<?xml version="1.0"?>
<div>:: <span class="kw">deftheorem </span>   defines <a href="aimloop.html#K25" title="AIMLOOP:func.25">\</a> <a onclick="hs(this)" href="javascript:()">AIMLOOP:def 45 : <br/></a><span> for <font color="Olive" title="b1">Q</font> being    <a href="algstr_0.html#L4" title="ALGSTR_0:struct.4">multLoopStr</a> <br/>  for <font color="Olive" title="b2">H1</font>, <font color="Olive" title="b3">H2</font>, <font color="Olive">b<sub>4</sub></font> being   <a href="struct_0.html#NM2" title="STRUCT_0:NM.2">Subset</a> of <font color="Olive" title="b1">Q</font> holds <br/> ( <font color="Olive">b<sub>4</sub></font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b2">H1</font> <a href="aimloop.html#K25" title="AIMLOOP:func.25">\</a> <font color="Olive" title="b3">H2</font> iff  for <font color="Olive" title="b5">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="b5">x</font> <a href="tarski.html#R2" title="TARSKI:pred.2">in</a> <font color="Olive">b<sub>4</sub></font> iff  ex <font color="Olive" title="b6">y</font>, <font color="Olive" title="b7">z</font> being   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Olive" title="b1">Q</font> st <br/>( <font color="Olive" title="b6">y</font> <a href="tarski.html#R2" title="TARSKI:pred.2">in</a> <font color="Olive" title="b2">H1</font> &amp; <font color="Olive" title="b7">z</font> <a href="tarski.html#R2" title="TARSKI:pred.2">in</a> <font color="Olive" title="b3">H2</font> &amp; <font color="Olive" title="b5">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b6">y</font> <a href="subset_1.html#K6" title="SUBSET_1:func.6">\</a> <font color="Olive" title="b7">z</font> ) ) );<br/></span></div>
