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<div><span class="kw">theorem </span><a NAME="T18"><span class="comment"><font color="firebrick">:: DICKSON:18</font></span><br/></a><div class="add"> for <font color="Olive" title="b1">R</font>, <font color="Olive" title="b2">S</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">m</font> being   <a href="struct_0.html#NM6" title="STRUCT_0:NM.6">Function</a> of <font color="Olive" title="b1">R</font>,<font color="Olive" title="b2">S</font>  st <font color="Olive" title="b1">R</font> is  <a href="dickson.html#V3" title="DICKSON:attr.3">quasi_ordered</a>  &amp; <font color="Olive" title="b2">S</font> is  <a href="orders_2.html#V5" title="ORDERS_2:attr.5">antisymmetric</a>  &amp; <font color="Olive" title="b2">S</font> <a href="dickson.html#K5" title="DICKSON:func.5">\~</a>  is  <a href="wellfnd1.html#V1" title="WELLFND1:attr.1">well_founded</a>  &amp; (  for <font color="Olive" title="b4">a</font>, <font color="Olive" title="b5">b</font> being   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Olive" title="b1">R</font> holds <br/> ( ( <font color="Olive" title="b4">a</font> <a href="orders_2.html#R1" title="ORDERS_2:pred.1">&lt;=</a> <font color="Olive" title="b5">b</font> implies <font color="Olive" title="b3">m</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Olive" title="b4">a</font> <a href="orders_2.html#R1" title="ORDERS_2:pred.1">&lt;=</a> <font color="Olive" title="b3">m</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Olive" title="b5">b</font> ) &amp; ( <font color="Olive" title="b3">m</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Olive" title="b4">a</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b3">m</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Olive" title="b5">b</font> implies <span class="p1"><a href="yellow_3.html#K7" title="YELLOW_3:func.7">[</a><span class="default"><font color="Olive" title="b4">a</font>,<font color="Olive" title="b5">b</font></span><a href="yellow_3.html#K7" title="YELLOW_3:func.7">]</a></span> <a href="tarski.html#R2" title="TARSKI:pred.2">in</a>  <a href="dickson.html#K1" title="DICKSON:func.1">EqRel</a> <font color="Olive" title="b1">R</font> ) ) ) holds <br/><font color="Olive" title="b1">R</font> <a href="dickson.html#K5" title="DICKSON:func.5">\~</a>  is  <a href="wellfnd1.html#V1" title="WELLFND1:attr.1">well_founded</a> </div></div>
