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<div>:: <span class="kw">deftheorem </span>   defines <a href="abcmiz_1.html#V11" title="ABCMIZ_1:attr.11">smooth</a> <a onclick="hs(this)" href="javascript:()">ABCMIZ_1:def 53 : <br/></a><span> for <font color="Olive" title="b1">L</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> holds <br/> ( <font color="Olive" title="b1">L</font> is  <a href="abcmiz_1.html#V11" title="ABCMIZ_1:attr.11">smooth</a>  iff  ex <font color="Olive" title="b2">C</font> being   <a href="abcmiz_1.html#V3" title="ABCMIZ_1:attr.3">initialized</a>  <a href="abcmiz_1.html#NM5" title="ABCMIZ_1:NM.5">ConstructorSignature</a> ex <font color="Olive" title="b3">f</font> being   <a href="struct_0.html#NM6" title="STRUCT_0:NM.6">Function</a> of <font color="Olive" title="b1">L</font>,<a href="abcmiz_1.html#K49" title="ABCMIZ_1:func.49">VarPoset</a> st <br/>(  the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Olive" title="b1">L</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a>  <a href="abcmiz_1.html#K39" title="ABCMIZ_1:func.39">QuasiTypes</a> <font color="Olive" title="b2">C</font> &amp; <font color="Olive" title="b3">f</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="abcmiz_1.html#K50" title="ABCMIZ_1:func.50">vars-function</a> <font color="Olive" title="b2">C</font></span>)</span> <a href="partfun1.html#K2" title="PARTFUN1:func.2">|</a>  the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Olive" title="b1">L</font> &amp; (  for <font color="Olive" title="b4">x</font>, <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="b1">L</font> holds  <font color="Olive" title="b3">f</font> <a href="waybel_0.html#R4" title="WAYBEL_0:pred.4">preserves_sup_of</a> <span class="p1"><a href="domain_1.html#K7" title="DOMAIN_1:func.7">{</a><span class="default"><font color="Olive" title="b4">x</font>,<font color="Olive" title="b5">y</font></span><a href="domain_1.html#K7" title="DOMAIN_1:func.7">}</a></span> ) ) );<br/></span></div>
