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<a NAME="E1:9_1_1"/><i><font color="Green" title="E2">A1</font></i>: 
 <a href="scmfsa_1.html#K2" title="SCMFSA_1:func.2">SCM+FSA-Memory</a>  <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <span class="p1">(<span class="default"><a href="tarski.html#K3" title="TARSKI:func.3">union</a> <span class="p2"><a href="tarski.html#K2" title="TARSKI:func.2">{</a><span class="default"><a href="numbers.html#K4" title="NUMBERS:func.4">INT</a> ,<span class="p3">(<span class="default"><a href="numbers.html#K4" title="NUMBERS:func.4">INT</a>  <a href="finseq_1.html#K13" title="FINSEQ_1:func.13">*</a> </span>)</span></span><a href="tarski.html#K2" title="TARSKI:func.2">}</a></span></span>)</span> <a href="xboole_0.html#K2" title="XBOOLE_0:func.2">\/</a> <a href="scmfsa_1.html#K2" title="SCMFSA_1:func.2">SCM+FSA-Memory</a> 
 
<b>by </b><i><a class="ref" href="xboole_1.html#T7" title="XBOOLE_1:th.7">XBOOLE_1:7</a></i>;<br/>
<a NAME="E2:9_1_1"/><i><font color="Green" title="E3">A2</font></i>: 
<span class="p1">{<span class="default"> <span class="p2"><a href="tarski.html#K4" title="TARSKI:func.4">[</a><span class="default"><font color="Olive" title="b1">J</font>,<span class="p3"><a href="finseq_4.html#K3" title="FINSEQ_4:func.3">&lt;*</a><span class="default"><font color="Olive" title="b2">c</font>,<font color="Olive" title="b4">f</font>,<font color="Olive" title="b3">b</font></span><a href="finseq_4.html#K3" title="FINSEQ_4:func.3">*&gt;</a></span></span><a href="tarski.html#K4" title="TARSKI:func.4">]</a></span> where <font color="Olive" title="b1">J</font> is    <a href="subset_1.html#M2" title="SUBSET_1:mode.2">Element</a> of  <a href="card_1.html#K7" title="CARD_1:func.7">Segm</a> 13, <font color="Olive" title="b2">c</font>, <font color="Olive" title="b3">b</font> is    <a href="subset_1.html#M2" title="SUBSET_1:mode.2">Element</a> of  <a href="scmfsa_1.html#K3" title="SCMFSA_1:func.3">SCM+FSA-Data-Loc</a> , <font color="Olive" title="b4">f</font> is    <a href="subset_1.html#M2" title="SUBSET_1:mode.2">Element</a> of  <a href="scmfsa_1.html#K4" title="SCMFSA_1:func.4">SCM+FSA-Data*-Loc</a>  : <font color="Olive" title="b1">J</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <span class="p1"><a href="tarski.html#K2" title="TARSKI:func.2">{</a><span class="default">9,10</span><a href="tarski.html#K2" title="TARSKI:func.2">}</a></span> </span>}</span>  <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <span class="p1"><a href="zfmisc_1.html#K2" title="ZFMISC_1:func.2">[:</a><span class="default"><a href="scmfsa_1.html#K5" title="SCMFSA_1:func.5">NAT</a> ,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="tarski.html#K3" title="TARSKI:func.3">union</a> <span class="p5"><a href="tarski.html#K2" title="TARSKI:func.2">{</a><span class="default"><a href="numbers.html#K4" title="NUMBERS:func.4">INT</a> ,<span class="p0">(<span class="default"><a href="numbers.html#K4" title="NUMBERS:func.4">INT</a>  <a href="finseq_1.html#K13" title="FINSEQ_1:func.13">*</a> </span>)</span></span><a href="tarski.html#K2" title="TARSKI:func.2">}</a></span></span>)</span> <a href="xboole_0.html#K2" title="XBOOLE_0:func.2">\/</a> <a href="scmfsa_1.html#K2" title="SCMFSA_1:func.2">SCM+FSA-Memory</a> </span>)</span> <a href="finseq_1.html#K13" title="FINSEQ_1:func.13">*</a> </span>)</span></span><a href="zfmisc_1.html#K2" title="ZFMISC_1:func.2">:]</a></span>
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="9_1_1_1"><b>proof </b></a><div class="add">

<b>let </b><font color="Maroon" title="c1">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="c1">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <span class="p1">{<span class="default"> <span class="p2"><a href="tarski.html#K4" title="TARSKI:func.4">[</a><span class="default"><font color="Olive" title="b1">J</font>,<span class="p3"><a href="finseq_4.html#K3" title="FINSEQ_4:func.3">&lt;*</a><span class="default"><font color="Olive" title="b2">c</font>,<font color="Olive" title="b4">f</font>,<font color="Olive" title="b3">b</font></span><a href="finseq_4.html#K3" title="FINSEQ_4:func.3">*&gt;</a></span></span><a href="tarski.html#K4" title="TARSKI:func.4">]</a></span> where <font color="Olive" title="b1">J</font> is    <a href="subset_1.html#M2" title="SUBSET_1:mode.2">Element</a> of  <a href="card_1.html#K7" title="CARD_1:func.7">Segm</a> 13, <font color="Olive" title="b2">c</font>, <font color="Olive" title="b3">b</font> is    <a href="subset_1.html#M2" title="SUBSET_1:mode.2">Element</a> of  <a href="scmfsa_1.html#K3" title="SCMFSA_1:func.3">SCM+FSA-Data-Loc</a> , <font color="Olive" title="b4">f</font> is    <a href="subset_1.html#M2" title="SUBSET_1:mode.2">Element</a> of  <a href="scmfsa_1.html#K4" title="SCMFSA_1:func.4">SCM+FSA-Data*-Loc</a>  : <font color="Olive" title="b1">J</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <span class="p1"><a href="tarski.html#K2" title="TARSKI:func.2">{</a><span class="default">9,10</span><a href="tarski.html#K2" title="TARSKI:func.2">}</a></span> </span>}</span>  or <font color="Maroon" title="c1">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <span class="p1"><a href="zfmisc_1.html#K2" title="ZFMISC_1:func.2">[:</a><span class="default"><a href="scmfsa_1.html#K5" title="SCMFSA_1:func.5">NAT</a> ,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="tarski.html#K3" title="TARSKI:func.3">union</a> <span class="p5"><a href="tarski.html#K2" title="TARSKI:func.2">{</a><span class="default"><a href="numbers.html#K4" title="NUMBERS:func.4">INT</a> ,<span class="p0">(<span class="default"><a href="numbers.html#K4" title="NUMBERS:func.4">INT</a>  <a href="finseq_1.html#K13" title="FINSEQ_1:func.13">*</a> </span>)</span></span><a href="tarski.html#K2" title="TARSKI:func.2">}</a></span></span>)</span> <a href="xboole_0.html#K2" title="XBOOLE_0:func.2">\/</a> <a href="scmfsa_1.html#K2" title="SCMFSA_1:func.2">SCM+FSA-Memory</a> </span>)</span> <a href="finseq_1.html#K13" title="FINSEQ_1:func.13">*</a> </span>)</span></span><a href="zfmisc_1.html#K2" title="ZFMISC_1:func.2">:]</a></span> )</span><br/>

<b>assume </b><a NAME="E1:9_1_1_1"/>
<font color="Maroon" title="c1">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <span class="p1">{<span class="default"> <span class="p2"><a href="tarski.html#K4" title="TARSKI:func.4">[</a><span class="default"><font color="Olive" title="b1">J</font>,<span class="p3"><a href="finseq_4.html#K3" title="FINSEQ_4:func.3">&lt;*</a><span class="default"><font color="Olive" title="b2">c</font>,<font color="Olive" title="b4">f</font>,<font color="Olive" title="b3">b</font></span><a href="finseq_4.html#K3" title="FINSEQ_4:func.3">*&gt;</a></span></span><a href="tarski.html#K4" title="TARSKI:func.4">]</a></span> where <font color="Olive" title="b1">J</font> is    <a href="subset_1.html#M2" title="SUBSET_1:mode.2">Element</a> of  <a href="card_1.html#K7" title="CARD_1:func.7">Segm</a> 13, <font color="Olive" title="b2">c</font>, <font color="Olive" title="b3">b</font> is    <a href="subset_1.html#M2" title="SUBSET_1:mode.2">Element</a> of  <a href="scmfsa_1.html#K3" title="SCMFSA_1:func.3">SCM+FSA-Data-Loc</a> , <font color="Olive" title="b4">f</font> is    <a href="subset_1.html#M2" title="SUBSET_1:mode.2">Element</a> of  <a href="scmfsa_1.html#K4" title="SCMFSA_1:func.4">SCM+FSA-Data*-Loc</a>  : <font color="Olive" title="b1">J</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <span class="p1"><a href="tarski.html#K2" title="TARSKI:func.2">{</a><span class="default">9,10</span><a href="tarski.html#K2" title="TARSKI:func.2">}</a></span> </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="c1">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <span class="p1"><a href="zfmisc_1.html#K2" title="ZFMISC_1:func.2">[:</a><span class="default"><a href="scmfsa_1.html#K5" title="SCMFSA_1:func.5">NAT</a> ,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="tarski.html#K3" title="TARSKI:func.3">union</a> <span class="p5"><a href="tarski.html#K2" title="TARSKI:func.2">{</a><span class="default"><a href="numbers.html#K4" title="NUMBERS:func.4">INT</a> ,<span class="p0">(<span class="default"><a href="numbers.html#K4" title="NUMBERS:func.4">INT</a>  <a href="finseq_1.html#K13" title="FINSEQ_1:func.13">*</a> </span>)</span></span><a href="tarski.html#K2" title="TARSKI:func.2">}</a></span></span>)</span> <a href="xboole_0.html#K2" title="XBOOLE_0:func.2">\/</a> <a href="scmfsa_1.html#K2" title="SCMFSA_1:func.2">SCM+FSA-Memory</a> </span>)</span> <a href="finseq_1.html#K13" title="FINSEQ_1:func.13">*</a> </span>)</span></span><a href="zfmisc_1.html#K2" title="ZFMISC_1:func.2">:]</a></span></span><br/>

<b>then consider </b><font color="Maroon" title="c2">J</font> being    <a href="subset_1.html#M2" title="SUBSET_1:mode.2">Element</a> of  <a href="card_1.html#K7" title="CARD_1:func.7">Segm</a> 13, <font color="Maroon" title="c3">c</font>, <font color="Maroon" title="c4">b</font> being    <a href="subset_1.html#M2" title="SUBSET_1:mode.2">Element</a> of  <a href="scmfsa_1.html#K3" title="SCMFSA_1:func.3">SCM+FSA-Data-Loc</a> , <font color="Maroon" title="c5">f</font> being    <a href="subset_1.html#M2" title="SUBSET_1:mode.2">Element</a> of  <a href="scmfsa_1.html#K4" title="SCMFSA_1:func.4">SCM+FSA-Data*-Loc</a> <b> such that </b><br/><a NAME="E3:9_1_1_1"/><i><font color="Green" title="E4">A3</font></i>: 
( <font color="Maroon" title="c1">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1"><a href="tarski.html#K4" title="TARSKI:func.4">[</a><span class="default"><font color="Maroon" title="c2">J</font>,<span class="p2"><a href="finseq_4.html#K3" title="FINSEQ_4:func.3">&lt;*</a><span class="default"><font color="Maroon" title="c3">c</font>,<font color="Maroon" title="c5">f</font>,<font color="Maroon" title="c4">b</font></span><a href="finseq_4.html#K3" title="FINSEQ_4:func.3">*&gt;</a></span></span><a href="tarski.html#K4" title="TARSKI:func.4">]</a></span> &amp; <font color="Maroon" title="c2">J</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <span class="p1"><a href="tarski.html#K2" title="TARSKI:func.2">{</a><span class="default">9,10</span><a href="tarski.html#K2" title="TARSKI:func.2">}</a></span> )
 ;<br/>
<b>reconsider </b><font color="Maroon" title="c6">c</font> = <font color="Maroon" title="c3">c</font>, <font color="Maroon" title="c7">f</font> = <font color="Maroon" title="c5">f</font>, <font color="Maroon" title="c8">b</font> = <font color="Maroon" title="c4">b</font> as    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of <span class="p1">(<span class="default"><a href="tarski.html#K3" title="TARSKI:func.3">union</a> <span class="p2"><a href="tarski.html#K2" title="TARSKI:func.2">{</a><span class="default"><a href="numbers.html#K4" title="NUMBERS:func.4">INT</a> ,<span class="p3">(<span class="default"><a href="numbers.html#K4" title="NUMBERS:func.4">INT</a>  <a href="finseq_1.html#K13" title="FINSEQ_1:func.13">*</a> </span>)</span></span><a href="tarski.html#K2" title="TARSKI:func.2">}</a></span></span>)</span> <a href="xboole_0.html#K2" title="XBOOLE_0:func.2">\/</a> <a href="scmfsa_1.html#K2" title="SCMFSA_1:func.2">SCM+FSA-Memory</a>  <b>by </b><i><a class="txt" href="scmfsa_1.html#E1:9_1_1"><i><font color="Green" title="E2">A1</font></i></a>, <a class="ref" href="tarski.html#D3" title="TARSKI:def.3">TARSKI:def 3</a></i>;<br/>
<a NAME="E5:9_1_1_1"/>
<span class="p1"><a href="finseq_4.html#K3" title="FINSEQ_4:func.3">&lt;*</a><span class="default"><font color="Maroon" title="c6">c</font>,<font color="Maroon" title="c7">f</font>,<font color="Maroon" title="c8">b</font></span><a href="finseq_4.html#K3" title="FINSEQ_4:func.3">*&gt;</a></span> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="tarski.html#K3" title="TARSKI:func.3">union</a> <span class="p3"><a href="tarski.html#K2" title="TARSKI:func.2">{</a><span class="default"><a href="numbers.html#K4" title="NUMBERS:func.4">INT</a> ,<span class="p4">(<span class="default"><a href="numbers.html#K4" title="NUMBERS:func.4">INT</a>  <a href="finseq_1.html#K13" title="FINSEQ_1:func.13">*</a> </span>)</span></span><a href="tarski.html#K2" title="TARSKI:func.2">}</a></span></span>)</span> <a href="xboole_0.html#K2" title="XBOOLE_0:func.2">\/</a> <a href="scmfsa_1.html#K2" title="SCMFSA_1:func.2">SCM+FSA-Memory</a> </span>)</span> <a href="finseq_1.html#K13" title="FINSEQ_1:func.13">*</a> 
 
<b>by </b><i><a class="ref" href="finseq_1.html#D11" title="FINSEQ_1:def.11">FINSEQ_1:def 11</a></i>;<br/>
<b>hence </b><a NAME="E6:9_1_1_1"/>
<font color="Maroon" title="c1">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <span class="p1"><a href="zfmisc_1.html#K2" title="ZFMISC_1:func.2">[:</a><span class="default"><a href="scmfsa_1.html#K5" title="SCMFSA_1:func.5">NAT</a> ,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="tarski.html#K3" title="TARSKI:func.3">union</a> <span class="p5"><a href="tarski.html#K2" title="TARSKI:func.2">{</a><span class="default"><a href="numbers.html#K4" title="NUMBERS:func.4">INT</a> ,<span class="p0">(<span class="default"><a href="numbers.html#K4" title="NUMBERS:func.4">INT</a>  <a href="finseq_1.html#K13" title="FINSEQ_1:func.13">*</a> </span>)</span></span><a href="tarski.html#K2" title="TARSKI:func.2">}</a></span></span>)</span> <a href="xboole_0.html#K2" title="XBOOLE_0:func.2">\/</a> <a href="scmfsa_1.html#K2" title="SCMFSA_1:func.2">SCM+FSA-Memory</a> </span>)</span> <a href="finseq_1.html#K13" title="FINSEQ_1:func.13">*</a> </span>)</span></span><a href="zfmisc_1.html#K2" title="ZFMISC_1:func.2">:]</a></span>
 <b>by </b><i><a class="txt" href="scmfsa_1.html#E3:9_1_1_1"><i><font color="Green" title="E4">A3</font></i></a>, <a class="ref" href="zfmisc_1.html#T106" title="ZFMISC_1:th.106">ZFMISC_1:106</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="E3:9_1_1"/><i><font color="Green" title="E4">A4</font></i>: 
<span class="p1">{<span class="default"> <span class="p2"><a href="tarski.html#K4" title="TARSKI:func.4">[</a><span class="default"><font color="Olive" title="b1">K</font>,<span class="p3"><a href="finseq_4.html#K2" title="FINSEQ_4:func.2">&lt;*</a><span class="default"><font color="Olive" title="b2">c1</font>,<font color="Olive" title="b3">f1</font></span><a href="finseq_4.html#K2" title="FINSEQ_4:func.2">*&gt;</a></span></span><a href="tarski.html#K4" title="TARSKI:func.4">]</a></span> where <font color="Olive" title="b1">K</font> is    <a href="subset_1.html#M2" title="SUBSET_1:mode.2">Element</a> of  <a href="card_1.html#K7" title="CARD_1:func.7">Segm</a> 13, <font color="Olive" title="b2">c1</font> is    <a href="subset_1.html#M2" title="SUBSET_1:mode.2">Element</a> of  <a href="scmfsa_1.html#K3" title="SCMFSA_1:func.3">SCM+FSA-Data-Loc</a> , <font color="Olive" title="b3">f1</font> is    <a href="subset_1.html#M2" title="SUBSET_1:mode.2">Element</a> of  <a href="scmfsa_1.html#K4" title="SCMFSA_1:func.4">SCM+FSA-Data*-Loc</a>  : <font color="Olive" title="b1">K</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <span class="p1"><a href="tarski.html#K2" title="TARSKI:func.2">{</a><span class="default">11,12</span><a href="tarski.html#K2" title="TARSKI:func.2">}</a></span> </span>}</span>  <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <span class="p1"><a href="zfmisc_1.html#K2" title="ZFMISC_1:func.2">[:</a><span class="default"><a href="scmfsa_1.html#K5" title="SCMFSA_1:func.5">NAT</a> ,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="tarski.html#K3" title="TARSKI:func.3">union</a> <span class="p5"><a href="tarski.html#K2" title="TARSKI:func.2">{</a><span class="default"><a href="numbers.html#K4" title="NUMBERS:func.4">INT</a> ,<span class="p0">(<span class="default"><a href="numbers.html#K4" title="NUMBERS:func.4">INT</a>  <a href="finseq_1.html#K13" title="FINSEQ_1:func.13">*</a> </span>)</span></span><a href="tarski.html#K2" title="TARSKI:func.2">}</a></span></span>)</span> <a href="xboole_0.html#K2" title="XBOOLE_0:func.2">\/</a> <a href="scmfsa_1.html#K2" title="SCMFSA_1:func.2">SCM+FSA-Memory</a> </span>)</span> <a href="finseq_1.html#K13" title="FINSEQ_1:func.13">*</a> </span>)</span></span><a href="zfmisc_1.html#K2" title="ZFMISC_1:func.2">:]</a></span>
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="9_1_1_2"><b>proof </b></a><div class="add">

<b>let </b><font color="Maroon" title="c1">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="c1">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <span class="p1">{<span class="default"> <span class="p2"><a href="tarski.html#K4" title="TARSKI:func.4">[</a><span class="default"><font color="Olive" title="b1">K</font>,<span class="p3"><a href="finseq_4.html#K2" title="FINSEQ_4:func.2">&lt;*</a><span class="default"><font color="Olive" title="b2">c1</font>,<font color="Olive" title="b3">f1</font></span><a href="finseq_4.html#K2" title="FINSEQ_4:func.2">*&gt;</a></span></span><a href="tarski.html#K4" title="TARSKI:func.4">]</a></span> where <font color="Olive" title="b1">K</font> is    <a href="subset_1.html#M2" title="SUBSET_1:mode.2">Element</a> of  <a href="card_1.html#K7" title="CARD_1:func.7">Segm</a> 13, <font color="Olive" title="b2">c1</font> is    <a href="subset_1.html#M2" title="SUBSET_1:mode.2">Element</a> of  <a href="scmfsa_1.html#K3" title="SCMFSA_1:func.3">SCM+FSA-Data-Loc</a> , <font color="Olive" title="b3">f1</font> is    <a href="subset_1.html#M2" title="SUBSET_1:mode.2">Element</a> of  <a href="scmfsa_1.html#K4" title="SCMFSA_1:func.4">SCM+FSA-Data*-Loc</a>  : <font color="Olive" title="b1">K</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <span class="p1"><a href="tarski.html#K2" title="TARSKI:func.2">{</a><span class="default">11,12</span><a href="tarski.html#K2" title="TARSKI:func.2">}</a></span> </span>}</span>  or <font color="Maroon" title="c1">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <span class="p1"><a href="zfmisc_1.html#K2" title="ZFMISC_1:func.2">[:</a><span class="default"><a href="scmfsa_1.html#K5" title="SCMFSA_1:func.5">NAT</a> ,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="tarski.html#K3" title="TARSKI:func.3">union</a> <span class="p5"><a href="tarski.html#K2" title="TARSKI:func.2">{</a><span class="default"><a href="numbers.html#K4" title="NUMBERS:func.4">INT</a> ,<span class="p0">(<span class="default"><a href="numbers.html#K4" title="NUMBERS:func.4">INT</a>  <a href="finseq_1.html#K13" title="FINSEQ_1:func.13">*</a> </span>)</span></span><a href="tarski.html#K2" title="TARSKI:func.2">}</a></span></span>)</span> <a href="xboole_0.html#K2" title="XBOOLE_0:func.2">\/</a> <a href="scmfsa_1.html#K2" title="SCMFSA_1:func.2">SCM+FSA-Memory</a> </span>)</span> <a href="finseq_1.html#K13" title="FINSEQ_1:func.13">*</a> </span>)</span></span><a href="zfmisc_1.html#K2" title="ZFMISC_1:func.2">:]</a></span> )</span><br/>

<b>assume </b><a NAME="E1:9_1_1_2"/>
<font color="Maroon" title="c1">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <span class="p1">{<span class="default"> <span class="p2"><a href="tarski.html#K4" title="TARSKI:func.4">[</a><span class="default"><font color="Olive" title="b1">K</font>,<span class="p3"><a href="finseq_4.html#K2" title="FINSEQ_4:func.2">&lt;*</a><span class="default"><font color="Olive" title="b2">c</font>,<font color="Olive" title="b3">f</font></span><a href="finseq_4.html#K2" title="FINSEQ_4:func.2">*&gt;</a></span></span><a href="tarski.html#K4" title="TARSKI:func.4">]</a></span> where <font color="Olive" title="b1">K</font> is    <a href="subset_1.html#M2" title="SUBSET_1:mode.2">Element</a> of  <a href="card_1.html#K7" title="CARD_1:func.7">Segm</a> 13, <font color="Olive" title="b2">c</font> is    <a href="subset_1.html#M2" title="SUBSET_1:mode.2">Element</a> of  <a href="scmfsa_1.html#K3" title="SCMFSA_1:func.3">SCM+FSA-Data-Loc</a> , <font color="Olive" title="b3">f</font> is    <a href="subset_1.html#M2" title="SUBSET_1:mode.2">Element</a> of  <a href="scmfsa_1.html#K4" title="SCMFSA_1:func.4">SCM+FSA-Data*-Loc</a>  : <font color="Olive" title="b1">K</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <span class="p1"><a href="tarski.html#K2" title="TARSKI:func.2">{</a><span class="default">11,12</span><a href="tarski.html#K2" title="TARSKI:func.2">}</a></span> </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="c1">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <span class="p1"><a href="zfmisc_1.html#K2" title="ZFMISC_1:func.2">[:</a><span class="default"><a href="scmfsa_1.html#K5" title="SCMFSA_1:func.5">NAT</a> ,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="tarski.html#K3" title="TARSKI:func.3">union</a> <span class="p5"><a href="tarski.html#K2" title="TARSKI:func.2">{</a><span class="default"><a href="numbers.html#K4" title="NUMBERS:func.4">INT</a> ,<span class="p0">(<span class="default"><a href="numbers.html#K4" title="NUMBERS:func.4">INT</a>  <a href="finseq_1.html#K13" title="FINSEQ_1:func.13">*</a> </span>)</span></span><a href="tarski.html#K2" title="TARSKI:func.2">}</a></span></span>)</span> <a href="xboole_0.html#K2" title="XBOOLE_0:func.2">\/</a> <a href="scmfsa_1.html#K2" title="SCMFSA_1:func.2">SCM+FSA-Memory</a> </span>)</span> <a href="finseq_1.html#K13" title="FINSEQ_1:func.13">*</a> </span>)</span></span><a href="zfmisc_1.html#K2" title="ZFMISC_1:func.2">:]</a></span></span><br/>

<b>then consider </b><font color="Maroon" title="c2">K</font> being    <a href="subset_1.html#M2" title="SUBSET_1:mode.2">Element</a> of  <a href="card_1.html#K7" title="CARD_1:func.7">Segm</a> 13, <font color="Maroon" title="c3">c</font> being    <a href="subset_1.html#M2" title="SUBSET_1:mode.2">Element</a> of  <a href="scmfsa_1.html#K3" title="SCMFSA_1:func.3">SCM+FSA-Data-Loc</a> , <font color="Maroon" title="c4">f</font> being    <a href="subset_1.html#M2" title="SUBSET_1:mode.2">Element</a> of  <a href="scmfsa_1.html#K4" title="SCMFSA_1:func.4">SCM+FSA-Data*-Loc</a> <b> such that </b><br/><a NAME="E3:9_1_1_2"/><i><font color="Green" title="E5">A5</font></i>: 
( <font color="Maroon" title="c1">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1"><a href="tarski.html#K4" title="TARSKI:func.4">[</a><span class="default"><font color="Maroon" title="c2">K</font>,<span class="p2"><a href="finseq_4.html#K2" title="FINSEQ_4:func.2">&lt;*</a><span class="default"><font color="Maroon" title="c3">c</font>,<font color="Maroon" title="c4">f</font></span><a href="finseq_4.html#K2" title="FINSEQ_4:func.2">*&gt;</a></span></span><a href="tarski.html#K4" title="TARSKI:func.4">]</a></span> &amp; <font color="Maroon" title="c2">K</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <span class="p1"><a href="tarski.html#K2" title="TARSKI:func.2">{</a><span class="default">11,12</span><a href="tarski.html#K2" title="TARSKI:func.2">}</a></span> )
 ;<br/>
<b>reconsider </b><font color="Maroon" title="c5">c</font> = <font color="Maroon" title="c3">c</font>, <font color="Maroon" title="c6">f</font> = <font color="Maroon" title="c4">f</font> as    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of <span class="p1">(<span class="default"><a href="tarski.html#K3" title="TARSKI:func.3">union</a> <span class="p2"><a href="tarski.html#K2" title="TARSKI:func.2">{</a><span class="default"><a href="numbers.html#K4" title="NUMBERS:func.4">INT</a> ,<span class="p3">(<span class="default"><a href="numbers.html#K4" title="NUMBERS:func.4">INT</a>  <a href="finseq_1.html#K13" title="FINSEQ_1:func.13">*</a> </span>)</span></span><a href="tarski.html#K2" title="TARSKI:func.2">}</a></span></span>)</span> <a href="xboole_0.html#K2" title="XBOOLE_0:func.2">\/</a> <a href="scmfsa_1.html#K2" title="SCMFSA_1:func.2">SCM+FSA-Memory</a>  <b>by </b><i><a class="txt" href="scmfsa_1.html#E1:9_1_1"><i><font color="Green" title="E2">A1</font></i></a>, <a class="ref" href="tarski.html#D3" title="TARSKI:def.3">TARSKI:def 3</a></i>;<br/>
<a NAME="E5:9_1_1_2"/>
<span class="p1"><a href="finseq_4.html#K2" title="FINSEQ_4:func.2">&lt;*</a><span class="default"><font color="Maroon" title="c5">c</font>,<font color="Maroon" title="c6">f</font></span><a href="finseq_4.html#K2" title="FINSEQ_4:func.2">*&gt;</a></span> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="tarski.html#K3" title="TARSKI:func.3">union</a> <span class="p3"><a href="tarski.html#K2" title="TARSKI:func.2">{</a><span class="default"><a href="numbers.html#K4" title="NUMBERS:func.4">INT</a> ,<span class="p4">(<span class="default"><a href="numbers.html#K4" title="NUMBERS:func.4">INT</a>  <a href="finseq_1.html#K13" title="FINSEQ_1:func.13">*</a> </span>)</span></span><a href="tarski.html#K2" title="TARSKI:func.2">}</a></span></span>)</span> <a href="xboole_0.html#K2" title="XBOOLE_0:func.2">\/</a> <a href="scmfsa_1.html#K2" title="SCMFSA_1:func.2">SCM+FSA-Memory</a> </span>)</span> <a href="finseq_1.html#K13" title="FINSEQ_1:func.13">*</a> 
 
<b>by </b><i><a class="ref" href="finseq_1.html#D11" title="FINSEQ_1:def.11">FINSEQ_1:def 11</a></i>;<br/>
<b>hence </b><a NAME="E6:9_1_1_2"/>
<font color="Maroon" title="c1">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <span class="p1"><a href="zfmisc_1.html#K2" title="ZFMISC_1:func.2">[:</a><span class="default"><a href="scmfsa_1.html#K5" title="SCMFSA_1:func.5">NAT</a> ,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="tarski.html#K3" title="TARSKI:func.3">union</a> <span class="p5"><a href="tarski.html#K2" title="TARSKI:func.2">{</a><span class="default"><a href="numbers.html#K4" title="NUMBERS:func.4">INT</a> ,<span class="p0">(<span class="default"><a href="numbers.html#K4" title="NUMBERS:func.4">INT</a>  <a href="finseq_1.html#K13" title="FINSEQ_1:func.13">*</a> </span>)</span></span><a href="tarski.html#K2" title="TARSKI:func.2">}</a></span></span>)</span> <a href="xboole_0.html#K2" title="XBOOLE_0:func.2">\/</a> <a href="scmfsa_1.html#K2" title="SCMFSA_1:func.2">SCM+FSA-Memory</a> </span>)</span> <a href="finseq_1.html#K13" title="FINSEQ_1:func.13">*</a> </span>)</span></span><a href="zfmisc_1.html#K2" title="ZFMISC_1:func.2">:]</a></span>
 <b>by </b><i><a class="txt" href="scmfsa_1.html#E3:9_1_1_2"><i><font color="Green" title="E5">A5</font></i></a>, <a class="ref" href="zfmisc_1.html#T106" title="ZFMISC_1:th.106">ZFMISC_1:106</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="E4:9_1_1"/>
 <a href="tarski.html#K3" title="TARSKI:func.3">union</a> <span class="p1"><a href="tarski.html#K1" title="TARSKI:func.1">{</a><span class="default"><a href="numbers.html#K4" title="NUMBERS:func.4">INT</a> </span><a href="tarski.html#K1" title="TARSKI:func.1">}</a></span> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a>  <a href="tarski.html#K3" title="TARSKI:func.3">union</a> <span class="p1"><a href="tarski.html#K2" title="TARSKI:func.2">{</a><span class="default"><a href="numbers.html#K4" title="NUMBERS:func.4">INT</a> ,<span class="p2">(<span class="default"><a href="numbers.html#K4" title="NUMBERS:func.4">INT</a>  <a href="finseq_1.html#K13" title="FINSEQ_1:func.13">*</a> </span>)</span></span><a href="tarski.html#K2" title="TARSKI:func.2">}</a></span>
 
<b>by </b><i><a class="ref" href="zfmisc_1.html#T12" title="ZFMISC_1:th.12">ZFMISC_1:12</a>, <a class="ref" href="zfmisc_1.html#T95" title="ZFMISC_1:th.95">ZFMISC_1:95</a></i>;<br/>
<a NAME="E5:9_1_1"/><b>then </b>
<span class="p1">(<span class="default"><a href="tarski.html#K3" title="TARSKI:func.3">union</a> <span class="p2"><a href="tarski.html#K1" title="TARSKI:func.1">{</a><span class="default"><a href="numbers.html#K4" title="NUMBERS:func.4">INT</a> </span><a href="tarski.html#K1" title="TARSKI:func.1">}</a></span></span>)</span> <a href="xboole_0.html#K2" title="XBOOLE_0:func.2">\/</a> <a href="ami_2.html#K3" title="AMI_2:func.3">SCM-Memory</a>  <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <span class="p1">(<span class="default"><a href="tarski.html#K3" title="TARSKI:func.3">union</a> <span class="p2"><a href="tarski.html#K2" title="TARSKI:func.2">{</a><span class="default"><a href="numbers.html#K4" title="NUMBERS:func.4">INT</a> ,<span class="p3">(<span class="default"><a href="numbers.html#K4" title="NUMBERS:func.4">INT</a>  <a href="finseq_1.html#K13" title="FINSEQ_1:func.13">*</a> </span>)</span></span><a href="tarski.html#K2" title="TARSKI:func.2">}</a></span></span>)</span> <a href="xboole_0.html#K2" title="XBOOLE_0:func.2">\/</a> <a href="scmfsa_1.html#K2" title="SCMFSA_1:func.2">SCM+FSA-Memory</a> 
 
<b>by </b><i><a class="ref" href="scmfsa_1.html#T1" target="_self" title="SCMFSA_1:th.1">Th1</a>, <a class="ref" href="xboole_1.html#T13" title="XBOOLE_1:th.13">XBOOLE_1:13</a></i>;<br/>
<a NAME="E6:9_1_1"/><b>then </b>
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="tarski.html#K3" title="TARSKI:func.3">union</a> <span class="p3"><a href="tarski.html#K1" title="TARSKI:func.1">{</a><span class="default"><a href="numbers.html#K4" title="NUMBERS:func.4">INT</a> </span><a href="tarski.html#K1" title="TARSKI:func.1">}</a></span></span>)</span> <a href="xboole_0.html#K2" title="XBOOLE_0:func.2">\/</a> <a href="ami_2.html#K3" title="AMI_2:func.3">SCM-Memory</a> </span>)</span> <a href="finseq_1.html#K13" title="FINSEQ_1:func.13">*</a>  <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="tarski.html#K3" title="TARSKI:func.3">union</a> <span class="p3"><a href="tarski.html#K2" title="TARSKI:func.2">{</a><span class="default"><a href="numbers.html#K4" title="NUMBERS:func.4">INT</a> ,<span class="p4">(<span class="default"><a href="numbers.html#K4" title="NUMBERS:func.4">INT</a>  <a href="finseq_1.html#K13" title="FINSEQ_1:func.13">*</a> </span>)</span></span><a href="tarski.html#K2" title="TARSKI:func.2">}</a></span></span>)</span> <a href="xboole_0.html#K2" title="XBOOLE_0:func.2">\/</a> <a href="scmfsa_1.html#K2" title="SCMFSA_1:func.2">SCM+FSA-Memory</a> </span>)</span> <a href="finseq_1.html#K13" title="FINSEQ_1:func.13">*</a> 
 
<b>by </b><i><a class="ref" href="finseq_1.html#T83" title="FINSEQ_1:th.83">FINSEQ_1:83</a></i>;<br/>
<a NAME="E7:9_1_1"/><b>then </b>
<span class="p1"><a href="zfmisc_1.html#K2" title="ZFMISC_1:func.2">[:</a><span class="default"><a href="scmfsa_1.html#K5" title="SCMFSA_1:func.5">NAT</a> ,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="tarski.html#K3" title="TARSKI:func.3">union</a> <span class="p5"><a href="tarski.html#K1" title="TARSKI:func.1">{</a><span class="default"><a href="numbers.html#K4" title="NUMBERS:func.4">INT</a> </span><a href="tarski.html#K1" title="TARSKI:func.1">}</a></span></span>)</span> <a href="xboole_0.html#K2" title="XBOOLE_0:func.2">\/</a> <a href="ami_2.html#K3" title="AMI_2:func.3">SCM-Memory</a> </span>)</span> <a href="finseq_1.html#K13" title="FINSEQ_1:func.13">*</a> </span>)</span></span><a href="zfmisc_1.html#K2" title="ZFMISC_1:func.2">:]</a></span> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <span class="p1"><a href="zfmisc_1.html#K2" title="ZFMISC_1:func.2">[:</a><span class="default"><a href="scmfsa_1.html#K5" title="SCMFSA_1:func.5">NAT</a> ,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="tarski.html#K3" title="TARSKI:func.3">union</a> <span class="p5"><a href="tarski.html#K2" title="TARSKI:func.2">{</a><span class="default"><a href="numbers.html#K4" title="NUMBERS:func.4">INT</a> ,<span class="p0">(<span class="default"><a href="numbers.html#K4" title="NUMBERS:func.4">INT</a>  <a href="finseq_1.html#K13" title="FINSEQ_1:func.13">*</a> </span>)</span></span><a href="tarski.html#K2" title="TARSKI:func.2">}</a></span></span>)</span> <a href="xboole_0.html#K2" title="XBOOLE_0:func.2">\/</a> <a href="scmfsa_1.html#K2" title="SCMFSA_1:func.2">SCM+FSA-Memory</a> </span>)</span> <a href="finseq_1.html#K13" title="FINSEQ_1:func.13">*</a> </span>)</span></span><a href="zfmisc_1.html#K2" title="ZFMISC_1:func.2">:]</a></span>
 
<b>by </b><i><a class="ref" href="zfmisc_1.html#T119" title="ZFMISC_1:th.119">ZFMISC_1:119</a></i>;<br/>
<a NAME="E8:9_1_1"/><b>then </b>
 <a href="ami_2.html#K6" title="AMI_2:func.6">SCM-Instr</a>  <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <span class="p1"><a href="zfmisc_1.html#K2" title="ZFMISC_1:func.2">[:</a><span class="default"><a href="scmfsa_1.html#K5" title="SCMFSA_1:func.5">NAT</a> ,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="tarski.html#K3" title="TARSKI:func.3">union</a> <span class="p5"><a href="tarski.html#K2" title="TARSKI:func.2">{</a><span class="default"><a href="numbers.html#K4" title="NUMBERS:func.4">INT</a> ,<span class="p0">(<span class="default"><a href="numbers.html#K4" title="NUMBERS:func.4">INT</a>  <a href="finseq_1.html#K13" title="FINSEQ_1:func.13">*</a> </span>)</span></span><a href="tarski.html#K2" title="TARSKI:func.2">}</a></span></span>)</span> <a href="xboole_0.html#K2" title="XBOOLE_0:func.2">\/</a> <a href="scmfsa_1.html#K2" title="SCMFSA_1:func.2">SCM+FSA-Memory</a> </span>)</span> <a href="finseq_1.html#K13" title="FINSEQ_1:func.13">*</a> </span>)</span></span><a href="zfmisc_1.html#K2" title="ZFMISC_1:func.2">:]</a></span>
 
<b>by </b><i><a class="ref" href="xboole_1.html#T1" title="XBOOLE_1:th.1">XBOOLE_1:1</a></i>;<br/>
<a NAME="E9:9_1_1"/><b>then </b>
<a href="ami_2.html#K6" title="AMI_2:func.6">SCM-Instr</a>  <a href="xboole_0.html#K2" title="XBOOLE_0:func.2">\/</a> <span class="p1">{<span class="default"> <span class="p2"><a href="tarski.html#K4" title="TARSKI:func.4">[</a><span class="default"><font color="Olive" title="b1">J</font>,<span class="p3"><a href="finseq_4.html#K3" title="FINSEQ_4:func.3">&lt;*</a><span class="default"><font color="Olive" title="b2">c</font>,<font color="Olive" title="b4">f</font>,<font color="Olive" title="b3">b</font></span><a href="finseq_4.html#K3" title="FINSEQ_4:func.3">*&gt;</a></span></span><a href="tarski.html#K4" title="TARSKI:func.4">]</a></span> where <font color="Olive" title="b1">J</font> is    <a href="subset_1.html#M2" title="SUBSET_1:mode.2">Element</a> of  <a href="card_1.html#K7" title="CARD_1:func.7">Segm</a> 13, <font color="Olive" title="b2">c</font>, <font color="Olive" title="b3">b</font> is    <a href="subset_1.html#M2" title="SUBSET_1:mode.2">Element</a> of  <a href="scmfsa_1.html#K3" title="SCMFSA_1:func.3">SCM+FSA-Data-Loc</a> , <font color="Olive" title="b4">f</font> is    <a href="subset_1.html#M2" title="SUBSET_1:mode.2">Element</a> of  <a href="scmfsa_1.html#K4" title="SCMFSA_1:func.4">SCM+FSA-Data*-Loc</a>  : <font color="Olive" title="b1">J</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <span class="p1"><a href="tarski.html#K2" title="TARSKI:func.2">{</a><span class="default">9,10</span><a href="tarski.html#K2" title="TARSKI:func.2">}</a></span> </span>}</span>  <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <span class="p1"><a href="zfmisc_1.html#K2" title="ZFMISC_1:func.2">[:</a><span class="default"><a href="scmfsa_1.html#K5" title="SCMFSA_1:func.5">NAT</a> ,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="tarski.html#K3" title="TARSKI:func.3">union</a> <span class="p5"><a href="tarski.html#K2" title="TARSKI:func.2">{</a><span class="default"><a href="numbers.html#K4" title="NUMBERS:func.4">INT</a> ,<span class="p0">(<span class="default"><a href="numbers.html#K4" title="NUMBERS:func.4">INT</a>  <a href="finseq_1.html#K13" title="FINSEQ_1:func.13">*</a> </span>)</span></span><a href="tarski.html#K2" title="TARSKI:func.2">}</a></span></span>)</span> <a href="xboole_0.html#K2" title="XBOOLE_0:func.2">\/</a> <a href="scmfsa_1.html#K2" title="SCMFSA_1:func.2">SCM+FSA-Memory</a> </span>)</span> <a href="finseq_1.html#K13" title="FINSEQ_1:func.13">*</a> </span>)</span></span><a href="zfmisc_1.html#K2" title="ZFMISC_1:func.2">:]</a></span>
 
<b>by </b><i><a class="txt" href="scmfsa_1.html#E2:9_1_1"><i><font color="Green" title="E3">A2</font></i></a>, <a class="ref" href="xboole_1.html#T8" title="XBOOLE_1:th.8">XBOOLE_1:8</a></i>;<br/>
<b>hence </b><a NAME="E10:9_1_1"/>
<span class="p1">(<span class="default"><a href="ami_2.html#K6" title="AMI_2:func.6">SCM-Instr</a>  <a href="xboole_0.html#K2" title="XBOOLE_0:func.2">\/</a> <span class="p2">{<span class="default"> <span class="p3"><a href="tarski.html#K4" title="TARSKI:func.4">[</a><span class="default"><font color="Olive" title="b1">J</font>,<span class="p4"><a href="finseq_4.html#K3" title="FINSEQ_4:func.3">&lt;*</a><span class="default"><font color="Olive" title="b2">c</font>,<font color="Olive" title="b4">f</font>,<font color="Olive" title="b3">b</font></span><a href="finseq_4.html#K3" title="FINSEQ_4:func.3">*&gt;</a></span></span><a href="tarski.html#K4" title="TARSKI:func.4">]</a></span> where <font color="Olive" title="b1">J</font> is    <a href="subset_1.html#M2" title="SUBSET_1:mode.2">Element</a> of  <a href="card_1.html#K7" title="CARD_1:func.7">Segm</a> 13, <font color="Olive" title="b2">c</font>, <font color="Olive" title="b3">b</font> is    <a href="subset_1.html#M2" title="SUBSET_1:mode.2">Element</a> of  <a href="scmfsa_1.html#K3" title="SCMFSA_1:func.3">SCM+FSA-Data-Loc</a> , <font color="Olive" title="b4">f</font> is    <a href="subset_1.html#M2" title="SUBSET_1:mode.2">Element</a> of  <a href="scmfsa_1.html#K4" title="SCMFSA_1:func.4">SCM+FSA-Data*-Loc</a>  : <font color="Olive" title="b1">J</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <span class="p1"><a href="tarski.html#K2" title="TARSKI:func.2">{</a><span class="default">9,10</span><a href="tarski.html#K2" title="TARSKI:func.2">}</a></span> </span>}</span> </span>)</span> <a href="xboole_0.html#K2" title="XBOOLE_0:func.2">\/</a> <span class="p1">{<span class="default"> <span class="p2"><a href="tarski.html#K4" title="TARSKI:func.4">[</a><span class="default"><font color="Olive" title="b1">K</font>,<span class="p3"><a href="finseq_4.html#K2" title="FINSEQ_4:func.2">&lt;*</a><span class="default"><font color="Olive" title="b2">c1</font>,<font color="Olive" title="b3">f1</font></span><a href="finseq_4.html#K2" title="FINSEQ_4:func.2">*&gt;</a></span></span><a href="tarski.html#K4" title="TARSKI:func.4">]</a></span> where <font color="Olive" title="b1">K</font> is    <a href="subset_1.html#M2" title="SUBSET_1:mode.2">Element</a> of  <a href="card_1.html#K7" title="CARD_1:func.7">Segm</a> 13, <font color="Olive" title="b2">c1</font> is    <a href="subset_1.html#M2" title="SUBSET_1:mode.2">Element</a> of  <a href="scmfsa_1.html#K3" title="SCMFSA_1:func.3">SCM+FSA-Data-Loc</a> , <font color="Olive" title="b3">f1</font> is    <a href="subset_1.html#M2" title="SUBSET_1:mode.2">Element</a> of  <a href="scmfsa_1.html#K4" title="SCMFSA_1:func.4">SCM+FSA-Data*-Loc</a>  : <font color="Olive" title="b1">K</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <span class="p1"><a href="tarski.html#K2" title="TARSKI:func.2">{</a><span class="default">11,12</span><a href="tarski.html#K2" title="TARSKI:func.2">}</a></span> </span>}</span>  is   <a href="subset_1.html#NM2" title="SUBSET_1:NM.2">Subset</a> of <span class="p1"><a href="zfmisc_1.html#K2" title="ZFMISC_1:func.2">[:</a><span class="default"><a href="scmfsa_1.html#K5" title="SCMFSA_1:func.5">NAT</a> ,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="tarski.html#K3" title="TARSKI:func.3">union</a> <span class="p5"><a href="tarski.html#K2" title="TARSKI:func.2">{</a><span class="default"><a href="numbers.html#K4" title="NUMBERS:func.4">INT</a> ,<span class="p0">(<span class="default"><a href="numbers.html#K4" title="NUMBERS:func.4">INT</a>  <a href="finseq_1.html#K13" title="FINSEQ_1:func.13">*</a> </span>)</span></span><a href="tarski.html#K2" title="TARSKI:func.2">}</a></span></span>)</span> <a href="xboole_0.html#K2" title="XBOOLE_0:func.2">\/</a> <a href="scmfsa_1.html#K2" title="SCMFSA_1:func.2">SCM+FSA-Memory</a> </span>)</span> <a href="finseq_1.html#K13" title="FINSEQ_1:func.13">*</a> </span>)</span></span><a href="zfmisc_1.html#K2" title="ZFMISC_1:func.2">:]</a></span>
 <b>by </b><i><a class="txt" href="scmfsa_1.html#E3:9_1_1"><i><font color="Green" title="E4">A4</font></i></a>, <a class="ref" href="xboole_1.html#T8" title="XBOOLE_1:th.8">XBOOLE_1:8</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>
