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<span class="kw">let </span><font color="Maroon" title="c1">R</font> be   <a href="roughs_1.html#NM1" title="ROUGHS_1:NM.1">Approximation_Space</a>; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide">  for <font color="Olive" title="b1">x</font> being   <a href="struct_0.html#NM2" title="STRUCT_0:NM.2">Subset</a> of <font color="Maroon" title="c1">R</font>  holds <span class="p1">(<span class="default"><a href="roughs_5.html#K5" title="ROUGHS_5:func.5">f_0</a> <font color="Maroon" title="c1">R</font></span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Olive" title="b1">x</font> is  <a href="roughs_1.html#NV5" title="ROUGHS_1:NV.5">exact</a> </span><br/><span class="kw">let </span><font color="Maroon" title="c2">x</font> be   <a href="struct_0.html#NM2" title="STRUCT_0:NM.2">Subset</a> of <font color="Maroon" title="c1">R</font>; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" 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="roughs_5.html#K5" title="ROUGHS_5:func.5">f_0</a> <font color="Maroon" title="c1">R</font></span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c2">x</font> is  <a href="roughs_1.html#NV5" title="ROUGHS_1:NV.5">exact</a> </span><br/>



<span class="p1">(<span class="default"><a href="roughs_5.html#K5" title="ROUGHS_5:func.5">f_0</a> <font color="Maroon" title="c1">R</font></span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c2">x</font> = 
<span class="p1">(<span class="default"><a href="roughs_2.html#K4" title="ROUGHS_2:func.4">UAp</a> <font color="Maroon" title="c1">R</font></span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c2">x</font>
<span class="kw">by</span> <span class="lab"><a class="ref" href="roughs_5.html#T13" target="_self" onmouseover="rs('roughs_5/T13')" onmouseout="rh()">UApF0</a></span>
<br/>.= 
 <a href="roughs_1.html#K4" title="ROUGHS_1:func.4">UAp</a> <font color="Maroon" title="c2">x</font>
<span class="kw">by</span> <span class="lab"><a class="ref" href="roughs_2.html#D11" onmouseover="rs('roughs_2/D11')" onmouseout="rh()">ROUGHS_2:def 11</a></span>
;<br/>
<span class="kw">hence </span><a NAME="E2:20"/>
<span class="p1">(<span class="default"><a href="roughs_5.html#K5" title="ROUGHS_5:func.5">f_0</a> <font color="Maroon" title="c1">R</font></span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c2">x</font> is  <a href="roughs_1.html#NV5" title="ROUGHS_1:NV.5">exact</a> 
 ; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" 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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