<?xml version="1.0"?>
<div><span class="kw">theorem </span><span class="lab"><font color="Green" title="E14">Th8</font></span>: <a NAME="T8"><span class="comment"><font color="firebrick">:: SCMPDS_I:8</font></span><br/></a><div class="add"> for <font color="Olive" title="b1">x</font> being    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of  <a href="scmpds_i.html#K1" title="SCMPDS_I:func.1">SCMPDS-Instr</a>   holds <br/>( ( <font color="Olive" title="b1">x</font> <a href="tarski.html#R2" title="TARSKI:pred.2">in</a> <span class="p1"><a href="tarski.html#K1" title="TARSKI:func.1">{</a><span class="default"><span class="p2"><a href="xtuple_0.html#K3" title="XTUPLE_0:func.3">[</a><span class="default"><a href="numbers.html#K5" title="NUMBERS:func.5">0</a>,<a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a>,<a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a></span><a href="xtuple_0.html#K3" title="XTUPLE_0:func.3">]</a></span></span><a href="tarski.html#K1" title="TARSKI:func.1">}</a></span> &amp;  <a href="compos_0.html#K1" title="COMPOS_0:func.1">InsCode</a> <font color="Olive" title="b1">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="numbers.html#K5" title="NUMBERS:func.5">0</a>  ) or ( <font color="Olive" title="b1">x</font> <a href="tarski.html#R2" title="TARSKI:pred.2">in</a> <span class="p1"> { <span class="default"> <span class="p2"><a href="xtuple_0.html#K3" title="XTUPLE_0:func.3">[</a><span class="default">14,<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="b2">l</font></span><a href="finseq_1.html#K12" title="FINSEQ_1:func.12">*&gt;</a></span></span><a href="xtuple_0.html#K3" title="XTUPLE_0:func.3">]</a></span> where <font color="Olive" title="b2">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>  &amp;  <a href="compos_0.html#K1" title="COMPOS_0:func.1">InsCode</a> <font color="Olive" title="b1">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 14 ) or ( <font color="Olive" title="b1">x</font> <a href="tarski.html#R2" title="TARSKI:pred.2">in</a> <span class="p1"> { <span class="default"> <span class="p2"><a href="xtuple_0.html#K3" title="XTUPLE_0: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="b2">sp</font></span><a href="finseq_1.html#K12" title="FINSEQ_1:func.12">*&gt;</a></span></span><a href="xtuple_0.html#K3" title="XTUPLE_0:func.3">]</a></span> where <font color="Olive" title="b2">sp</font> is    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of  <a href="scm_inst.html#K2" title="SCM_INST:func.2">SCM-Data-Loc</a>  : verum </span> } </span>  &amp;  <a href="compos_0.html#K1" title="COMPOS_0:func.1">InsCode</a> <font color="Olive" title="b1">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 1 ) or ( <font color="Olive" title="b1">x</font> <a href="tarski.html#R2" title="TARSKI:pred.2">in</a> <span class="p1"> { <span class="default"> <span class="p2"><a href="xtuple_0.html#K3" title="XTUPLE_0:func.3">[</a><span class="default"><font color="Olive" title="b2">I</font>,<a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a>,<span class="p3"><a href="scmpds_i.html#K2" title="SCMPDS_I:func.2">&lt;*</a><span class="default"><font color="Olive" title="b3">v</font>,<font color="Olive" title="b4">c</font></span><a href="scmpds_i.html#K2" title="SCMPDS_I:func.2">*&gt;</a></span></span><a href="xtuple_0.html#K3" title="XTUPLE_0:func.3">]</a></span> where <font color="Olive" title="b2">I</font> is    <a href="subset_1.html#M2" title="SUBSET_1:mode.2">Element</a> of  <a href="card_1.html#K5" title="CARD_1:func.5">Segm</a> 15, <font color="Olive" title="b3">v</font> is    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of  <a href="scm_inst.html#K2" title="SCM_INST:func.2">SCM-Data-Loc</a> , <font color="Olive" title="b4">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="b2">I</font> <a href="tarski.html#R2" title="TARSKI: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>  &amp; (  <a href="compos_0.html#K1" title="COMPOS_0:func.1">InsCode</a> <font color="Olive" title="b1">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 2 or  <a href="compos_0.html#K1" title="COMPOS_0:func.1">InsCode</a> <font color="Olive" title="b1">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 3 ) ) or ( <font color="Olive" title="b1">x</font> <a href="tarski.html#R2" title="TARSKI:pred.2">in</a> <span class="p1"> { <span class="default"> <span class="p2"><a href="xtuple_0.html#K3" title="XTUPLE_0:func.3">[</a><span class="default"><font color="Olive" title="b2">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="b3">v</font>,<font color="Olive" title="b4">c1</font>,<font color="Olive" title="b5">c2</font></span><a href="finseq_1.html#K11" title="FINSEQ_1:func.11">*&gt;</a></span></span><a href="xtuple_0.html#K3" title="XTUPLE_0:func.3">]</a></span> where <font color="Olive" title="b2">I</font> is    <a href="subset_1.html#M2" title="SUBSET_1:mode.2">Element</a> of  <a href="card_1.html#K5" title="CARD_1:func.5">Segm</a> 15, <font color="Olive" title="b3">v</font> is    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of  <a href="scm_inst.html#K2" title="SCM_INST:func.2">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="b2">I</font> <a href="tarski.html#R2" title="TARSKI: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>  &amp; (  <a href="compos_0.html#K1" title="COMPOS_0:func.1">InsCode</a> <font color="Olive" title="b1">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 4 or  <a href="compos_0.html#K1" title="COMPOS_0:func.1">InsCode</a> <font color="Olive" title="b1">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 5 or  <a href="compos_0.html#K1" title="COMPOS_0:func.1">InsCode</a> <font color="Olive" title="b1">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 6 or  <a href="compos_0.html#K1" title="COMPOS_0:func.1">InsCode</a> <font color="Olive" title="b1">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 7 or  <a href="compos_0.html#K1" title="COMPOS_0:func.1">InsCode</a> <font color="Olive" title="b1">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 8 ) ) or ( <font color="Olive" title="b1">x</font> <a href="tarski.html#R2" title="TARSKI:pred.2">in</a> <span class="p1"> { <span class="default"> <span class="p2"><a href="xtuple_0.html#K3" title="XTUPLE_0:func.3">[</a><span class="default"><font color="Olive" title="b2">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="b3">v1</font>,<font color="Olive" title="b4">v2</font>,<font color="Olive" title="b5">c1</font>,<font color="Olive" title="b6">c2</font></span><a href="finseq_4.html#K7" title="FINSEQ_4:func.7">*&gt;</a></span></span><a href="xtuple_0.html#K3" title="XTUPLE_0:func.3">]</a></span> where <font color="Olive" title="b2">I</font> is    <a href="subset_1.html#M2" title="SUBSET_1:mode.2">Element</a> of  <a href="card_1.html#K5" title="CARD_1:func.5">Segm</a> 15, <font color="Olive" title="b3">v1</font>, <font color="Olive" title="b4">v2</font> is    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of  <a href="scm_inst.html#K2" title="SCM_INST:func.2">SCM-Data-Loc</a> , <font color="Olive" title="b5">c1</font>, <font color="Olive" title="b6">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="b2">I</font> <a href="tarski.html#R2" title="TARSKI: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>  &amp; (  <a href="compos_0.html#K1" title="COMPOS_0:func.1">InsCode</a> <font color="Olive" title="b1">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 9 or  <a href="compos_0.html#K1" title="COMPOS_0:func.1">InsCode</a> <font color="Olive" title="b1">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 10 or  <a href="compos_0.html#K1" title="COMPOS_0:func.1">InsCode</a> <font color="Olive" title="b1">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 11 or  <a href="compos_0.html#K1" title="COMPOS_0:func.1">InsCode</a> <font color="Olive" title="b1">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 12 or  <a href="compos_0.html#K1" title="COMPOS_0:func.1">InsCode</a> <font color="Olive" title="b1">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 13 ) ) )</div></div>
