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<div><span class="kw">theorem </span><span class="lab"><font color="Green" title="E10">Th7</font></span>: <a NAME="T7"><span class="comment"><font color="firebrick">:: SCMRINGI:7</font></span><br/></a><div class="add"> for <font color="Olive" title="b1">S</font> being   non  <a href="struct_0.html#V2" title="STRUCT_0:attr.2">empty</a>   <a href="struct_0.html#L1" title="STRUCT_0:struct.1">1-sorted</a> <br/>  for <font color="Olive" title="b2">x</font> being    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of  <a href="scmringi.html#K1" title="SCMRINGI:func.1">SCM-Instr</a> <font color="Olive" title="b1">S</font>  holds <br/>( ( <font color="Olive" title="b2">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="b2">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="b2">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="b3">I</font>,<a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a>,<span class="p3"><a href="finseq_4.html#K2" title="FINSEQ_4:func.2">&lt;*</a><span class="default"><font color="Olive" title="b4">a</font>,<font color="Olive" title="b5">b</font></span><a href="finseq_4.html#K2" title="FINSEQ_4:func.2">*&gt;</a></span></span><a href="xtuple_0.html#K3" title="XTUPLE_0:func.3">]</a></span> where <font color="Olive" title="b3">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> 8, <font color="Olive" title="b4">a</font>, <font color="Olive" title="b5">b</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="b3">I</font> <a href="tarski.html#R2" title="TARSKI:pred.2">in</a> <span class="p1"><a href="enumset1.html#K2" title="ENUMSET1:func.2">{</a><span class="default">1,2,3,4</span><a href="enumset1.html#K2" title="ENUMSET1:func.2">}</a></span> </span> } </span>  &amp; (  <a href="compos_0.html#K1" title="COMPOS_0:func.1">InsCode</a> <font color="Olive" title="b2">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 1 or  <a href="compos_0.html#K1" title="COMPOS_0:func.1">InsCode</a> <font color="Olive" title="b2">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="b2">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 3 or  <a href="compos_0.html#K1" title="COMPOS_0:func.1">InsCode</a> <font color="Olive" title="b2">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 4 ) ) or ( <font color="Olive" title="b2">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">6,<span class="p3"><a href="finseq_1.html#K9" title="FINSEQ_1:func.9">&lt;*</a><span class="default"><font color="Olive" title="b3">i</font></span><a href="finseq_1.html#K9" title="FINSEQ_1:func.9">*&gt;</a></span>,<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> where <font color="Olive" title="b3">i</font> is   <a href="ordinal1.html#NM6" title="ORDINAL1:NM.6">Nat</a> : verum </span> } </span>  &amp;  <a href="compos_0.html#K1" title="COMPOS_0:func.1">InsCode</a> <font color="Olive" title="b2">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 6 ) or ( <font color="Olive" title="b2">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">7,<span class="p3"><a href="finseq_1.html#K9" title="FINSEQ_1:func.9">&lt;*</a><span class="default"><font color="Olive" title="b3">i</font></span><a href="finseq_1.html#K9" title="FINSEQ_1:func.9">*&gt;</a></span>,<span class="p3"><a href="finseq_1.html#K12" title="FINSEQ_1:func.12">&lt;*</a><span class="default"><font color="Olive" title="b4">a</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="b3">i</font> is   <a href="ordinal1.html#NM6" title="ORDINAL1:NM.6">Nat</a>, <font color="Olive" title="b4">a</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="b2">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 7 ) or ( <font color="Olive" title="b2">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">5,<a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a>,<span class="p3"><a href="scmringi.html#K7" title="SCMRINGI:func.7">&lt;*</a><span class="default"><font color="Olive" title="b3">a</font>,<font color="Olive" title="b4">r</font></span><a href="scmringi.html#K7" title="SCMRINGI:func.7">*&gt;</a></span></span><a href="xtuple_0.html#K3" title="XTUPLE_0:func.3">]</a></span> where <font color="Olive" title="b3">a</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">r</font> is   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Olive" title="b1">S</font> : verum </span> } </span>  &amp;  <a href="compos_0.html#K1" title="COMPOS_0:func.1">InsCode</a> <font color="Olive" title="b2">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 5 ) )</div></div>
