </b>
( <font color="Maroon" title="c10">b</font> <a href="orders_2.html#R2" title="ORDERS_2:pred.2">&lt;</a> <font color="Maroon" title="c8">a2</font> &amp; <font color="Maroon" title="c10">b</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c4">fC2</font> )
 
<b>by </b><i><a class="txt" href="#E3:67_4"><i><font color="Green" title="E50">A19</font></i></a>, <a class="txt" href="#E2:67_4_1"><i><font color="Green" title="E53">A24</font></i></a>, <a class="ref" href="orders_2.html#T29" target="_self" title="ORDERS_2:th.29">Th29</a>, <a class="ref" href="orders_2.html#T57" target="_self" title="ORDERS_2:th.57">Th57</a></i>;<br/>
<a NAME="E6:67_4_1"/><b>then </b>
<font color="Maroon" title="c10">b</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="orders_2.html#K3" title="ORDERS_2:func.3">InitSegm</a> <font color="Maroon" title="c4">fC2</font>,<font color="Maroon" title="c8">a2</font>
 
<b>by </b><i><a class="ref" href="orders_2.html#T57" target="_self" title="ORDERS_2:th.57">Th57</a></i>;<br/>
<a NAME="E7:67_4_1"/><b>then </b>
<font color="Maroon" title="c10">b</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c3">fC1</font>
 
<b>by </b><i><a class="txt" href="#E4:67_4"><i><font color="Green" title="E51">A20</font></i></a>, <a class="ref" href="orders_2.html#T57" target="_self" title="ORDERS_2:th.57">Th57</a></i>;<br/>
<b>hence </b><a NAME="E8:67_4_1"/>
<font color="Maroon" title="c9">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="orders_2.html#K3" title="ORDERS_2:func.3">InitSegm</a> <font color="Maroon" title="c3">fC1</font>,<font color="Maroon" title="c7">a1</font>
 <b>by </b><i><a class="txt" href="#E4:67_4_1"><i><font color="Green" title="E54">A25</font></i></a>, <a class="ref" href="orders_2.html#T57" target="_self" title="ORDERS_2:th.57">Th57</a></i>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> verum</span><br/>


</div><b>end;</b></div><b>hence </b><a NAME="E9:67_4"/>
<font color="Maroon" title="c7">a1</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c6">N</font>
 <b>by </b><i><a class="txt" href="#E7:67_4"><i><font color="Green" title="E52">A21</font></i></a></i>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> verum</span><br/></div><b>end;</b></div>
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="67_5"><b>now </b></a><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="67_5_1"><b>per </b></a><a class="txt" onclick="hs(this)" href="javascript:()"><b>cases </b></a><span class="hide"><a NAME="E1:67_5_1"/>
( ( <font color="Maroon" title="c6">N</font> is    <a href="orders_2.html#M1" title="ORDERS_2:mode.1">Initial_Segm</a> of <font color="Maroon" title="c3">fC1</font> &amp; <font color="Maroon" title="c6">N</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c4">fC2</font> ) or ( <font color="Maroon" title="c6">N</font> is    <a href="orders_2.html#M1" title="ORDERS_2:mode.1">Initial_Segm</a> of <font color="Maroon" title="c4">fC2</font> &amp; <font color="Maroon" title="c6">N</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c3">fC1</font> ) or ( <font color="Maroon" title="c6">N</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c3">fC1</font> &amp; <font color="Maroon" title="c6">N</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c4">fC2</font> ) or ( <font color="Maroon" title="c6">N</font> is    <a href="orders_2.html#M1" title="ORDERS_2:mode.1">Initial_Segm</a> of <font color="Maroon" title="c3">fC1</font> &amp; <font color="Maroon" title="c6">N</font> is    <a href="orders_2.html#M1" title="ORDERS_2:mode.1">Initial_Segm</a> of <font color="Maroon" title="c4">fC2</font> ) )
 </span><b>by </b><i><a class="txt" href="#E2:67"><i><font color="Green" title="E42">A2</font></i></a>, <a class="txt" href="#E4:67"><i><font color="Green" title="E43">A3</font></i></a>, <a class="txt" href="#E5:67"><i><font color="Green" title="E44">A4</font></i></a>, <a class="txt" href="#E6:67"><i><font color="Green" title="E45">A14</font></i></a>, <a class="txt" href="#E7:67"><i><font color="Green" title="E46">A15</font></i></a>, <a class="txt" href="#E8:67"><i><font color="Green" title="E47">A16</font></i></a>, <a class="ref" href="orders_2.html#T73" target="_self" title="ORDERS_2:th.73">Th73</a></i>;<br/><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="67_5_1_1"><b>suppose </b></a><a NAME="E1:67_5_1_1"/>
( <font color="Maroon" title="c6">N</font> is    <a href="orders_2.html#M1" title="ORDERS_2:mode.1">Initial_Segm</a> of <font color="Maroon" title="c3">fC1</font> &amp; <font color="Maroon" title="c6">N</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c4">fC2</font> )
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> ( <font color="Maroon" title="c3">fC1</font> is    <a href="orders_2.html#M1" title="ORDERS_2:mode.1">Initial_Segm</a> of <font color="Maroon" title="c4">fC2</font> iff <font color="Maroon" title="c4">fC2</font> is  not    <a href="orders_2.html#M1" title="ORDERS_2:mode.1">Initial_Segm</a> of <font color="Maroon" title="c3">fC1</font> )</span><br/><div class="add"><a NAME="E2:67_5_1_1"/><b>then </b>
( <font color="Maroon" title="c4">fC2</font> is    <a href="orders_2.html#M1" title="ORDERS_2:mode.1">Initial_Segm</a> of <font color="Maroon" title="c3">fC1</font> &amp; <font color="Maroon" title="c3">fC1</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a>  <a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a>  )
 <b>by </b><i><a class="ref" href="orders_2.html#D16" target="_self" title="ORDERS_2:def.16">Def16</a></i>;<br/><b>hence </b><a NAME="E3:67_5_1_1"/>
( <font color="Maroon" title="c3">fC1</font> is    <a href="orders_2.html#M1" title="ORDERS_2:mode.1">Initial_Segm</a> of <font color="Maroon" title="c4">fC2</font> iff <font color="Maroon" title="c4">fC2</font> is  not    <a href="orders_2.html#M1" title="ORDERS_2:mode.1">Initial_Segm</a> of <font color="Maroon" title="c3">fC1</font> )
 <b>by </b><i><a class="ref" href="orders_2.html#T69" target="_self" title="ORDERS_2:th.69">Th69</a></i>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> verum</span><br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="67_5_1_2"><b>suppose </b></a><a NAME="E1:67_5_1_2"/>
( <font color="Maroon" title="c6">N</font> is    <a href="orders_2.html#M1" title="ORDERS_2:mode.1">Initial_Segm</a> of <font color="Maroon" title="c4">fC2</font> &amp; <font color="Maroon" title="c6">N</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c3">fC1</font> )
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> ( <font color="Maroon" title="c3">fC1</font> is    <a href="orders_2.html#M1" title="ORDERS_2:mode.1">Initial_Segm</a> of <font color="Maroon" title="c4">fC2</font> iff <font color="Maroon" title="c4">fC2</font> is  not    <a href="orders_2.html#M1" title="ORDERS_2:mode.1">Initial_Segm</a> of <font color="Maroon" title="c3">fC1</font> )</span><br/><div class="add"><a NAME="E2:67_5_1_2"/><b>then </b>
( <font color="Maroon" title="c3">fC1</font> is    <a href="orders_2.html#M1" title="ORDERS_2:mode.1">Initial_Segm</a> of <font color="Maroon" title="c4">fC2</font> &amp; <font color="Maroon" title="c4">fC2</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a>  <a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a>  )
 <b>by </b><i><a class="ref" href="orders_2.html#D16" target="_self" title="ORDERS_2:def.16">Def16</a></i>;<br/><b>hence </b><a NAME="E3:67_5_1_2"/>
( <font color="Maroon" title="c3">fC1</font> is    <a href="orders_2.html#M1" title="ORDERS_2:mode.1">Initial_Segm</a> of <font color="Maroon" title="c4">fC2</font> iff <font color="Maroon" title="c4">fC2</font> is  not    <a href="orders_2.html#M1" title="ORDERS_2:mode.1">Initial_Segm</a> of <font color="Maroon" title="c3">fC1</font> )
 <b>by </b><i><a class="ref" href="orders_2.html#T69" target="_self" title="ORDERS_2:th.69">Th69</a></i>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> verum</span><br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="67_5_1_3"><b>suppose </b></a><a NAME="E1:67_5_1_3"/>
( <font color="Maroon" title="c6">N</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c3">fC1</font> &amp; <font color="Maroon" title="c6">N</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c4">fC2</font> )
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> ( <font color="Maroon" title="c3">fC1</font> is    <a href="orders_2.html#M1" title="ORDERS_2:mode.1">Initial_Segm</a> of <font color="Maroon" title="c4">fC2</font> iff <font color="Maroon" title="c4">fC2</font> is  not    <a href="orders_2.html#M1" title="ORDERS_2:mode.1">Initial_Segm</a> of <font color="Maroon" title="c3">fC1</font> )</span><br/><div class="add"><b>hence </b><a NAME="E2:67_5_1_3"/>
( <font color="Maroon" title="c3">fC1</font> is    <a href="orders_2.html#M1" title="ORDERS_2:mode.1">Initial_Segm</a> of <font color="Maroon" title="c4">fC2</font> iff <font color="Maroon" title="c4">fC2</font> is  not    <a href="orders_2.html#M1" title="ORDERS_2:mode.1">Initial_Segm</a> of <font color="Maroon" title="c3">fC1</font> )
 <b>by </b><i><a class="txt" href="#E1:67"><i><font color="Green" title="E41">A1</font></i></a></i>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> verum</span><br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="67_5_1_4"><b>suppose </b></a><a NAME="E1:67_5_1_4"/><i><font color="Green" title="E48">A26</font></i>: 
( <font color="Maroon" title="c6">N</font> is    <a href="orders_2.html#M1" title="ORDERS_2:mode.1">Initial_Segm</a> of <font color="Maroon" title="c3">fC1</font> &amp; <font color="Maroon" title="c6">N</font> is    <a href="orders_2.html#M1" title="ORDERS_2:mode.1">Initial_Segm</a> of <font color="Maroon" title="c4">fC2</font> )
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> ( <font color="Maroon" title="c3">fC1</font> is    <a href="orders_2.html#M1" title="ORDERS_2:mode.1">Initial_Segm</a> of <font color="Maroon" title="c4">fC2</font> iff <font color="Maroon" title="c4">fC2</font> is  not    <a href="orders_2.html#M1" title="ORDERS_2:mode.1">Initial_Segm</a> of <font color="Maroon" title="c3">fC1</font> )</span><br/><div class="add"><a NAME="E2:67_5_1_4"/>
<font color="Maroon" title="c3">fC1</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a>  <a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a> 
 <b>by </b><i><a class="ref" href="orders_2.html#D16" target="_self" title="ORDERS_2:def.16">Def16</a></i>;<br/><b>then consider </b><font color="Maroon" title="c7">a</font> being   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Maroon" title="c1">A</font><b> such that </b><br/><a NAME="E4:67_5_1_4"/><i><font color="Green" title="E49">A27</font></i>: 
<font color="Maroon" title="c7">a</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c3">fC1</font>
 <b>and </b><br/><a NAME="E5:67_5_1_4"/><i><font color="Green" title="E50">A28</font></i>: 
<font color="Maroon" title="c6">N</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="orders_2.html#K3" title="ORDERS_2:func.3">InitSegm</a> <font color="Maroon" title="c3">fC1</font>,<font color="Maroon" title="c7">a</font>
 <b>by </b><i><a class="txt" href="#E1:67_5_1_4"><i><font color="Green" title="E48">A26</font></i></a>, <a class="ref" href="orders_2.html#D15" target="_self" title="ORDERS_2:def.15">Def15</a></i>;<br/><a NAME="E6:67_5_1_4"/>
<font color="Maroon" title="c4">fC2</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a>  <a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a> 
 <b>by </b><i><a class="ref" href="orders_2.html#D16" target="_self" title="ORDERS_2:def.16">Def16</a></i>;<br/><b>then consider </b><font color="Maroon" title="c8">b</font> being   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Maroon" title="c1">A</font><b> such that </b><br/><a NAME="E8:67_5_1_4"/><i><font color="Green" title="E51">A29</font></i>: 
<font color="Maroon" title="c8">b</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c4">fC2</font>
 <b>and </b><br/><a NAME="E9:67_5_1_4"/><i><font color="Green" title="E52">A30</font></i>: 
<font color="Maroon" title="c6">N</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="orders_2.html#K3" title="ORDERS_2:func.3">InitSegm</a> <font color="Maroon" title="c4">fC2</font>,<font color="Maroon" title="c8">b</font>
 <b>by </b><i><a class="txt" href="#E1:67_5_1_4"><i><font color="Green" title="E48">A26</font></i></a>, <a class="ref" href="orders_2.html#D15" target="_self" title="ORDERS_2:def.15">Def15</a></i>;<br/><i><font color="Green" title="E53">A31</font></i>: <font color="Maroon" title="c7">a</font> = 
<font color="Maroon" title="c2">f</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p1">(<span class="default"><a href="orders_2.html#K1" title="ORDERS_2:func.1">UpperCone</a> <span class="p2">(<span class="default"><a href="orders_2.html#K3" title="ORDERS_2:func.3">InitSegm</a> <font color="Maroon" title="c4">fC2</font>,<font color="Maroon" title="c8">b</font></span>)</span></span>)</span>
<b>by </b><i><a class="txt" href="#E4:67_5_1_4"><i><font color="Green" title="E49">A27</font></i></a>, <a class="txt" href="#E5:67_5_1_4"><i><font color="Green" title="E50">A28</font></i></a>, <a class="txt" href="#E9:67_5_1_4"><i><font color="Green" title="E52">A30</font></i></a>, <a class="ref" href="orders_2.html#D16" target="_self" title="ORDERS_2:def.16">Def16</a></i>
<br/>.= 
<font color="Maroon" title="c8">b</font>
<b>by </b><i><a class="txt" href="#E8:67_5_1_4"><i><font color="Green" title="E51">A29</font></i></a>, <a class="ref" href="orders_2.html#D16" target="_self" title="ORDERS_2:def.16">Def16</a></i>
;<br/><a NAME="E11:67_5_1_4"/><b>then </b>
<font color="Maroon" title="c7">a</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c3">fC1</font> <a href="subset_1.html#K9" title="SUBSET_1:func.9">/\</a> <font color="Maroon" title="c4">fC2</font>
 <b>by </b><i><a class="txt" href="#E4:67_5_1_4"><i><font color="Green" title="E49">A27</font></i></a>, <a class="txt" href="#E8:67_5_1_4"><i><font color="Green" title="E51">A29</font></i></a>, <a class="ref" href="xboole_0.html#D4" title="XBOOLE_0:def.4">XBOOLE_0:def 4</a></i>;<br/><a NAME="E12:67_5_1_4"/><b>then </b>
<font color="Maroon" title="c7">a</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c6">N</font>
 <b>by </b><i><a class="txt" href="#E5:67_5_1_4"><i><font color="Green" title="E50">A28</font></i></a>, <a class="txt" href="#E9:67_5_1_4"><i><font color="Green" title="E52">A30</font></i></a>, <a class="txt" href="#E10:67_5_1_4"><i><font color="Green" title="E53">A31</font></i></a></i>;<br/><b>hence </b><a NAME="E13:67_5_1_4"/>
( <font color="Maroon" title="c3">fC1</font> is    <a href="orders_2.html#M1" title="ORDERS_2:mode.1">Initial_Segm</a> of <font color="Maroon" title="c4">fC2</font> iff <font color="Maroon" title="c4">fC2</font> is  not    <a href="orders_2.html#M1" title="ORDERS_2:mode.1">Initial_Segm</a> of <font color="Maroon" title="c3">fC1</font> )
 <b>by </b><i><a class="txt" href="#E5:67_5_1_4"><i><font color="Green" title="E50">A28</font></i></a>, <a class="ref" href="orders_2.html#T62" target="_self" title="ORDERS_2:th.62">Th62</a></i>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> verum</span><br/></div><b>end;</b></div></div><b>end;</b></div></div><b>end;</b></div>
<b>hence </b><a NAME="E10:67"/>
( <font color="Maroon" title="c3">fC1</font> is    <a href="orders_2.html#M1" title="ORDERS_2:mode.1">Initial_Segm</a> of <font color="Maroon" title="c4">fC2</font> iff <font color="Maroon" title="c4">fC2</font> is  not    <a href="orders_2.html#M1" title="ORDERS_2:mode.1">Initial_Segm</a> of <font color="Maroon" title="c3">fC1</font> )
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> verum</span><br/>


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