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<span class="kw">let </span><font color="Maroon" title="c1">I</font> be    <a href="hidden.html#M2" title="HIDDEN:mode.2">set</a> ; <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">  for <font color="Olive" title="b1">X</font>, <font color="Olive" title="b2">Y</font>, <font color="Olive" title="b3">Z</font> being   <a href="pboole.html#NM1" title="PBOOLE:NM.1">ManySortedSet</a> of <font color="Maroon" title="c1">I</font>  st ( <font color="Olive" title="b1">X</font> <a href="pboole.html#R4" title="PBOOLE:pred.4">overlaps</a> <font color="Olive" title="b2">Y</font> or <font color="Olive" title="b1">X</font> <a href="pboole.html#R4" title="PBOOLE:pred.4">overlaps</a> <font color="Olive" title="b3">Z</font> ) holds <br/><font color="Olive" title="b1">X</font> <a href="pboole.html#R4" title="PBOOLE:pred.4">overlaps</a> <font color="Olive" title="b2">Y</font> <a href="pboole.html#K2" title="PBOOLE:func.2">(\/)</a> <font color="Olive" title="b3">Z</font></span><br/><span class="kw">let </span><font color="Maroon" title="c2">X</font>, <font color="Maroon" title="c3">Y</font>, <font color="Maroon" title="c4">Z</font> be   <a href="pboole.html#NM1" title="PBOOLE:NM.1">ManySortedSet</a> of <font color="Maroon" title="c1">I</font>; <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"> ( ( <font color="Maroon" title="c2">X</font> <a href="pboole.html#R4" title="PBOOLE:pred.4">overlaps</a> <font color="Maroon" title="c3">Y</font> or <font color="Maroon" title="c2">X</font> <a href="pboole.html#R4" title="PBOOLE:pred.4">overlaps</a> <font color="Maroon" title="c4">Z</font> ) implies <font color="Maroon" title="c2">X</font> <a href="pboole.html#R4" title="PBOOLE:pred.4">overlaps</a> <font color="Maroon" title="c3">Y</font> <a href="pboole.html#K2" title="PBOOLE:func.2">(\/)</a> <font color="Maroon" title="c4">Z</font> )</span><br/>







<span class="kw">assume </span><a NAME="E1:95"/><span class="lab"><font color="Green" title="E55">A1</font></span>: 
( <font color="Maroon" title="c2">X</font> <a href="pboole.html#R4" title="PBOOLE:pred.4">overlaps</a> <font color="Maroon" title="c3">Y</font> or <font color="Maroon" title="c2">X</font> <a href="pboole.html#R4" title="PBOOLE:pred.4">overlaps</a> <font color="Maroon" title="c4">Z</font> )
 ; <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"> <font color="Maroon" title="c2">X</font> <a href="pboole.html#R4" title="PBOOLE:pred.4">overlaps</a> <font color="Maroon" title="c3">Y</font> <a href="pboole.html#K2" title="PBOOLE:func.2">(\/)</a> <font color="Maroon" title="c4">Z</font></span><br/>

<div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="95_1"><span class="kw">per </span></a><a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="kw">cases </span></a><span class="hide"><a NAME="E1:95_1"/>
( <font color="Maroon" title="c2">X</font> <a href="pboole.html#R4" title="PBOOLE:pred.4">overlaps</a> <font color="Maroon" title="c3">Y</font> or <font color="Maroon" title="c2">X</font> <a href="pboole.html#R4" title="PBOOLE:pred.4">overlaps</a> <font color="Maroon" title="c4">Z</font> )
 </span><span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:95"><span class="lab"><font color="Green" title="E55">A1</font></span></a></span>;<br/><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="95_1_1"><span class="kw">suppose </span></a><a NAME="E1:95_1_1"/>
<font color="Maroon" title="c2">X</font> <a href="pboole.html#R4" title="PBOOLE:pred.4">overlaps</a> <font color="Maroon" title="c3">Y</font>
 ; <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"> <font color="Maroon" title="c2">X</font> <a href="pboole.html#R4" title="PBOOLE:pred.4">overlaps</a> <font color="Maroon" title="c3">Y</font> <a href="pboole.html#K2" title="PBOOLE:func.2">(\/)</a> <font color="Maroon" title="c4">Z</font></span><br/><div class="add"><span class="kw">then </span><span class="kw">consider </span><font color="Maroon" title="c5">x</font> being   <a href="pboole.html#NM1" title="PBOOLE:NM.1">ManySortedSet</a> of <font color="Maroon" title="c1">I</font><span class="kw"> such that </span><br/><a NAME="E3:95_1_1"/><span class="lab"><font color="Green" title="E56">A2</font></span>: 
<font color="Maroon" title="c5">x</font> <a href="pboole.html#R1" title="PBOOLE:pred.1">in</a> <font color="Maroon" title="c2">X</font>
 <span class="kw">and </span><br/><a NAME="E4:95_1_1"/><span class="lab"><font color="Green" title="E57">A3</font></span>: 
<font color="Maroon" title="c5">x</font> <a href="pboole.html#R1" title="PBOOLE:pred.1">in</a> <font color="Maroon" title="c3">Y</font>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="pboole.html#T11" target="_self" onmouseover="rs('pboole/T11')" onmouseout="rh()">Th11</a></span>;<br/><a NAME="E5:95_1_1"/>
<font color="Maroon" title="c5">x</font> <a href="pboole.html#R1" title="PBOOLE:pred.1">in</a> <font color="Maroon" title="c3">Y</font> <a href="pboole.html#K2" title="PBOOLE:func.2">(\/)</a> <font color="Maroon" title="c4">Z</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E4:95_1_1"><span class="lab"><font color="Green" title="E57">A3</font></span></a>, <a class="ref" href="pboole.html#T7" target="_self" onmouseover="rs('pboole/T7')" onmouseout="rh()">Th7</a></span>;<br/><span class="kw">hence </span><a NAME="E6:95_1_1"/>
<font color="Maroon" title="c2">X</font> <a href="pboole.html#R4" title="PBOOLE:pred.4">overlaps</a> <font color="Maroon" title="c3">Y</font> <a href="pboole.html#K2" title="PBOOLE:func.2">(\/)</a> <font color="Maroon" title="c4">Z</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E3:95_1_1"><span class="lab"><font color="Green" title="E56">A2</font></span></a>, <a class="ref" href="pboole.html#T10" target="_self" onmouseover="rs('pboole/T10')" onmouseout="rh()">Th10</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/></div><span class="kw">end;</span></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="95_1_2"><span class="kw">suppose </span></a><a NAME="E1:95_1_2"/>
<font color="Maroon" title="c2">X</font> <a href="pboole.html#R4" title="PBOOLE:pred.4">overlaps</a> <font color="Maroon" title="c4">Z</font>
 ; <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"> <font color="Maroon" title="c2">X</font> <a href="pboole.html#R4" title="PBOOLE:pred.4">overlaps</a> <font color="Maroon" title="c3">Y</font> <a href="pboole.html#K2" title="PBOOLE:func.2">(\/)</a> <font color="Maroon" title="c4">Z</font></span><br/><div class="add"><span class="kw">then </span><span class="kw">consider </span><font color="Maroon" title="c5">x</font> being   <a href="pboole.html#NM1" title="PBOOLE:NM.1">ManySortedSet</a> of <font color="Maroon" title="c1">I</font><span class="kw"> such that </span><br/><a NAME="E3:95_1_2"/><span class="lab"><font color="Green" title="E56">A4</font></span>: 
<font color="Maroon" title="c5">x</font> <a href="pboole.html#R1" title="PBOOLE:pred.1">in</a> <font color="Maroon" title="c2">X</font>
 <span class="kw">and </span><br/><a NAME="E4:95_1_2"/><span class="lab"><font color="Green" title="E57">A5</font></span>: 
<font color="Maroon" title="c5">x</font> <a href="pboole.html#R1" title="PBOOLE:pred.1">in</a> <font color="Maroon" title="c4">Z</font>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="pboole.html#T11" target="_self" onmouseover="rs('pboole/T11')" onmouseout="rh()">Th11</a></span>;<br/><a NAME="E5:95_1_2"/>
<font color="Maroon" title="c5">x</font> <a href="pboole.html#R1" title="PBOOLE:pred.1">in</a> <font color="Maroon" title="c3">Y</font> <a href="pboole.html#K2" title="PBOOLE:func.2">(\/)</a> <font color="Maroon" title="c4">Z</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E4:95_1_2"><span class="lab"><font color="Green" title="E57">A5</font></span></a>, <a class="ref" href="pboole.html#T7" target="_self" onmouseover="rs('pboole/T7')" onmouseout="rh()">Th7</a></span>;<br/><span class="kw">hence </span><a NAME="E6:95_1_2"/>
<font color="Maroon" title="c2">X</font> <a href="pboole.html#R4" title="PBOOLE:pred.4">overlaps</a> <font color="Maroon" title="c3">Y</font> <a href="pboole.html#K2" title="PBOOLE:func.2">(\/)</a> <font color="Maroon" title="c4">Z</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E3:95_1_2"><span class="lab"><font color="Green" title="E56">A4</font></span></a>, <a class="ref" href="pboole.html#T10" target="_self" onmouseover="rs('pboole/T10')" onmouseout="rh()">Th10</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/></div><span class="kw">end;</span></div></div><span class="kw">end;</span></div>

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