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<div>:: <span class="kw">deftheorem </span>   defines <a href="c0sp1.html#V3" title="C0SP1:attr.3">multiplicatively-closed</a> <a onclick="hs(this)" href="javascript:()">C0SP1:def 4 : <br/></a><span> for <font color="Olive" title="b1">V</font> being   non  <a href="struct_0.html#V2" title="STRUCT_0:attr.2">empty</a>   <a href="algstr_0.html#L5" title="ALGSTR_0:struct.5">multLoopStr_0</a> <br/>  for <font color="Olive" title="b2">V1</font> being   <a href="struct_0.html#NM2" title="STRUCT_0:NM.2">Subset</a> of <font color="Olive" title="b1">V</font> holds <br/> ( <font color="Olive" title="b2">V1</font> is  <a href="c0sp1.html#V3" title="C0SP1:attr.3">multiplicatively-closed</a>  iff (  <a href="struct_0.html#K5" title="STRUCT_0:func.5">1.</a> <font color="Olive" title="b1">V</font> <a href="tarski.html#R2" title="TARSKI:pred.2">in</a> <font color="Olive" title="b2">V1</font> &amp; (  for <font color="Olive" title="b3">v</font>, <font color="Olive" title="b4">u</font> being   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Olive" title="b1">V</font>  st <font color="Olive" title="b3">v</font> <a href="tarski.html#R2" title="TARSKI:pred.2">in</a> <font color="Olive" title="b2">V1</font> &amp; <font color="Olive" title="b4">u</font> <a href="tarski.html#R2" title="TARSKI:pred.2">in</a> <font color="Olive" title="b2">V1</font> holds <br/><font color="Olive" title="b3">v</font> <a href="algstr_0.html#K6" title="ALGSTR_0:func.6">*</a> <font color="Olive" title="b4">u</font> <a href="tarski.html#R2" title="TARSKI:pred.2">in</a> <font color="Olive" title="b2">V1</font> ) ) );<br/></span></div>
