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<span class="kw">let </span><font color="Maroon" title="c1">X</font> be   <a href="roughs_1.html#NM2" title="ROUGHS_1:NM.2">Tolerance_Space</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   <a href="interva1.html#M2" title="INTERVA1:mode.2">RoughSet</a> of <font color="Maroon" title="c1">X</font> holds  <font color="Olive" title="b1">A</font> <a href="interva1.html#K16" title="INTERVA1:func.16">_\/_</a> <span class="p1">(<span class="default"><font color="Olive" title="b1">A</font> <a href="interva1.html#K17" title="INTERVA1:func.17">_/\_</a> <font color="Olive" title="b2">B</font></span>)</span> <a href="interva1.html#R2" title="INTERVA1:pred.2">=</a> <font color="Olive" title="b1">A</font></span><br/><span class="kw">let </span><font color="Maroon" title="c2">A</font>, <font color="Maroon" title="c3">B</font> be    <a href="interva1.html#M2" title="INTERVA1:mode.2">RoughSet</a> of <font color="Maroon" title="c1">X</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#K16" title="INTERVA1:func.16">_\/_</a> <span class="p1">(<span class="default"><font color="Maroon" title="c2">A</font> <a href="interva1.html#K17" title="INTERVA1:func.17">_/\_</a> <font color="Maroon" title="c3">B</font></span>)</span> <a href="interva1.html#R2" title="INTERVA1:pred.2">=</a> <font color="Maroon" title="c2">A</font></span><br/>





<span class="lab"><font color="Green" title="E62">A1</font></span>:  <a href="interva1.html#K14" title="INTERVA1:func.14">LAp</a> <span class="p1">(<span class="default"><font color="Maroon" title="c2">A</font> <a href="interva1.html#K16" title="INTERVA1:func.16">_\/_</a> <span class="p2">(<span class="default"><font color="Maroon" title="c2">A</font> <a href="interva1.html#K17" title="INTERVA1:func.17">_/\_</a> <font color="Maroon" title="c3">B</font></span>)</span></span>)</span> = 
<span class="p1">(<span class="default"><a href="interva1.html#K14" title="INTERVA1:func.14">LAp</a> <font color="Maroon" title="c2">A</font></span>)</span> <a href="subset_1.html#K4" title="SUBSET_1:func.4">\/</a> <span class="p1">(<span class="default"><a href="interva1.html#K14" title="INTERVA1:func.14">LAp</a> <span class="p2">(<span class="default"><font color="Maroon" title="c2">A</font> <a href="interva1.html#K17" title="INTERVA1:func.17">_/\_</a> <font color="Maroon" title="c3">B</font></span>)</span></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="ref" href="interva1.html#T56" target="_self" title="INTERVA1:th.56">Th1</a></span>
<br/>.= 
<span class="p1">(<span class="default"><a href="interva1.html#K14" title="INTERVA1:func.14">LAp</a> <font color="Maroon" title="c2">A</font></span>)</span> <a href="subset_1.html#K4" title="SUBSET_1:func.4">\/</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="interva1.html#K14" title="INTERVA1:func.14">LAp</a> <font color="Maroon" title="c2">A</font></span>)</span> <a href="subset_1.html#K9" title="SUBSET_1:func.9">/\</a> <span class="p2">(<span class="default"><a href="interva1.html#K14" title="INTERVA1:func.14">LAp</a> <font color="Maroon" title="c3">B</font></span>)</span></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="ref" href="interva1.html#T58" target="_self" title="INTERVA1:th.58">Th3</a></span>
<br/>.= 
 <a href="interva1.html#K14" title="INTERVA1:func.14">LAp</a> <font color="Maroon" title="c2">A</font>
<span class="kw">by</span> <span class="lab"><a class="ref" href="xboole_1.html#T22" title="XBOOLE_1:th.22">XBOOLE_1:22</a></span>
;<br/>
 <a href="interva1.html#K15" title="INTERVA1:func.15">UAp</a> <span class="p1">(<span class="default"><font color="Maroon" title="c2">A</font> <a href="interva1.html#K16" title="INTERVA1:func.16">_\/_</a> <span class="p2">(<span class="default"><font color="Maroon" title="c2">A</font> <a href="interva1.html#K17" title="INTERVA1:func.17">_/\_</a> <font color="Maroon" title="c3">B</font></span>)</span></span>)</span> = 
<span class="p1">(<span class="default"><a href="interva1.html#K15" title="INTERVA1:func.15">UAp</a> <font color="Maroon" title="c2">A</font></span>)</span> <a href="subset_1.html#K4" title="SUBSET_1:func.4">\/</a> <span class="p1">(<span class="default"><a href="interva1.html#K15" title="INTERVA1:func.15">UAp</a> <span class="p2">(<span class="default"><font color="Maroon" title="c2">A</font> <a href="interva1.html#K17" title="INTERVA1:func.17">_/\_</a> <font color="Maroon" title="c3">B</font></span>)</span></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="ref" href="interva1.html#T57" target="_self" title="INTERVA1:th.57">Th2</a></span>
<br/>.= 
<span class="p1">(<span class="default"><a href="interva1.html#K15" title="INTERVA1:func.15">UAp</a> <font color="Maroon" title="c2">A</font></span>)</span> <a href="subset_1.html#K4" title="SUBSET_1:func.4">\/</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="interva1.html#K15" title="INTERVA1:func.15">UAp</a> <font color="Maroon" title="c2">A</font></span>)</span> <a href="subset_1.html#K9" title="SUBSET_1:func.9">/\</a> <span class="p2">(<span class="default"><a href="interva1.html#K15" title="INTERVA1:func.15">UAp</a> <font color="Maroon" title="c3">B</font></span>)</span></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="ref" href="interva1.html#T59" target="_self" title="INTERVA1:th.59">Th4</a></span>
<br/>.= 
 <a href="interva1.html#K15" title="INTERVA1:func.15">UAp</a> <font color="Maroon" title="c2">A</font>
<span class="kw">by</span> <span class="lab"><a class="ref" href="xboole_1.html#T22" title="XBOOLE_1:th.22">XBOOLE_1:22</a></span>
;<br/>
<span class="kw">hence </span><a NAME="E3:85"/>
<font color="Maroon" title="c2">A</font> <a href="interva1.html#K16" title="INTERVA1:func.16">_\/_</a> <span class="p1">(<span class="default"><font color="Maroon" title="c2">A</font> <a href="interva1.html#K17" title="INTERVA1:func.17">_/\_</a> <font color="Maroon" title="c3">B</font></span>)</span> <a href="interva1.html#R2" title="INTERVA1:pred.2">=</a> <font color="Maroon" title="c2">A</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:85"><span class="lab"><font color="Green" title="E62">A1</font></span></a>, <a class="ref" href="interva1.html#D17" target="_self" title="INTERVA1:def.17">Def5</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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