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<span class="kw">thus </span><a NAME="E1:3_1_1"/>
 not  <a href="scmpds_2.html#K1" title="SCMPDS_2:func.1">SCMPDS</a>  is  <a href="struct_0.html#V2" title="STRUCT_0:attr.2">empty</a> 
 <span class="kw">by</span> <span class="lab"><a class="ref" href="struct_0.html#D1" title="STRUCT_0:def.1">STRUCT_0:def 1</a></span>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide">  <a href="scmpds_2.html#K1" title="SCMPDS_2:func.1">SCMPDS</a>  is  <a href="compos_1.html#V3" title="COMPOS_1:attr.3">standard-ins</a> </span><br/>

<span class="kw">consider </span><font color="Maroon" title="c1">X</font> being   non  <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a>   <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a> <span class="kw"> such that </span><br/><a NAME="E3:3_1_1"/><span class="lab"><font color="Green" title="E1">A1</font></span>: 
 <a href="relat_1.html#K2" title="RELAT_1:func.2">proj2</a> <a href="scmpds_1.html#K1" title="SCMPDS_1:func.1">SCMPDS-Instr</a> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <font color="Maroon" title="c1">X</font> <a href="finseq_1.html#K13" title="FINSEQ_1:func.13">*</a> 
 <span class="kw">by</span> <span class="lab"><a class="ref" href="finseq_1.html#T85" title="FINSEQ_1:th.85">FINSEQ_1:85</a></span>;<br/>
<span class="kw">take </span>
<font color="Maroon" title="c1">X</font>
; <span class="comment"><font color="firebrick">:: according to </font></span><a class="ref" href="compos_1.html#D4" title="COMPOS_1:def.4">COMPOS_1:def 4</a> <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide">  the <a href="compos_1.html#U1" title="COMPOS_1:sel.1">Instructions</a> of <a href="scmpds_2.html#K1" title="SCMPDS_2:func.1">SCMPDS</a> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <span class="p1"><a href="zfmisc_1.html#K3" title="ZFMISC_1:func.3">[:</a><span class="default"><a href="numbers.html#K5" title="NUMBERS:func.5">NAT</a>,<span class="p2">(<span class="default"><a href="numbers.html#K5" title="NUMBERS:func.5">NAT</a> <a href="finseq_1.html#K13" title="FINSEQ_1:func.13">*</a></span>)</span>,<span class="p2">(<span class="default"><font color="Maroon" title="c1">X</font> <a href="finseq_1.html#K13" title="FINSEQ_1:func.13">*</a></span>)</span></span><a href="zfmisc_1.html#K3" title="ZFMISC_1:func.3">:]</a></span></span><br/>

<span class="kw">let </span><font color="Maroon" title="c2">x</font> be    <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a> ; <span class="comment"><font color="firebrick">:: according to </font></span><a class="ref" href="tarski.html#D3" title="TARSKI:def.3">TARSKI:def 3</a> <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> (  not <font color="Maroon" title="c2">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  the <a href="compos_1.html#U1" title="COMPOS_1:sel.1">Instructions</a> of <a href="scmpds_2.html#K1" title="SCMPDS_2:func.1">SCMPDS</a> or <font color="Maroon" title="c2">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <span class="p1"><a href="zfmisc_1.html#K3" title="ZFMISC_1:func.3">[:</a><span class="default"><a href="numbers.html#K5" title="NUMBERS:func.5">NAT</a>,<span class="p2">(<span class="default"><a href="numbers.html#K5" title="NUMBERS:func.5">NAT</a> <a href="finseq_1.html#K13" title="FINSEQ_1:func.13">*</a></span>)</span>,<span class="p2">(<span class="default"><font color="Maroon" title="c1">X</font> <a href="finseq_1.html#K13" title="FINSEQ_1:func.13">*</a></span>)</span></span><a href="zfmisc_1.html#K3" title="ZFMISC_1:func.3">:]</a></span> )</span><br/>

<span class="kw">assume </span><a NAME="E4:3_1_1"/><span class="lab"><font color="Green" title="E2">A2</font></span>: 
<font color="Maroon" title="c2">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  the <a href="compos_1.html#U1" title="COMPOS_1:sel.1">Instructions</a> of <a href="scmpds_2.html#K1" title="SCMPDS_2:func.1">SCMPDS</a>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> <font color="Maroon" title="c2">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <span class="p1"><a href="zfmisc_1.html#K3" title="ZFMISC_1:func.3">[:</a><span class="default"><a href="numbers.html#K5" title="NUMBERS:func.5">NAT</a>,<span class="p2">(<span class="default"><a href="numbers.html#K5" title="NUMBERS:func.5">NAT</a> <a href="finseq_1.html#K13" title="FINSEQ_1:func.13">*</a></span>)</span>,<span class="p2">(<span class="default"><font color="Maroon" title="c1">X</font> <a href="finseq_1.html#K13" title="FINSEQ_1:func.13">*</a></span>)</span></span><a href="zfmisc_1.html#K3" title="ZFMISC_1:func.3">:]</a></span></span><br/>

<a NAME="E5:3_1_1"/><span class="lab"><font color="Green" title="E3">A3</font></span>: 
 <a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a>  <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <a href="numbers.html#K5" title="NUMBERS:func.5">NAT</a> <a href="finseq_1.html#K13" title="FINSEQ_1:func.13">*</a> 
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="finseq_1.html#T49" title="FINSEQ_1:th.49">FINSEQ_1:49</a></span>;<br/>
<div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="3_1_1_1"><span class="kw">per </span></a><a class="txt" onclick="hs(this)" href="javascript:()"><span class="kw">cases </span></a><span class="hide"><a NAME="E1:3_1_1_1"/>
( <font color="Maroon" title="c2">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3"> { <span class="default"> <span class="p4"><a href="mcart_1.html#K3" title="MCART_1:func.3">[</a><span class="default"><a href="numbers.html#K6" title="NUMBERS:func.6">0</a>,<a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a>,<span class="p5"><a href="finseq_1.html#K12" title="FINSEQ_1:func.12">&lt;*</a><span class="default"><font color="Olive" title="b1">l</font></span><a href="finseq_1.html#K12" title="FINSEQ_1:func.12">*&gt;</a></span></span><a href="mcart_1.html#K3" title="MCART_1:func.3">]</a></span> where <font color="Olive" title="b1">l</font> is    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of  <a href="numbers.html#K4" title="NUMBERS:func.4">INT</a>  : verum </span> } </span>  <a href="xboole_0.html#K2" title="XBOOLE_0:func.2">\/</a> <span class="p3"> { <span class="default"> <span class="p4"><a href="mcart_1.html#K3" title="MCART_1:func.3">[</a><span class="default">1,<a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a>,<span class="p5"><a href="finseq_1.html#K12" title="FINSEQ_1:func.12">&lt;*</a><span class="default"><font color="Olive" title="b1">sp</font></span><a href="finseq_1.html#K12" title="FINSEQ_1:func.12">*&gt;</a></span></span><a href="mcart_1.html#K3" title="MCART_1:func.3">]</a></span> where <font color="Olive" title="b1">sp</font> is    <a href="subset_1.html#M2" title="SUBSET_1:mode.2">Element</a> of  <a href="ami_2.html#K4" title="AMI_2:func.4">SCM-Data-Loc</a>  : verum </span> } </span> </span>)</span> <a href="xboole_0.html#K2" title="XBOOLE_0:func.2">\/</a> <span class="p2"> { <span class="default"> <span class="p3"><a href="mcart_1.html#K3" title="MCART_1:func.3">[</a><span class="default"><font color="Olive" title="b1">I</font>,<a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a>,<span class="p4"><a href="scmpds_1.html#K9" title="SCMPDS_1:func.9">&lt;*</a><span class="default"><font color="Olive" title="b2">v</font>,<font color="Olive" title="b3">c</font></span><a href="scmpds_1.html#K9" title="SCMPDS_1:func.9">*&gt;</a></span></span><a href="mcart_1.html#K3" title="MCART_1:func.3">]</a></span> where <font color="Olive" title="b1">I</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> 14, <font color="Olive" title="b2">v</font> is    <a href="subset_1.html#M2" title="SUBSET_1:mode.2">Element</a> of  <a href="ami_2.html#K4" title="AMI_2:func.4">SCM-Data-Loc</a> , <font color="Olive" title="b3">c</font> is    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of  <a href="numbers.html#K4" title="NUMBERS:func.4">INT</a>  : <font color="Olive" title="b1">I</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <span class="p1"><a href="tarski.html#K2" title="TARSKI:func.2">{</a><span class="default">2,3</span><a href="tarski.html#K2" title="TARSKI:func.2">}</a></span> </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="mcart_1.html#K3" title="MCART_1:func.3">[</a><span class="default"><font color="Olive" title="b1">I</font>,<a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a>,<span class="p3"><a href="finseq_1.html#K11" title="FINSEQ_1:func.11">&lt;*</a><span class="default"><font color="Olive" title="b2">v</font>,<font color="Olive" title="b3">c1</font>,<font color="Olive" title="b4">c2</font></span><a href="finseq_1.html#K11" title="FINSEQ_1:func.11">*&gt;</a></span></span><a href="mcart_1.html#K3" title="MCART_1:func.3">]</a></span> where <font color="Olive" title="b1">I</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> 14, <font color="Olive" title="b2">v</font> is    <a href="subset_1.html#M2" title="SUBSET_1:mode.2">Element</a> of  <a href="ami_2.html#K4" title="AMI_2:func.4">SCM-Data-Loc</a> , <font color="Olive" title="b3">c1</font>, <font color="Olive" title="b4">c2</font> is    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of  <a href="numbers.html#K4" title="NUMBERS:func.4">INT</a>  : <font color="Olive" title="b1">I</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <span class="p1"><a href="enumset1.html#K3" title="ENUMSET1:func.3">{</a><span class="default">4,5,6,7,8</span><a href="enumset1.html#K3" title="ENUMSET1:func.3">}</a></span> </span> } </span>  or <font color="Maroon" title="c2">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <span class="p1"> { <span class="default"> <span class="p2"><a href="mcart_1.html#K3" title="MCART_1:func.3">[</a><span class="default"><font color="Olive" title="b1">I</font>,<a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a>,<span class="p3"><a href="finseq_4.html#K7" title="FINSEQ_4:func.7">&lt;*</a><span class="default"><font color="Olive" title="b2">v1</font>,<font color="Olive" title="b3">v2</font>,<font color="Olive" title="b4">c1</font>,<font color="Olive" title="b5">c2</font></span><a href="finseq_4.html#K7" title="FINSEQ_4:func.7">*&gt;</a></span></span><a href="mcart_1.html#K3" title="MCART_1:func.3">]</a></span> where <font color="Olive" title="b1">I</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> 14, <font color="Olive" title="b2">v1</font>, <font color="Olive" title="b3">v2</font> is    <a href="subset_1.html#M2" title="SUBSET_1:mode.2">Element</a> of  <a href="ami_2.html#K4" title="AMI_2:func.4">SCM-Data-Loc</a> , <font color="Olive" title="b4">c1</font>, <font color="Olive" title="b5">c2</font> is    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of  <a href="numbers.html#K4" title="NUMBERS:func.4">INT</a>  : <font color="Olive" title="b1">I</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <span class="p1"><a href="enumset1.html#K3" title="ENUMSET1:func.3">{</a><span class="default">9,10,11,12,13</span><a href="enumset1.html#K3" title="ENUMSET1:func.3">}</a></span> </span> } </span>  )
 </span><span class="kw">by</span> <span class="lab"><a class="txt" href="#E4:3_1_1"><span class="lab"><font color="Green" title="E2">A2</font></span></a>, <a class="ref" href="xboole_0.html#D3" title="XBOOLE_0:def.3">XBOOLE_0:def 3</a></span>;<br/><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="3_1_1_1_1"><span class="kw">suppose </span></a><a NAME="E1:3_1_1_1_1"/><span class="lab"><font color="Green" title="E4">A4</font></span>: 
<font color="Maroon" title="c2">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3"> { <span class="default"> <span class="p4"><a href="mcart_1.html#K3" title="MCART_1:func.3">[</a><span class="default"><a href="numbers.html#K6" title="NUMBERS:func.6">0</a>,<a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a>,<span class="p5"><a href="finseq_1.html#K12" title="FINSEQ_1:func.12">&lt;*</a><span class="default"><font color="Olive" title="b1">l</font></span><a href="finseq_1.html#K12" title="FINSEQ_1:func.12">*&gt;</a></span></span><a href="mcart_1.html#K3" title="MCART_1:func.3">]</a></span> where <font color="Olive" title="b1">l</font> is    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of  <a href="numbers.html#K4" title="NUMBERS:func.4">INT</a>  : verum </span> } </span>  <a href="xboole_0.html#K2" title="XBOOLE_0:func.2">\/</a> <span class="p3"> { <span class="default"> <span class="p4"><a href="mcart_1.html#K3" title="MCART_1:func.3">[</a><span class="default">1,<a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a>,<span class="p5"><a href="finseq_1.html#K12" title="FINSEQ_1:func.12">&lt;*</a><span class="default"><font color="Olive" title="b1">sp</font></span><a href="finseq_1.html#K12" title="FINSEQ_1:func.12">*&gt;</a></span></span><a href="mcart_1.html#K3" title="MCART_1:func.3">]</a></span> where <font color="Olive" title="b1">sp</font> is    <a href="subset_1.html#M2" title="SUBSET_1:mode.2">Element</a> of  <a href="ami_2.html#K4" title="AMI_2:func.4">SCM-Data-Loc</a>  : verum </span> } </span> </span>)</span> <a href="xboole_0.html#K2" title="XBOOLE_0:func.2">\/</a> <span class="p2"> { <span class="default"> <span class="p3"><a href="mcart_1.html#K3" title="MCART_1:func.3">[</a><span class="default"><font color="Olive" title="b1">I</font>,<a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a>,<span class="p4"><a href="scmpds_1.html#K9" title="SCMPDS_1:func.9">&lt;*</a><span class="default"><font color="Olive" title="b2">v</font>,<font color="Olive" title="b3">c</font></span><a href="scmpds_1.html#K9" title="SCMPDS_1:func.9">*&gt;</a></span></span><a href="mcart_1.html#K3" title="MCART_1:func.3">]</a></span> where <font color="Olive" title="b1">I</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> 14, <font color="Olive" title="b2">v</font> is    <a href="subset_1.html#M2" title="SUBSET_1:mode.2">Element</a> of  <a href="ami_2.html#K4" title="AMI_2:func.4">SCM-Data-Loc</a> , <font color="Olive" title="b3">c</font> is    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of  <a href="numbers.html#K4" title="NUMBERS:func.4">INT</a>  : <font color="Olive" title="b1">I</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <span class="p1"><a href="tarski.html#K2" title="TARSKI:func.2">{</a><span class="default">2,3</span><a href="tarski.html#K2" title="TARSKI:func.2">}</a></span> </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="mcart_1.html#K3" title="MCART_1:func.3">[</a><span class="default"><font color="Olive" title="b1">I</font>,<a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a>,<span class="p3"><a href="finseq_1.html#K11" title="FINSEQ_1:func.11">&lt;*</a><span class="default"><font color="Olive" title="b2">v</font>,<font color="Olive" title="b3">c1</font>,<font color="Olive" title="b4">c2</font></span><a href="finseq_1.html#K11" title="FINSEQ_1:func.11">*&gt;</a></span></span><a href="mcart_1.html#K3" title="MCART_1:func.3">]</a></span> where <font color="Olive" title="b1">I</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> 14, <font color="Olive" title="b2">v</font> is    <a href="subset_1.html#M2" title="SUBSET_1:mode.2">Element</a> of  <a href="ami_2.html#K4" title="AMI_2:func.4">SCM-Data-Loc</a> , <font color="Olive" title="b3">c1</font>, <font color="Olive" title="b4">c2</font> is    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of  <a href="numbers.html#K4" title="NUMBERS:func.4">INT</a>  : <font color="Olive" title="b1">I</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <span class="p1"><a href="enumset1.html#K3" title="ENUMSET1:func.3">{</a><span class="default">4,5,6,7,8</span><a href="enumset1.html#K3" title="ENUMSET1:func.3">}</a></span> </span> } </span> 
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> <font color="Maroon" title="c2">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <span class="p1"><a href="zfmisc_1.html#K3" title="ZFMISC_1:func.3">[:</a><span class="default"><a href="numbers.html#K5" title="NUMBERS:func.5">NAT</a>,<span class="p2">(<span class="default"><a href="numbers.html#K5" title="NUMBERS:func.5">NAT</a> <a href="finseq_1.html#K13" title="FINSEQ_1:func.13">*</a></span>)</span>,<span class="p2">(<span class="default"><font color="Maroon" title="c1">X</font> <a href="finseq_1.html#K13" title="FINSEQ_1:func.13">*</a></span>)</span></span><a href="zfmisc_1.html#K3" title="ZFMISC_1:func.3">:]</a></span></span><br/><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="3_1_1_1_1_1"><span class="kw">per </span></a><a class="txt" onclick="hs(this)" href="javascript:()"><span class="kw">cases </span></a><span class="hide"><a NAME="E1:3_1_1_1_1_1"/>
( <font color="Maroon" title="c2">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <span class="p1">(<span class="default"><span class="p2"> { <span class="default"> <span class="p3"><a href="mcart_1.html#K3" title="MCART_1:func.3">[</a><span class="default"><a href="numbers.html#K6" title="NUMBERS:func.6">0</a>,<a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a>,<span class="p4"><a href="finseq_1.html#K12" title="FINSEQ_1:func.12">&lt;*</a><span class="default"><font color="Olive" title="b1">l</font></span><a href="finseq_1.html#K12" title="FINSEQ_1:func.12">*&gt;</a></span></span><a href="mcart_1.html#K3" title="MCART_1:func.3">]</a></span> where <font color="Olive" title="b1">l</font> is    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of  <a href="numbers.html#K4" title="NUMBERS:func.4">INT</a>  : verum </span> } </span>  <a href="xboole_0.html#K2" title="XBOOLE_0:func.2">\/</a> <span class="p2"> { <span class="default"> <span class="p3"><a href="mcart_1.html#K3" title="MCART_1:func.3">[</a><span class="default">1,<a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a>,<span class="p4"><a href="finseq_1.html#K12" title="FINSEQ_1:func.12">&lt;*</a><span class="default"><font color="Olive" title="b1">sp</font></span><a href="finseq_1.html#K12" title="FINSEQ_1:func.12">*&gt;</a></span></span><a href="mcart_1.html#K3" title="MCART_1:func.3">]</a></span> where <font color="Olive" title="b1">sp</font> is    <a href="subset_1.html#M2" title="SUBSET_1:mode.2">Element</a> of  <a href="ami_2.html#K4" title="AMI_2:func.4">SCM-Data-Loc</a>  : verum </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="mcart_1.html#K3" title="MCART_1:func.3">[</a><span class="default"><font color="Olive" title="b1">I</font>,<a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a>,<span class="p3"><a href="scmpds_1.html#K9" title="SCMPDS_1:func.9">&lt;*</a><span class="default"><font color="Olive" title="b2">v</font>,<font color="Olive" title="b3">c</font></span><a href="scmpds_1.html#K9" title="SCMPDS_1:func.9">*&gt;</a></span></span><a href="mcart_1.html#K3" title="MCART_1:func.3">]</a></span> where <font color="Olive" title="b1">I</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> 14, <font color="Olive" title="b2">v</font> is    <a href="subset_1.html#M2" title="SUBSET_1:mode.2">Element</a> of  <a href="ami_2.html#K4" title="AMI_2:func.4">SCM-Data-Loc</a> , <font color="Olive" title="b3">c</font> is    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of  <a href="numbers.html#K4" title="NUMBERS:func.4">INT</a>  : <font color="Olive" title="b1">I</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <span class="p1"><a href="tarski.html#K2" title="TARSKI:func.2">{</a><span class="default">2,3</span><a href="tarski.html#K2" title="TARSKI:func.2">}</a></span> </span> } </span>  or <font color="Maroon" title="c2">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <span class="p1"> { <span class="default"> <span class="p2"><a href="mcart_1.html#K3" title="MCART_1:func.3">[</a><span class="default"><font color="Olive" title="b1">I</font>,<a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a>,<span class="p3"><a href="finseq_1.html#K11" title="FINSEQ_1:func.11">&lt;*</a><span class="default"><font color="Olive" title="b2">v</font>,<font color="Olive" title="b3">c1</font>,<font color="Olive" title="b4">c2</font></span><a href="finseq_1.html#K11" title="FINSEQ_1:func.11">*&gt;</a></span></span><a href="mcart_1.html#K3" title="MCART_1:func.3">]</a></span> where <font color="Olive" title="b1">I</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> 14, <font color="Olive" title="b2">v</font> is    <a href="subset_1.html#M2" title="SUBSET_1:mode.2">Element</a> of  <a href="ami_2.html#K4" title="AMI_2:func.4">SCM-Data-Loc</a> , <font color="Olive" title="b3">c1</font>, <font color="Olive" title="b4">c2</font> is    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of  <a href="numbers.html#K4" title="NUMBERS:func.4">INT</a>  : <font color="Olive" title="b1">I</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <span class="p1"><a href="enumset1.html#K3" title="ENUMSET1:func.3">{</a><span class="default">4,5,6,7,8</span><a href="enumset1.html#K3" title="ENUMSET1:func.3">}</a></span> </span> } </span>  )
 </span><span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:3_1_1_1_1"><span class="lab"><font color="Green" title="E4">A4</font></span></a>, <a class="ref" href="xboole_0.html#D3" title="XBOOLE_0:def.3">XBOOLE_0:def 3</a></span>;<br/><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="3_1_1_1_1_1_1"><span class="kw">suppose </span></a><a NAME="E1:3_1_1_1_1_1_1"/><span class="lab"><font color="Green" title="E5">A5</font></span>: 
<font color="Maroon" title="c2">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <span class="p1">(<span class="default"><span class="p2"> { <span class="default"> <span class="p3"><a href="mcart_1.html#K3" title="MCART_1:func.3">[</a><span class="default"><a href="numbers.html#K6" title="NUMBERS:func.6">0</a>,<a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a>,<span class="p4"><a href="finseq_1.html#K12" title="FINSEQ_1:func.12">&lt;*</a><span class="default"><font color="Olive" title="b1">l</font></span><a href="finseq_1.html#K12" title="FINSEQ_1:func.12">*&gt;</a></span></span><a href="mcart_1.html#K3" title="MCART_1:func.3">]</a></span> where <font color="Olive" title="b1">l</font> is    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of  <a href="numbers.html#K4" title="NUMBERS:func.4">INT</a>  : verum </span> } </span>  <a href="xboole_0.html#K2" title="XBOOLE_0:func.2">\/</a> <span class="p2"> { <span class="default"> <span class="p3"><a href="mcart_1.html#K3" title="MCART_1:func.3">[</a><span class="default">1,<a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a>,<span class="p4"><a href="finseq_1.html#K12" title="FINSEQ_1:func.12">&lt;*</a><span class="default"><font color="Olive" title="b1">sp</font></span><a href="finseq_1.html#K12" title="FINSEQ_1:func.12">*&gt;</a></span></span><a href="mcart_1.html#K3" title="MCART_1:func.3">]</a></span> where <font color="Olive" title="b1">sp</font> is    <a href="subset_1.html#M2" title="SUBSET_1:mode.2">Element</a> of  <a href="ami_2.html#K4" title="AMI_2:func.4">SCM-Data-Loc</a>  : verum </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="mcart_1.html#K3" title="MCART_1:func.3">[</a><span class="default"><font color="Olive" title="b1">I</font>,<a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a>,<span class="p3"><a href="scmpds_1.html#K9" title="SCMPDS_1:func.9">&lt;*</a><span class="default"><font color="Olive" title="b2">v</font>,<font color="Olive" title="b3">c</font></span><a href="scmpds_1.html#K9" title="SCMPDS_1:func.9">*&gt;</a></span></span><a href="mcart_1.html#K3" title="MCART_1:func.3">]</a></span> where <font color="Olive" title="b1">I</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> 14, <font color="Olive" title="b2">v</font> is    <a href="subset_1.html#M2" title="SUBSET_1:mode.2">Element</a> of  <a href="ami_2.html#K4" title="AMI_2:func.4">SCM-Data-Loc</a> , <font color="Olive" title="b3">c</font> is    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of  <a href="numbers.html#K4" title="NUMBERS:func.4">INT</a>  : <font color="Olive" title="b1">I</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <span class="p1"><a href="tarski.html#K2" title="TARSKI:func.2">{</a><span class="default">2,3</span><a href="tarski.html#K2" title="TARSKI:func.2">}</a></span> </span> } </span> 
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> <font color="Maroon" title="c2">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <span class="p1"><a href="zfmisc_1.html#K3" title="ZFMISC_1:func.3">[:</a><span class="default"><a href="numbers.html#K5" title="NUMBERS:func.5">NAT</a>,<span class="p2">(<span class="default"><a href="numbers.html#K5" title="NUMBERS:func.5">NAT</a> <a href="finseq_1.html#K13" title="FINSEQ_1:func.13">*</a></span>)</span>,<span class="p2">(<span class="default"><font color="Maroon" title="c1">X</font> <a href="finseq_1.html#K13" title="FINSEQ_1:func.13">*</a></span>)</span></span><a href="zfmisc_1.html#K3" title="ZFMISC_1:func.3">:]</a></span></span><br/><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="3_1_1_1_1_1_1_1"><span class="kw">per </span></a><a class="txt" onclick="hs(this)" href="javascript:()"><span class="kw">cases </span></a><span class="hide"><a NAME="E1:3_1_1_1_1_1_1_1"/>
( <font color="Maroon" title="c2">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <span class="p1"> { <span class="default"> <span class="p2"><a href="mcart_1.html#K3" title="MCART_1:func.3">[</a><span class="default"><a href="numbers.html#K6" title="NUMBERS:func.6">0</a>,<a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a>,<span class="p3"><a href="finseq_1.html#K12" title="FINSEQ_1:func.12">&lt;*</a><span class="default"><font color="Olive" title="b1">l</font></span><a href="finseq_1.html#K12" title="FINSEQ_1:func.12">*&gt;</a></span></span><a href="mcart_1.html#K3" title="MCART_1:func.3">]</a></span> where <font color="Olive" title="b1">l</font> is    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of  <a href="numbers.html#K4" title="NUMBERS:func.4">INT</a>  : verum </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="mcart_1.html#K3" title="MCART_1:func.3">[</a><span class="default">1,<a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a>,<span class="p3"><a href="finseq_1.html#K12" title="FINSEQ_1:func.12">&lt;*</a><span class="default"><font color="Olive" title="b1">sp</font></span><a href="finseq_1.html#K12" title="FINSEQ_1:func.12">*&gt;</a></span></span><a href="mcart_1.html#K3" title="MCART_1:func.3">]</a></span> where <font color="Olive" title="b1">sp</font> is    <a href="subset_1.html#M2" title="SUBSET_1:mode.2">Element</a> of  <a href="ami_2.html#K4" title="AMI_2:func.4">SCM-Data-Loc</a>  : verum </span> } </span>  or <font color="Maroon" title="c2">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <span class="p1"> { <span class="default"> <span class="p2"><a href="mcart_1.html#K3" title="MCART_1:func.3">[</a><span class="default"><font color="Olive" title="b1">I</font>,<a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a>,<span class="p3"><a href="scmpds_1.html#K9" title="SCMPDS_1:func.9">&lt;*</a><span class="default"><font color="Olive" title="b2">v</font>,<font color="Olive" title="b3">c</font></span><a href="scmpds_1.html#K9" title="SCMPDS_1:func.9">*&gt;</a></span></span><a href="mcart_1.html#K3" title="MCART_1:func.3">]</a></span> where <font color="Olive" title="b1">I</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> 14, <font color="Olive" title="b2">v</font> is    <a href="subset_1.html#M2" title="SUBSET_1:mode.2">Element</a> of  <a href="ami_2.html#K4" title="AMI_2:func.4">SCM-Data-Loc</a> , <font color="Olive" title="b3">c</font> is    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of  <a href="numbers.html#K4" title="NUMBERS:func.4">INT</a>  : <font color="Olive" title="b1">I</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <span class="p1"><a href="tarski.html#K2" title="TARSKI:func.2">{</a><span class="default">2,3</span><a href="tarski.html#K2" title="TARSKI:func.2">}</a></span> </span> } </span>  )
 </span><span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:3_1_1_1_1_1_1"><span class="lab"><font color="Green" title="E5">A5</font></span></a>, <a class="ref" href="xboole_0.html#D3" title="XBOOLE_0:def.3">XBOOLE_0:def 3</a></span>;<br/><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="3_1_1_1_1_1_1_1_1"><span class="kw">suppose </span></a><a NAME="E1:3_1_1_1_1_1_1_1_1"/><span class="lab"><font color="Green" title="E6">A6</font></span>: 
<font color="Maroon" title="c2">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <span class="p1"> { <span class="default"> <span class="p2"><a href="mcart_1.html#K3" title="MCART_1:func.3">[</a><span class="default"><a href="numbers.html#K6" title="NUMBERS:func.6">0</a>,<a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a>,<span class="p3"><a href="finseq_1.html#K12" title="FINSEQ_1:func.12">&lt;*</a><span class="default"><font color="Olive" title="b1">l</font></span><a href="finseq_1.html#K12" title="FINSEQ_1:func.12">*&gt;</a></span></span><a href="mcart_1.html#K3" title="MCART_1:func.3">]</a></span> where <font color="Olive" title="b1">l</font> is    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of  <a href="numbers.html#K4" title="NUMBERS:func.4">INT</a>  : verum </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="mcart_1.html#K3" title="MCART_1:func.3">[</a><span class="default">1,<a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a>,<span class="p3"><a href="finseq_1.html#K12" title="FINSEQ_1:func.12">&lt;*</a><span class="default"><font color="Olive" title="b1">sp</font></span><a href="finseq_1.html#K12" title="FINSEQ_1:func.12">*&gt;</a></span></span><a href="mcart_1.html#K3" title="MCART_1:func.3">]</a></span> where <font color="Olive" title="b1">sp</font> is    <a href="subset_1.html#M2" title="SUBSET_1:mode.2">Element</a> of  <a href="ami_2.html#K4" title="AMI_2:func.4">SCM-Data-Loc</a>  : verum </span> } </span> 
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> <font color="Maroon" title="c2">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <span class="p1"><a href="zfmisc_1.html#K3" title="ZFMISC_1:func.3">[:</a><span class="default"><a href="numbers.html#K5" title="NUMBERS:func.5">NAT</a>,<span class="p2">(<span class="default"><a href="numbers.html#K5" title="NUMBERS:func.5">NAT</a> <a href="finseq_1.html#K13" title="FINSEQ_1:func.13">*</a></span>)</span>,<span class="p2">(<span class="default"><font color="Maroon" title="c1">X</font> <a href="finseq_1.html#K13" title="FINSEQ_1:func.13">*</a></span>)</span></span><a href="zfmisc_1.html#K3" title="ZFMISC_1:func.3">:]</a></span></span><br/><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="3_1_1_1_1_1_1_1_1_1"><span class="kw">per </span></a><a class="txt" onclick="hs(this)" href="javascript:()"><span class="kw">cases </span></a><span class="hide"><a NAME="E1:3_1_1_1_1_1_1_1_1_1"/>
( <font color="Maroon" title="c2">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <span class="p1"> { <span class="default"> <span class="p2"><a href="mcart_1.html#K3" title="MCART_1:func.3">[</a><span class="default"><a href="numbers.html#K6" title="NUMBERS:func.6">0</a>,<a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a>,<span class="p3"><a href="finseq_1.html#K12" title="FINSEQ_1:func.12">&lt;*</a><span class="default"><font color="Olive" title="b1">l</font></span><a href="finseq_1.html#K12" title="FINSEQ_1:func.12">*&gt;</a></span></span><a href="mcart_1.html#K3" title="MCART_1:func.3">]</a></span> where <font color="Olive" title="b1">l</font> is    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of  <a href="numbers.html#K4" title="NUMBERS:func.4">INT</a>  : verum </span> } </span>  or <font color="Maroon" title="c2">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <span class="p1"> { <span class="default"> <span class="p2"><a href="mcart_1.html#K3" title="MCART_1:func.3">[</a><span class="default">1,<a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a>,<span class="p3"><a href="finseq_1.html#K12" title="FINSEQ_1:func.12">&lt;*</a><span class="default"><font color="Olive" title="b1">sp</font></span><a href="finseq_1.html#K12" title="FINSEQ_1:func.12">*&gt;</a></span></span><a href="mcart_1.html#K3" title="MCART_1:func.3">]</a></span> where <font color="Olive" title="b1">sp</font> is    <a href="subset_1.html#M2" title="SUBSET_1:mode.2">Element</a> of  <a href="ami_2.html#K4" title="AMI_2:func.4">SCM-Data-Loc</a>  : verum </span> } </span>  )
 </span><span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:3_1_1_1_1_1_1_1_1"><span class="lab"><font color="Green" title="E6">A6</font></span></a>, <a class="ref" href="xboole_0.html#D3" title="XBOOLE_0:def.3">XBOOLE_0:def 3</a></span>;<br/><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="3_1_1_1_1_1_1_1_1_1_1"><span class="kw">suppose </span></a><a NAME="E1:3_1_1_1_1_1_1_1_1_1_1"/>
<font color="Maroon" title="c2">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <span class="p1"> { <span class="default"> <span class="p2"><a href="mcart_1.html#K3" title="MCART_1:func.3">[</a><span class="default"><a href="numbers.html#K6" title="NUMBERS:func.6">0</a>,<a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a>,<span class="p3"><a href="finseq_1.html#K12" title="FINSEQ_1:func.12">&lt;*</a><span class="default"><font color="Olive" title="b1">l</font></span><a href="finseq_1.html#K12" title="FINSEQ_1:func.12">*&gt;</a></span></span><a href="mcart_1.html#K3" title="MCART_1:func.3">]</a></span> where <font color="Olive" title="b1">l</font> is    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of  <a href="numbers.html#K4" title="NUMBERS:func.4">INT</a>  : verum </span> } </span> 
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> <font color="Maroon" title="c2">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <span class="p1"><a href="zfmisc_1.html#K3" title="ZFMISC_1:func.3">[:</a><span class="default"><a href="numbers.html#K5" title="NUMBERS:func.5">NAT</a>,<span class="p2">(<span class="default"><a href="numbers.html#K5" title="NUMBERS:func.5">NAT</a> <a href="finseq_1.html#K13" title="FINSEQ_1:func.13">*</a></span>)</span>,<span class="p2">(<span class="default"><font color="Maroon" title="c1">X</font> <a href="finseq_1.html#K13" title="FINSEQ_1:func.13">*</a></span>)</span></span><a href="zfmisc_1.html#K3" title="ZFMISC_1:func.3">:]</a></span></span><br/><div class="add"><span class="kw">then </span><span class="kw">consider </span><font color="Maroon" title="c3">l</font> being    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of  <a href="numbers.html#K4" title="NUMBERS:func.4">INT</a> <span class="kw"> such that </span><br/><a NAME="E3:3_1_1_1_1_1_1_1_1_1_1"/><span class="lab"><font color="Green" title="E7">A7</font></span>: 
<font color="Maroon" title="c2">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1"><a href="mcart_1.html#K3" title="MCART_1:func.3">[</a><span class="default"><a href="numbers.html#K6" title="NUMBERS:func.6">0</a>,<a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a>,<span class="p2"><a href="finseq_1.html#K12" title="FINSEQ_1:func.12">&lt;*</a><span class="default"><font color="Maroon" title="c3">l</font></span><a href="finseq_1.html#K12" title="FINSEQ_1:func.12">*&gt;</a></span></span><a href="mcart_1.html#K3" title="MCART_1:func.3">]</a></span>
 ;<br/><a NAME="E4:3_1_1_1_1_1_1_1_1_1_1"/>
<span class="p1"><a href="finseq_1.html#K12" title="FINSEQ_1:func.12">&lt;*</a><span class="default"><font color="Maroon" title="c3">l</font></span><a href="finseq_1.html#K12" title="FINSEQ_1:func.12">*&gt;</a></span> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="relat_1.html#K2" title="RELAT_1:func.2">proj2</a> <a href="scmpds_1.html#K1" title="SCMPDS_1:func.1">SCMPDS-Instr</a>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E4:3_1_1"><span class="lab"><font color="Green" title="E2">A2</font></span></a>, <a class="txt" href="#E3:3_1_1_1_1_1_1_1_1_1_1"><span class="lab"><font color="Green" title="E7">A7</font></span></a>, <a class="ref" href="relat_1.html#D5" title="RELAT_1:def.5">RELAT_1:def 5</a></span>;<br/><a NAME="E5:3_1_1_1_1_1_1_1_1_1_1"/><span class="kw">then </span>
<span class="p1"><a href="finseq_1.html#K12" title="FINSEQ_1:func.12">&lt;*</a><span class="default"><font color="Maroon" title="c3">l</font></span><a href="finseq_1.html#K12" title="FINSEQ_1:func.12">*&gt;</a></span> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c1">X</font> <a href="finseq_1.html#K13" title="FINSEQ_1:func.13">*</a> 
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E3:3_1_1"><span class="lab"><font color="Green" title="E1">A1</font></span></a></span>;<br/><span class="kw">hence </span><a NAME="E6:3_1_1_1_1_1_1_1_1_1_1"/>
<font color="Maroon" title="c2">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <span class="p1"><a href="zfmisc_1.html#K3" title="ZFMISC_1:func.3">[:</a><span class="default"><a href="numbers.html#K5" title="NUMBERS:func.5">NAT</a>,<span class="p2">(<span class="default"><a href="numbers.html#K5" title="NUMBERS:func.5">NAT</a> <a href="finseq_1.html#K13" title="FINSEQ_1:func.13">*</a></span>)</span>,<span class="p2">(<span class="default"><font color="Maroon" title="c1">X</font> <a href="finseq_1.html#K13" title="FINSEQ_1:func.13">*</a></span>)</span></span><a href="zfmisc_1.html#K3" title="ZFMISC_1:func.3">:]</a></span>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E3:3_1_1_1_1_1_1_1_1_1_1"><span class="lab"><font color="Green" title="E7">A7</font></span></a>, <a class="txt" href="#E5:3_1_1"><span class="lab"><font color="Green" title="E3">A3</font></span></a>, <a class="ref" href="mcart_1.html#T69" title="MCART_1:th.69">MCART_1:69</a></span>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> verum</span><br/></div><span class="kw">end;</span></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="3_1_1_1_1_1_1_1_1_1_2"><span class="kw">suppose </span></a><a NAME="E1:3_1_1_1_1_1_1_1_1_1_2"/>
<font color="Maroon" title="c2">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <span class="p1"> { <span class="default"> <span class="p2"><a href="mcart_1.html#K3" title="MCART_1:func.3">[</a><span class="default">1,<a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a>,<span class="p3"><a href="finseq_1.html#K12" title="FINSEQ_1:func.12">&lt;*</a><span class="default"><font color="Olive" title="b1">sp</font></span><a href="finseq_1.html#K12" title="FINSEQ_1:func.12">*&gt;</a></span></span><a href="mcart_1.html#K3" title="MCART_1:func.3">]</a></span> where <font color="Olive" title="b1">sp</font> is    <a href="subset_1.html#M2" title="SUBSET_1:mode.2">Element</a> of  <a href="ami_2.html#K4" title="AMI_2:func.4">SCM-Data-Loc</a>  : verum </span> } </span> 
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> <font color="Maroon" title="c2">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <span class="p1"><a href="zfmisc_1.html#K3" title="ZFMISC_1:func.3">[:</a><span class="default"><a href="numbers.html#K5" title="NUMBERS:func.5">NAT</a>,<span class="p2">(<span class="default"><a href="numbers.html#K5" title="NUMBERS:func.5">NAT</a> <a href="finseq_1.html#K13" title="FINSEQ_1:func.13">*</a></span>)</span>,<span class="p2">(<span class="default"><font color="Maroon" title="c1">X</font> <a href="finseq_1.html#K13" title="FINSEQ_1:func.13">*</a></span>)</span></span><a href="zfmisc_1.html#K3" title="ZFMISC_1:func.3">:]</a></span></span><br/><div class="add"><span class="kw">then </span><span class="kw">consider </span><font color="Maroon" title="c3">sp</font> being    <a href="subset_1.html#M2" title="SUBSET_1:mode.2">Element</a> of  <a href="ami_2.html#K4" title="AMI_2:func.4">SCM-Data-Loc</a> <span class="kw"> such that </span><br/><a NAME="E3:3_1_1_1_1_1_1_1_1_1_2"/><span class="lab"><font color="Green" title="E7">A8</font></span>: 
<font color="Maroon" title="c2">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1"><a href="mcart_1.html#K3" title="MCART_1:func.3">[</a><span class="default">1,<a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a>,<span class="p2"><a href="finseq_1.html#K12" title="FINSEQ_1:func.12">&lt;*</a><span class="default"><font color="Maroon" title="c3">sp</font></span><a href="finseq_1.html#K12" title="FINSEQ_1:func.12">*&gt;</a></span></span><a href="mcart_1.html#K3" title="MCART_1:func.3">]</a></span>
 ;<br/><a NAME="E4:3_1_1_1_1_1_1_1_1_1_2"/>
<span class="p1"><a href="finseq_1.html#K12" title="FINSEQ_1:func.12">&lt;*</a><span class="default"><font color="Maroon" title="c3">sp</font></span><a href="finseq_1.html#K12" title="FINSEQ_1:func.12">*&gt;</a></span> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="relat_1.html#K2" title="RELAT_1:func.2">proj2</a> <a href="scmpds_1.html#K1" title="SCMPDS_1:func.1">SCMPDS-Instr</a>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E4:3_1_1"><span class="lab"><font color="Green" title="E2">A2</font></span></a>, <a class="txt" href="#E3:3_1_1_1_1_1_1_1_1_1_2"><span class="lab"><font color="Green" title="E7">A8</font></span></a>, <a class="ref" href="relat_1.html#D5" title="RELAT_1:def.5">RELAT_1:def 5</a></span>;<br/><a NAME="E5:3_1_1_1_1_1_1_1_1_1_2"/><span class="kw">then </span>
<span class="p1"><a href="finseq_1.html#K12" title="FINSEQ_1:func.12">&lt;*</a><span class="default"><font color="Maroon" title="c3">sp</font></span><a href="finseq_1.html#K12" title="FINSEQ_1:func.12">*&gt;</a></span> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c1">X</font> <a href="finseq_1.html#K13" title="FINSEQ_1:func.13">*</a> 
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E3:3_1_1"><span class="lab"><font color="Green" title="E1">A1</font></span></a></span>;<br/><span class="kw">hence </span><a NAME="E6:3_1_1_1_1_1_1_1_1_1_2"/>
<font color="Maroon" title="c2">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <span class="p1"><a href="zfmisc_1.html#K3" title="ZFMISC_1:func.3">[:</a><span class="default"><a href="numbers.html#K5" title="NUMBERS:func.5">NAT</a>,<span class="p2">(<span class="default"><a href="numbers.html#K5" title="NUMBERS:func.5">NAT</a> <a href="finseq_1.html#K13" title="FINSEQ_1:func.13">*</a></span>)</span>,<span class="p2">(<span class="default"><font color="Maroon" title="c1">X</font> <a href="finseq_1.html#K13" title="FINSEQ_1:func.13">*</a></span>)</span></span><a href="zfmisc_1.html#K3" title="ZFMISC_1:func.3">:]</a></span>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E3:3_1_1_1_1_1_1_1_1_1_2"><span class="lab"><font color="Green" title="E7">A8</font></span></a>, <a class="txt" href="#E5:3_1_1"><span class="lab"><font color="Green" title="E3">A3</font></span></a>, <a class="ref" href="mcart_1.html#T69" title="MCART_1:th.69">MCART_1:69</a></span>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> verum</span><br/></div><span class="kw">end;</span></div></div><span class="kw">end;</span></div></div><span class="kw">end;</span></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="3_1_1_1_1_1_1_1_2"><span class="kw">suppose </span></a><a NAME="E1:3_1_1_1_1_1_1_1_2"/>
<font color="Maroon" title="c2">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <span class="p1"> { <span class="default"> <span class="p2"><a href="mcart_1.html#K3" title="MCART_1:func.3">[</a><span class="default"><font color="Olive" title="b1">I</font>,<a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a>,<span class="p3"><a href="scmpds_1.html#K9" title="SCMPDS_1:func.9">&lt;*</a><span class="default"><font color="Olive" title="b2">v</font>,<font color="Olive" title="b3">c</font></span><a href="scmpds_1.html#K9" title="SCMPDS_1:func.9">*&gt;</a></span></span><a href="mcart_1.html#K3" title="MCART_1:func.3">]</a></span> where <font color="Olive" title="b1">I</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> 14, <font color="Olive" title="b2">v</font> is    <a href="subset_1.html#M2" title="SUBSET_1:mode.2">Element</a> of  <a href="ami_2.html#K4" title="AMI_2:func.4">SCM-Data-Loc</a> , <font color="Olive" title="b3">c</font> is    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of  <a href="numbers.html#K4" title="NUMBERS:func.4">INT</a>  : <font color="Olive" title="b1">I</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <span class="p1"><a href="tarski.html#K2" title="TARSKI:func.2">{</a><span class="default">2,3</span><a href="tarski.html#K2" title="TARSKI:func.2">}</a></span> </span> } </span> 
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> <font color="Maroon" title="c2">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <span class="p1"><a href="zfmisc_1.html#K3" title="ZFMISC_1:func.3">[:</a><span class="default"><a href="numbers.html#K5" title="NUMBERS:func.5">NAT</a>,<span class="p2">(<span class="default"><a href="numbers.html#K5" title="NUMBERS:func.5">NAT</a> <a href="finseq_1.html#K13" title="FINSEQ_1:func.13">*</a></span>)</span>,<span class="p2">(<span class="default"><font color="Maroon" title="c1">X</font> <a href="finseq_1.html#K13" title="FINSEQ_1:func.13">*</a></span>)</span></span><a href="zfmisc_1.html#K3" title="ZFMISC_1:func.3">:]</a></span></span><br/><div class="add"><span class="kw">then </span><span class="kw">consider </span><font color="Maroon" title="c3">I</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> 14, <font color="Maroon" title="c4">v</font> being    <a href="subset_1.html#M2" title="SUBSET_1:mode.2">Element</a> of  <a href="ami_2.html#K4" title="AMI_2:func.4">SCM-Data-Loc</a> , <font color="Maroon" title="c5">c</font> being    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of  <a href="numbers.html#K4" title="NUMBERS:func.4">INT</a> <span class="kw"> such that </span><br/><a NAME="E3:3_1_1_1_1_1_1_1_2"/><span class="lab"><font color="Green" title="E6">A9</font></span>: 
( <font color="Maroon" title="c2">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1"><a href="mcart_1.html#K3" title="MCART_1:func.3">[</a><span class="default"><font color="Maroon" title="c3">I</font>,<a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a>,<span class="p2"><a href="scmpds_1.html#K9" title="SCMPDS_1:func.9">&lt;*</a><span class="default"><font color="Maroon" title="c4">v</font>,<font color="Maroon" title="c5">c</font></span><a href="scmpds_1.html#K9" title="SCMPDS_1:func.9">*&gt;</a></span></span><a href="mcart_1.html#K3" title="MCART_1:func.3">]</a></span> &amp; <font color="Maroon" title="c3">I</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <span class="p1"><a href="tarski.html#K2" title="TARSKI:func.2">{</a><span class="default">2,3</span><a href="tarski.html#K2" title="TARSKI:func.2">}</a></span> )
 ;<br/><a NAME="E4:3_1_1_1_1_1_1_1_2"/>
<span class="p1"><a href="scmpds_1.html#K9" title="SCMPDS_1:func.9">&lt;*</a><span class="default"><font color="Maroon" title="c4">v</font>,<font color="Maroon" title="c5">c</font></span><a href="scmpds_1.html#K9" title="SCMPDS_1:func.9">*&gt;</a></span> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="relat_1.html#K2" title="RELAT_1:func.2">proj2</a> <a href="scmpds_1.html#K1" title="SCMPDS_1:func.1">SCMPDS-Instr</a>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E4:3_1_1"><span class="lab"><font color="Green" title="E2">A2</font></span></a>, <a class="txt" href="#E3:3_1_1_1_1_1_1_1_2"><span class="lab"><font color="Green" title="E6">A9</font></span></a>, <a class="ref" href="relat_1.html#D5" title="RELAT_1:def.5">RELAT_1:def 5</a></span>;<br/><a NAME="E5:3_1_1_1_1_1_1_1_2"/><span class="kw">then </span>
<span class="p1"><a href="scmpds_1.html#K9" title="SCMPDS_1:func.9">&lt;*</a><span class="default"><font color="Maroon" title="c4">v</font>,<font color="Maroon" title="c5">c</font></span><a href="scmpds_1.html#K9" title="SCMPDS_1:func.9">*&gt;</a></span> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c1">X</font> <a href="finseq_1.html#K13" title="FINSEQ_1:func.13">*</a> 
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E3:3_1_1"><span class="lab"><font color="Green" title="E1">A1</font></span></a></span>;<br/><span class="kw">hence </span><a NAME="E6:3_1_1_1_1_1_1_1_2"/>
<font color="Maroon" title="c2">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <span class="p1"><a href="zfmisc_1.html#K3" title="ZFMISC_1:func.3">[:</a><span class="default"><a href="numbers.html#K5" title="NUMBERS:func.5">NAT</a>,<span class="p2">(<span class="default"><a href="numbers.html#K5" title="NUMBERS:func.5">NAT</a> <a href="finseq_1.html#K13" title="FINSEQ_1:func.13">*</a></span>)</span>,<span class="p2">(<span class="default"><font color="Maroon" title="c1">X</font> <a href="finseq_1.html#K13" title="FINSEQ_1:func.13">*</a></span>)</span></span><a href="zfmisc_1.html#K3" title="ZFMISC_1:func.3">:]</a></span>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E3:3_1_1_1_1_1_1_1_2"><span class="lab"><font color="Green" title="E6">A9</font></span></a>, <a class="txt" href="#E5:3_1_1"><span class="lab"><font color="Green" title="E3">A3</font></span></a>, <a class="ref" href="mcart_1.html#T69" title="MCART_1:th.69">MCART_1:69</a></span>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> verum</span><br/></div><span class="kw">end;</span></div></div><span class="kw">end;</span></div></div><span class="kw">end;</span></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="3_1_1_1_1_1_2"><span class="kw">suppose </span></a><a NAME="E1:3_1_1_1_1_1_2"/>
<font color="Maroon" title="c2">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <span class="p1"> { <span class="default"> <span class="p2"><a href="mcart_1.html#K3" title="MCART_1:func.3">[</a><span class="default"><font color="Olive" title="b1">I</font>,<a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a>,<span class="p3"><a href="finseq_1.html#K11" title="FINSEQ_1:func.11">&lt;*</a><span class="default"><font color="Olive" title="b2">v</font>,<font color="Olive" title="b3">c1</font>,<font color="Olive" title="b4">c2</font></span><a href="finseq_1.html#K11" title="FINSEQ_1:func.11">*&gt;</a></span></span><a href="mcart_1.html#K3" title="MCART_1:func.3">]</a></span> where <font color="Olive" title="b1">I</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> 14, <font color="Olive" title="b2">v</font> is    <a href="subset_1.html#M2" title="SUBSET_1:mode.2">Element</a> of  <a href="ami_2.html#K4" title="AMI_2:func.4">SCM-Data-Loc</a> , <font color="Olive" title="b3">c1</font>, <font color="Olive" title="b4">c2</font> is    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of  <a href="numbers.html#K4" title="NUMBERS:func.4">INT</a>  : <font color="Olive" title="b1">I</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <span class="p1"><a href="enumset1.html#K3" title="ENUMSET1:func.3">{</a><span class="default">4,5,6,7,8</span><a href="enumset1.html#K3" title="ENUMSET1:func.3">}</a></span> </span> } </span> 
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> <font color="Maroon" title="c2">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <span class="p1"><a href="zfmisc_1.html#K3" title="ZFMISC_1:func.3">[:</a><span class="default"><a href="numbers.html#K5" title="NUMBERS:func.5">NAT</a>,<span class="p2">(<span class="default"><a href="numbers.html#K5" title="NUMBERS:func.5">NAT</a> <a href="finseq_1.html#K13" title="FINSEQ_1:func.13">*</a></span>)</span>,<span class="p2">(<span class="default"><font color="Maroon" title="c1">X</font> <a href="finseq_1.html#K13" title="FINSEQ_1:func.13">*</a></span>)</span></span><a href="zfmisc_1.html#K3" title="ZFMISC_1:func.3">:]</a></span></span><br/><div class="add"><span class="kw">then </span><span class="kw">consider </span><font color="Maroon" title="c3">I</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> 14, <font color="Maroon" title="c4">v</font> being    <a href="subset_1.html#M2" title="SUBSET_1:mode.2">Element</a> of  <a href="ami_2.html#K4" title="AMI_2:func.4">SCM-Data-Loc</a> , <font color="Maroon" title="c5">c1</font>, <font color="Maroon" title="c6">c2</font> being    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of  <a href="numbers.html#K4" title="NUMBERS:func.4">INT</a> <span class="kw"> such that </span><br/><a NAME="E3:3_1_1_1_1_1_2"/><span class="lab"><font color="Green" title="E5">A10</font></span>: 
( <font color="Maroon" title="c2">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1"><a href="mcart_1.html#K3" title="MCART_1:func.3">[</a><span class="default"><font color="Maroon" title="c3">I</font>,<a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a>,<span class="p2"><a href="finseq_1.html#K11" title="FINSEQ_1:func.11">&lt;*</a><span class="default"><font color="Maroon" title="c4">v</font>,<font color="Maroon" title="c5">c1</font>,<font color="Maroon" title="c6">c2</font></span><a href="finseq_1.html#K11" title="FINSEQ_1:func.11">*&gt;</a></span></span><a href="mcart_1.html#K3" title="MCART_1:func.3">]</a></span> &amp; <font color="Maroon" title="c3">I</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <span class="p1"><a href="enumset1.html#K3" title="ENUMSET1:func.3">{</a><span class="default">4,5,6,7,8</span><a href="enumset1.html#K3" title="ENUMSET1:func.3">}</a></span> )
 ;<br/><a NAME="E4:3_1_1_1_1_1_2"/>
<span class="p1"><a href="finseq_1.html#K11" title="FINSEQ_1:func.11">&lt;*</a><span class="default"><font color="Maroon" title="c4">v</font>,<font color="Maroon" title="c5">c1</font>,<font color="Maroon" title="c6">c2</font></span><a href="finseq_1.html#K11" title="FINSEQ_1:func.11">*&gt;</a></span> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="relat_1.html#K2" title="RELAT_1:func.2">proj2</a> <a href="scmpds_1.html#K1" title="SCMPDS_1:func.1">SCMPDS-Instr</a>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E4:3_1_1"><span class="lab"><font color="Green" title="E2">A2</font></span></a>, <a class="txt" href="#E3:3_1_1_1_1_1_2"><span class="lab"><font color="Green" title="E5">A10</font></span></a>, <a class="ref" href="relat_1.html#D5" title="RELAT_1:def.5">RELAT_1:def 5</a></span>;<br/><a NAME="E5:3_1_1_1_1_1_2"/><span class="kw">then </span>
<span class="p1"><a href="finseq_1.html#K11" title="FINSEQ_1:func.11">&lt;*</a><span class="default"><font color="Maroon" title="c4">v</font>,<font color="Maroon" title="c5">c1</font>,<font color="Maroon" title="c6">c2</font></span><a href="finseq_1.html#K11" title="FINSEQ_1:func.11">*&gt;</a></span> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c1">X</font> <a href="finseq_1.html#K13" title="FINSEQ_1:func.13">*</a> 
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E3:3_1_1"><span class="lab"><font color="Green" title="E1">A1</font></span></a></span>;<br/><span class="kw">hence </span><a NAME="E6:3_1_1_1_1_1_2"/>
<font color="Maroon" title="c2">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <span class="p1"><a href="zfmisc_1.html#K3" title="ZFMISC_1:func.3">[:</a><span class="default"><a href="numbers.html#K5" title="NUMBERS:func.5">NAT</a>,<span class="p2">(<span class="default"><a href="numbers.html#K5" title="NUMBERS:func.5">NAT</a> <a href="finseq_1.html#K13" title="FINSEQ_1:func.13">*</a></span>)</span>,<span class="p2">(<span class="default"><font color="Maroon" title="c1">X</font> <a href="finseq_1.html#K13" title="FINSEQ_1:func.13">*</a></span>)</span></span><a href="zfmisc_1.html#K3" title="ZFMISC_1:func.3">:]</a></span>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E3:3_1_1_1_1_1_2"><span class="lab"><font color="Green" title="E5">A10</font></span></a>, <a class="txt" href="#E5:3_1_1"><span class="lab"><font color="Green" title="E3">A3</font></span></a>, <a class="ref" href="mcart_1.html#T69" title="MCART_1:th.69">MCART_1:69</a></span>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> verum</span><br/></div><span class="kw">end;</span></div></div><span class="kw">end;</span></div></div><span class="kw">end;</span></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="3_1_1_1_2"><span class="kw">suppose </span></a><a NAME="E1:3_1_1_1_2"/>
<font color="Maroon" title="c2">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <span class="p1"> { <span class="default"> <span class="p2"><a href="mcart_1.html#K3" title="MCART_1:func.3">[</a><span class="default"><font color="Olive" title="b1">I</font>,<a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a>,<span class="p3"><a href="finseq_4.html#K7" title="FINSEQ_4:func.7">&lt;*</a><span class="default"><font color="Olive" title="b2">v1</font>,<font color="Olive" title="b3">v2</font>,<font color="Olive" title="b4">c1</font>,<font color="Olive" title="b5">c2</font></span><a href="finseq_4.html#K7" title="FINSEQ_4:func.7">*&gt;</a></span></span><a href="mcart_1.html#K3" title="MCART_1:func.3">]</a></span> where <font color="Olive" title="b1">I</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> 14, <font color="Olive" title="b2">v1</font>, <font color="Olive" title="b3">v2</font> is    <a href="subset_1.html#M2" title="SUBSET_1:mode.2">Element</a> of  <a href="ami_2.html#K4" title="AMI_2:func.4">SCM-Data-Loc</a> , <font color="Olive" title="b4">c1</font>, <font color="Olive" title="b5">c2</font> is    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of  <a href="numbers.html#K4" title="NUMBERS:func.4">INT</a>  : <font color="Olive" title="b1">I</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <span class="p1"><a href="enumset1.html#K3" title="ENUMSET1:func.3">{</a><span class="default">9,10,11,12,13</span><a href="enumset1.html#K3" title="ENUMSET1:func.3">}</a></span> </span> } </span> 
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> <font color="Maroon" title="c2">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <span class="p1"><a href="zfmisc_1.html#K3" title="ZFMISC_1:func.3">[:</a><span class="default"><a href="numbers.html#K5" title="NUMBERS:func.5">NAT</a>,<span class="p2">(<span class="default"><a href="numbers.html#K5" title="NUMBERS:func.5">NAT</a> <a href="finseq_1.html#K13" title="FINSEQ_1:func.13">*</a></span>)</span>,<span class="p2">(<span class="default"><font color="Maroon" title="c1">X</font> <a href="finseq_1.html#K13" title="FINSEQ_1:func.13">*</a></span>)</span></span><a href="zfmisc_1.html#K3" title="ZFMISC_1:func.3">:]</a></span></span><br/><div class="add"><span class="kw">then </span><span class="kw">consider </span><font color="Maroon" title="c3">I</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> 14, <font color="Maroon" title="c4">v1</font>, <font color="Maroon" title="c5">v2</font> being    <a href="subset_1.html#M2" title="SUBSET_1:mode.2">Element</a> of  <a href="ami_2.html#K4" title="AMI_2:func.4">SCM-Data-Loc</a> , <font color="Maroon" title="c6">c1</font>, <font color="Maroon" title="c7">c2</font> being    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of  <a href="numbers.html#K4" title="NUMBERS:func.4">INT</a> <span class="kw"> such that </span><br/><a NAME="E3:3_1_1_1_2"/><span class="lab"><font color="Green" title="E4">A11</font></span>: 
( <font color="Maroon" title="c2">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1"><a href="mcart_1.html#K3" title="MCART_1:func.3">[</a><span class="default"><font color="Maroon" title="c3">I</font>,<a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a>,<span class="p2"><a href="finseq_4.html#K7" title="FINSEQ_4:func.7">&lt;*</a><span class="default"><font color="Maroon" title="c4">v1</font>,<font color="Maroon" title="c5">v2</font>,<font color="Maroon" title="c6">c1</font>,<font color="Maroon" title="c7">c2</font></span><a href="finseq_4.html#K7" title="FINSEQ_4:func.7">*&gt;</a></span></span><a href="mcart_1.html#K3" title="MCART_1:func.3">]</a></span> &amp; <font color="Maroon" title="c3">I</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <span class="p1"><a href="enumset1.html#K3" title="ENUMSET1:func.3">{</a><span class="default">9,10,11,12,13</span><a href="enumset1.html#K3" title="ENUMSET1:func.3">}</a></span> )
 ;<br/><a NAME="E4:3_1_1_1_2"/>
<span class="p1"><a href="finseq_4.html#K7" title="FINSEQ_4:func.7">&lt;*</a><span class="default"><font color="Maroon" title="c4">v1</font>,<font color="Maroon" title="c5">v2</font>,<font color="Maroon" title="c6">c1</font>,<font color="Maroon" title="c7">c2</font></span><a href="finseq_4.html#K7" title="FINSEQ_4:func.7">*&gt;</a></span> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="relat_1.html#K2" title="RELAT_1:func.2">proj2</a> <a href="scmpds_1.html#K1" title="SCMPDS_1:func.1">SCMPDS-Instr</a>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E4:3_1_1"><span class="lab"><font color="Green" title="E2">A2</font></span></a>, <a class="txt" href="#E3:3_1_1_1_2"><span class="lab"><font color="Green" title="E4">A11</font></span></a>, <a class="ref" href="relat_1.html#D5" title="RELAT_1:def.5">RELAT_1:def 5</a></span>;<br/><a NAME="E5:3_1_1_1_2"/><span class="kw">then </span>
<span class="p1"><a href="finseq_4.html#K7" title="FINSEQ_4:func.7">&lt;*</a><span class="default"><font color="Maroon" title="c4">v1</font>,<font color="Maroon" title="c5">v2</font>,<font color="Maroon" title="c6">c1</font>,<font color="Maroon" title="c7">c2</font></span><a href="finseq_4.html#K7" title="FINSEQ_4:func.7">*&gt;</a></span> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c1">X</font> <a href="finseq_1.html#K13" title="FINSEQ_1:func.13">*</a> 
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E3:3_1_1"><span class="lab"><font color="Green" title="E1">A1</font></span></a></span>;<br/><span class="kw">hence </span><a NAME="E6:3_1_1_1_2"/>
<font color="Maroon" title="c2">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <span class="p1"><a href="zfmisc_1.html#K3" title="ZFMISC_1:func.3">[:</a><span class="default"><a href="numbers.html#K5" title="NUMBERS:func.5">NAT</a>,<span class="p2">(<span class="default"><a href="numbers.html#K5" title="NUMBERS:func.5">NAT</a> <a href="finseq_1.html#K13" title="FINSEQ_1:func.13">*</a></span>)</span>,<span class="p2">(<span class="default"><font color="Maroon" title="c1">X</font> <a href="finseq_1.html#K13" title="FINSEQ_1:func.13">*</a></span>)</span></span><a href="zfmisc_1.html#K3" title="ZFMISC_1:func.3">:]</a></span>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E3:3_1_1_1_2"><span class="lab"><font color="Green" title="E4">A11</font></span></a>, <a class="txt" href="#E5:3_1_1"><span class="lab"><font color="Green" title="E3">A3</font></span></a>, <a class="ref" href="mcart_1.html#T69" title="MCART_1:th.69">MCART_1:69</a></span>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> verum</span><br/></div><span class="kw">end;</span></div></div><span class="kw">end;</span></div>

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