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<div><span class="kw">theorem </span><a NAME="T37"><span class="comment"><font color="firebrick">:: ROUGHS_5:37</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>  holds <br/> ( <span class="p1">(<span class="default"><a href="roughs_5.html#K5" title="ROUGHS_5:func.5">f_0</a> <font color="Olive" title="b1">R</font></span>)</span> <a href="partfun1.html#K1" title="PARTFUN1:func.1">*</a> <span class="p1">(<span class="default"><a href="roughs_5.html#K5" title="ROUGHS_5:func.5">f_0</a> <font color="Olive" title="b1">R</font></span>)</span> <a href="funct_2.html#R2" title="FUNCT_2:pred.2">=</a>  <a href="roughs_5.html#K5" title="ROUGHS_5:func.5">f_0</a> <font color="Olive" title="b1">R</font> iff <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#K5" title="ROUGHS_5:func.5">f_0</a> <font color="Olive" title="b1">R</font></span>)</span></span>)</span> <a href="partfun1.html#K1" title="PARTFUN1:func.1">*</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#K5" title="ROUGHS_5:func.5">f_0</a> <font color="Olive" title="b1">R</font></span>)</span></span>)</span> <a href="funct_2.html#R2" title="FUNCT_2:pred.2">=</a>  <a href="roughs_2.html#K5" title="ROUGHS_2:func.5">Flip</a> <span class="p1">(<span class="default"><a href="roughs_5.html#K5" title="ROUGHS_5:func.5">f_0</a> <font color="Olive" title="b1">R</font></span>)</span> )</div></div>
