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<b>let </b><font color="Maroon" title="c1">A</font> be   <a href="roughs_1.html#NM2" title="ROUGHS_1:NM.2">Tolerance_Space</a>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> for <font color="Olive" title="b1">X</font>, <font color="Olive" title="b2">Y</font>, <font color="Olive" title="b3">Z</font> being  <a href="struct_0.html#NM2" title="STRUCT_0:NM.2">Subset</a> of <font color="Maroon" title="c1">A</font>  st <font color="Olive" title="b1">X</font> <a href="roughs_1.html#R1" title="ROUGHS_1:pred.1">_c=</a> <font color="Olive" title="b2">Y</font> &amp; <font color="Olive" title="b2">Y</font> <a href="roughs_1.html#R1" title="ROUGHS_1:pred.1">_c=</a> <font color="Olive" title="b3">Z</font> holds <br/><font color="Olive" title="b1">X</font> <a href="roughs_1.html#R1" title="ROUGHS_1:pred.1">_c=</a> <font color="Olive" title="b3">Z</font></span><br/><b>let </b><font color="Maroon" title="c2">X</font>, <font color="Maroon" title="c3">Y</font>, <font color="Maroon" title="c4">Z</font> be   <a href="struct_0.html#NM2" title="STRUCT_0:NM.2">Subset</a> of <font color="Maroon" title="c1">A</font>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> ( <font color="Maroon" title="c2">X</font> <a href="roughs_1.html#R1" title="ROUGHS_1:pred.1">_c=</a> <font color="Maroon" title="c3">Y</font> &amp; <font color="Maroon" title="c3">Y</font> <a href="roughs_1.html#R1" title="ROUGHS_1:pred.1">_c=</a> <font color="Maroon" title="c4">Z</font> implies <font color="Maroon" title="c2">X</font> <a href="roughs_1.html#R1" title="ROUGHS_1:pred.1">_c=</a> <font color="Maroon" title="c4">Z</font> )</span><br/>







<b>assume </b><a NAME="E1:90"/>
( <font color="Maroon" title="c2">X</font> <a href="roughs_1.html#R1" title="ROUGHS_1:pred.1">_c=</a> <font color="Maroon" title="c3">Y</font> &amp; <font color="Maroon" title="c3">Y</font> <a href="roughs_1.html#R1" title="ROUGHS_1:pred.1">_c=</a> <font color="Maroon" title="c4">Z</font> )
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> <font color="Maroon" title="c2">X</font> <a href="roughs_1.html#R1" title="ROUGHS_1:pred.1">_c=</a> <font color="Maroon" title="c4">Z</font></span><br/>

<a NAME="E2:90"/><b>then </b>
(  <a href="roughs_1.html#K3" title="ROUGHS_1:func.3">LAp</a> <font color="Maroon" title="c2">X</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a>  <a href="roughs_1.html#K3" title="ROUGHS_1:func.3">LAp</a> <font color="Maroon" title="c3">Y</font> &amp;  <a href="roughs_1.html#K3" title="ROUGHS_1:func.3">LAp</a> <font color="Maroon" title="c3">Y</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a>  <a href="roughs_1.html#K3" title="ROUGHS_1:func.3">LAp</a> <font color="Maroon" title="c4">Z</font> )
 
<b>by </b><i><a class="ref" href="roughs_1.html#D11" target="_self" title="ROUGHS_1:def.11">Def11</a></i>;<br/>
<a NAME="E3:90"/><b>then </b>
 <a href="roughs_1.html#K3" title="ROUGHS_1:func.3">LAp</a> <font color="Maroon" title="c2">X</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a>  <a href="roughs_1.html#K3" title="ROUGHS_1:func.3">LAp</a> <font color="Maroon" title="c4">Z</font>
 
<b>by </b><i><a class="ref" href="xboole_1.html#T1" title="XBOOLE_1:th.1">XBOOLE_1:1</a></i>;<br/>
<b>hence </b><a NAME="E4:90"/>
<font color="Maroon" title="c2">X</font> <a href="roughs_1.html#R1" title="ROUGHS_1:pred.1">_c=</a> <font color="Maroon" title="c4">Z</font>
 <b>by </b><i><a class="ref" href="roughs_1.html#D11" target="_self" title="ROUGHS_1:def.11">Def11</a></i>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> verum</span><br/>


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