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<b>let </b><font color="Maroon">c<sub>1</sub></font> be  non <a href="realset2.html#V3">trivial</a> <a href="lattice2.html#NM2">H_Lattice</a>;<br/>

<a NAME="E1:57"/>
for <font color="Olive">b<sub>1</sub></font>, <font color="Olive">b<sub>2</sub></font> being  <a href="struct_0.html#NM1">Element</a> of <font color="Maroon">c<sub>1</sub></font> holds <span class="p1">(<span class="default"><a href="openlatt.html#K18" target="_self">StoneH</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="funct_2.html#K3">.</a> <span class="p1">(<span class="default"><font color="Olive">b<sub>1</sub></font> <a href="filter_0.html#K4">=&gt;</a> <font color="Olive">b<sub>2</sub></font></span>)</span> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="openlatt.html#K18" target="_self">StoneH</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="funct_2.html#K3">.</a> <font color="Olive">b<sub>1</sub></font></span>)</span> <a href="filter_0.html#K4">=&gt;</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="openlatt.html#K18" target="_self">StoneH</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="funct_2.html#K3">.</a> <font color="Olive">b<sub>2</sub></font></span>)</span>
 
<b>by </b><i><a class="ref" href="openlatt.html#T39" target="_self">Th39</a></i>;<br/>
<b>hence </b><a NAME="E2:57"/>
 <a href="openlatt.html#K18" target="_self">StoneH</a> <font color="Maroon">c<sub>1</sub></font> <a href="lattice4.html#R1">preserves_implication</a> 
 <b>by </b><i><a class="ref" href="lattice4.html#D6">LATTICE4:def 6</a></i>;<br/>


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