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<div><span class="kw">theorem </span><a NAME="T30"><span class="comment"><font color="firebrick">:: FIELD_16:30</font></span><br/></a><div class="add"> for <font color="Olive" title="b1">R</font> being   non  <a href="struct_0.html#V6" title="STRUCT_0:attr.6">degenerated</a>   <a href="group_1.html#V1" title="GROUP_1:attr.1">unital</a>   <a href="algstr_0.html#L6" title="ALGSTR_0:struct.6">doubleLoopStr</a> <br/>  for <font color="Olive" title="b2">a</font> being   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Olive" title="b1">R</font><br/>  for <font color="Olive" title="b3">n</font> being   non  <a href="zfmisc_1.html#V1" title="ZFMISC_1:attr.1">trivial</a>  <a href="ordinal1.html#NM6" title="ORDINAL1:NM.6">Nat</a> holds <br/> ( <span class="p1">(<span class="default"><a href="field_16.html#K6" title="FIELD_16:func.6">X^</a> (<font color="Olive" title="b3">n</font>,<font color="Olive" title="b1">R</font>)</span>)</span> <a href="nat_1.html#K8" title="NAT_1:func.8">.</a> 1 <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="algstr_0.html#K4" title="ALGSTR_0:func.4">-</a> <span class="p1">(<span class="default"><a href="struct_0.html#K5" title="STRUCT_0:func.5">1.</a> <font color="Olive" title="b1">R</font></span>)</span> &amp; <span class="p1">(<span class="default"><a href="field_16.html#K6" title="FIELD_16:func.6">X^</a> (<font color="Olive" title="b3">n</font>,<font color="Olive" title="b1">R</font>)</span>)</span> <a href="nat_1.html#K8" title="NAT_1:func.8">.</a> <font color="Olive" title="b3">n</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="struct_0.html#K5" title="STRUCT_0:func.5">1.</a> <font color="Olive" title="b1">R</font> &amp; (  for <font color="Olive" title="b4">m</font> being   <a href="ordinal1.html#NM6" title="ORDINAL1:NM.6">Nat</a>  st <font color="Olive" title="b4">m</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> 1 &amp; <font color="Olive" title="b4">m</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Olive" title="b3">n</font> holds <br/><span class="p1">(<span class="default"><a href="field_16.html#K6" title="FIELD_16:func.6">X^</a> (<font color="Olive" title="b3">n</font>,<font color="Olive" title="b1">R</font>)</span>)</span> <a href="nat_1.html#K8" title="NAT_1:func.8">.</a> <font color="Olive" title="b4">m</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="struct_0.html#K4" title="STRUCT_0:func.4">0.</a> <font color="Olive" title="b1">R</font> ) ) <span class="kw">by</span> <span class="lab"><a class="txt" href="field_16.html#E42"><span class="lab"><font color="Green" title="E35">Lm10</font></span></a>, <a class="txt" href="field_16.html#E43"><span class="lab"><font color="Green" title="E36">Lm11</font></span></a></span>;<br/></div></div>
