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<div><span class="kw">theorem </span><a NAME="T47"><span class="comment"><font color="firebrick">:: ROUGHS_5:47</font></span><br/></a><div class="add"> for <font color="Olive" title="b1">R</font> being   non  <a href="struct_0.html#V2" title="STRUCT_0:attr.2">empty</a>   <a href="orders_2.html#L1" title="ORDERS_2:struct.1">RelStr</a> <br/>  for <font color="Olive" title="b2">x</font>, <font color="Olive" title="b3">y</font> being   <a href="struct_0.html#NM2" title="STRUCT_0:NM.2">Subset</a> of <font color="Olive" title="b1">R</font> holds  <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> <span class="p3">(<span class="default"><a href="roughs_5.html#K6" title="ROUGHS_5:func.6">f_1</a> <font color="Olive" title="b1">R</font></span>)</span></span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Olive" title="b2">x</font></span>)</span> <a href="subset_1.html#K4" title="SUBSET_1:func.4">\/</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> <span class="p3">(<span class="default"><a href="roughs_5.html#K6" title="ROUGHS_5:func.6">f_1</a> <font color="Olive" title="b1">R</font></span>)</span></span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Olive" title="b3">y</font></span>)</span> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <span class="p1">(<span class="default"><a href="roughs_2.html#K5" title="ROUGHS_2:func.5">Flip</a> <span class="p2">(<span class="default"><a href="roughs_5.html#K6" title="ROUGHS_5:func.6">f_1</a> <font color="Olive" title="b1">R</font></span>)</span></span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <span class="p1">(<span class="default"><font color="Olive" title="b2">x</font> <a href="subset_1.html#K4" title="SUBSET_1:func.4">\/</a> <font color="Olive" title="b3">y</font></span>)</span> <span class="kw">by</span> <span class="lab"><a class="ref" href="roughs_5.html#T45" target="_self" onmouseover="rs('roughs_5/T45')" onmouseout="rh()">Propk</a></span>;<br/></div></div>
