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<b>let </b><font color="Maroon" title="c1">H</font> be  non <a href="struct_0.html#V7" title="STRUCT_0:attr.7">trivial</a> <a href="lattice2.html#NM2" title="LATTICE2:NM.2">H_Lattice</a>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide">  <a href="openlatt.html#K18" title="OPENLATT:func.18">StoneH</a> <font color="Maroon" title="c1">H</font> <a href="lattice4.html#R1" title="LATTICE4:pred.1">preserves_implication</a> </span><br/>

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for <font color="Olive" title="b1">p'</font>, <font color="Olive" title="b2">q'</font> being  <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Maroon" title="c1">H</font> holds  <span class="p1">(<span class="default"><a href="openlatt.html#K18" title="OPENLATT:func.18">StoneH</a> <font color="Maroon" title="c1">H</font></span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <span class="p1">(<span class="default"><font color="Olive" title="b1">p'</font> <a href="filter_0.html#K4" title="FILTER_0:func.4">=&gt;</a> <font color="Olive" title="b2">q'</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="openlatt.html#K18" title="OPENLATT:func.18">StoneH</a> <font color="Maroon" title="c1">H</font></span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Olive" title="b1">p'</font></span>)</span> <a href="filter_0.html#K4" title="FILTER_0:func.4">=&gt;</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="openlatt.html#K18" title="OPENLATT:func.18">StoneH</a> <font color="Maroon" title="c1">H</font></span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Olive" title="b2">q'</font></span>)</span>
 
<b>by </b><i><a class="ref" href="openlatt.html#T39" target="_self" title="OPENLATT:th.39">Th39</a></i>;<br/>
<b>hence </b><a NAME="E2:56"/>
 <a href="openlatt.html#K18" title="OPENLATT:func.18">StoneH</a> <font color="Maroon" title="c1">H</font> <a href="lattice4.html#R1" title="LATTICE4:pred.1">preserves_implication</a> 
 <b>by </b><i><a class="ref" href="lattice4.html#D6" title="LATTICE4:def.6">LATTICE4:def 6</a></i>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> verum</span><br/>


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