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<div><span class="kw">theorem </span><span class="lab"><font color="Green" title="E18">Th31</font></span>: <a NAME="T32"><span class="comment"><font color="firebrick">:: SCMRING3:32</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">a</font> being   <a href="scmring2.html#NM1" title="SCMRING2:NM.1">Data-Location</a> of <font color="Olive" title="b1">R</font><br/>  for <font color="Olive" title="b3">il</font>, <font color="Olive" title="b4">i1</font> being   <a href="ordinal1.html#NM6" title="ORDINAL1:NM.6">Nat</a> holds <br/> ( <font color="Olive" title="b4">i1</font> <a href="tarski.html#R2" title="TARSKI:pred.2">in</a>  <a href="amistd_1.html#K1" title="AMISTD_1:func.1">NIC</a> (<span class="p1">(<span class="default"><font color="Olive" title="b2">a</font> <a href="scmring2.html#K9" title="SCMRING2:func.9">=0_goto</a> <font color="Olive" title="b4">i1</font></span>)</span>,<font color="Olive" title="b3">il</font>) &amp;  <a href="amistd_1.html#K1" title="AMISTD_1:func.1">NIC</a> (<span class="p1">(<span class="default"><font color="Olive" title="b2">a</font> <a href="scmring2.html#K9" title="SCMRING2:func.9">=0_goto</a> <font color="Olive" title="b4">i1</font></span>)</span>,<font color="Olive" title="b3">il</font>) <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <span class="p1"><a href="tarski.html#K2" title="TARSKI:func.2">{</a><span class="default"><font color="Olive" title="b4">i1</font>,<span class="p2">(<span class="default"><font color="Olive" title="b3">il</font> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 1</span>)</span></span><a href="tarski.html#K2" title="TARSKI:func.2">}</a></span> )</div></div>
