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<a NAME="E1:10_1_1"/>
 for <font color="Olive" title="b1">a</font>, <font color="Olive" title="b2">b</font> being   <a href="subset_1.html#NM2" title="SUBSET_1:NM.2">Subset</a> of <font color="Maroon" title="c1">A</font> holds  <font color="Maroon" title="c2">f</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <span class="p1">(<span class="default"><font color="Olive" title="b1">a</font> <a href="subset_1.html#K4" title="SUBSET_1:func.4">\/</a> <font color="Olive" title="b2">b</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><font color="Maroon" title="c2">f</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Olive" title="b1">a</font></span>)</span> <a href="subset_1.html#K4" title="SUBSET_1:func.4">\/</a> <span class="p1">(<span class="default"><font color="Maroon" title="c2">f</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Olive" title="b2">b</font></span>)</span>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="roughs_4.html#D9" onmouseover="rs('roughs_4/D9')" onmouseout="rh()">ROUGHS_4:def 9</a></span>;<br/>
<a NAME="E2:10_1_1"/><span class="kw">then </span>
 for <font color="Olive" title="b1">a</font>, <font color="Olive" title="b2">b</font> being   <a href="subset_1.html#NM2" title="SUBSET_1:NM.2">Subset</a> of <font color="Maroon" title="c1">A</font> holds  <span class="p1">(<span class="default"><a href="roughs_2.html#K5" title="ROUGHS_2:func.5">Flip</a> <font color="Maroon" title="c2">f</font></span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <span class="p1">(<span class="default"><font color="Olive" title="b1">a</font> <a href="subset_1.html#K9" title="SUBSET_1:func.9">/\</a> <font color="Olive" title="b2">b</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="roughs_2.html#K5" title="ROUGHS_2:func.5">Flip</a> <font color="Maroon" title="c2">f</font></span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Olive" title="b1">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="roughs_2.html#K5" title="ROUGHS_2:func.5">Flip</a> <font color="Maroon" title="c2">f</font></span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Olive" title="b2">b</font></span>)</span>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="roughs_2.html#T21" onmouseover="rs('roughs_2/T21')" onmouseout="rh()">ROUGHS_2:21</a></span>;<br/>
<span class="kw">hence </span><a NAME="E3:10_1_1"/>
 <a href="roughs_2.html#K5" title="ROUGHS_2:func.5">Flip</a> <font color="Maroon" title="c2">f</font> is  <a href="roughs_4.html#V10" title="ROUGHS_4:attr.10">/\-preserving</a> 
 <span class="kw">by</span> <span class="lab"><a class="ref" href="roughs_4.html#D10" onmouseover="rs('roughs_4/D10')" onmouseout="rh()">ROUGHS_4:def 10</a></span>; <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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