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<span class="kw">let </span><font color="Maroon" title="c1">I</font> be    <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a> ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide">  for <font color="Olive" title="b1">Y</font>, <font color="Olive" title="b2">Z</font>, <font color="Olive" title="b3">X</font> being   <a href="pboole.html#NM1" title="PBOOLE:NM.1">ManySortedSet</a> of <font color="Maroon" title="c1">I</font>  st  not <font color="Olive" title="b1">Y</font> <a href="pboole.html#R4" title="PBOOLE:pred.4">overlaps</a> <font color="Olive" title="b2">Z</font> holds <br/> not <font color="Olive" title="b3">X</font> <a href="pboole.html#K3" title="PBOOLE:func.3">/\</a> <font color="Olive" title="b1">Y</font> <a href="pboole.html#R4" title="PBOOLE:pred.4">overlaps</a> <font color="Olive" title="b3">X</font> <a href="pboole.html#K3" title="PBOOLE:func.3">/\</a> <font color="Olive" title="b2">Z</font></span><br/><span class="kw">let </span><font color="Maroon" title="c2">Y</font>, <font color="Maroon" title="c3">Z</font>, <font color="Maroon" title="c4">X</font> be   <a href="pboole.html#NM1" title="PBOOLE:NM.1">ManySortedSet</a> of <font color="Maroon" title="c1">I</font>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> (  not <font color="Maroon" title="c2">Y</font> <a href="pboole.html#R4" title="PBOOLE:pred.4">overlaps</a> <font color="Maroon" title="c3">Z</font> implies  not <font color="Maroon" title="c4">X</font> <a href="pboole.html#K3" title="PBOOLE:func.3">/\</a> <font color="Maroon" title="c2">Y</font> <a href="pboole.html#R4" title="PBOOLE:pred.4">overlaps</a> <font color="Maroon" title="c4">X</font> <a href="pboole.html#K3" title="PBOOLE:func.3">/\</a> <font color="Maroon" title="c3">Z</font> )</span><br/>







<span class="kw">assume </span><a NAME="E1:107"/><span class="lab"><font color="Green" title="E64">A1</font></span>: 
 not <font color="Maroon" title="c2">Y</font> <a href="pboole.html#R4" title="PBOOLE:pred.4">overlaps</a> <font color="Maroon" title="c3">Z</font>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide">  not <font color="Maroon" title="c4">X</font> <a href="pboole.html#K3" title="PBOOLE:func.3">/\</a> <font color="Maroon" title="c2">Y</font> <a href="pboole.html#R4" title="PBOOLE:pred.4">overlaps</a> <font color="Maroon" title="c4">X</font> <a href="pboole.html#K3" title="PBOOLE:func.3">/\</a> <font color="Maroon" title="c3">Z</font></span><br/>

<a NAME="E2:107"/>
( <font color="Maroon" title="c4">X</font> <a href="pboole.html#K3" title="PBOOLE:func.3">/\</a> <font color="Maroon" title="c2">Y</font> <a href="pboole.html#R2" title="PBOOLE:pred.2">c=</a> <font color="Maroon" title="c2">Y</font> &amp; <font color="Maroon" title="c4">X</font> <a href="pboole.html#K3" title="PBOOLE:func.3">/\</a> <font color="Maroon" title="c3">Z</font> <a href="pboole.html#R2" title="PBOOLE:pred.2">c=</a> <font color="Maroon" title="c3">Z</font> )
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="pboole.html#T15" target="_self" title="PBOOLE:th.15">Th17</a></span>;<br/>
<span class="kw">hence </span><a NAME="E3:107"/>
 not <font color="Maroon" title="c4">X</font> <a href="pboole.html#K3" title="PBOOLE:func.3">/\</a> <font color="Maroon" title="c2">Y</font> <a href="pboole.html#R4" title="PBOOLE:pred.4">overlaps</a> <font color="Maroon" title="c4">X</font> <a href="pboole.html#K3" title="PBOOLE:func.3">/\</a> <font color="Maroon" title="c3">Z</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:107"><span class="lab"><font color="Green" title="E64">A1</font></span></a>, <a class="ref" href="pboole.html#T101" target="_self" title="PBOOLE:th.101">Th110</a></span>; <a class="txt" 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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