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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>, <font color="Olive" title="b3">C</font> being   <a href="interva1.html#M2" title="INTERVA1:mode.2">RoughSet</a> of <font color="Maroon" title="c1">X</font> holds  <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#K17" title="INTERVA1:func.17">_/\_</a> <font color="Olive" title="b3">C</font> <a href="interva1.html#R2" title="INTERVA1:pred.2">=</a> <font color="Olive" title="b1">A</font> <a href="interva1.html#K17" title="INTERVA1:func.17">_/\_</a> <span class="p1">(<span class="default"><font color="Olive" title="b2">B</font> <a href="interva1.html#K17" title="INTERVA1:func.17">_/\_</a> <font color="Olive" title="b3">C</font></span>)</span></span><br/><span class="kw">let </span><font color="Maroon" title="c2">A</font>, <font color="Maroon" title="c3">B</font>, <font color="Maroon" title="c4">C</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"> <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#K17" title="INTERVA1:func.17">_/\_</a> <font color="Maroon" title="c4">C</font> <a href="interva1.html#R2" title="INTERVA1:pred.2">=</a> <font color="Maroon" title="c2">A</font> <a href="interva1.html#K17" title="INTERVA1:func.17">_/\_</a> <span class="p1">(<span class="default"><font color="Maroon" title="c3">B</font> <a href="interva1.html#K17" title="INTERVA1:func.17">_/\_</a> <font color="Maroon" title="c4">C</font></span>)</span></span><br/>







<a NAME="E1:83"/><span class="lab"><font color="Green" title="E60">a</font></span>: 
<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> <a href="subset_1.html#K9" title="SUBSET_1:func.9">/\</a> <span class="p1">(<span class="default"><a href="interva1.html#K14" title="INTERVA1:func.14">LAp</a> <font color="Maroon" title="c4">C</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</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> <a href="subset_1.html#K9" title="SUBSET_1:func.9">/\</a> <span class="p1">(<span class="default"><a href="interva1.html#K14" title="INTERVA1:func.14">LAp</a> <font color="Maroon" title="c4">C</font></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 NAME="E2:83"/><span class="lab"><font color="Green" title="E61">s</font></span>: 
<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> <a href="subset_1.html#K9" title="SUBSET_1:func.9">/\</a> <span class="p1">(<span class="default"><a href="interva1.html#K14" title="INTERVA1:func.14">LAp</a> <font color="Maroon" title="c4">C</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <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#K9" title="SUBSET_1:func.9">/\</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="c3">B</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="c4">C</font></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/>
<a NAME="E3:83"/><span class="lab"><font color="Green" title="E62">q</font></span>: 
<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> <a href="subset_1.html#K9" title="SUBSET_1:func.9">/\</a> <span class="p1">(<span class="default"><a href="interva1.html#K15" title="INTERVA1:func.15">UAp</a> <font color="Maroon" title="c4">C</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</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> <a href="subset_1.html#K9" title="SUBSET_1:func.9">/\</a> <span class="p1">(<span class="default"><a href="interva1.html#K15" title="INTERVA1:func.15">UAp</a> <font color="Maroon" title="c4">C</font></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 NAME="E4:83"/><span class="lab"><font color="Green" title="E63">w</font></span>: 
<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> <a href="subset_1.html#K9" title="SUBSET_1:func.9">/\</a> <span class="p1">(<span class="default"><a href="interva1.html#K15" title="INTERVA1:func.15">UAp</a> <font color="Maroon" title="c4">C</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <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#K9" title="SUBSET_1:func.9">/\</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="c3">B</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="c4">C</font></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/>
<a NAME="E5:83"/>
<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#K9" title="SUBSET_1:func.9">/\</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="c3">B</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="c4">C</font></span>)</span></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <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#K9" title="SUBSET_1:func.9">/\</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="c3">B</font> <a href="interva1.html#K17" title="INTERVA1:func.17">_/\_</a> <font color="Maroon" title="c4">C</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/>
<span class="kw">hence </span><a NAME="E6:83"/>
<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#K17" title="INTERVA1:func.17">_/\_</a> <font color="Maroon" title="c4">C</font> <a href="interva1.html#R2" title="INTERVA1:pred.2">=</a> <font color="Maroon" title="c2">A</font> <a href="interva1.html#K17" title="INTERVA1:func.17">_/\_</a> <span class="p1">(<span class="default"><font color="Maroon" title="c3">B</font> <a href="interva1.html#K17" title="INTERVA1:func.17">_/\_</a> <font color="Maroon" title="c4">C</font></span>)</span>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:83"><span class="lab"><font color="Green" title="E60">a</font></span></a>, <a class="txt" href="#E2:83"><span class="lab"><font color="Green" title="E61">s</font></span></a>, <a class="ref" href="interva1.html#T58" target="_self" title="INTERVA1:th.58">Th3</a>, <a class="txt" href="#E3:83"><span class="lab"><font color="Green" title="E62">q</font></span></a>, <a class="txt" href="#E4:83"><span class="lab"><font color="Green" title="E63">w</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/>


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