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<div><span class="kw">theorem </span><a NAME="T41"><span class="comment"><font color="firebrick">:: MONOID_0:41</font></span><br/></a><div class="add"> for <font color="Olive" title="b1">G</font> being   non  <a href="struct_0.html#V2" title="STRUCT_0:attr.2">empty</a>   <a href="algstr_0.html#V15" title="ALGSTR_0:attr.15">strict</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>  holds <br/> ( <font color="Olive" title="b1">G</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="monoid_0.html#K3" title="MONOID_0:func.3">INT.Group</a>  iff  the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Olive" title="b1">G</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="numbers.html#K4" title="NUMBERS:func.4">INT</a>  ) <span class="kw">by</span> <span class="lab"><a class="ref" href="monoid_0.html#T26" target="_self" onmouseover="rs('monoid_0/T26')" onmouseout="rh()">Th26</a>, <a class="ref" href="gr_cy_1.html#D3" onmouseover="rs('gr_cy_1/D3')" onmouseout="rh()">GR_CY_1:def 3</a></span>;<br/></div></div>
