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<div><span class="kw">theorem </span><a NAME="T18"><span class="comment"><font color="firebrick">:: MONOID_1:18</font></span><br/></a><div class="add"> for <font color="Olive" title="b1">x</font>, <font color="Olive" title="b2">X</font> being    <a href="hidden.html#M2" title="HIDDEN:mode.2">set</a> <br/>  for <font color="Olive" title="b3">G</font> being   non  <a href="struct_0.html#V2" title="STRUCT_0:attr.2">empty</a>   <a href="algstr_0.html#L3" title="ALGSTR_0:struct.3">multMagma</a>  holds <br/> ( <font color="Olive" title="b1">x</font> is   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <span class="p1">(<span class="default"><a href="monoid_1.html#K9" title="MONOID_1:func.9">.:</a> (<font color="Olive" title="b3">G</font>,<font color="Olive" title="b2">X</font>)</span>)</span> iff <font color="Olive" title="b1">x</font> is   <a href="funct_2.html#NM1" title="FUNCT_2:NM.1">Function</a> of <font color="Olive" title="b2">X</font>, the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Olive" title="b3">G</font> )</div></div>
