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<span class="kw">let </span><font color="Maroon" title="c1">R</font> be   <a href="vectsp_1.html#NM3" title="VECTSP_1:NM.3">Ring</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">R</font>  st  <a href="compos_0.html#K5" title="COMPOS_0:func.5">InsCode</a> <font color="Olive" title="b1">I</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 7 holds <br/> <a href="finseq_1.html#K4" title="FINSEQ_1:func.4">dom</a> <span class="p1">(<span class="default"><a href="compos_0.html#K2" title="COMPOS_0:func.2">JumpPart</a> <font color="Olive" title="b1">I</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="finseq_1.html#K2" title="FINSEQ_1:func.2">Seg</a> 1</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">R</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#K5" title="COMPOS_0:func.5">InsCode</a> <font color="Maroon" title="c2">I</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 7 implies  <a href="finseq_1.html#K4" title="FINSEQ_1:func.4">dom</a> <span class="p1">(<span class="default"><a href="compos_0.html#K2" title="COMPOS_0:func.2">JumpPart</a> <font color="Maroon" title="c2">I</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="finseq_1.html#K2" title="FINSEQ_1:func.2">Seg</a> 1 )</span><br/>



<span class="kw">assume </span><a NAME="E1:23"/>
 <a href="compos_0.html#K5" title="COMPOS_0:func.5">InsCode</a> <font color="Maroon" title="c2">I</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 7
 ; <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="finseq_1.html#K4" title="FINSEQ_1:func.4">dom</a> <span class="p1">(<span class="default"><a href="compos_0.html#K2" title="COMPOS_0:func.2">JumpPart</a> <font color="Maroon" title="c2">I</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="finseq_1.html#K2" title="FINSEQ_1:func.2">Seg</a> 1</span><br/>

<a NAME="E2:23"/><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">7,<span class="p3"><a href="finseq_1.html#K9" title="FINSEQ_1:func.9">&lt;*</a><span class="default"><font color="Olive" title="b1">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="b2">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="b1">i</font> is   <a href="ordinal1.html#NM6" title="ORDINAL1:NM.6">Nat</a>, <font color="Olive" title="b2">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> 
 
<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/>
<span class="kw">then </span><span class="kw">consider </span><font color="Maroon" title="c3">i</font> being   <a href="ordinal1.html#NM6" title="ORDINAL1:NM.6">Nat</a>, <font color="Maroon" title="c4">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> <span class="kw"> such that </span><br/><a NAME="E4:23"/><span class="lab"><font color="Green" title="E16">A1</font></span>: 
<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">7,<span class="p2"><a href="finseq_1.html#K9" title="FINSEQ_1:func.9">&lt;*</a><span class="default"><font color="Maroon" title="c3">i</font></span><a href="finseq_1.html#K9" title="FINSEQ_1:func.9">*&gt;</a></span>,<span class="p2"><a href="finseq_1.html#K12" title="FINSEQ_1:func.12">&lt;*</a><span class="default"><font color="Maroon" title="c4">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>
 ;<br/>
<a NAME="E5:23"/>
 <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> <span class="p1"><a href="finseq_1.html#K9" title="FINSEQ_1:func.9">&lt;*</a><span class="default"><font color="Maroon" title="c3">i</font></span><a href="finseq_1.html#K9" title="FINSEQ_1:func.9">*&gt;</a></span>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E4:23"><span class="lab"><font color="Green" title="E16">A1</font></span></a></span>;<br/>
<span class="kw">hence </span><a NAME="E6:23"/>
 <a href="finseq_1.html#K4" title="FINSEQ_1:func.4">dom</a> <span class="p1">(<span class="default"><a href="compos_0.html#K2" title="COMPOS_0:func.2">JumpPart</a> <font color="Maroon" title="c2">I</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="finseq_1.html#K2" title="FINSEQ_1:func.2">Seg</a> 1
 <span class="kw">by</span> <span class="lab"><a class="ref" href="finseq_1.html#T38" onmouseover="rs('finseq_1/T38')" onmouseout="rh()">FINSEQ_1:38</a></span>; <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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