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<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#K3" title="INTERVA1:func.3">_/\_</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#K9" title="SUBSET_1:func.9">/\</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 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#K9" title="SUBSET_1:func.9">/\</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><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#K3" title="INTERVA1:func.3">_/\_</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#K9" title="SUBSET_1:func.9">/\</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="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#K9" title="SUBSET_1:func.9">/\</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><br/>





<a NAME="E1:24"/><span class="lab"><font color="Green" title="E20">v1</font></span>: 
<font color="Maroon" title="c2">A</font> <a href="interva1.html#K3" title="INTERVA1:func.3">_/\_</a> <font color="Maroon" title="c3">B</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</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#K9" title="SUBSET_1:func.9">/\</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="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#K9" title="SUBSET_1:func.9">/\</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>
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="24_1"><span class="kw">proof </span></a><div class="add">

<span class="kw">let </span><font color="Maroon" title="c4">x</font> be    <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a> ; <span class="comment"><font color="Red">:: according to </font></span><a class="ref" href="tarski.html#D3" title="TARSKI:def.3">TARSKI:def 3</a> <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> (  not <font color="Maroon" title="c4">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c2">A</font> <a href="interva1.html#K3" title="INTERVA1:func.3">_/\_</a> <font color="Maroon" title="c3">B</font> or <font color="Maroon" title="c4">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</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#K9" title="SUBSET_1:func.9">/\</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="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#K9" title="SUBSET_1:func.9">/\</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><br/>

<span class="kw">assume </span><a NAME="E1:24_1"/>
<font color="Maroon" title="c4">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c2">A</font> <a href="interva1.html#K3" title="INTERVA1:func.3">_/\_</a> <font color="Maroon" title="c3">B</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="c4">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</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#K9" title="SUBSET_1:func.9">/\</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="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#K9" title="SUBSET_1:func.9">/\</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><br/>

<span class="kw">then </span><span class="kw">consider </span><font color="Maroon" title="c5">X</font>, <font color="Maroon" title="c6">Y</font> being    <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a> <span class="kw"> such that </span><br/><a NAME="E3:24_1"/><span class="lab"><font color="Green" title="E21">v2</font></span>: 
( <font color="Maroon" title="c5">X</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c2">A</font> &amp; <font color="Maroon" title="c6">Y</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c3">B</font> &amp; <font color="Maroon" title="c4">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c5">X</font> <a href="xboole_0.html#K3" title="XBOOLE_0:func.3">/\</a> <font color="Maroon" title="c6">Y</font> )
 <span class="kw">by</span> <span class="lab"><a class="ref" href="setfam_1.html#D5" title="SETFAM_1:def.5">SETFAM_1:def 5</a></span>;<br/>
<a NAME="E4:24_1"/>
( <font color="Maroon" title="c2">A</font> <a href="interva1.html#K5" title="INTERVA1:func.5">``1</a>  <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <font color="Maroon" title="c5">X</font> &amp; <font color="Maroon" title="c3">B</font> <a href="interva1.html#K5" title="INTERVA1:func.5">``1</a>  <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <font color="Maroon" title="c6">Y</font> &amp; <font color="Maroon" title="c5">X</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <font color="Maroon" title="c2">A</font> <a href="interva1.html#K6" title="INTERVA1:func.6">``2</a>  &amp; <font color="Maroon" title="c6">Y</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</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="txt" href="#E3:24_1"><span class="lab"><font color="Green" title="E21">v2</font></span></a>, <a class="ref" href="interva1.html#T14" target="_self" title="INTERVA1:th.14">Wazne</a></span>;<br/>
<a NAME="E5:24_1"/><span class="kw">then </span>
( <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> <a href="subset_1.html#K9" title="SUBSET_1:func.9">/\</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> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <font color="Maroon" title="c4">x</font> &amp; <font color="Maroon" title="c4">x</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <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> <a href="subset_1.html#K9" title="SUBSET_1:func.9">/\</a> <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="xboole_1.html#T27" title="XBOOLE_1:th.27">XBOOLE_1:27</a>, <a class="txt" href="#E3:24_1"><span class="lab"><font color="Green" title="E21">v2</font></span></a></span>;<br/>
<span class="kw">hence </span><a NAME="E6:24_1"/>
<font color="Maroon" title="c4">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</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#K9" title="SUBSET_1:func.9">/\</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="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#K9" title="SUBSET_1:func.9">/\</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="kw">by</span> <span class="lab"><a class="ref" href="interva1.html#T1" target="_self" title="INTERVA1:th.1">Lemacik</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><span class="kw">end;</span></div>
<a NAME="E2:24"/>
 <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#K9" title="SUBSET_1:func.9">/\</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="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#K9" title="SUBSET_1:func.9">/\</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> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <font color="Maroon" title="c2">A</font> <a href="interva1.html#K3" title="INTERVA1:func.3">_/\_</a> <font color="Maroon" title="c3">B</font>
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="24_2"><span class="kw">proof </span></a><div class="add">

<span class="kw">let </span><font color="Maroon" title="c4">x</font> be    <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a> ; <span class="comment"><font color="Red">:: according to </font></span><a class="ref" href="tarski.html#D3" title="TARSKI:def.3">TARSKI:def 3</a> <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> (  not <font color="Maroon" title="c4">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</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#K9" title="SUBSET_1:func.9">/\</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="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#K9" title="SUBSET_1:func.9">/\</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> or <font color="Maroon" title="c4">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c2">A</font> <a href="interva1.html#K3" title="INTERVA1:func.3">_/\_</a> <font color="Maroon" title="c3">B</font> )</span><br/>

<span class="kw">assume </span><a NAME="E1:24_2"/>
<font color="Maroon" title="c4">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</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#K9" title="SUBSET_1:func.9">/\</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="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#K9" title="SUBSET_1:func.9">/\</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>
 ; <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="c4">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c2">A</font> <a href="interva1.html#K3" title="INTERVA1:func.3">_/\_</a> <font color="Maroon" title="c3">B</font></span><br/>

<span class="kw">then </span><span class="kw">consider </span><font color="Maroon" title="c5">Z</font> being    <a href="subset_1.html#M2" title="SUBSET_1:mode.2">Element</a> of  <a href="setfam_1.html#K9" title="SETFAM_1:func.9">bool</a> <font color="Maroon" title="c1">U</font><span class="kw"> such that </span><br/><a NAME="E3:24_2"/><span class="lab"><font color="Green" title="E21">z2</font></span>: 
( <font color="Maroon" title="c4">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c5">Z</font> &amp; <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> <a href="subset_1.html#K9" title="SUBSET_1:func.9">/\</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> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <font color="Maroon" title="c5">Z</font> &amp; <font color="Maroon" title="c5">Z</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <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> <a href="subset_1.html#K9" title="SUBSET_1:func.9">/\</a> <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> )
 ;<br/>
<a NAME="E4:24_2"/>
<font color="Maroon" title="c2">A</font> <a href="interva1.html#K5" title="INTERVA1:func.5">``1</a>  <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <span class="p1">(<span class="default"><font color="Maroon" title="c5">Z</font> <a href="subset_1.html#K4" title="SUBSET_1:func.4">\/</a> <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></span>)</span> <a href="subset_1.html#K9" title="SUBSET_1:func.9">/\</a> <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>
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="24_2_1"><span class="kw">proof </span></a><div class="add">

<span class="kw">let </span><font color="Maroon" title="c6">x</font> be    <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a> ; <span class="comment"><font color="Red">:: according to </font></span><a class="ref" href="tarski.html#D3" title="TARSKI:def.3">TARSKI:def 3</a> <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> (  not <font color="Maroon" title="c6">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c2">A</font> <a href="interva1.html#K5" title="INTERVA1:func.5">``1</a>  or <font color="Maroon" title="c6">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <span class="p1">(<span class="default"><font color="Maroon" title="c5">Z</font> <a href="subset_1.html#K4" title="SUBSET_1:func.4">\/</a> <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></span>)</span> <a href="subset_1.html#K9" title="SUBSET_1:func.9">/\</a> <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><br/>

<span class="kw">assume </span><a NAME="E1:24_2_1"/><span class="lab"><font color="Green" title="E22">a0</font></span>: 
<font color="Maroon" title="c6">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c2">A</font> <a href="interva1.html#K5" title="INTERVA1:func.5">``1</a> 
 ; <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="c6">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <span class="p1">(<span class="default"><font color="Maroon" title="c5">Z</font> <a href="subset_1.html#K4" title="SUBSET_1:func.4">\/</a> <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></span>)</span> <a href="subset_1.html#K9" title="SUBSET_1:func.9">/\</a> <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><br/>

<span class="kw">assume </span><a NAME="E2:24_2_1"/><span class="lab"><font color="Green" title="E23">aa</font></span>: 
not <font color="Maroon" title="c6">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <span class="p1">(<span class="default"><font color="Maroon" title="c5">Z</font> <a href="subset_1.html#K4" title="SUBSET_1:func.4">\/</a> <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></span>)</span> <a href="subset_1.html#K9" title="SUBSET_1:func.9">/\</a> <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>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> contradiction</span><br/>

<div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="24_2_1_1"><span class="kw">per </span></a><a class="txt" onclick="hs(this)" href="javascript:()"><span class="kw">cases </span></a><span class="hide"><a NAME="E1:24_2_1_1"/>
(  not <font color="Maroon" title="c6">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c5">Z</font> <a href="subset_1.html#K4" title="SUBSET_1:func.4">\/</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> or  not <font color="Maroon" title="c6">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c2">A</font> <a href="interva1.html#K6" title="INTERVA1:func.6">``2</a>  )
 </span><span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:24_2_1"><span class="lab"><font color="Green" title="E23">aa</font></span></a>, <a class="ref" href="xboole_0.html#D4" title="XBOOLE_0:def.4">XBOOLE_0:def 4</a></span>;<br/><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="24_2_1_1_1"><span class="kw">suppose </span></a><a NAME="E1:24_2_1_1_1"/>
not <font color="Maroon" title="c6">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c5">Z</font> <a href="subset_1.html#K4" title="SUBSET_1:func.4">\/</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>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> contradiction</span><br/><div class="add"><span class="kw">hence </span><a NAME="E2:24_2_1_1_1"/>
contradiction
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:24_2_1"><span class="lab"><font color="Green" title="E22">a0</font></span></a>, <a class="ref" href="xboole_0.html#D3" title="XBOOLE_0:def.3">XBOOLE_0:def 3</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><span class="kw">end;</span></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="24_2_1_1_2"><span class="kw">suppose </span></a><a NAME="E1:24_2_1_1_2"/><span class="lab"><font color="Green" title="E24">b1</font></span>: 
not <font color="Maroon" title="c6">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c2">A</font> <a href="interva1.html#K6" title="INTERVA1:func.6">``2</a> 
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> contradiction</span><br/><div class="add"><a NAME="E2:24_2_1_1_2"/>
( <font color="Maroon" title="c2">A</font> <a href="interva1.html#K5" title="INTERVA1:func.5">``1</a>  <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <font color="Maroon" title="c2">A</font> <a href="interva1.html#K6" title="INTERVA1:func.6">``2</a>  &amp; <font color="Maroon" title="c6">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c2">A</font> <a href="interva1.html#K5" title="INTERVA1:func.5">``1</a>  )
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:24_2_1"><span class="lab"><font color="Green" title="E22">a0</font></span></a>, <a class="ref" href="interva1.html#T16" target="_self" title="INTERVA1:th.16">wazne2</a></span>;<br/><span class="kw">hence </span><a NAME="E3:24_2_1_1_2"/>
contradiction
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:24_2_1_1_2"><span class="lab"><font color="Green" title="E24">b1</font></span></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><span class="kw">end;</span></div></div><span class="kw">end;</span></div>

</div><span class="kw">end;</span></div>
<a NAME="E5:24_2"/><span class="kw">then </span>
( <font color="Maroon" title="c2">A</font> <a href="interva1.html#K5" title="INTERVA1:func.5">``1</a>  <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <span class="p1">(<span class="default"><font color="Maroon" title="c5">Z</font> <a href="subset_1.html#K4" title="SUBSET_1:func.4">\/</a> <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></span>)</span> <a href="subset_1.html#K9" title="SUBSET_1:func.9">/\</a> <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; <span class="p1">(<span class="default"><font color="Maroon" title="c5">Z</font> <a href="subset_1.html#K4" title="SUBSET_1:func.4">\/</a> <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></span>)</span> <a href="subset_1.html#K9" title="SUBSET_1:func.9">/\</a> <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> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</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="ref" href="xboole_1.html#T17" title="XBOOLE_1:th.17">XBOOLE_1:17</a></span>;<br/>
<a NAME="E6:24_2"/><span class="kw">then </span><span class="lab"><font color="Green" title="E22">e1</font></span>: 
<span class="p1">(<span class="default"><font color="Maroon" title="c5">Z</font> <a href="subset_1.html#K4" title="SUBSET_1:func.4">\/</a> <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></span>)</span> <a href="subset_1.html#K9" title="SUBSET_1:func.9">/\</a> <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> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c2">A</font>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="interva1.html#T14" target="_self" title="INTERVA1:th.14">Wazne</a></span>;<br/>
<a NAME="E7:24_2"/>
<font color="Maroon" title="c3">B</font> <a href="interva1.html#K5" title="INTERVA1:func.5">``1</a>  <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <span class="p1">(<span class="default"><font color="Maroon" title="c5">Z</font> <a href="subset_1.html#K4" title="SUBSET_1:func.4">\/</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> <a href="subset_1.html#K9" title="SUBSET_1:func.9">/\</a> <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>
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="24_2_2"><span class="kw">proof </span></a><div class="add">

<span class="kw">let </span><font color="Maroon" title="c6">x</font> be    <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a> ; <span class="comment"><font color="Red">:: according to </font></span><a class="ref" href="tarski.html#D3" title="TARSKI:def.3">TARSKI:def 3</a> <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> (  not <font color="Maroon" title="c6">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c3">B</font> <a href="interva1.html#K5" title="INTERVA1:func.5">``1</a>  or <font color="Maroon" title="c6">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <span class="p1">(<span class="default"><font color="Maroon" title="c5">Z</font> <a href="subset_1.html#K4" title="SUBSET_1:func.4">\/</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> <a href="subset_1.html#K9" title="SUBSET_1:func.9">/\</a> <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><br/>

<span class="kw">assume </span><a NAME="E1:24_2_2"/><span class="lab"><font color="Green" title="E23">a1</font></span>: 
<font color="Maroon" title="c6">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c3">B</font> <a href="interva1.html#K5" title="INTERVA1:func.5">``1</a> 
 ; <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="c6">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <span class="p1">(<span class="default"><font color="Maroon" title="c5">Z</font> <a href="subset_1.html#K4" title="SUBSET_1:func.4">\/</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> <a href="subset_1.html#K9" title="SUBSET_1:func.9">/\</a> <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><br/>

<a NAME="E2:24_2_2"/><span class="kw">then </span><span class="lab"><font color="Green" title="E24">a2</font></span>: 
<font color="Maroon" title="c6">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c5">Z</font> <a href="subset_1.html#K4" title="SUBSET_1:func.4">\/</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="kw">by</span> <span class="lab"><a class="ref" href="xboole_0.html#D3" title="XBOOLE_0:def.3">XBOOLE_0:def 3</a></span>;<br/>
<a NAME="E3:24_2_2"/>
<font color="Maroon" title="c3">B</font> <a href="interva1.html#K5" title="INTERVA1:func.5">``1</a>  <a href="tarski.html#R1" title="TARSKI:pred.1">c=</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#T16" target="_self" title="INTERVA1:th.16">wazne2</a></span>;<br/>
<span class="kw">hence </span><a NAME="E4:24_2_2"/>
<font color="Maroon" title="c6">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <span class="p1">(<span class="default"><font color="Maroon" title="c5">Z</font> <a href="subset_1.html#K4" title="SUBSET_1:func.4">\/</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> <a href="subset_1.html#K9" title="SUBSET_1:func.9">/\</a> <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="txt" href="#E1:24_2_2"><span class="lab"><font color="Green" title="E23">a1</font></span></a>, <a class="txt" href="#E2:24_2_2"><span class="lab"><font color="Green" title="E24">a2</font></span></a>, <a class="ref" href="xboole_0.html#D4" title="XBOOLE_0:def.4">XBOOLE_0:def 4</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><span class="kw">end;</span></div>
<a NAME="E8:24_2"/><span class="kw">then </span>
( <font color="Maroon" title="c3">B</font> <a href="interva1.html#K5" title="INTERVA1:func.5">``1</a>  <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <span class="p1">(<span class="default"><font color="Maroon" title="c5">Z</font> <a href="subset_1.html#K4" title="SUBSET_1:func.4">\/</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> <a href="subset_1.html#K9" title="SUBSET_1:func.9">/\</a> <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> &amp; <span class="p1">(<span class="default"><font color="Maroon" title="c5">Z</font> <a href="subset_1.html#K4" title="SUBSET_1:func.4">\/</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> <a href="subset_1.html#K9" title="SUBSET_1:func.9">/\</a> <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> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</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="xboole_1.html#T17" title="XBOOLE_1:th.17">XBOOLE_1:17</a></span>;<br/>
<a NAME="E9:24_2"/><span class="kw">then </span><span class="lab"><font color="Green" title="E23">e2</font></span>: 
<span class="p1">(<span class="default"><font color="Maroon" title="c5">Z</font> <a href="subset_1.html#K4" title="SUBSET_1:func.4">\/</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> <a href="subset_1.html#K9" title="SUBSET_1:func.9">/\</a> <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> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c3">B</font>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="interva1.html#T14" target="_self" title="INTERVA1:th.14">Wazne</a></span>;<br/>
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c5">Z</font> <a href="subset_1.html#K4" title="SUBSET_1:func.4">\/</a> <span class="p3">(<span class="default"><font color="Maroon" title="c2">A</font> <a href="interva1.html#K5" title="INTERVA1:func.5">``1</a> </span>)</span></span>)</span> <a href="subset_1.html#K9" title="SUBSET_1:func.9">/\</a> <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></span>)</span> <a href="subset_1.html#K9" title="SUBSET_1:func.9">/\</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c5">Z</font> <a href="subset_1.html#K4" title="SUBSET_1:func.4">\/</a> <span class="p3">(<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> <a href="subset_1.html#K9" title="SUBSET_1:func.9">/\</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"><span class="p3">(<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#K9" title="SUBSET_1:func.9">/\</a> <span class="p3">(<span class="default"><font color="Maroon" title="c5">Z</font> <a href="subset_1.html#K4" title="SUBSET_1:func.4">\/</a> <span class="p4">(<span class="default"><font color="Maroon" title="c2">A</font> <a href="interva1.html#K5" title="INTERVA1:func.5">``1</a> </span>)</span></span>)</span></span>)</span> <a href="subset_1.html#K9" title="SUBSET_1:func.9">/\</a> <span class="p2">(<span class="default"><font color="Maroon" title="c5">Z</font> <a href="subset_1.html#K4" title="SUBSET_1:func.4">\/</a> <span class="p3">(<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>)</span> <a href="subset_1.html#K9" title="SUBSET_1:func.9">/\</a> <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="xboole_1.html#T16" title="XBOOLE_1:th.16">XBOOLE_1:16</a></span>
<br/>.= 
<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#K9" title="SUBSET_1:func.9">/\</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon" title="c5">Z</font> <a href="subset_1.html#K4" title="SUBSET_1:func.4">\/</a> <span class="p4">(<span class="default"><font color="Maroon" title="c2">A</font> <a href="interva1.html#K5" title="INTERVA1:func.5">``1</a> </span>)</span></span>)</span> <a href="subset_1.html#K9" title="SUBSET_1:func.9">/\</a> <span class="p3">(<span class="default"><font color="Maroon" title="c5">Z</font> <a href="subset_1.html#K4" title="SUBSET_1:func.4">\/</a> <span class="p4">(<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>)</span></span>)</span> <a href="subset_1.html#K9" title="SUBSET_1:func.9">/\</a> <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="xboole_1.html#T16" title="XBOOLE_1:th.16">XBOOLE_1:16</a></span>
<br/>.= 
<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#K9" title="SUBSET_1:func.9">/\</a> <span class="p2">(<span class="default"><font color="Maroon" title="c5">Z</font> <a href="subset_1.html#K4" title="SUBSET_1:func.4">\/</a> <span class="p3">(<span class="default"><span class="p4">(<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#K9" title="SUBSET_1:func.9">/\</a> <span class="p4">(<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>)</span></span>)</span> <a href="subset_1.html#K9" title="SUBSET_1:func.9">/\</a> <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="xboole_1.html#T24" title="XBOOLE_1:th.24">XBOOLE_1:24</a></span>
<br/>.= 
<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#K9" title="SUBSET_1:func.9">/\</a> <font color="Maroon" title="c5">Z</font></span>)</span> <a href="subset_1.html#K9" title="SUBSET_1:func.9">/\</a> <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="txt" href="#E3:24_2"><span class="lab"><font color="Green" title="E21">z2</font></span></a>, <a class="ref" href="xboole_1.html#T12" title="XBOOLE_1:th.12">XBOOLE_1:12</a></span>
<br/>.= 
<font color="Maroon" title="c5">Z</font> <a href="subset_1.html#K9" title="SUBSET_1:func.9">/\</a> <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#K9" title="SUBSET_1:func.9">/\</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="kw">by</span> <span class="lab"><a class="ref" href="xboole_1.html#T16" title="XBOOLE_1:th.16">XBOOLE_1:16</a></span>
<br/>.= 
<font color="Maroon" title="c5">Z</font>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E3:24_2"><span class="lab"><font color="Green" title="E21">z2</font></span></a>, <a class="ref" href="xboole_1.html#T28" title="XBOOLE_1:th.28">XBOOLE_1:28</a></span>
;<br/>
<span class="kw">hence </span><a NAME="E11:24_2"/>
<font color="Maroon" title="c4">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c2">A</font> <a href="interva1.html#K3" title="INTERVA1:func.3">_/\_</a> <font color="Maroon" title="c3">B</font>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="setfam_1.html#D5" title="SETFAM_1:def.5">SETFAM_1:def 5</a>, <a class="txt" href="#E3:24_2"><span class="lab"><font color="Green" title="E21">z2</font></span></a>, <a class="txt" href="#E6:24_2"><span class="lab"><font color="Green" title="E22">e1</font></span></a>, <a class="txt" href="#E9:24_2"><span class="lab"><font color="Green" title="E23">e2</font></span></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><span class="kw">end;</span></div>
<span class="kw">hence </span><a NAME="E3:24"/>
<font color="Maroon" title="c2">A</font> <a href="interva1.html#K3" title="INTERVA1:func.3">_/\_</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#K9" title="SUBSET_1:func.9">/\</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="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#K9" title="SUBSET_1:func.9">/\</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="kw">by</span> <span class="lab"><a class="txt" href="#E1:24"><span class="lab"><font color="Green" title="E20">v1</font></span></a>, <a class="ref" href="xboole_0.html#D10" title="XBOOLE_0:def.10">XBOOLE_0:def 10</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>
