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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">K</font>, <font color="Olive" title="b2">L</font>, <font color="Olive" title="b3">M</font> being   <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of  <a href="interva1.html#K18" title="INTERVA1:func.18">RoughSets</a> <font color="Maroon" title="c1">X</font> holds  the <a href="lattices.html#U1" title="LATTICES:sel.1">L_meet</a> of <span class="p1">(<span class="default"><a href="interva1.html#K21" title="INTERVA1:func.21">RSLattice</a> <font color="Maroon" title="c1">X</font></span>)</span> <a href="binop_1.html#K1" title="BINOP_1:func.1">.</a> <font color="Olive" title="b1">K</font>,<span class="p1">(<span class="default">the <a href="lattices.html#U2" title="LATTICES:sel.2">L_join</a> of <span class="p2">(<span class="default"><a href="interva1.html#K21" title="INTERVA1:func.21">RSLattice</a> <font color="Maroon" title="c1">X</font></span>)</span> <a href="binop_1.html#K1" title="BINOP_1:func.1">.</a> <font color="Olive" title="b2">L</font>,<font color="Olive" title="b3">M</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> the <a href="lattices.html#U2" title="LATTICES:sel.2">L_join</a> of <span class="p1">(<span class="default"><a href="interva1.html#K21" title="INTERVA1:func.21">RSLattice</a> <font color="Maroon" title="c1">X</font></span>)</span> <a href="binop_1.html#K1" title="BINOP_1:func.1">.</a> <span class="p1">(<span class="default">the <a href="lattices.html#U1" title="LATTICES:sel.1">L_meet</a> of <span class="p2">(<span class="default"><a href="interva1.html#K21" title="INTERVA1:func.21">RSLattice</a> <font color="Maroon" title="c1">X</font></span>)</span> <a href="binop_1.html#K1" title="BINOP_1:func.1">.</a> <font color="Olive" title="b1">K</font>,<font color="Olive" title="b2">L</font></span>)</span>,<span class="p1">(<span class="default">the <a href="lattices.html#U1" title="LATTICES:sel.1">L_meet</a> of <span class="p2">(<span class="default"><a href="interva1.html#K21" title="INTERVA1:func.21">RSLattice</a> <font color="Maroon" title="c1">X</font></span>)</span> <a href="binop_1.html#K1" title="BINOP_1:func.1">.</a> <font color="Olive" title="b1">K</font>,<font color="Olive" title="b3">M</font></span>)</span></span><br/><span class="kw">let </span><font color="Maroon" title="c2">K</font>, <font color="Maroon" title="c3">L</font>, <font color="Maroon" title="c4">M</font> be    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of  <a href="interva1.html#K18" title="INTERVA1:func.18">RoughSets</a> <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"> the <a href="lattices.html#U1" title="LATTICES:sel.1">L_meet</a> of <span class="p1">(<span class="default"><a href="interva1.html#K21" title="INTERVA1:func.21">RSLattice</a> <font color="Maroon" title="c1">X</font></span>)</span> <a href="binop_1.html#K1" title="BINOP_1:func.1">.</a> <font color="Maroon" title="c2">K</font>,<span class="p1">(<span class="default">the <a href="lattices.html#U2" title="LATTICES:sel.2">L_join</a> of <span class="p2">(<span class="default"><a href="interva1.html#K21" title="INTERVA1:func.21">RSLattice</a> <font color="Maroon" title="c1">X</font></span>)</span> <a href="binop_1.html#K1" title="BINOP_1:func.1">.</a> <font color="Maroon" title="c3">L</font>,<font color="Maroon" title="c4">M</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> the <a href="lattices.html#U2" title="LATTICES:sel.2">L_join</a> of <span class="p1">(<span class="default"><a href="interva1.html#K21" title="INTERVA1:func.21">RSLattice</a> <font color="Maroon" title="c1">X</font></span>)</span> <a href="binop_1.html#K1" title="BINOP_1:func.1">.</a> <span class="p1">(<span class="default">the <a href="lattices.html#U1" title="LATTICES:sel.1">L_meet</a> of <span class="p2">(<span class="default"><a href="interva1.html#K21" title="INTERVA1:func.21">RSLattice</a> <font color="Maroon" title="c1">X</font></span>)</span> <a href="binop_1.html#K1" title="BINOP_1:func.1">.</a> <font color="Maroon" title="c2">K</font>,<font color="Maroon" title="c3">L</font></span>)</span>,<span class="p1">(<span class="default">the <a href="lattices.html#U1" title="LATTICES:sel.1">L_meet</a> of <span class="p2">(<span class="default"><a href="interva1.html#K21" title="INTERVA1:func.21">RSLattice</a> <font color="Maroon" title="c1">X</font></span>)</span> <a href="binop_1.html#K1" title="BINOP_1:func.1">.</a> <font color="Maroon" title="c2">K</font>,<font color="Maroon" title="c4">M</font></span>)</span></span><br/>







<span class="kw">set </span><font color="Maroon" title="c5">G</font> =  <a href="interva1.html#K21" title="INTERVA1:func.21">RSLattice</a> <font color="Maroon" title="c1">X</font>;<br/>
<span class="kw">reconsider </span><font color="Maroon" title="c6">K9</font> = <font color="Maroon" title="c2">K</font>, <font color="Maroon" title="c7">L9</font> = <font color="Maroon" title="c3">L</font>, <font color="Maroon" title="c8">M9</font> = <font color="Maroon" title="c4">M</font> as    <a href="interva1.html#M2" title="INTERVA1:mode.2">RoughSet</a> of <font color="Maroon" title="c1">X</font> <span class="kw">by</span> <span class="lab"><a class="ref" href="interva1.html#D20" target="_self" title="INTERVA1:def.20">DefRSX</a></span>;<br/>
<a NAME="E2:99"/><span class="lab"><font color="Green" title="E71">XX</font></span>: 
<font color="Maroon" title="c7">L9</font> <a href="interva1.html#K16" title="INTERVA1:func.16">_\/_</a> <font color="Maroon" title="c8">M9</font> is    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of  <a href="interva1.html#K18" title="INTERVA1:func.18">RoughSets</a> <font color="Maroon" title="c1">X</font>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="interva1.html#D20" target="_self" title="INTERVA1:def.20">DefRSX</a></span>;<br/>
<a NAME="E3:99"/><span class="lab"><font color="Green" title="E72">XY</font></span>: 
<font color="Maroon" title="c6">K9</font> <a href="interva1.html#K17" title="INTERVA1:func.17">_/\_</a> <font color="Maroon" title="c7">L9</font> is    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of  <a href="interva1.html#K18" title="INTERVA1:func.18">RoughSets</a> <font color="Maroon" title="c1">X</font>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="interva1.html#D20" target="_self" title="INTERVA1:def.20">DefRSX</a></span>;<br/>
<a NAME="E4:99"/><span class="lab"><font color="Green" title="E73">XQ</font></span>: 
<font color="Maroon" title="c6">K9</font> <a href="interva1.html#K17" title="INTERVA1:func.17">_/\_</a> <font color="Maroon" title="c8">M9</font> is    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of  <a href="interva1.html#K18" title="INTERVA1:func.18">RoughSets</a> <font color="Maroon" title="c1">X</font>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="interva1.html#D20" target="_self" title="INTERVA1:def.20">DefRSX</a></span>;<br/>
the <a href="lattices.html#U1" title="LATTICES:sel.1">L_meet</a> of <span class="p1">(<span class="default"><a href="interva1.html#K21" title="INTERVA1:func.21">RSLattice</a> <font color="Maroon" title="c1">X</font></span>)</span> <a href="binop_1.html#K1" title="BINOP_1:func.1">.</a> <font color="Maroon" title="c2">K</font>,<span class="p1">(<span class="default">the <a href="lattices.html#U2" title="LATTICES:sel.2">L_join</a> of <span class="p2">(<span class="default"><a href="interva1.html#K21" title="INTERVA1:func.21">RSLattice</a> <font color="Maroon" title="c1">X</font></span>)</span> <a href="binop_1.html#K1" title="BINOP_1:func.1">.</a> <font color="Maroon" title="c3">L</font>,<font color="Maroon" title="c4">M</font></span>)</span> = 
the <a href="lattices.html#U1" title="LATTICES:sel.1">L_meet</a> of <span class="p1">(<span class="default"><a href="interva1.html#K21" title="INTERVA1:func.21">RSLattice</a> <font color="Maroon" title="c1">X</font></span>)</span> <a href="binop_1.html#K1" title="BINOP_1:func.1">.</a> <font color="Maroon" title="c2">K</font>,<span class="p1">(<span class="default"><font color="Maroon" title="c7">L9</font> <a href="interva1.html#K16" title="INTERVA1:func.16">_\/_</a> <font color="Maroon" title="c8">M9</font></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="ref" href="interva1.html#D23" target="_self" title="INTERVA1:def.23">Def8</a></span>
<br/>.= 
<font color="Maroon" title="c6">K9</font> <a href="interva1.html#K17" title="INTERVA1:func.17">_/\_</a> <span class="p1">(<span class="default"><font color="Maroon" title="c7">L9</font> <a href="interva1.html#K16" title="INTERVA1:func.16">_\/_</a> <font color="Maroon" title="c8">M9</font></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="ref" href="interva1.html#D23" target="_self" title="INTERVA1:def.23">Def8</a>, <a class="txt" href="#E2:99"><span class="lab"><font color="Green" title="E71">XX</font></span></a></span>
<br/>.= 
<span class="p1">(<span class="default"><font color="Maroon" title="c6">K9</font> <a href="interva1.html#K17" title="INTERVA1:func.17">_/\_</a> <font color="Maroon" title="c7">L9</font></span>)</span> <a href="interva1.html#K16" title="INTERVA1:func.16">_\/_</a> <span class="p1">(<span class="default"><font color="Maroon" title="c6">K9</font> <a href="interva1.html#K17" title="INTERVA1:func.17">_/\_</a> <font color="Maroon" title="c8">M9</font></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="ref" href="interva1.html#T66" target="_self" title="INTERVA1:th.66">Th9</a></span>
<br/>.= 
the <a href="lattices.html#U2" title="LATTICES:sel.2">L_join</a> of <span class="p1">(<span class="default"><a href="interva1.html#K21" title="INTERVA1:func.21">RSLattice</a> <font color="Maroon" title="c1">X</font></span>)</span> <a href="binop_1.html#K1" title="BINOP_1:func.1">.</a> <span class="p1">(<span class="default"><font color="Maroon" title="c6">K9</font> <a href="interva1.html#K17" title="INTERVA1:func.17">_/\_</a> <font color="Maroon" title="c7">L9</font></span>)</span>,<span class="p1">(<span class="default"><font color="Maroon" title="c6">K9</font> <a href="interva1.html#K17" title="INTERVA1:func.17">_/\_</a> <font color="Maroon" title="c8">M9</font></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="ref" href="interva1.html#D23" target="_self" title="INTERVA1:def.23">Def8</a>, <a class="txt" href="#E3:99"><span class="lab"><font color="Green" title="E72">XY</font></span></a>, <a class="txt" href="#E4:99"><span class="lab"><font color="Green" title="E73">XQ</font></span></a></span>
<br/>.= 
the <a href="lattices.html#U2" title="LATTICES:sel.2">L_join</a> of <span class="p1">(<span class="default"><a href="interva1.html#K21" title="INTERVA1:func.21">RSLattice</a> <font color="Maroon" title="c1">X</font></span>)</span> <a href="binop_1.html#K1" title="BINOP_1:func.1">.</a> <span class="p1">(<span class="default">the <a href="lattices.html#U1" title="LATTICES:sel.1">L_meet</a> of <span class="p2">(<span class="default"><a href="interva1.html#K21" title="INTERVA1:func.21">RSLattice</a> <font color="Maroon" title="c1">X</font></span>)</span> <a href="binop_1.html#K1" title="BINOP_1:func.1">.</a> <font color="Maroon" title="c2">K</font>,<font color="Maroon" title="c3">L</font></span>)</span>,<span class="p1">(<span class="default"><font color="Maroon" title="c6">K9</font> <a href="interva1.html#K17" title="INTERVA1:func.17">_/\_</a> <font color="Maroon" title="c8">M9</font></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="ref" href="interva1.html#D23" target="_self" title="INTERVA1:def.23">Def8</a></span>
<br/>.= 
the <a href="lattices.html#U2" title="LATTICES:sel.2">L_join</a> of <span class="p1">(<span class="default"><a href="interva1.html#K21" title="INTERVA1:func.21">RSLattice</a> <font color="Maroon" title="c1">X</font></span>)</span> <a href="binop_1.html#K1" title="BINOP_1:func.1">.</a> <span class="p1">(<span class="default">the <a href="lattices.html#U1" title="LATTICES:sel.1">L_meet</a> of <span class="p2">(<span class="default"><a href="interva1.html#K21" title="INTERVA1:func.21">RSLattice</a> <font color="Maroon" title="c1">X</font></span>)</span> <a href="binop_1.html#K1" title="BINOP_1:func.1">.</a> <font color="Maroon" title="c2">K</font>,<font color="Maroon" title="c3">L</font></span>)</span>,<span class="p1">(<span class="default">the <a href="lattices.html#U1" title="LATTICES:sel.1">L_meet</a> of <span class="p2">(<span class="default"><a href="interva1.html#K21" title="INTERVA1:func.21">RSLattice</a> <font color="Maroon" title="c1">X</font></span>)</span> <a href="binop_1.html#K1" title="BINOP_1:func.1">.</a> <font color="Maroon" title="c2">K</font>,<font color="Maroon" title="c4">M</font></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="ref" href="interva1.html#D23" target="_self" title="INTERVA1:def.23">Def8</a></span>
;<br/>
<span class="kw">hence </span><a NAME="E6:99"/>
the <a href="lattices.html#U1" title="LATTICES:sel.1">L_meet</a> of <span class="p1">(<span class="default"><a href="interva1.html#K21" title="INTERVA1:func.21">RSLattice</a> <font color="Maroon" title="c1">X</font></span>)</span> <a href="binop_1.html#K1" title="BINOP_1:func.1">.</a> <font color="Maroon" title="c2">K</font>,<span class="p1">(<span class="default">the <a href="lattices.html#U2" title="LATTICES:sel.2">L_join</a> of <span class="p2">(<span class="default"><a href="interva1.html#K21" title="INTERVA1:func.21">RSLattice</a> <font color="Maroon" title="c1">X</font></span>)</span> <a href="binop_1.html#K1" title="BINOP_1:func.1">.</a> <font color="Maroon" title="c3">L</font>,<font color="Maroon" title="c4">M</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> the <a href="lattices.html#U2" title="LATTICES:sel.2">L_join</a> of <span class="p1">(<span class="default"><a href="interva1.html#K21" title="INTERVA1:func.21">RSLattice</a> <font color="Maroon" title="c1">X</font></span>)</span> <a href="binop_1.html#K1" title="BINOP_1:func.1">.</a> <span class="p1">(<span class="default">the <a href="lattices.html#U1" title="LATTICES:sel.1">L_meet</a> of <span class="p2">(<span class="default"><a href="interva1.html#K21" title="INTERVA1:func.21">RSLattice</a> <font color="Maroon" title="c1">X</font></span>)</span> <a href="binop_1.html#K1" title="BINOP_1:func.1">.</a> <font color="Maroon" title="c2">K</font>,<font color="Maroon" title="c3">L</font></span>)</span>,<span class="p1">(<span class="default">the <a href="lattices.html#U1" title="LATTICES:sel.1">L_meet</a> of <span class="p2">(<span class="default"><a href="interva1.html#K21" title="INTERVA1:func.21">RSLattice</a> <font color="Maroon" title="c1">X</font></span>)</span> <a href="binop_1.html#K1" title="BINOP_1:func.1">.</a> <font color="Maroon" title="c2">K</font>,<font color="Maroon" title="c4">M</font></span>)</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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