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<div><span class="kw">theorem </span><span class="lab"><font color="Green" title="E45">Th39</font></span>: <a NAME="T39"><span class="comment"><font color="firebrick">:: MONOID_0:39</font></span><br/></a><div class="add"> for <font color="Olive" title="b1">N</font> being   non  <a href="struct_0.html#V2" title="STRUCT_0:attr.2">empty</a>   <a href="monoid_0.html#M2" title="MONOID_0:mode.2">SubStr</a> of  <a href="monoid_0.html#K2" title="MONOID_0:func.2">&lt;REAL,+&gt;</a> <br/>  for <font color="Olive" title="b2">a</font>, <font color="Olive" title="b3">b</font> being   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Olive" title="b1">N</font><br/>  for <font color="Olive" title="b4">x</font>, <font color="Olive" title="b5">y</font> being   <a href="xreal_0.html#NM1" title="XREAL_0:NM.1">Real</a>  st <font color="Olive" title="b2">a</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b4">x</font> &amp; <font color="Olive" title="b3">b</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b5">y</font> holds <br/><font color="Olive" title="b2">a</font> <a href="algstr_0.html#K6" title="ALGSTR_0:func.6">*</a> <font color="Olive" title="b3">b</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b4">x</font> <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> <font color="Olive" title="b5">y</font></div></div>
