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<div>:: <span class="kw">deftheorem </span>   defines <a href="lattice3.html#V5" title="LATTICE3:attr.5">\/-distributive</a> <a onclick="hs(this)" href="javascript:()">LATTICE3:def 19 : <br/></a><span> for <font color="Olive" title="b1">IT</font> being   non  <a href="struct_0.html#V2" title="STRUCT_0:attr.2">empty</a>   <a href="lattices.html#L3" title="LATTICES:struct.3">LattStr</a>  holds <br/> ( <font color="Olive" title="b1">IT</font> is  <a href="lattice3.html#V5" title="LATTICE3:attr.5">\/-distributive</a>  iff  for <font color="Olive" title="b2">X</font> being    <a href="hidden.html#M2" title="HIDDEN:mode.2">set</a> <br/>  for <font color="Olive" title="b3">a</font>, <font color="Olive" title="b4">b</font>, <font color="Olive" title="b5">c</font> being   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Olive" title="b1">IT</font>  st <font color="Olive" title="b2">X</font> <a href="lattice3.html#R4" title="LATTICE3:pred.4">is_less_than</a> <font color="Olive" title="b3">a</font> &amp; (  for <font color="Olive" title="b6">d</font> being   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Olive" title="b1">IT</font>  st <font color="Olive" title="b2">X</font> <a href="lattice3.html#R4" title="LATTICE3:pred.4">is_less_than</a> <font color="Olive" title="b6">d</font> holds <br/><font color="Olive" title="b3">a</font> <a href="lattices.html#R1" title="LATTICES:pred.1">[=</a> <font color="Olive" title="b6">d</font> ) &amp; <span class="p1"> { <span class="default"> <span class="p2">(<span class="default"><font color="Olive" title="b4">b</font> <a href="lattices.html#K2" title="LATTICES:func.2">"/\"</a> <font color="Olive" title="b6">a9</font></span>)</span> where <font color="Olive" title="b6">a9</font> is   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Olive" title="b1">IT</font> : <font color="Olive" title="b6">a9</font> <a href="tarski.html#R2" title="TARSKI:pred.2">in</a> <font color="Olive" title="b2">X</font> </span> } </span>  <a href="lattice3.html#R4" title="LATTICE3:pred.4">is_less_than</a> <font color="Olive" title="b5">c</font> &amp; (  for <font color="Olive" title="b6">d</font> being   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Olive" title="b1">IT</font>  st <span class="p1"> { <span class="default"> <span class="p2">(<span class="default"><font color="Olive" title="b4">b</font> <a href="lattices.html#K2" title="LATTICES:func.2">"/\"</a> <font color="Olive" title="b7">a9</font></span>)</span> where <font color="Olive" title="b7">a9</font> is   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Olive" title="b1">IT</font> : <font color="Olive" title="b7">a9</font> <a href="tarski.html#R2" title="TARSKI:pred.2">in</a> <font color="Olive" title="b2">X</font> </span> } </span>  <a href="lattice3.html#R4" title="LATTICE3:pred.4">is_less_than</a> <font color="Olive" title="b6">d</font> holds <br/><font color="Olive" title="b5">c</font> <a href="lattices.html#R1" title="LATTICES:pred.1">[=</a> <font color="Olive" title="b6">d</font> ) holds <br/><font color="Olive" title="b4">b</font> <a href="lattices.html#K2" title="LATTICES:func.2">"/\"</a> <font color="Olive" title="b3">a</font> <a href="lattices.html#R1" title="LATTICES:pred.1">[=</a> <font color="Olive" title="b5">c</font> );<br/></span></div>
