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<div><span class="kw">theorem </span><span class="lab"><font color="Green" title="E9">Th7</font></span>: <a NAME="T7"><span class="comment"><font color="firebrick">:: SCMRING2:7</font></span><br/></a><div class="add"> for <font color="Olive" title="b1">R</font> being   <a href="vectsp_1.html#NM3" title="VECTSP_1:NM.3">Ring</a><br/>  for <font color="Olive" title="b2">I</font> being    <a href="hidden.html#M2" title="HIDDEN:mode.2">set</a>  holds <br/> ( <font color="Olive" title="b2">I</font> is   <a href="compos_1.html#NM1" title="COMPOS_1:NM.1">Instruction</a> of <span class="p1">(<span class="default"><a href="scmring2.html#K1" title="SCMRING2:func.1">SCM</a> <font color="Olive" title="b1">R</font></span>)</span> iff ( <font color="Olive" title="b2">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"><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> or  ex <font color="Olive" title="b3">a</font>, <font color="Olive" title="b4">b</font> being   <a href="scmring2.html#NM1" title="SCMRING2:NM.1">Data-Location</a> of <font color="Olive" title="b1">R</font> st <font color="Olive" title="b2">I</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b3">a</font> <a href="scmring2.html#K3" title="SCMRING2:func.3">:=</a> <font color="Olive" title="b4">b</font> or  ex <font color="Olive" title="b3">a</font>, <font color="Olive" title="b4">b</font> being   <a href="scmring2.html#NM1" title="SCMRING2:NM.1">Data-Location</a> of <font color="Olive" title="b1">R</font> st <font color="Olive" title="b2">I</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="scmring2.html#K4" title="SCMRING2:func.4">AddTo</a> (<font color="Olive" title="b3">a</font>,<font color="Olive" title="b4">b</font>) or  ex <font color="Olive" title="b3">a</font>, <font color="Olive" title="b4">b</font> being   <a href="scmring2.html#NM1" title="SCMRING2:NM.1">Data-Location</a> of <font color="Olive" title="b1">R</font> st <font color="Olive" title="b2">I</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="scmring2.html#K5" title="SCMRING2:func.5">SubFrom</a> (<font color="Olive" title="b3">a</font>,<font color="Olive" title="b4">b</font>) or  ex <font color="Olive" title="b3">a</font>, <font color="Olive" title="b4">b</font> being   <a href="scmring2.html#NM1" title="SCMRING2:NM.1">Data-Location</a> of <font color="Olive" title="b1">R</font> st <font color="Olive" title="b2">I</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="scmring2.html#K6" title="SCMRING2:func.6">MultBy</a> (<font color="Olive" title="b3">a</font>,<font color="Olive" title="b4">b</font>) or  ex <font color="Olive" title="b3">i1</font> being   <a href="ordinal1.html#NM6" title="ORDINAL1:NM.6">Nat</a> st <font color="Olive" title="b2">I</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="scmring2.html#K8" title="SCMRING2:func.8">goto</a> (<font color="Olive" title="b3">i1</font>,<font color="Olive" title="b1">R</font>) or  ex <font color="Olive" title="b3">a</font> being   <a href="scmring2.html#NM1" title="SCMRING2:NM.1">Data-Location</a> of <font color="Olive" title="b1">R</font> ex <font color="Olive" title="b4">i1</font> being   <a href="ordinal1.html#NM6" title="ORDINAL1:NM.6">Nat</a> st <font color="Olive" title="b2">I</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b3">a</font> <a href="scmring2.html#K9" title="SCMRING2:func.9">=0_goto</a> <font color="Olive" title="b4">i1</font> or  ex <font color="Olive" title="b3">a</font> being   <a href="scmring2.html#NM1" title="SCMRING2:NM.1">Data-Location</a> of <font color="Olive" title="b1">R</font> ex <font color="Olive" title="b4">r</font> being   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Olive" title="b1">R</font> st <font color="Olive" title="b2">I</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b3">a</font> <a href="scmring2.html#K7" title="SCMRING2:func.7">:=</a> <font color="Olive" title="b4">r</font> ) )</div></div>
