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<div><span class="kw">theorem </span><a NAME="T57"><span class="comment"><font color="firebrick">:: MONOID_1:57</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#L3" title="ALGSTR_0:struct.3">multMagma</a>  holds <br/> ( ( <font color="Olive" title="b1">G</font> is  <a href="group_1.html#V5" title="GROUP_1:attr.5">commutative</a>  implies  <a href="monoid_1.html#K20" title="MONOID_1:func.20">bool</a> <font color="Olive" title="b1">G</font> is  <a href="group_1.html#V5" title="GROUP_1:attr.5">commutative</a>  ) &amp; ( <font color="Olive" title="b1">G</font> is  <a href="group_1.html#V3" title="GROUP_1:attr.3">associative</a>  implies  <a href="monoid_1.html#K20" title="MONOID_1:func.20">bool</a> <font color="Olive" title="b1">G</font> is  <a href="group_1.html#V3" title="GROUP_1:attr.3">associative</a>  ) &amp; ( <font color="Olive" title="b1">G</font> is  <a href="monoid_0.html#V17" title="MONOID_0:attr.17">uniquely-decomposable</a>  implies  <a href="monoid_1.html#K20" title="MONOID_1:func.20">bool</a> <font color="Olive" title="b1">G</font> is  <a href="monoid_0.html#V17" title="MONOID_0:attr.17">uniquely-decomposable</a>  ) )</div></div>
