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<div>:: <span class="kw">deftheorem </span><span class="lab"><font color="Green" title="E52">Def38</font></span>   defines <a href="aimloop.html#K20" title="AIMLOOP:func.20">Mlt</a> <a onclick="hs(this)" href="javascript:()">AIMLOOP:def 40 : <br/></a><span> for <font color="Olive" title="b1">Q</font> being   <a href="algstr_1.html#NM2" title="ALGSTR_1:NM.2">multLoop</a><br/>  for <font color="Olive" title="b2">H</font> being   <a href="struct_0.html#NM2" title="STRUCT_0:NM.2">Subset</a> of <font color="Olive" title="b1">Q</font><br/>  for <font color="Olive">b<sub>3</sub></font> being   <a href="aimloop.html#V17" title="AIMLOOP:attr.17">composition-closed</a>   <a href="aimloop.html#V18" title="AIMLOOP:attr.18">inverse-closed</a>  <a href="subset_1.html#NM2" title="SUBSET_1:NM.2">Subset</a> of <span class="p1">(<span class="default"><a href="aimloop.html#K1" title="AIMLOOP:func.1">Funcs</a> (<font color="Olive" title="b1">Q</font>,<font color="Olive" title="b1">Q</font>)</span>)</span> holds <br/> ( <font color="Olive">b<sub>3</sub></font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="aimloop.html#K20" title="AIMLOOP:func.20">Mlt</a> <font color="Olive" title="b2">H</font> iff ( <font color="Olive" title="b2">H</font> <a href="aimloop.html#R1" title="AIMLOOP:pred.1">left-right-mult-closed</a> <font color="Olive">b<sub>3</sub></font> &amp; (  for <font color="Olive" title="b4">X</font> being   <a href="aimloop.html#V17" title="AIMLOOP:attr.17">composition-closed</a>   <a href="aimloop.html#V18" title="AIMLOOP:attr.18">inverse-closed</a>  <a href="subset_1.html#NM2" title="SUBSET_1:NM.2">Subset</a> of <span class="p1">(<span class="default"><a href="aimloop.html#K1" title="AIMLOOP:func.1">Funcs</a> (<font color="Olive" title="b1">Q</font>,<font color="Olive" title="b1">Q</font>)</span>)</span>  st <font color="Olive" title="b2">H</font> <a href="aimloop.html#R1" title="AIMLOOP:pred.1">left-right-mult-closed</a> <font color="Olive" title="b4">X</font> holds <br/><font color="Olive">b<sub>3</sub></font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <font color="Olive" title="b4">X</font> ) ) );<br/></span></div>
