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<div>:: <span class="kw">deftheorem </span><span class="lab"><font color="Green" title="E4">Def4</font></span>   defines <a href="yellow21.html#V2" title="YELLOW21:attr.2">lattice-wise</a> <a onclick="hs(this)" href="javascript:()">YELLOW21:def 4 : <br/></a><span> for <font color="Olive" title="b1">C</font> being   <a href="altcat_1.html#NM4" title="ALTCAT_1:NM.4">category</a> holds <br/> ( <font color="Olive" title="b1">C</font> is  <a href="yellow21.html#V2" title="YELLOW21:attr.2">lattice-wise</a>  iff ( <font color="Olive" title="b1">C</font> is  <a href="altcat_1.html#V9" title="ALTCAT_1:attr.9">semi-functional</a>  &amp; <font color="Olive" title="b1">C</font> is  <a href="yellow18.html#V3" title="YELLOW18:attr.3">set-id-inheriting</a>  &amp; (  for <font color="Olive" title="b2">a</font> being   <a href="altcat_1.html#NM1" title="ALTCAT_1:NM.1">Object</a> of <font color="Olive" title="b1">C</font> holds  <font color="Olive" title="b2">a</font> is   <a href="waybel_0.html#NM8" title="WAYBEL_0:NM.8">LATTICE</a> ) &amp; (  for <font color="Olive" title="b2">a</font>, <font color="Olive" title="b3">b</font> being   <a href="altcat_1.html#NM1" title="ALTCAT_1:NM.1">Object</a> of <font color="Olive" title="b1">C</font><br/>  for <font color="Olive" title="b4">A</font>, <font color="Olive" title="b5">B</font> being   <a href="waybel_0.html#NM8" title="WAYBEL_0:NM.8">LATTICE</a>  st <font color="Olive" title="b4">A</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b2">a</font> &amp; <font color="Olive" title="b5">B</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b3">b</font> holds <br/><span class="p1"><a href="altcat_1.html#K1" title="ALTCAT_1:func.1">&lt;^</a><span class="default"><font color="Olive" title="b2">a</font>,<font color="Olive" title="b3">b</font></span><a href="altcat_1.html#K1" title="ALTCAT_1:func.1">^&gt;</a></span> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a>  <a href="orders_3.html#K1" title="ORDERS_3:func.1">MonFuncs</a> (<font color="Olive" title="b4">A</font>,<font color="Olive" title="b5">B</font>) ) ) );<br/></span></div>
