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<div><span class="kw">theorem </span><span class="lab"><font color="Green" title="E1">Th1</font></span>: <a NAME="T1"><span class="comment"><font color="firebrick">:: OSALG_3:1</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#NM1" title="ORDERS_2:NM.1">Poset</a><br/>  for <font color="Olive" title="b2">F</font> being   <a href="pboole.html#NM2" title="PBOOLE:NM.2">ManySortedFunction</a> of  the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Olive" title="b1">R</font>  st <font color="Olive" title="b2">F</font> is  <a href="osalg_3.html#V1" title="OSALG_3:attr.1">order-sorted</a>  holds <br/> for <font color="Olive" title="b3">s1</font>, <font color="Olive" title="b4">s2</font> being   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Olive" title="b1">R</font>  st <font color="Olive" title="b3">s1</font> <a href="orders_2.html#R3" title="ORDERS_2:pred.3">&lt;=</a> <font color="Olive" title="b4">s2</font> holds <br/>(  <a href="relat_1.html#NK1" title="RELAT_1:NK.1">dom</a> <span class="p1">(<span class="default"><font color="Olive" title="b2">F</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Olive" title="b3">s1</font></span>)</span> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a>  <a href="relat_1.html#NK1" title="RELAT_1:NK.1">dom</a> <span class="p1">(<span class="default"><font color="Olive" title="b2">F</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Olive" title="b4">s2</font></span>)</span> &amp; <font color="Olive" title="b2">F</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Olive" title="b3">s1</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <font color="Olive" title="b2">F</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Olive" title="b4">s2</font> )</div></div>
