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

<b>set </b><font color="Maroon">U1</font> = <span class="p1">(<span class="default"><a href="tarski.html#K3">union</a> <span class="p2"><a href="tarski.html#K1">{</a><span class="default"><a href="numbers.html#K4">INT</a> </span><a href="tarski.html#K1">}</a></span></span>)</span> <a href="xboole_0.html#K2">\/</a> <a href="numbers.html#K5">NAT</a> ;<br/>
<b>set </b><font color="Maroon">UU</font> = <span class="p1"><a href="zfmisc_1.html#K2">[:</a><span class="default"><span class="p2">(<span class="default"><a href="gr_cy_1.html#K1">Segm</a> 14</span>)</span>,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="tarski.html#K3">union</a> <span class="p5"><a href="tarski.html#K1">{</a><span class="default"><a href="numbers.html#K4">INT</a> </span><a href="tarski.html#K1">}</a></span></span>)</span> <a href="xboole_0.html#K2">\/</a> <a href="numbers.html#K5">NAT</a> </span>)</span> <a href="finseq_1.html#K13">*</a> </span>)</span></span><a href="zfmisc_1.html#K2">:]</a></span>;<br/>
<a NAME="E1:4_1_1"/><i><font color="Green">E46</font></i>: 
 <a href="numbers.html#K5">NAT</a>  <a href="tarski.html#R1">c=</a> <span class="p1">(<span class="default"><a href="tarski.html#K3">union</a> <span class="p2"><a href="tarski.html#K1">{</a><span class="default"><a href="numbers.html#K4">INT</a> </span><a href="tarski.html#K1">}</a></span></span>)</span> <a href="xboole_0.html#K2">\/</a> <a href="numbers.html#K5">NAT</a> 
 
<b>by </b><i><a class="ref" href="xboole_1.html#T7">XBOOLE_1:7</a></i>;<br/>
<a NAME="E2:4_1_1"/><i><font color="Green">E60</font></i>: 
<span class="p1">{<span class="default"> <span class="p2"><a href="tarski.html#K4">[</a><span class="default"><font color="Olive">I1</font>,<span class="p3"><a href="finseq_4.html#K8">&lt;*</a><span class="default"><font color="Olive">d1</font>,<font color="Olive">d2</font>,<font color="Olive">k1</font>,<font color="Olive">k2</font></span><a href="finseq_4.html#K8">*&gt;</a></span></span><a href="tarski.html#K4">]</a></span> where <font color="Olive">I1</font> is    <a href="subset_1.html#M2">Element</a> of  <a href="gr_cy_1.html#K1">Segm</a> 14, <font color="Olive">d1</font> is    <a href="subset_1.html#M2">Element</a> of  <a href="ami_2.html#K2">SCM-Data-Loc</a> , <font color="Olive">d2</font> is    <a href="subset_1.html#M2">Element</a> of  <a href="ami_2.html#K2">SCM-Data-Loc</a> , <font color="Olive">k1</font> is    <a href="subset_1.html#M1">Element</a> of  <a href="numbers.html#K4">INT</a> , <font color="Olive">k2</font> is    <a href="subset_1.html#M1">Element</a> of  <a href="numbers.html#K4">INT</a>  : <font color="Olive">I1</font> <a href="hidden.html#R2">in</a> <span class="p1"><a href="enumset1.html#K3">{</a><span class="default">9,10,11,12,13</span><a href="enumset1.html#K3">}</a></span> </span>}</span>  <a href="tarski.html#R1">c=</a> <span class="p1"><a href="zfmisc_1.html#K2">[:</a><span class="default"><span class="p2">(<span class="default"><a href="gr_cy_1.html#K1">Segm</a> 14</span>)</span>,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="tarski.html#K3">union</a> <span class="p5"><a href="tarski.html#K1">{</a><span class="default"><a href="numbers.html#K4">INT</a> </span><a href="tarski.html#K1">}</a></span></span>)</span> <a href="xboole_0.html#K2">\/</a> <a href="numbers.html#K5">NAT</a> </span>)</span> <a href="finseq_1.html#K13">*</a> </span>)</span></span><a href="zfmisc_1.html#K2">:]</a></span>
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="4_1_1_1"><b>proof </b></a><div class="add">

<b>let </b><font color="Maroon">x</font> be    <a href="hidden.html#M1">set</a> ; <i><font color="Red">:: according to </font></i><a class="ref" href="tarski.html#D3">TARSKI:def 3</a><br/>

<b>assume </b><a NAME="E1:4_1_1_1"/>
<font color="Maroon">x</font> <a href="hidden.html#R2">in</a> <span class="p1">{<span class="default"> <span class="p2"><a href="tarski.html#K4">[</a><span class="default"><font color="Olive">I1</font>,<span class="p3"><a href="finseq_4.html#K8">&lt;*</a><span class="default"><font color="Olive">d1</font>,<font color="Olive">d2</font>,<font color="Olive">k1</font>,<font color="Olive">k2</font></span><a href="finseq_4.html#K8">*&gt;</a></span></span><a href="tarski.html#K4">]</a></span> where <font color="Olive">I1</font> is    <a href="subset_1.html#M2">Element</a> of  <a href="gr_cy_1.html#K1">Segm</a> 14, <font color="Olive">d1</font> is    <a href="subset_1.html#M2">Element</a> of  <a href="ami_2.html#K2">SCM-Data-Loc</a> , <font color="Olive">d2</font> is    <a href="subset_1.html#M2">Element</a> of  <a href="ami_2.html#K2">SCM-Data-Loc</a> , <font color="Olive">k1</font> is    <a href="subset_1.html#M1">Element</a> of  <a href="numbers.html#K4">INT</a> , <font color="Olive">k2</font> is    <a href="subset_1.html#M1">Element</a> of  <a href="numbers.html#K4">INT</a>  : <font color="Olive">I1</font> <a href="hidden.html#R2">in</a> <span class="p1"><a href="enumset1.html#K3">{</a><span class="default">9,10,11,12,13</span><a href="enumset1.html#K3">}</a></span> </span>}</span> 
 ;<br/>

<b>then consider </b><font color="Maroon">I1</font> being    <a href="subset_1.html#M2">Element</a> of  <a href="gr_cy_1.html#K1">Segm</a> 14, <font color="Maroon">d1</font> being    <a href="subset_1.html#M2">Element</a> of  <a href="ami_2.html#K2">SCM-Data-Loc</a> , <font color="Maroon">d2</font> being    <a href="subset_1.html#M2">Element</a> of  <a href="ami_2.html#K2">SCM-Data-Loc</a> , <font color="Maroon">k1</font> being    <a href="subset_1.html#M1">Element</a> of  <a href="numbers.html#K4">INT</a> , <font color="Maroon">k2</font> being    <a href="subset_1.html#M1">Element</a> of  <a href="numbers.html#K4">INT</a> <b> such that </b><br/><a NAME="E3:4_1_1_1"/><i><font color="Green">E63</font></i>: 
<font color="Maroon">x</font> <a href="hidden.html#R1">=</a> <span class="p1"><a href="tarski.html#K4">[</a><span class="default"><font color="Maroon">I1</font>,<span class="p2"><a href="finseq_4.html#K8">&lt;*</a><span class="default"><font color="Maroon">d1</font>,<font color="Maroon">d2</font>,<font color="Maroon">k1</font>,<font color="Maroon">k2</font></span><a href="finseq_4.html#K8">*&gt;</a></span></span><a href="tarski.html#K4">]</a></span>
 <b>and </b><br/><a NAME="E4:4_1_1_1"/>
<font color="Maroon">I1</font> <a href="hidden.html#R2">in</a> <span class="p1"><a href="enumset1.html#K3">{</a><span class="default">9,10,11,12,13</span><a href="enumset1.html#K3">}</a></span>
 ;<br/>
<b>reconsider </b><font color="Maroon">d1</font> = <font color="Maroon">d1</font>, <font color="Maroon">d2</font> = <font color="Maroon">d2</font> as    <a href="subset_1.html#M1">Element</a> of <span class="p1">(<span class="default"><a href="tarski.html#K3">union</a> <span class="p2"><a href="tarski.html#K1">{</a><span class="default"><a href="numbers.html#K4">INT</a> </span><a href="tarski.html#K1">}</a></span></span>)</span> <a href="xboole_0.html#K2">\/</a> <a href="numbers.html#K5">NAT</a>  <b>by </b><i>, <a class="ref" href="tarski.html#D3">TARSKI:def 3</a></i>;<br/>
<b>reconsider </b><font color="Maroon">k1</font> = <font color="Maroon">k1</font>, <font color="Maroon">k2</font> = <font color="Maroon">k2</font> as    <a href="subset_1.html#M1">Element</a> of <span class="p1">(<span class="default"><a href="tarski.html#K3">union</a> <span class="p2"><a href="tarski.html#K1">{</a><span class="default"><a href="numbers.html#K4">INT</a> </span><a href="tarski.html#K1">}</a></span></span>)</span> <a href="xboole_0.html#K2">\/</a> <a href="numbers.html#K5">NAT</a>  <b>by </b><i/>;<br/>
<a NAME="E7:4_1_1_1"/>
<span class="p1"><a href="finseq_4.html#K10">&lt;*</a><span class="default"><font color="Maroon">d1</font>,<font color="Maroon">d2</font>,<font color="Maroon">k1</font>,<font color="Maroon">k2</font></span><a href="finseq_4.html#K10">*&gt;</a></span> <a href="hidden.html#R2">in</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="tarski.html#K3">union</a> <span class="p3"><a href="tarski.html#K1">{</a><span class="default"><a href="numbers.html#K4">INT</a> </span><a href="tarski.html#K1">}</a></span></span>)</span> <a href="xboole_0.html#K2">\/</a> <a href="numbers.html#K5">NAT</a> </span>)</span> <a href="finseq_1.html#K13">*</a> 
 
<b>by </b><i><a class="ref" href="finseq_1.html#D11">FINSEQ_1:def 11</a></i>;<br/>
<b>hence </b><a NAME="E8:4_1_1_1"/>
<font color="Maroon">x</font> <a href="hidden.html#R2">in</a> <span class="p1"><a href="zfmisc_1.html#K2">[:</a><span class="default"><span class="p2">(<span class="default"><a href="gr_cy_1.html#K1">Segm</a> 14</span>)</span>,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="tarski.html#K3">union</a> <span class="p5"><a href="tarski.html#K1">{</a><span class="default"><a href="numbers.html#K4">INT</a> </span><a href="tarski.html#K1">}</a></span></span>)</span> <a href="xboole_0.html#K2">\/</a> <a href="numbers.html#K5">NAT</a> </span>)</span> <a href="finseq_1.html#K13">*</a> </span>)</span></span><a href="zfmisc_1.html#K2">:]</a></span>
 <b>by </b><i>, <a class="ref" href="zfmisc_1.html#T106">ZFMISC_1:106</a></i>;<br/>


</div><b>end;</b></div>
<a NAME="E3:4_1_1"/><i><font color="Green">E64</font></i>: 
<span class="p1">{<span class="default"> <span class="p2"><a href="tarski.html#K4">[</a><span class="default"><font color="Olive">I2</font>,<span class="p3"><a href="finseq_1.html#K11">&lt;*</a><span class="default"><font color="Olive">d3</font>,<font color="Olive">k3</font>,<font color="Olive">k4</font></span><a href="finseq_1.html#K11">*&gt;</a></span></span><a href="tarski.html#K4">]</a></span> where <font color="Olive">I2</font> is    <a href="subset_1.html#M2">Element</a> of  <a href="gr_cy_1.html#K1">Segm</a> 14, <font color="Olive">d3</font> is    <a href="subset_1.html#M2">Element</a> of  <a href="ami_2.html#K2">SCM-Data-Loc</a> , <font color="Olive">k3</font> is    <a href="subset_1.html#M1">Element</a> of  <a href="numbers.html#K4">INT</a> , <font color="Olive">k4</font> is    <a href="subset_1.html#M1">Element</a> of  <a href="numbers.html#K4">INT</a>  : <font color="Olive">I2</font> <a href="hidden.html#R2">in</a> <span class="p1"><a href="enumset1.html#K3">{</a><span class="default">4,5,6,7,8</span><a href="enumset1.html#K3">}</a></span> </span>}</span>  <a href="tarski.html#R1">c=</a> <span class="p1"><a href="zfmisc_1.html#K2">[:</a><span class="default"><span class="p2">(<span class="default"><a href="gr_cy_1.html#K1">Segm</a> 14</span>)</span>,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="tarski.html#K3">union</a> <span class="p5"><a href="tarski.html#K1">{</a><span class="default"><a href="numbers.html#K4">INT</a> </span><a href="tarski.html#K1">}</a></span></span>)</span> <a href="xboole_0.html#K2">\/</a> <a href="numbers.html#K5">NAT</a> </span>)</span> <a href="finseq_1.html#K13">*</a> </span>)</span></span><a href="zfmisc_1.html#K2">:]</a></span>
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="4_1_1_2"><b>proof </b></a><div class="add">

<b>let </b><font color="Maroon">x</font> be    <a href="hidden.html#M1">set</a> ; <i><font color="Red">:: according to </font></i><a class="ref" href="tarski.html#D3">TARSKI:def 3</a><br/>

<b>assume </b><a NAME="E1:4_1_1_2"/>
<font color="Maroon">x</font> <a href="hidden.html#R2">in</a> <span class="p1">{<span class="default"> <span class="p2"><a href="tarski.html#K4">[</a><span class="default"><font color="Olive">I2</font>,<span class="p3"><a href="finseq_1.html#K11">&lt;*</a><span class="default"><font color="Olive">d3</font>,<font color="Olive">k3</font>,<font color="Olive">k4</font></span><a href="finseq_1.html#K11">*&gt;</a></span></span><a href="tarski.html#K4">]</a></span> where <font color="Olive">I2</font> is    <a href="subset_1.html#M2">Element</a> of  <a href="gr_cy_1.html#K1">Segm</a> 14, <font color="Olive">d3</font> is    <a href="subset_1.html#M2">Element</a> of  <a href="ami_2.html#K2">SCM-Data-Loc</a> , <font color="Olive">k3</font> is    <a href="subset_1.html#M1">Element</a> of  <a href="numbers.html#K4">INT</a> , <font color="Olive">k4</font> is    <a href="subset_1.html#M1">Element</a> of  <a href="numbers.html#K4">INT</a>  : <font color="Olive">I2</font> <a href="hidden.html#R2">in</a> <span class="p1"><a href="enumset1.html#K3">{</a><span class="default">4,5,6,7,8</span><a href="enumset1.html#K3">}</a></span> </span>}</span> 
 ;<br/>

<b>then consider </b><font color="Maroon">I2</font> being    <a href="subset_1.html#M2">Element</a> of  <a href="gr_cy_1.html#K1">Segm</a> 14, <font color="Maroon">d3</font> being    <a href="subset_1.html#M2">Element</a> of  <a href="ami_2.html#K2">SCM-Data-Loc</a> , <font color="Maroon">k3</font> being    <a href="subset_1.html#M1">Element</a> of  <a href="numbers.html#K4">INT</a> , <font color="Maroon">k4</font> being    <a href="subset_1.html#M1">Element</a> of  <a href="numbers.html#K4">INT</a> <b> such that </b><br/><a NAME="E3:4_1_1_2"/><i><font color="Green">E67</font></i>: 
<font color="Maroon">x</font> <a href="hidden.html#R1">=</a> <span class="p1"><a href="tarski.html#K4">[</a><span class="default"><font color="Maroon">I2</font>,<span class="p2"><a href="finseq_1.html#K11">&lt;*</a><span class="default"><font color="Maroon">d3</font>,<font color="Maroon">k3</font>,<font color="Maroon">k4</font></span><a href="finseq_1.html#K11">*&gt;</a></span></span><a href="tarski.html#K4">]</a></span>
 <b>and </b><br/><a NAME="E4:4_1_1_2"/>
<font color="Maroon">I2</font> <a href="hidden.html#R2">in</a> <span class="p1"><a href="enumset1.html#K3">{</a><span class="default">4,5,6,7,8</span><a href="enumset1.html#K3">}</a></span>
 ;<br/>
<b>reconsider </b><font color="Maroon">d3</font> = <font color="Maroon">d3</font> as    <a href="subset_1.html#M1">Element</a> of <span class="p1">(<span class="default"><a href="tarski.html#K3">union</a> <span class="p2"><a href="tarski.html#K1">{</a><span class="default"><a href="numbers.html#K4">INT</a> </span><a href="tarski.html#K1">}</a></span></span>)</span> <a href="xboole_0.html#K2">\/</a> <a href="numbers.html#K5">NAT</a>  <b>by </b><i>, <a class="ref" href="tarski.html#D3">TARSKI:def 3</a></i>;<br/>
<b>reconsider </b><font color="Maroon">k3</font> = <font color="Maroon">k3</font>, <font color="Maroon">k4</font> = <font color="Maroon">k4</font> as    <a href="subset_1.html#M1">Element</a> of <span class="p1">(<span class="default"><a href="tarski.html#K3">union</a> <span class="p2"><a href="tarski.html#K1">{</a><span class="default"><a href="numbers.html#K4">INT</a> </span><a href="tarski.html#K1">}</a></span></span>)</span> <a href="xboole_0.html#K2">\/</a> <a href="numbers.html#K5">NAT</a>  <b>by </b><i/>;<br/>
<a NAME="E7:4_1_1_2"/>
<span class="p1"><a href="finseq_4.html#K3">&lt;*</a><span class="default"><font color="Maroon">d3</font>,<font color="Maroon">k3</font>,<font color="Maroon">k4</font></span><a href="finseq_4.html#K3">*&gt;</a></span> <a href="hidden.html#R2">in</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="tarski.html#K3">union</a> <span class="p3"><a href="tarski.html#K1">{</a><span class="default"><a href="numbers.html#K4">INT</a> </span><a href="tarski.html#K1">}</a></span></span>)</span> <a href="xboole_0.html#K2">\/</a> <a href="numbers.html#K5">NAT</a> </span>)</span> <a href="finseq_1.html#K13">*</a> 
 
<b>by </b><i><a class="ref" href="finseq_1.html#D11">FINSEQ_1:def 11</a></i>;<br/>
<b>hence </b><a NAME="E8:4_1_1_2"/>
<font color="Maroon">x</font> <a href="hidden.html#R2">in</a> <span class="p1"><a href="zfmisc_1.html#K2">[:</a><span class="default"><span class="p2">(<span class="default"><a href="gr_cy_1.html#K1">Segm</a> 14</span>)</span>,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="tarski.html#K3">union</a> <span class="p5"><a href="tarski.html#K1">{</a><span class="default"><a href="numbers.html#K4">INT</a> </span><a href="tarski.html#K1">}</a></span></span>)</span> <a href="xboole_0.html#K2">\/</a> <a href="numbers.html#K5">NAT</a> </span>)</span> <a href="finseq_1.html#K13">*</a> </span>)</span></span><a href="zfmisc_1.html#K2">:]</a></span>
 <b>by </b><i>, <a class="ref" href="zfmisc_1.html#T106">ZFMISC_1:106</a></i>;<br/>


</div><b>end;</b></div>
<a NAME="E4:4_1_1"/><i><font color="Green">E68</font></i>: 
<span class="p1">{<span class="default"> <span class="p2"><a href="tarski.html#K4">[</a><span class="default">0,<span class="p3"><a href="finseq_1.html#K12">&lt;*</a><span class="default"><font color="Olive">k5</font></span><a href="finseq_1.html#K12">*&gt;</a></span></span><a href="tarski.html#K4">]</a></span> where <font color="Olive">k5</font> is    <a href="subset_1.html#M1">Element</a> of  <a href="numbers.html#K4">INT</a>  : verum </span>}</span>  <a href="tarski.html#R1">c=</a> <span class="p1"><a href="zfmisc_1.html#K2">[:</a><span class="default"><span class="p2">(<span class="default"><a href="gr_cy_1.html#K1">Segm</a> 14</span>)</span>,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="tarski.html#K3">union</a> <span class="p5"><a href="tarski.html#K1">{</a><span class="default"><a href="numbers.html#K4">INT</a> </span><a href="tarski.html#K1">}</a></span></span>)</span> <a href="xboole_0.html#K2">\/</a> <a href="numbers.html#K5">NAT</a> </span>)</span> <a href="finseq_1.html#K13">*</a> </span>)</span></span><a href="zfmisc_1.html#K2">:]</a></span>
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="4_1_1_3"><b>proof </b></a><div class="add">

<b>let </b><font color="Maroon">x</font> be    <a href="hidden.html#M1">set</a> ; <i><font color="Red">:: according to </font></i><a class="ref" href="tarski.html#D3">TARSKI:def 3</a><br/>

<b>assume </b><a NAME="E1:4_1_1_3"/>
<font color="Maroon">x</font> <a href="hidden.html#R2">in</a> <span class="p1">{<span class="default"> <span class="p2"><a href="tarski.html#K4">[</a><span class="default">0,<span class="p3"><a href="finseq_1.html#K12">&lt;*</a><span class="default"><font color="Olive">k5</font></span><a href="finseq_1.html#K12">*&gt;</a></span></span><a href="tarski.html#K4">]</a></span> where <font color="Olive">k5</font> is    <a href="subset_1.html#M1">Element</a> of  <a href="numbers.html#K4">INT</a>  : verum </span>}</span> 
 ;<br/>

<b>then consider </b><font color="Maroon">k5</font> being    <a href="subset_1.html#M1">Element</a> of  <a href="numbers.html#K4">INT</a> <b> such that </b><br/><a NAME="E3:4_1_1_3"/><i><font color="Green">E70</font></i>: 
<font color="Maroon">x</font> <a href="hidden.html#R1">=</a> <span class="p1"><a href="tarski.html#K4">[</a><span class="default">0,<span class="p2"><a href="finseq_1.html#K12">&lt;*</a><span class="default"><font color="Maroon">k5</font></span><a href="finseq_1.html#K12">*&gt;</a></span></span><a href="tarski.html#K4">]</a></span>
 <b>and </b><br/><a NAME="E4:4_1_1_3"/>
verum
 ;<br/>
<b>reconsider </b><font color="Maroon">k5</font> = <font color="Maroon">k5</font> as    <a href="subset_1.html#M1">Element</a> of <span class="p1">(<span class="default"><a href="tarski.html#K3">union</a> <span class="p2"><a href="tarski.html#K1">{</a><span class="default"><a href="numbers.html#K4">INT</a> </span><a href="tarski.html#K1">}</a></span></span>)</span> <a href="xboole_0.html#K2">\/</a> <a href="numbers.html#K5">NAT</a>  <b>by </b><i/>;<br/>
<a NAME="E6:4_1_1_3"/><i><font color="Green">E71</font></i>: 
0 <a href="hidden.html#R2">in</a>  <a href="gr_cy_1.html#K1">Segm</a> 14
 
<b>by </b><i><a class="ref" href="gr_cy_1.html#T10">GR_CY_1:10</a></i>;<br/>
<a NAME="E7:4_1_1_3"/>
<span class="p1"><a href="finseq_1.html#K12">&lt;*</a><span class="default"><font color="Maroon">k5</font></span><a href="finseq_1.html#K12">*&gt;</a></span> <a href="hidden.html#R2">in</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="tarski.html#K3">union</a> <span class="p3"><a href="tarski.html#K1">{</a><span class="default"><a href="numbers.html#K4">INT</a> </span><a href="tarski.html#K1">}</a></span></span>)</span> <a href="xboole_0.html#K2">\/</a> <a href="numbers.html#K5">NAT</a> </span>)</span> <a href="finseq_1.html#K13">*</a> 
 
<b>by </b><i><a class="ref" href="finseq_1.html#D11">FINSEQ_1:def 11</a></i>;<br/>
<b>hence </b><a NAME="E8:4_1_1_3"/>
<font color="Maroon">x</font> <a href="hidden.html#R2">in</a> <span class="p1"><a href="zfmisc_1.html#K2">[:</a><span class="default"><span class="p2">(<span class="default"><a href="gr_cy_1.html#K1">Segm</a> 14</span>)</span>,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="tarski.html#K3">union</a> <span class="p5"><a href="tarski.html#K1">{</a><span class="default"><a href="numbers.html#K4">INT</a> </span><a href="tarski.html#K1">}</a></span></span>)</span> <a href="xboole_0.html#K2">\/</a> <a href="numbers.html#K5">NAT</a> </span>)</span> <a href="finseq_1.html#K13">*</a> </span>)</span></span><a href="zfmisc_1.html#K2">:]</a></span>
 <b>by </b><i>, , <a class="ref" href="zfmisc_1.html#T106">ZFMISC_1:106</a></i>;<br/>


</div><b>end;</b></div>
<a NAME="E5:4_1_1"/><i><font color="Green">E72</font></i>: 
<span class="p1">{<span class="default"> <span class="p2"><a href="tarski.html#K4">[</a><span class="default">1,<span class="p3"><a href="finseq_1.html#K12">&lt;*</a><span class="default"><font color="Olive">d4</font></span><a href="finseq_1.html#K12">*&gt;</a></span></span><a href="tarski.html#K4">]</a></span> where <font color="Olive">d4</font> is    <a href="subset_1.html#M2">Element</a> of  <a href="ami_2.html#K2">SCM-Data-Loc</a>  : verum </span>}</span>  <a href="tarski.html#R1">c=</a> <span class="p1"><a href="zfmisc_1.html#K2">[:</a><span class="default"><span class="p2">(<span class="default"><a href="gr_cy_1.html#K1">Segm</a> 14</span>)</span>,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="tarski.html#K3">union</a> <span class="p5"><a href="tarski.html#K1">{</a><span class="default"><a href="numbers.html#K4">INT</a> </span><a href="tarski.html#K1">}</a></span></span>)</span> <a href="xboole_0.html#K2">\/</a> <a href="numbers.html#K5">NAT</a> </span>)</span> <a href="finseq_1.html#K13">*</a> </span>)</span></span><a href="zfmisc_1.html#K2">:]</a></span>
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="4_1_1_4"><b>proof </b></a><div class="add">

<b>let </b><font color="Maroon">x</font> be    <a href="hidden.html#M1">set</a> ; <i><font color="Red">:: according to </font></i><a class="ref" href="tarski.html#D3">TARSKI:def 3</a><br/>

<b>assume </b><a NAME="E1:4_1_1_4"/>
<font color="Maroon">x</font> <a href="hidden.html#R2">in</a> <span class="p1">{<span class="default"> <span class="p2"><a href="tarski.html#K4">[</a><span class="default">1,<span class="p3"><a href="finseq_1.html#K12">&lt;*</a><span class="default"><font color="Olive">d4</font></span><a href="finseq_1.html#K12">*&gt;</a></span></span><a href="tarski.html#K4">]</a></span> where <font color="Olive">d4</font> is    <a href="subset_1.html#M2">Element</a> of  <a href="ami_2.html#K2">SCM-Data-Loc</a>  : verum </span>}</span> 
 ;<br/>

<b>then consider </b><font color="Maroon">d4</font> being    <a href="subset_1.html#M2">Element</a> of  <a href="ami_2.html#K2">SCM-Data-Loc</a> <b> such that </b><br/><a NAME="E3:4_1_1_4"/><i><font color="Green">E73</font></i>: 
<font color="Maroon">x</font> <a href="hidden.html#R1">=</a> <span class="p1"><a href="tarski.html#K4">[</a><span class="default">1,<span class="p2"><a href="finseq_1.html#K12">&lt;*</a><span class="default"><font color="Maroon">d4</font></span><a href="finseq_1.html#K12">*&gt;</a></span></span><a href="tarski.html#K4">]</a></span>
 <b>and </b><br/><a NAME="E4:4_1_1_4"/>
verum
 ;<br/>
<b>reconsider </b><font color="Maroon">d4</font> = <font color="Maroon">d4</font> as    <a href="subset_1.html#M1">Element</a> of <span class="p1">(<span class="default"><a href="tarski.html#K3">union</a> <span class="p2"><a href="tarski.html#K1">{</a><span class="default"><a href="numbers.html#K4">INT</a> </span><a href="tarski.html#K1">}</a></span></span>)</span> <a href="xboole_0.html#K2">\/</a> <a href="numbers.html#K5">NAT</a>  <b>by </b><i>, <a class="ref" href="tarski.html#D3">TARSKI:def 3</a></i>;<br/>
<a NAME="E6:4_1_1_4"/><i><font color="Green">E74</font></i>: 
1 <a href="hidden.html#R2">in</a>  <a href="gr_cy_1.html#K1">Segm</a> 14
 
<b>by </b><i><a class="ref" href="gr_cy_1.html#T10">GR_CY_1:10</a></i>;<br/>
<a NAME="E7:4_1_1_4"/>
<span class="p1"><a href="finseq_1.html#K12">&lt;*</a><span class="default"><font color="Maroon">d4</font></span><a href="finseq_1.html#K12">*&gt;</a></span> <a href="hidden.html#R2">in</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="tarski.html#K3">union</a> <span class="p3"><a href="tarski.html#K1">{</a><span class="default"><a href="numbers.html#K4">INT</a> </span><a href="tarski.html#K1">}</a></span></span>)</span> <a href="xboole_0.html#K2">\/</a> <a href="numbers.html#K5">NAT</a> </span>)</span> <a href="finseq_1.html#K13">*</a> 
 
<b>by </b><i><a class="ref" href="finseq_1.html#D11">FINSEQ_1:def 11</a></i>;<br/>
<b>hence </b><a NAME="E8:4_1_1_4"/>
<font color="Maroon">x</font> <a href="hidden.html#R2">in</a> <span class="p1"><a href="zfmisc_1.html#K2">[:</a><span class="default"><span class="p2">(<span class="default"><a href="gr_cy_1.html#K1">Segm</a> 14</span>)</span>,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="tarski.html#K3">union</a> <span class="p5"><a href="tarski.html#K1">{</a><span class="default"><a href="numbers.html#K4">INT</a> </span><a href="tarski.html#K1">}</a></span></span>)</span> <a href="xboole_0.html#K2">\/</a> <a href="numbers.html#K5">NAT</a> </span>)</span> <a href="finseq_1.html#K13">*</a> </span>)</span></span><a href="zfmisc_1.html#K2">:]</a></span>
 <b>by </b><i>, , <a class="ref" href="zfmisc_1.html#T106">ZFMISC_1:106</a></i>;<br/>


</div><b>end;</b></div>
<a NAME="E6:4_1_1"/><i><font color="Green">E75</font></i>: 
<span class="p1">{<span class="default"> <span class="p2"><a href="tarski.html#K4">[</a><span class="default"><font color="Olive">I4</font>,<span class="p3"><a href="finseq_1.html#K10">&lt;*</a><span class="default"><font color="Olive">d5</font>,<font color="Olive">r</font></span><a href="finseq_1.html#K10">*&gt;</a></span></span><a href="tarski.html#K4">]</a></span> where <font color="Olive">I4</font> is    <a href="subset_1.html#M2">Element</a> of  <a href="gr_cy_1.html#K1">Segm</a> 14, <font color="Olive">d5</font> is    <a href="subset_1.html#M2">Element</a> of  <a href="ami_2.html#K2">SCM-Data-Loc</a> , <font color="Olive">r</font> is    <a href="subset_1.html#M1">Element</a> of  <a href="numbers.html#K4">INT</a>  : <font color="Olive">I4</font> <a href="hidden.html#R2">in</a> <span class="p1"><a href="tarski.html#K2">{</a><span class="default">2,3</span><a href="tarski.html#K2">}</a></span> </span>}</span>  <a href="tarski.html#R1">c=</a> <span class="p1"><a href="zfmisc_1.html#K2">[:</a><span class="default"><span class="p2">(<span class="default"><a href="gr_cy_1.html#K1">Segm</a> 14</span>)</span>,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="tarski.html#K3">union</a> <span class="p5"><a href="tarski.html#K1">{</a><span class="default"><a href="numbers.html#K4">INT</a> </span><a href="tarski.html#K1">}</a></span></span>)</span> <a href="xboole_0.html#K2">\/</a> <a href="numbers.html#K5">NAT</a> </span>)</span> <a href="finseq_1.html#K13">*</a> </span>)</span></span><a href="zfmisc_1.html#K2">:]</a></span>
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="4_1_1_5"><b>proof </b></a><div class="add">

<b>let </b><font color="Maroon">x</font> be    <a href="hidden.html#M1">set</a> ; <i><font color="Red">:: according to </font></i><a class="ref" href="tarski.html#D3">TARSKI:def 3</a><br/>

<b>assume </b><a NAME="E1:4_1_1_5"/>
<font color="Maroon">x</font> <a href="hidden.html#R2">in</a> <span class="p1">{<span class="default"> <span class="p2"><a href="tarski.html#K4">[</a><span class="default"><font color="Olive">I4</font>,<span class="p3"><a href="finseq_1.html#K10">&lt;*</a><span class="default"><font color="Olive">d5</font>,<font color="Olive">r</font></span><a href="finseq_1.html#K10">*&gt;</a></span></span><a href="tarski.html#K4">]</a></span> where <font color="Olive">I4</font> is    <a href="subset_1.html#M2">Element</a> of  <a href="gr_cy_1.html#K1">Segm</a> 14, <font color="Olive">d5</font> is    <a href="subset_1.html#M2">Element</a> of  <a href="ami_2.html#K2">SCM-Data-Loc</a> , <font color="Olive">r</font> is    <a href="subset_1.html#M1">Element</a> of  <a href="numbers.html#K4">INT</a>  : <font color="Olive">I4</font> <a href="hidden.html#R2">in</a> <span class="p1"><a href="tarski.html#K2">{</a><span class="default">2,3</span><a href="tarski.html#K2">}</a></span> </span>}</span> 
 ;<br/>

<b>then consider </b><font color="Maroon">I4</font> being    <a href="subset_1.html#M2">Element</a> of  <a href="gr_cy_1.html#K1">Segm</a> 14, <font color="Maroon">d5</font> being    <a href="subset_1.html#M2">Element</a> of  <a href="ami_2.html#K2">SCM-Data-Loc</a> , <font color="Maroon">r</font> being    <a href="subset_1.html#M1">Element</a> of  <a href="numbers.html#K4">INT</a> <b> such that </b><br/><a NAME="E3:4_1_1_5"/><i><font color="Green">E77</font></i>: 
<font color="Maroon">x</font> <a href="hidden.html#R1">=</a> <span class="p1"><a href="tarski.html#K4">[</a><span class="default"><font color="Maroon">I4</font>,<span class="p2"><a href="finseq_1.html#K10">&lt;*</a><span class="default"><font color="Maroon">d5</font>,<font color="Maroon">r</font></span><a href="finseq_1.html#K10">*&gt;</a></span></span><a href="tarski.html#K4">]</a></span>
 <b>and </b><br/><a NAME="E4:4_1_1_5"/>
<font color="Maroon">I4</font> <a href="hidden.html#R2">in</a> <span class="p1"><a href="tarski.html#K2">{</a><span class="default">2,3</span><a href="tarski.html#K2">}</a></span>
 ;<br/>
<b>reconsider </b><font color="Maroon">d5</font> = <font color="Maroon">d5</font>, <font color="Maroon">r</font> = <font color="Maroon">r</font> as    <a href="subset_1.html#M1">Element</a> of <span class="p1">(<span class="default"><a href="tarski.html#K3">union</a> <span class="p2"><a href="tarski.html#K1">{</a><span class="default"><a href="numbers.html#K4">INT</a> </span><a href="tarski.html#K1">}</a></span></span>)</span> <a href="xboole_0.html#K2">\/</a> <a href="numbers.html#K5">NAT</a>  <b>by </b><i>, , <a class="ref" href="tarski.html#D3">TARSKI:def 3</a></i>;<br/>
<a NAME="E6:4_1_1_5"/>
<span class="p1"><a href="finseq_4.html#K2">&lt;*</a><span class="default"><font color="Maroon">d5</font>,<font color="Maroon">r</font></span><a href="finseq_4.html#K2">*&gt;</a></span> <a href="hidden.html#R2">in</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="tarski.html#K3">union</a> <span class="p3"><a href="tarski.html#K1">{</a><span class="default"><a href="numbers.html#K4">INT</a> </span><a href="tarski.html#K1">}</a></span></span>)</span> <a href="xboole_0.html#K2">\/</a> <a href="numbers.html#K5">NAT</a> </span>)</span> <a href="finseq_1.html#K13">*</a> 
 
<b>by </b><i><a class="ref" href="finseq_1.html#D11">FINSEQ_1:def 11</a></i>;<br/>
<b>hence </b><a NAME="E7:4_1_1_5"/>
<font color="Maroon">x</font> <a href="hidden.html#R2">in</a> <span class="p1"><a href="zfmisc_1.html#K2">[:</a><span class="default"><span class="p2">(<span class="default"><a href="gr_cy_1.html#K1">Segm</a> 14</span>)</span>,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="tarski.html#K3">union</a> <span class="p5"><a href="tarski.html#K1">{</a><span class="default"><a href="numbers.html#K4">INT</a> </span><a href="tarski.html#K1">}</a></span></span>)</span> <a href="xboole_0.html#K2">\/</a> <a href="numbers.html#K5">NAT</a> </span>)</span> <a href="finseq_1.html#K13">*</a> </span>)</span></span><a href="zfmisc_1.html#K2">:]</a></span>
 <b>by </b><i>, <a class="ref" href="zfmisc_1.html#T106">ZFMISC_1:106</a></i>;<br/>


</div><b>end;</b></div>
<b>set </b><font color="Maroon">S1</font> = <span class="p1">{<span class="default"> <span class="p2"><a href="tarski.html#K4">[</a><span class="default">0,<span class="p3"><a href="finseq_1.html#K12">&lt;*</a><span class="default"><font color="Olive">k5</font></span><a href="finseq_1.html#K12">*&gt;</a></span></span><a href="tarski.html#K4">]</a></span> where <font color="Olive">k5</font> is    <a href="subset_1.html#M1">Element</a> of  <a href="numbers.html#K4">INT</a>  : verum </span>}</span> ;<br/>
<b>set </b><font color="Maroon">S2</font> = <span class="p1">{<span class="default"> <span class="p2"><a href="tarski.html#K4">[</a><span class="default">1,<span class="p3"><a href="finseq_1.html#K12">&lt;*</a><span class="default"><font color="Olive">d4</font></span><a href="finseq_1.html#K12">*&gt;</a></span></span><a href="tarski.html#K4">]</a></span> where <font color="Olive">d4</font> is    <a href="subset_1.html#M2">Element</a> of  <a href="ami_2.html#K2">SCM-Data-Loc</a>  : verum </span>}</span> ;<br/>
<b>set </b><font color="Maroon">S3</font> = <span class="p1">{<span class="default"> <span class="p2"><a href="tarski.html#K4">[</a><span class="default"><font color="Olive">I4</font>,<span class="p3"><a href="finseq_1.html#K10">&lt;*</a><span class="default"><font color="Olive">d5</font>,<font color="Olive">r</font></span><a href="finseq_1.html#K10">*&gt;</a></span></span><a href="tarski.html#K4">]</a></span> where <font color="Olive">I4</font> is    <a href="subset_1.html#M2">Element</a> of  <a href="gr_cy_1.html#K1">Segm</a> 14, <font color="Olive">d5</font> is    <a href="subset_1.html#M2">Element</a> of  <a href="ami_2.html#K2">SCM-Data-Loc</a> , <font color="Olive">r</font> is    <a href="subset_1.html#M1">Element</a> of  <a href="numbers.html#K4">INT</a>  : <font color="Olive">I4</font> <a href="hidden.html#R2">in</a> <span class="p1"><a href="tarski.html#K2">{</a><span class="default">2,3</span><a href="tarski.html#K2">}</a></span> </span>}</span> ;<br/>
<a NAME="E7:4_1_1"/>
<span class="p1">{<span class="default"> <span class="p2"><a href="tarski.html#K4">[</a><span class="default">0,<span class="p3"><a href="finseq_1.html#K12">&lt;*</a><span class="default"><font color="Olive">k5</font></span><a href="finseq_1.html#K12">*&gt;</a></span></span><a href="tarski.html#K4">]</a></span> where <font color="Olive">k5</font> is    <a href="subset_1.html#M1">Element</a> of  <a href="numbers.html#K4">INT</a>  : verum </span>}</span>  <a href="xboole_0.html#K2">\/</a> <span class="p1">{<span class="default"> <span class="p2"><a href="tarski.html#K4">[</a><span class="default">1,<span class="p3"><a href="finseq_1.html#K12">&lt;*</a><span class="default"><font color="Olive">d4</font></span><a href="finseq_1.html#K12">*&gt;</a></span></span><a href="tarski.html#K4">]</a></span> where <font color="Olive">d4</font> is    <a href="subset_1.html#M2">Element</a> of  <a href="ami_2.html#K2">SCM-Data-Loc</a>  : verum </span>}</span>  <a href="tarski.html#R1">c=</a> <span class="p1"><a href="zfmisc_1.html#K2">[:</a><span class="default"><span class="p2">(<span class="default"><a href="gr_cy_1.html#K1">Segm</a> 14</span>)</span>,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="tarski.html#K3">union</a> <span class="p5"><a href="tarski.html#K1">{</a><span class="default"><a href="numbers.html#K4">INT</a> </span><a href="tarski.html#K1">}</a></span></span>)</span> <a href="xboole_0.html#K2">\/</a> <a href="numbers.html#K5">NAT</a> </span>)</span> <a href="finseq_1.html#K13">*</a> </span>)</span></span><a href="zfmisc_1.html#K2">:]</a></span>
 
<b>by </b><i>, , <a class="ref" href="xboole_1.html#T8">XBOOLE_1:8</a></i>;<br/>
<a NAME="E8:4_1_1"/><b>then </b>
<span class="p1">(<span class="default"><span class="p2">{<span class="default"> <span class="p3"><a href="tarski.html#K4">[</a><span class="default">0,<span class="p4"><a href="finseq_1.html#K12">&lt;*</a><span class="default"><font color="Olive">k5</font></span><a href="finseq_1.html#K12">*&gt;</a></span></span><a href="tarski.html#K4">]</a></span> where <font color="Olive">k5</font> is    <a href="subset_1.html#M1">Element</a> of  <a href="numbers.html#K4">INT</a>  : verum </span>}</span>  <a href="xboole_0.html#K2">\/</a> <span class="p2">{<span class="default"> <span class="p3"><a href="tarski.html#K4">[</a><span class="default">1,<span class="p4"><a href="finseq_1.html#K12">&lt;*</a><span class="default"><font color="Olive">d4</font></span><a href="finseq_1.html#K12">*&gt;</a></span></span><a href="tarski.html#K4">]</a></span> where <font color="Olive">d4</font> is    <a href="subset_1.html#M2">Element</a> of  <a href="ami_2.html#K2">SCM-Data-Loc</a>  : verum </span>}</span> </span>)</span> <a href="xboole_0.html#K2">\/</a> <span class="p1">{<span class="default"> <span class="p2"><a href="tarski.html#K4">[</a><span class="default"><font color="Olive">I4</font>,<span class="p3"><a href="finseq_1.html#K10">&lt;*</a><span class="default"><font color="Olive">d5</font>,<font color="Olive">r</font></span><a href="finseq_1.html#K10">*&gt;</a></span></span><a href="tarski.html#K4">]</a></span> where <font color="Olive">I4</font> is    <a href="subset_1.html#M2">Element</a> of  <a href="gr_cy_1.html#K1">Segm</a> 14, <font color="Olive">d5</font> is    <a href="subset_1.html#M2">Element</a> of  <a href="ami_2.html#K2">SCM-Data-Loc</a> , <font color="Olive">r</font> is    <a href="subset_1.html#M1">Element</a> of  <a href="numbers.html#K4">INT</a>  : <font color="Olive">I4</font> <a href="hidden.html#R2">in</a> <span class="p1"><a href="tarski.html#K2">{</a><span class="default">2,3</span><a href="tarski.html#K2">}</a></span> </span>}</span>  <a href="tarski.html#R1">c=</a> <span class="p1"><a href="zfmisc_1.html#K2">[:</a><span class="default"><span class="p2">(<span class="default"><a href="gr_cy_1.html#K1">Segm</a> 14</span>)</span>,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="tarski.html#K3">union</a> <span class="p5"><a href="tarski.html#K1">{</a><span class="default"><a href="numbers.html#K4">INT</a> </span><a href="tarski.html#K1">}</a></span></span>)</span> <a href="xboole_0.html#K2">\/</a> <a href="numbers.html#K5">NAT</a> </span>)</span> <a href="finseq_1.html#K13">*</a> </span>)</span></span><a href="zfmisc_1.html#K2">:]</a></span>
 
<b>by </b><i>, <a class="ref" href="xboole_1.html#T8">XBOOLE_1:8</a></i>;<br/>
<a NAME="E9:4_1_1"/><b>then </b>
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">{<span class="default"> <span class="p4"><a href="tarski.html#K4">[</a><span class="default">0,<span class="p5"><a href="finseq_1.html#K12">&lt;*</a><span class="default"><font color="Olive">k5</font></span><a href="finseq_1.html#K12">*&gt;</a></span></span><a href="tarski.html#K4">]</a></span> where <font color="Olive">k5</font> is    <a href="subset_1.html#M1">Element</a> of  <a href="numbers.html#K4">INT</a>  : verum </span>}</span>  <a href="xboole_0.html#K2">\/</a> <span class="p3">{<span class="default"> <span class="p4"><a href="tarski.html#K4">[</a><span class="default">1,<span class="p5"><a href="finseq_1.html#K12">&lt;*</a><span class="default"><font color="Olive">d4</font></span><a href="finseq_1.html#K12">*&gt;</a></span></span><a href="tarski.html#K4">]</a></span> where <font color="Olive">d4</font> is    <a href="subset_1.html#M2">Element</a> of  <a href="ami_2.html#K2">SCM-Data-Loc</a>  : verum </span>}</span> </span>)</span> <a href="xboole_0.html#K2">\/</a> <span class="p2">{<span class="default"> <span class="p3"><a href="tarski.html#K4">[</a><span class="default"><font color="Olive">I4</font>,<span class="p4"><a href="finseq_1.html#K10">&lt;*</a><span class="default"><font color="Olive">d5</font>,<font color="Olive">r</font></span><a href="finseq_1.html#K10">*&gt;</a></span></span><a href="tarski.html#K4">]</a></span> where <font color="Olive">I4</font> is    <a href="subset_1.html#M2">Element</a> of  <a href="gr_cy_1.html#K1">Segm</a> 14, <font color="Olive">d5</font> is    <a href="subset_1.html#M2">Element</a> of  <a href="ami_2.html#K2">SCM-Data-Loc</a> , <font color="Olive">r</font> is    <a href="subset_1.html#M1">Element</a> of  <a href="numbers.html#K4">INT</a>  : <font color="Olive">I4</font> <a href="hidden.html#R2">in</a> <span class="p1"><a href="tarski.html#K2">{</a><span class="default">2,3</span><a href="tarski.html#K2">}</a></span> </span>}</span> </span>)</span> <a href="xboole_0.html#K2">\/</a> <span class="p1">{<span class="default"> <span class="p2"><a href="tarski.html#K4">[</a><span class="default"><font color="Olive">I2</font>,<span class="p3"><a href="finseq_1.html#K11">&lt;*</a><span class="default"><font color="Olive">d3</font>,<font color="Olive">k3</font>,<font color="Olive">k4</font></span><a href="finseq_1.html#K11">*&gt;</a></span></span><a href="tarski.html#K4">]</a></span> where <font color="Olive">I2</font> is    <a href="subset_1.html#M2">Element</a> of  <a href="gr_cy_1.html#K1">Segm</a> 14, <font color="Olive">d3</font> is    <a href="subset_1.html#M2">Element</a> of  <a href="ami_2.html#K2">SCM-Data-Loc</a> , <font color="Olive">k3</font> is    <a href="subset_1.html#M1">Element</a> of  <a href="numbers.html#K4">INT</a> , <font color="Olive">k4</font> is    <a href="subset_1.html#M1">Element</a> of  <a href="numbers.html#K4">INT</a>  : <font color="Olive">I2</font> <a href="hidden.html#R2">in</a> <span class="p1"><a href="enumset1.html#K3">{</a><span class="default">4,5,6,7,8</span><a href="enumset1.html#K3">}</a></span> </span>}</span>  <a href="tarski.html#R1">c=</a> <span class="p1"><a href="zfmisc_1.html#K2">[:</a><span class="default"><span class="p2">(<span class="default"><a href="gr_cy_1.html#K1">Segm</a> 14</span>)</span>,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="tarski.html#K3">union</a> <span class="p5"><a href="tarski.html#K1">{</a><span class="default"><a href="numbers.html#K4">INT</a> </span><a href="tarski.html#K1">}</a></span></span>)</span> <a href="xboole_0.html#K2">\/</a> <a href="numbers.html#K5">NAT</a> </span>)</span> <a href="finseq_1.html#K13">*</a> </span>)</span></span><a href="zfmisc_1.html#K2">:]</a></span>
 
<b>by </b><i>, <a class="ref" href="xboole_1.html#T8">XBOOLE_1:8</a></i>;<br/>
<b>hence </b><a NAME="E10:4_1_1"/>
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">{<span class="default"> <span class="p5"><a href="tarski.html#K4">[</a><span class="default">0,<span class="p0"><a href="finseq_1.html#K12">&lt;*</a><span class="default"><font color="Olive">l</font></span><a href="finseq_1.html#K12">*&gt;</a></span></span><a href="tarski.html#K4">]</a></span> where <font color="Olive">l</font> is    <a href="subset_1.html#M1">Element</a> of  <a href="numbers.html#K4">INT</a>  : verum </span>}</span>  <a href="xboole_0.html#K2">\/</a> <span class="p4">{<span class="default"> <span class="p5"><a href="tarski.html#K4">[</a><span class="default">1,<span class="p0"><a href="finseq_1.html#K12">&lt;*</a><span class="default"><font color="Olive">sp</font></span><a href="finseq_1.html#K12">*&gt;</a></span></span><a href="tarski.html#K4">]</a></span> where <font color="Olive">sp</font> is    <a href="subset_1.html#M2">Element</a> of  <a href="ami_2.html#K2">SCM-Data-Loc</a>  : verum </span>}</span> </span>)</span> <a href="xboole_0.html#K2">\/</a> <span class="p3">{<span class="default"> <span class="p4"><a href="tarski.html#K4">[</a><span class="default"><font color="Olive">I</font>,<span class="p5"><a href="finseq_1.html#K10">&lt;*</a><span class="default"><font color="Olive">v</font>,<font color="Olive">c</font></span><a href="finseq_1.html#K10">*&gt;</a></span></span><a href="tarski.html#K4">]</a></span> where <font color="Olive">I</font> is    <a href="subset_1.html#M2">Element</a> of  <a href="gr_cy_1.html#K1">Segm</a> 14, <font color="Olive">v</font> is    <a href="subset_1.html#M2">Element</a> of  <a href="ami_2.html#K2">SCM-Data-Loc</a> , <font color="Olive">c</font> is    <a href="subset_1.html#M1">Element</a> of  <a href="numbers.html#K4">INT</a>  : <font color="Olive">I</font> <a href="hidden.html#R2">in</a> <span class="p1"><a href="tarski.html#K2">{</a><span class="default">2,3</span><a href="tarski.html#K2">}</a></span> </span>}</span> </span>)</span> <a href="xboole_0.html#K2">\/</a> <span class="p2">{<span class="default"> <span class="p3"><a href="tarski.html#K4">[</a><span class="default"><font color="Olive">I</font>,<span class="p4"><a href="finseq_1.html#K11">&lt;*</a><span class="default"><font color="Olive">v</font>,<font color="Olive">c1</font>,<font color="Olive">c2</font></span><a href="finseq_1.html#K11">*&gt;</a></span></span><a href="tarski.html#K4">]</a></span> where <font color="Olive">I</font> is    <a href="subset_1.html#M2">Element</a> of  <a href="gr_cy_1.html#K1">Segm</a> 14, <font color="Olive">v</font> is    <a href="subset_1.html#M2">Element</a> of  <a href="ami_2.html#K2">SCM-Data-Loc</a> , <font color="Olive">c1</font> is    <a href="subset_1.html#M1">Element</a> of  <a href="numbers.html#K4">INT</a> , <font color="Olive">c2</font> is    <a href="subset_1.html#M1">Element</a> of  <a href="numbers.html#K4">INT</a>  : <font color="Olive">I</font> <a href="hidden.html#R2">in</a> <span class="p1"><a href="enumset1.html#K3">{</a><span class="default">4,5,6,7,8</span><a href="enumset1.html#K3">}</a></span> </span>}</span> </span>)</span> <a href="xboole_0.html#K2">\/</a> <span class="p1">{<span class="default"> <span class="p2"><a href="tarski.html#K4">[</a><span class="default"><font color="Olive">I</font>,<span class="p3"><a href="finseq_4.html#K8">&lt;*</a><span class="default"><font color="Olive">v1</font>,<font color="Olive">v2</font>,<font color="Olive">c1</font>,<font color="Olive">c2</font></span><a href="finseq_4.html#K8">*&gt;</a></span></span><a href="tarski.html#K4">]</a></span> where <font color="Olive">I</font> is    <a href="subset_1.html#M2">Element</a> of  <a href="gr_cy_1.html#K1">Segm</a> 14, <font color="Olive">v1</font> is    <a href="subset_1.html#M2">Element</a> of  <a href="ami_2.html#K2">SCM-Data-Loc</a> , <font color="Olive">v2</font> is    <a href="subset_1.html#M2">Element</a> of  <a href="ami_2.html#K2">SCM-Data-Loc</a> , <font color="Olive">c1</font> is    <a href="subset_1.html#M1">Element</a> of  <a href="numbers.html#K4">INT</a> , <font color="Olive">c2</font> is    <a href="subset_1.html#M1">Element</a> of  <a href="numbers.html#K4">INT</a>  : <font color="Olive">I</font> <a href="hidden.html#R2">in</a> <span class="p1"><a href="enumset1.html#K3">{</a><span class="default">9,10,11,12,13</span><a href="enumset1.html#K3">}</a></span> </span>}</span>  is   <a href="subset_1.html#NM2">Subset</a> of <span class="p1"><a href="zfmisc_1.html#K2">[:</a><span class="default"><span class="p2">(<span class="default"><a href="gr_cy_1.html#K1">Segm</a> 14</span>)</span>,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="tarski.html#K3">union</a> <span class="p5"><a href="tarski.html#K1">{</a><span class="default"><a href="numbers.html#K4">INT</a> </span><a href="tarski.html#K1">}</a></span></span>)</span> <a href="xboole_0.html#K2">\/</a> <a href="numbers.html#K5">NAT</a> </span>)</span> <a href="finseq_1.html#K13">*</a> </span>)</span></span><a href="zfmisc_1.html#K2">:]</a></span>
 <b>by </b><i>, <a class="ref" href="xboole_1.html#T8">XBOOLE_1:8</a></i>;<br/>


</div>
