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<div><span class="kw">theorem </span><span class="lab"><font color="Green" title="E39">Th12</font></span>: <a NAME="T12"><span class="comment"><font color="firebrick">:: POSET_1:12</font></span><br/></a><div class="add"> for <font color="Olive" title="b1">P</font>, <font color="Olive" title="b2">Q</font> being   non  <a href="struct_0.html#V2" title="STRUCT_0:attr.2">empty</a>   <a href="orders_2.html#V1" title="ORDERS_2:attr.1">strict</a>   <a href="poset_1.html#V1" title="POSET_1:attr.1">chain-complete</a>  <a href="orders_2.html#NM1" title="ORDERS_2:NM.1">Poset</a><br/>  for <font color="Olive" title="b3">f</font> being   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <span class="p1">(<span class="default"><a href="poset_1.html#K6" title="POSET_1:func.6">ConPoset</a> (<font color="Olive" title="b1">P</font>,<font color="Olive" title="b2">Q</font>)</span>)</span>  st <font color="Olive" title="b3">f</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="poset_1.html#K9" title="POSET_1:func.9">min_func</a> (<font color="Olive" title="b1">P</font>,<font color="Olive" title="b2">Q</font>) holds <br/><font color="Olive" title="b3">f</font> <a href="lattice3.html#R1" title="LATTICE3:pred.1">is_&lt;=_than</a>  the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <span class="p1">(<span class="default"><a href="poset_1.html#K6" title="POSET_1:func.6">ConPoset</a> (<font color="Olive" title="b1">P</font>,<font color="Olive" title="b2">Q</font>)</span>)</span></div></div>
