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<div><span class="kw">theorem </span><span class="lab"><font color="Green" title="E47">Th27</font></span>: <a NAME="T30"><span class="comment"><font color="firebrick">:: AIMLOOP:30</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">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" title="b3">phi</font> being   <a href="funct_2.html#NM1" title="FUNCT_2:NM.1">Function</a> of <span class="p1">(<span class="default"><a href="zfmisc_1.html#K1" title="ZFMISC_1:func.1">bool</a> <span class="p2">(<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></span>)</span>,<span class="p1">(<span class="default"><a href="zfmisc_1.html#K1" title="ZFMISC_1:func.1">bool</a> <span class="p2">(<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></span>)</span>  st (  for <font color="Olive" title="b4">X</font> being   <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  <font color="Olive" title="b3">phi</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Olive" title="b4">X</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="aimloop.html#K19" title="AIMLOOP:func.19">MltClos1</a> (<font color="Olive" title="b2">H</font>,<font color="Olive" title="b4">X</font>) ) holds <br/> for <font color="Olive" title="b4">Y</font> being   <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="b3">phi</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Olive" title="b4">Y</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <font color="Olive" title="b4">Y</font> holds <br/>( (  for <font color="Olive" title="b5">u</font> being   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Olive" title="b1">Q</font>  st <font color="Olive" title="b5">u</font> <a href="tarski.html#R2" title="TARSKI:pred.2">in</a> <font color="Olive" title="b2">H</font> holds <br/><span class="p1">(<span class="default"><a href="funct_5.html#K11" title="FUNCT_5:func.11">curry</a>  the <a href="algstr_0.html#U2" title="ALGSTR_0:sel.2">multF</a> of <font color="Olive" title="b1">Q</font></span>)</span> <a href="funct_5.html#K10" title="FUNCT_5:func.10">.</a> <font color="Olive" title="b5">u</font> <a href="tarski.html#R2" title="TARSKI:pred.2">in</a> <font color="Olive" title="b4">Y</font> ) &amp; (  for <font color="Olive" title="b5">u</font> being   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Olive" title="b1">Q</font>  st <font color="Olive" title="b5">u</font> <a href="tarski.html#R2" title="TARSKI:pred.2">in</a> <font color="Olive" title="b2">H</font> holds <br/><span class="p1">(<span class="default"><a href="funct_5.html#K12" title="FUNCT_5:func.12">curry'</a>  the <a href="algstr_0.html#U2" title="ALGSTR_0:sel.2">multF</a> of <font color="Olive" title="b1">Q</font></span>)</span> <a href="funct_5.html#K10" title="FUNCT_5:func.10">.</a> <font color="Olive" title="b5">u</font> <a href="tarski.html#R2" title="TARSKI:pred.2">in</a> <font color="Olive" title="b4">Y</font> ) )</div></div>
