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<span class="kw">let </span><font color="Maroon" title="c1">S</font> be   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> ; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide">  for <font color="Olive" title="b1">i</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="Maroon" title="c1">S</font>  st  <a href="compos_0.html#K1" title="COMPOS_0:func.1">InsCode</a> <font color="Olive" title="b1">i</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 5 holds <br/> <a href="compos_0.html#K2" title="COMPOS_0:func.2">JumpPart</a> <font color="Olive" title="b1">i</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a> </span><br/><span class="kw">let </span><font color="Maroon" title="c2">i</font> be    <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="Maroon" title="c1">S</font>; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> (  <a href="compos_0.html#K1" title="COMPOS_0:func.1">InsCode</a> <font color="Maroon" title="c2">i</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 5 implies  <a href="compos_0.html#K2" title="COMPOS_0:func.2">JumpPart</a> <font color="Maroon" title="c2">i</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a>  )</span><br/>



<span class="kw">assume </span><a NAME="E1:21"/>
 <a href="compos_0.html#K1" title="COMPOS_0:func.1">InsCode</a> <font color="Maroon" title="c2">i</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 5
 ; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide">  <a href="compos_0.html#K2" title="COMPOS_0:func.2">JumpPart</a> <font color="Maroon" title="c2">i</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a> </span><br/>

<a NAME="E2:21"/><span class="kw">then </span>
<font color="Maroon" title="c2">i</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="b1">a</font>,<font color="Olive" title="b2">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="b1">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="b2">r</font> is   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Maroon" title="c1">S</font> : verum </span> } </span> 
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="scmringi.html#T7" target="_self" onmouseover="rs('scmringi/T7')" onmouseout="rh()">Th7</a></span>;<br/>
<a NAME="E3:21"/><span class="kw">then </span>
 ex <font color="Olive" title="b1">a</font> being    <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>  ex <font color="Olive" title="b2">r</font> being   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Maroon" title="c1">S</font> st <font color="Maroon" title="c2">i</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1"><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="p2"><a href="scmringi.html#K7" title="SCMRINGI:func.7">&lt;*</a><span class="default"><font color="Olive" title="b1">a</font>,<font color="Olive" title="b2">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>
 
;<br/>
<span class="kw">hence </span><a NAME="E4:21"/>
 <a href="compos_0.html#K2" title="COMPOS_0:func.2">JumpPart</a> <font color="Maroon" title="c2">i</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a> 
 ; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> verum</span><br/>


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