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<div><span class="kw">theorem </span><a NAME="T37"><span class="comment"><font color="firebrick">:: ORDERS_5:37</font></span><br/></a><div class="add"> for <font color="Olive" title="b1">A</font> being   <a href="orders_5.html#NM1" title="ORDERS_5:NM.1">Preorder</a><br/>  for <font color="Olive" title="b2">x</font>, <font color="Olive" title="b3">y</font> being   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Olive" title="b1">A</font>  st <font color="Olive" title="b2">x</font> <a href="orders_5.html#R1" title="ORDERS_5:pred.1">=~</a> <font color="Olive" title="b3">y</font> holds <br/><span class="p1">(<span class="default"><a href="orders_5.html#K5" title="ORDERS_5:func.5">proj</a> <font color="Olive" title="b1">A</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Olive" title="b2">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="orders_5.html#K5" title="ORDERS_5:func.5">proj</a> <font color="Olive" title="b1">A</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Olive" title="b3">y</font></div></div>
