<?xml version="1.0"?>
<div class="add">

<b>consider </b><font color="Maroon" title="c2">A</font> being    <a href="pboole.html#M1" title="PBOOLE:mode.1">ManySortedSet</a> of the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c1">S</font><b> such that </b><br/><a NAME="E2:34_1_1"/><i><font color="Green" title="E13">A1</font></i>: 
<span class="p1"><a href="pzfmisc1.html#K1" title="PZFMISC1:func.1">{</a><span class="default"><font color="Maroon" title="c2">A</font></span><a href="pzfmisc1.html#K1" title="PZFMISC1:func.1">}</a></span> <a href="pboole.html#R6" title="PBOOLE:pred.6">=</a> the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c1">S</font> <a href="pre_circ.html#K2" title="PRE_CIRC:func.2">--&gt;</a> <span class="p1"><a href="tarski.html#K1" title="TARSKI:func.1">{</a><span class="default"><a href="numbers.html#K6" title="NUMBERS:func.6">0</a> </span><a href="tarski.html#K1" title="TARSKI:func.1">}</a></span>
 <b>by </b><i><a class="ref" href="msualg_9.html#T6" target="_self" title="MSUALG_9:th.6">Th6</a></i>;<br/>
<b>thus </b><a NAME="E3:34_1_1"/>
( the <a href="msualg_1.html#U4" title="MSUALG_1:sel.4">Sorts</a> of <span class="p1">(<span class="default"><a href="msafree2.html#K8" title="MSAFREE2:func.8">Trivial_Algebra</a> <font color="Maroon" title="c1">S</font></span>)</span> is <a href="finset_1.html#V2" title="FINSET_1:attr.2">locally-finite</a> &amp; the <a href="msualg_1.html#U4" title="MSUALG_1:sel.4">Sorts</a> of <span class="p1">(<span class="default"><a href="msafree2.html#K8" title="MSAFREE2:func.8">Trivial_Algebra</a> <font color="Maroon" title="c1">S</font></span>)</span> is <a href="relat_1.html#V2" title="RELAT_1:attr.2">non-empty</a> )
 <b>by </b><i><a class="txt" href="msualg_9.html#E2:34_1_1"><i><font color="Green" title="E13">A1</font></i></a>, <a class="ref" href="msafree2.html#D12" title="MSAFREE2:def.12">MSAFREE2:def 12</a></i>;<br/>


</div>
