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<div><span class="kw">theorem </span><span class="lab"><font color="Green" title="E69">Th42</font></span>: <a NAME="T45"><span class="comment"><font color="firebrick">:: AIMLOOP:45</font></span><br/></a><div class="add"> 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">N</font> being   <a href="aimloop.html#NM3" title="AIMLOOP:NM.3">SubLoop</a> of <font color="Olive" title="b1">Q</font><br/>  for <font color="Olive" title="b3">f</font> being   <a href="struct_0.html#NM6" title="STRUCT_0:NM.6">Function</a> of <font color="Olive" title="b1">Q</font>,<font color="Olive" title="b1">Q</font>  st <font color="Olive" title="b3">f</font> <a href="tarski.html#R2" title="TARSKI:pred.2">in</a>  <a href="aimloop.html#K20" title="AIMLOOP:func.20">Mlt</a> <span class="p1">(<span class="default"><a href="aimloop.html#K16" title="AIMLOOP:func.16">@</a> <span class="p2">(<span class="default"><a href="struct_0.html#K2" title="STRUCT_0:func.2">[#]</a> <font color="Olive" title="b2">N</font></span>)</span></span>)</span> holds <br/> for <font color="Olive" title="b4">x</font> being   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Olive" title="b1">Q</font> holds <br/> ( <font color="Olive" title="b4">x</font> <a href="tarski.html#R2" title="TARSKI:pred.2">in</a>  <a href="aimloop.html#K16" title="AIMLOOP:func.16">@</a> <span class="p1">(<span class="default"><a href="struct_0.html#K2" title="STRUCT_0:func.2">[#]</a> <font color="Olive" title="b2">N</font></span>)</span> iff <font color="Olive" title="b3">f</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Olive" title="b4">x</font> <a href="tarski.html#R2" title="TARSKI:pred.2">in</a>  <a href="aimloop.html#K16" title="AIMLOOP:func.16">@</a> <span class="p1">(<span class="default"><a href="struct_0.html#K2" title="STRUCT_0:func.2">[#]</a> <font color="Olive" title="b2">N</font></span>)</span> )</div></div>
