<?xml version="1.0"?>
<div class="add">

<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">B</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> holds  <font color="Olive" title="b1">A</font> <a href="interva1.html#K9" title="INTERVA1:func.9">_\_</a> <font color="Olive" title="b2">B</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"><span class="p2">(<span class="default"><font color="Olive" title="b1">A</font> <a href="interva1.html#K5" title="INTERVA1:func.5">``1</a> </span>)</span> <a href="subset_1.html#K7" title="SUBSET_1:func.7">\</a> <span class="p2">(<span class="default"><font color="Olive" title="b2">B</font> <a href="interva1.html#K6" title="INTERVA1:func.6">``2</a> </span>)</span></span>)</span>,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Olive" title="b1">A</font> <a href="interva1.html#K6" title="INTERVA1:func.6">``2</a> </span>)</span> <a href="subset_1.html#K7" title="SUBSET_1:func.7">\</a> <span class="p2">(<span class="default"><font color="Olive" title="b2">B</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">B</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"> <font color="Maroon" title="c2">A</font> <a href="interva1.html#K9" title="INTERVA1:func.9">_\_</a> <font color="Maroon" title="c3">B</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"><span class="p2">(<span class="default"><font color="Maroon" title="c2">A</font> <a href="interva1.html#K5" title="INTERVA1:func.5">``1</a> </span>)</span> <a href="subset_1.html#K7" title="SUBSET_1:func.7">\</a> <span class="p2">(<span class="default"><font color="Maroon" title="c3">B</font> <a href="interva1.html#K6" title="INTERVA1:func.6">``2</a> </span>)</span></span>)</span>,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c2">A</font> <a href="interva1.html#K6" title="INTERVA1:func.6">``2</a> </span>)</span> <a href="subset_1.html#K7" title="SUBSET_1:func.7">\</a> <span class="p2">(<span class="default"><font color="Maroon" title="c3">B</font> <a href="interva1.html#K5" title="INTERVA1:func.5">``1</a> </span>)</span></span>)</span></span><br/>





<span class="kw">reconsider </span><font color="Maroon" title="c4">AA</font> = <font color="Maroon" title="c2">A</font>, <font color="Maroon" title="c5">BB</font> = <font color="Maroon" title="c3">B</font> as  non  <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a>   <a href="interva1.html#V1" title="INTERVA1:attr.1">ordered</a>  <a href="setfam_1.html#NM1" title="SETFAM_1:NM.1">Subset-Family</a> of <font color="Maroon" title="c1">U</font> <span class="kw">by</span> <span class="lab"><a class="ref" href="interva1.html#T26" target="_self" title="INTERVA1:th.26">CorNowosc1</a></span>;<br/>
<a NAME="E2:55"/>
( <font color="Maroon" title="c4">AA</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> &amp; <font color="Maroon" title="c5">BB</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="c3">B</font> <a href="interva1.html#K5" title="INTERVA1:func.5">``1</a> </span>)</span>,<span class="p1">(<span class="default"><font color="Maroon" title="c3">B</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="E3:55"/><span class="kw">then </span>
(  <a href="interva1.html#K7" title="INTERVA1:func.7">min</a> <font color="Maroon" title="c4">AA</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;  <a href="interva1.html#K7" title="INTERVA1:func.7">min</a> <font color="Maroon" title="c5">BB</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c3">B</font> <a href="interva1.html#K5" title="INTERVA1:func.5">``1</a>  &amp;  <a href="interva1.html#K8" title="INTERVA1:func.8">max</a> <font color="Maroon" title="c4">AA</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>  &amp;  <a href="interva1.html#K8" title="INTERVA1:func.8">max</a> <font color="Maroon" title="c5">BB</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c3">B</font> <a href="interva1.html#K6" title="INTERVA1:func.6">``2</a>  )
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="interva1.html#T27" target="_self" title="INTERVA1:th.27">nowosc2</a></span>;<br/>
<span class="kw">hence </span><a NAME="E4:55"/>
<font color="Maroon" title="c2">A</font> <a href="interva1.html#K9" title="INTERVA1:func.9">_\_</a> <font color="Maroon" title="c3">B</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"><span class="p2">(<span class="default"><font color="Maroon" title="c2">A</font> <a href="interva1.html#K5" title="INTERVA1:func.5">``1</a> </span>)</span> <a href="subset_1.html#K7" title="SUBSET_1:func.7">\</a> <span class="p2">(<span class="default"><font color="Maroon" title="c3">B</font> <a href="interva1.html#K6" title="INTERVA1:func.6">``2</a> </span>)</span></span>)</span>,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c2">A</font> <a href="interva1.html#K6" title="INTERVA1:func.6">``2</a> </span>)</span> <a href="subset_1.html#K7" title="SUBSET_1:func.7">\</a> <span class="p2">(<span class="default"><font color="Maroon" title="c3">B</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#T38" target="_self" title="INTERVA1:th.38">LemmaC0</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/>


</div>
