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 ex <font color="Olive" title="b1">A</font> being   <a href="pboole.html#NM1" title="PBOOLE:NM.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> st <span class="p1"><a href="pzfmisc1.html#K1" title="PZFMISC1:func.1">{</a><span class="default"><font color="Olive" title="b1">A</font></span><a href="pzfmisc1.html#K1" title="PZFMISC1:func.1">}</a></span> <a href="pboole.html#R8" title="PBOOLE:pred.8">=</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="funcop_1.html#K7" title="FUNCOP_1:func.7">--&gt;</a> <span class="p1"><a href="tarski.html#K1" title="TARSKI:func.1">{</a><span class="default"><a href="numbers.html#K5" title="NUMBERS:func.5">0</a></span><a href="tarski.html#K1" title="TARSKI:func.1">}</a></span>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="msualg_9.html#T5" target="_self" onmouseover="rs('msualg_9/T5')" onmouseout="rh()">Th5</a></span>;<br/>
<span class="kw">hence </span><a NAME="E2:32_1_1"/>
(  the <a href="msualg_1.html#U3" title="MSUALG_1:sel.3">Sorts</a> of <span class="p1">(<span class="default"><a href="msafree2.html#K7" title="MSAFREE2:func.7">Trivial_Algebra</a> <font color="Maroon" title="c1">S</font></span>)</span> is  <a href="finset_1.html#V2" title="FINSET_1:attr.2">finite-yielding</a>  &amp;  the <a href="msualg_1.html#U3" title="MSUALG_1:sel.3">Sorts</a> of <span class="p1">(<span class="default"><a href="msafree2.html#K7" title="MSAFREE2:func.7">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>  )
 <span class="kw">by</span> <span class="lab"><a class="ref" href="msafree2.html#D12" onmouseover="rs('msafree2/D12')" onmouseout="rh()">MSAFREE2:def 12</a></span>; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> verum</span><br/>


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