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<span class="kw">let </span><font color="Maroon" title="c1">U</font> be  non  <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a>   <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a> ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> for <font color="Olive" title="b1">A</font>, <font color="Olive" title="b2">C</font> being non  <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a>   <a href="interva1.html#M1" title="INTERVA1:mode.1">IntervalSet</a> of <font color="Maroon" title="c1">U</font><br/> for <font color="Olive" title="b3">X</font>, <font color="Olive" title="b4">Y</font> being  <a href="subset_1.html#NM2" title="SUBSET_1:NM.2">Subset</a> of <font color="Maroon" title="c1">U</font>  st <font color="Olive" title="b1">A</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="interva1.html#K2" title="INTERVA1:func.2">Inter</a> <font color="Olive" title="b3">X</font>,<font color="Olive" title="b4">Y</font> holds <br/><font color="Olive" title="b1">A</font> <a href="interva1.html#K9" title="INTERVA1:func.9">_\_</a> <font color="Olive" title="b2">C</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="interva1.html#K2" title="INTERVA1:func.2">Inter</a> <span class="p1">(<span class="default"><font color="Olive" title="b3">X</font> <a href="subset_1.html#K7" title="SUBSET_1:func.7">\</a> <span class="p2">(<span class="default"><font color="Olive" title="b2">C</font> <a href="interva1.html#K6" title="INTERVA1:func.6">``2</a> </span>)</span></span>)</span>,<span class="p1">(<span class="default"><font color="Olive" title="b4">Y</font> <a href="subset_1.html#K7" title="SUBSET_1:func.7">\</a> <span class="p2">(<span class="default"><font color="Olive" title="b2">C</font> <a href="interva1.html#K5" title="INTERVA1:func.5">``1</a> </span>)</span></span>)</span></span><br/><span class="kw">let </span><font color="Maroon" title="c2">A</font>, <font color="Maroon" title="c3">C</font> be  non  <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a>   <a href="interva1.html#M1" title="INTERVA1:mode.1">IntervalSet</a> of <font color="Maroon" title="c1">U</font>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> for <font color="Olive" title="b1">X</font>, <font color="Olive" title="b2">Y</font> being  <a href="subset_1.html#NM2" title="SUBSET_1:NM.2">Subset</a> of <font color="Maroon" title="c1">U</font>  st <font color="Maroon" title="c2">A</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="interva1.html#K2" title="INTERVA1:func.2">Inter</a> <font color="Olive" title="b1">X</font>,<font color="Olive" title="b2">Y</font> holds <br/><font color="Maroon" title="c2">A</font> <a href="interva1.html#K9" title="INTERVA1:func.9">_\_</a> <font color="Maroon" title="c3">C</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="interva1.html#K2" title="INTERVA1:func.2">Inter</a> <span class="p1">(<span class="default"><font color="Olive" title="b1">X</font> <a href="subset_1.html#K7" title="SUBSET_1:func.7">\</a> <span class="p2">(<span class="default"><font color="Maroon" title="c3">C</font> <a href="interva1.html#K6" title="INTERVA1:func.6">``2</a> </span>)</span></span>)</span>,<span class="p1">(<span class="default"><font color="Olive" title="b2">Y</font> <a href="subset_1.html#K7" title="SUBSET_1:func.7">\</a> <span class="p2">(<span class="default"><font color="Maroon" title="c3">C</font> <a href="interva1.html#K5" title="INTERVA1:func.5">``1</a> </span>)</span></span>)</span></span><br/><span class="kw">let </span><font color="Maroon" title="c4">X</font>, <font color="Maroon" title="c5">Y</font> be   <a href="subset_1.html#NM2" title="SUBSET_1:NM.2">Subset</a> of <font color="Maroon" title="c1">U</font>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> ( <font color="Maroon" title="c2">A</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="interva1.html#K2" title="INTERVA1:func.2">Inter</a> <font color="Maroon" title="c4">X</font>,<font color="Maroon" title="c5">Y</font> implies <font color="Maroon" title="c2">A</font> <a href="interva1.html#K9" title="INTERVA1:func.9">_\_</a> <font color="Maroon" title="c3">C</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="interva1.html#K2" title="INTERVA1:func.2">Inter</a> <span class="p1">(<span class="default"><font color="Maroon" title="c4">X</font> <a href="subset_1.html#K7" title="SUBSET_1:func.7">\</a> <span class="p2">(<span class="default"><font color="Maroon" title="c3">C</font> <a href="interva1.html#K6" title="INTERVA1:func.6">``2</a> </span>)</span></span>)</span>,<span class="p1">(<span class="default"><font color="Maroon" title="c5">Y</font> <a href="subset_1.html#K7" title="SUBSET_1:func.7">\</a> <span class="p2">(<span class="default"><font color="Maroon" title="c3">C</font> <a href="interva1.html#K5" title="INTERVA1:func.5">``1</a> </span>)</span></span>)</span> )</span><br/>







<span class="kw">assume </span><a NAME="E1:56"/><span class="lab"><font color="Green" title="E43">a0</font></span>: 
<font color="Maroon" title="c2">A</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="interva1.html#K2" title="INTERVA1:func.2">Inter</a> <font color="Maroon" title="c4">X</font>,<font color="Maroon" title="c5">Y</font>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> <font color="Maroon" title="c2">A</font> <a href="interva1.html#K9" title="INTERVA1:func.9">_\_</a> <font color="Maroon" title="c3">C</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="interva1.html#K2" title="INTERVA1:func.2">Inter</a> <span class="p1">(<span class="default"><font color="Maroon" title="c4">X</font> <a href="subset_1.html#K7" title="SUBSET_1:func.7">\</a> <span class="p2">(<span class="default"><font color="Maroon" title="c3">C</font> <a href="interva1.html#K6" title="INTERVA1:func.6">``2</a> </span>)</span></span>)</span>,<span class="p1">(<span class="default"><font color="Maroon" title="c5">Y</font> <a href="subset_1.html#K7" title="SUBSET_1:func.7">\</a> <span class="p2">(<span class="default"><font color="Maroon" title="c3">C</font> <a href="interva1.html#K5" title="INTERVA1:func.5">``1</a> </span>)</span></span>)</span></span><br/>

<a NAME="E2:56"/>
<font color="Maroon" title="c2">A</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="interva1.html#K2" title="INTERVA1:func.2">Inter</a> <span class="p1">(<span class="default"><font color="Maroon" title="c2">A</font> <a href="interva1.html#K5" title="INTERVA1:func.5">``1</a> </span>)</span>,<span class="p1">(<span class="default"><font color="Maroon" title="c2">A</font> <a href="interva1.html#K6" title="INTERVA1:func.6">``2</a> </span>)</span>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="interva1.html#T15" target="_self" title="INTERVA1:th.15">Wazne33</a></span>;<br/>
<a NAME="E3:56"/><span class="kw">then </span>
( <font color="Maroon" title="c4">X</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c2">A</font> <a href="interva1.html#K5" title="INTERVA1:func.5">``1</a>  &amp; <font color="Maroon" title="c5">Y</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c2">A</font> <a href="interva1.html#K6" title="INTERVA1:func.6">``2</a>  )
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:56"><span class="lab"><font color="Green" title="E43">a0</font></span></a>, <a class="ref" href="interva1.html#T6" target="_self" title="INTERVA1:th.6">Pik</a></span>;<br/>
<span class="kw">hence </span><a NAME="E4:56"/>
<font color="Maroon" title="c2">A</font> <a href="interva1.html#K9" title="INTERVA1:func.9">_\_</a> <font color="Maroon" title="c3">C</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="interva1.html#K2" title="INTERVA1:func.2">Inter</a> <span class="p1">(<span class="default"><font color="Maroon" title="c4">X</font> <a href="subset_1.html#K7" title="SUBSET_1:func.7">\</a> <span class="p2">(<span class="default"><font color="Maroon" title="c3">C</font> <a href="interva1.html#K6" title="INTERVA1:func.6">``2</a> </span>)</span></span>)</span>,<span class="p1">(<span class="default"><font color="Maroon" title="c5">Y</font> <a href="subset_1.html#K7" title="SUBSET_1:func.7">\</a> <span class="p2">(<span class="default"><font color="Maroon" title="c3">C</font> <a href="interva1.html#K5" title="INTERVA1:func.5">``1</a> </span>)</span></span>)</span>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="interva1.html#T40" target="_self" title="INTERVA1:th.40">Dif</a></span>; <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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