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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="firebrick">::  thesis: </font></span></a><span class="hide">  for <font color="Olive" title="b1">A</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"><a href="interva1.html#K23" title="INTERVA1:func.23">TRS</a> <font color="Maroon" title="c1">X</font></span>)</span> <a href="interva1.html#K17" title="INTERVA1:func.17">_/\_</a> <font color="Olive" title="b1">A</font> <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> 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="firebrick">::  thesis: </font></span></a><span class="hide"> <span class="p1">(<span class="default"><a href="interva1.html#K23" title="INTERVA1:func.23">TRS</a> <font color="Maroon" title="c1">X</font></span>)</span> <a href="interva1.html#K17" title="INTERVA1:func.17">_/\_</a> <font color="Maroon" title="c2">A</font> <a href="interva1.html#R2" title="INTERVA1:pred.2">=</a> <font color="Maroon" title="c2">A</font></span><br/>



<a NAME="E1:106"/><span class="lab"><font color="Green" title="E76">A1</font></span>: 
 <a href="interva1.html#K14" title="INTERVA1:func.14">LAp</a> <span class="p1">(<span class="default"><a href="interva1.html#K23" title="INTERVA1:func.23">TRS</a> <font color="Maroon" title="c1">X</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="struct_0.html#K2" title="STRUCT_0:func.2">[#]</a> <font color="Maroon" title="c1">X</font>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="mcart_1.html#T7" title="MCART_1:th.7">MCART_1:7</a></span>;<br/>
<a NAME="E2:106"/><span class="lab"><font color="Green" title="E77">A2</font></span>: 
 <a href="interva1.html#K15" title="INTERVA1:func.15">UAp</a> <span class="p1">(<span class="default"><a href="interva1.html#K23" title="INTERVA1:func.23">TRS</a> <font color="Maroon" title="c1">X</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="struct_0.html#K2" title="STRUCT_0:func.2">[#]</a> <font color="Maroon" title="c1">X</font>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="mcart_1.html#T7" title="MCART_1:th.7">MCART_1:7</a></span>;<br/>
<span class="lab"><font color="Green" title="E78">A3</font></span>:  <a href="interva1.html#K14" title="INTERVA1:func.14">LAp</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="interva1.html#K23" title="INTERVA1:func.23">TRS</a> <font color="Maroon" title="c1">X</font></span>)</span> <a href="interva1.html#K17" title="INTERVA1:func.17">_/\_</a> <font color="Maroon" title="c2">A</font></span>)</span> = 
<span class="p1">(<span class="default"><a href="interva1.html#K14" title="INTERVA1:func.14">LAp</a> <span class="p2">(<span class="default"><a href="interva1.html#K23" title="INTERVA1:func.23">TRS</a> <font color="Maroon" title="c1">X</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="c2">A</font></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="ref" href="interva1.html#T58" target="_self" title="INTERVA1:th.58">Th58</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="txt" href="#E1:106"><span class="lab"><font color="Green" title="E76">A1</font></span></a>, <a class="ref" href="xboole_1.html#T28" title="XBOOLE_1:th.28">XBOOLE_1:28</a></span>
;<br/>
 <a href="interva1.html#K15" title="INTERVA1:func.15">UAp</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="interva1.html#K23" title="INTERVA1:func.23">TRS</a> <font color="Maroon" title="c1">X</font></span>)</span> <a href="interva1.html#K17" title="INTERVA1:func.17">_/\_</a> <font color="Maroon" title="c2">A</font></span>)</span> = 
<span class="p1">(<span class="default"><a href="interva1.html#K15" title="INTERVA1:func.15">UAp</a> <span class="p2">(<span class="default"><a href="interva1.html#K23" title="INTERVA1:func.23">TRS</a> <font color="Maroon" title="c1">X</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="c2">A</font></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="ref" href="interva1.html#T59" target="_self" title="INTERVA1:th.59">Th59</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="txt" href="#E2:106"><span class="lab"><font color="Green" title="E77">A2</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="E5:106"/>
<span class="p1">(<span class="default"><a href="interva1.html#K23" title="INTERVA1:func.23">TRS</a> <font color="Maroon" title="c1">X</font></span>)</span> <a href="interva1.html#K17" title="INTERVA1:func.17">_/\_</a> <font color="Maroon" title="c2">A</font> <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="#E3:106"><span class="lab"><font color="Green" title="E78">A3</font></span></a>, <a class="ref" href="interva1.html#D17" target="_self" title="INTERVA1:def.17">Def17</a></span>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> verum</span><br/>


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