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<a NAME="E1:51_1_1"/>
 <a href="pboole.html#K1" title="PBOOLE:func.1">[[0]]</a> <font color="Maroon" title="c1">I</font> <a href="pboole.html#R2" title="PBOOLE:pred.2">c=</a>  <a href="mssubfam.html#K1" title="MSSUBFAM:func.1">bool</a> <font color="Maroon" title="c2">M</font>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="pboole.html#T49" title="PBOOLE:th.49">PBOOLE:49</a></span>;<br/>
<a NAME="E2:51_1_1"/><span class="kw">then </span>
 <a href="pboole.html#K1" title="PBOOLE:func.1">[[0]]</a> <font color="Maroon" title="c1">I</font> is    <a href="pboole.html#M3" title="PBOOLE:mode.3">ManySortedSubset</a> of  <a href="mssubfam.html#K1" title="MSSUBFAM:func.1">bool</a> <font color="Maroon" title="c2">M</font>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="pboole.html#D23" title="PBOOLE:def.23">PBOOLE:def 23</a></span>;<br/>
<span class="kw">hence </span><a NAME="E3:51_1_1"/>
 ex <font color="Olive">b<sub>1</sub></font> being  <a href="mssubfam.html#NM1" title="MSSUBFAM:NM.1">MSSubsetFamily</a> of <font color="Maroon" title="c2">M</font> st <br/>( <font color="Olive">b<sub>1</sub></font> is  <a href="relat_1.html#V3" title="RELAT_1:attr.3">empty-yielding</a>  &amp; <font color="Olive">b<sub>1</sub></font> is  <a href="finset_1.html#V2" title="FINSET_1:attr.2">finite-yielding</a>  )
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> verum</span><br/>


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