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<div><span class="kw">theorem </span><span class="lab"><font color="Green" title="E14">Th34</font></span>: <a NAME="T34"><span class="comment"><font color="firebrick">:: YELLOW_3:34</font></span><br/></a><div class="add"> for <font color="Olive" title="b1">S1</font>, <font color="Olive" title="b2">S2</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="b3">D</font> being   <a href="struct_0.html#NM2" title="STRUCT_0:NM.2">Subset</a> of <span class="p1"><a href="yellow_3.html#K3" title="YELLOW_3:func.3">[:</a><span class="default"><font color="Olive" title="b1">S1</font>,<font color="Olive" title="b2">S2</font></span><a href="yellow_3.html#K3" title="YELLOW_3:func.3">:]</a></span><br/>  for <font color="Olive" title="b4">x</font> being   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Olive" title="b1">S1</font><br/>  for <font color="Olive" title="b5">y</font> being   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Olive" title="b2">S2</font> holds <br/> ( <span class="p1"><a href="yellow_3.html#K7" title="YELLOW_3:func.7">[</a><span class="default"><font color="Olive" title="b4">x</font>,<font color="Olive" title="b5">y</font></span><a href="yellow_3.html#K7" title="YELLOW_3:func.7">]</a></span> <a href="lattice3.html#R1" title="LATTICE3:pred.1">is_&lt;=_than</a> <font color="Olive" title="b3">D</font> iff ( <font color="Olive" title="b4">x</font> <a href="lattice3.html#R1" title="LATTICE3:pred.1">is_&lt;=_than</a>  <a href="yellow_3.html#K4" title="YELLOW_3:func.4">proj1</a> <font color="Olive" title="b3">D</font> &amp; <font color="Olive" title="b5">y</font> <a href="lattice3.html#R1" title="LATTICE3:pred.1">is_&lt;=_than</a>  <a href="yellow_3.html#K5" title="YELLOW_3:func.5">proj2</a> <font color="Olive" title="b3">D</font> ) )</div></div>
