<?xml version="1.0"?>
<div>:: <span class="kw">deftheorem </span>   defines <a href="lattice4.html#R1" title="LATTICE4:pred.1">preserves_implication</a> <a onclick="hs(this)" href="javascript:()">LATTICE4:def 4 : <br/></a><span> for <font color="Olive" title="b1">L1</font>, <font color="Olive" title="b2">L2</font> being   <a href="lattices.html#NM1" title="LATTICES:NM.1">Lattice</a><br/>  for <font color="Olive" title="b3">f</font> being   <a href="lattice4.html#NM1" title="LATTICE4:NM.1">Homomorphism</a> of <font color="Olive" title="b1">L1</font>,<font color="Olive" title="b2">L2</font> holds <br/> ( <font color="Olive" title="b3">f</font> <a href="lattice4.html#R1" title="LATTICE4:pred.1">preserves_implication</a>  iff  for <font color="Olive" title="b4">a1</font>, <font color="Olive" title="b5">b1</font> being   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Olive" title="b1">L1</font> holds  <font color="Olive" title="b3">f</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <span class="p1">(<span class="default"><font color="Olive" title="b4">a1</font> <a href="filter_0.html#K4" title="FILTER_0:func.4">=&gt;</a> <font color="Olive" title="b5">b1</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><font color="Olive" title="b3">f</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Olive" title="b4">a1</font></span>)</span> <a href="filter_0.html#K4" title="FILTER_0:func.4">=&gt;</a> <span class="p1">(<span class="default"><font color="Olive" title="b3">f</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Olive" title="b5">b1</font></span>)</span> );<br/></span></div>
