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<b>let </b><font color="Maroon">H</font> be  non <a href="struct_0.html#V3">empty</a>  <a href="orders_2.html#L1">RelStr</a> ;<br/>

<b>assume </b><a NAME="E1:116"/><i><font color="Green">E32</font></i>: 
<font color="Maroon">H</font> <a href="waybel_1.html#NR13" target="_self">is_a_Heyting_algebra</a> 
 ;<br/>

<a NAME="E2:116"/><b>then </b><i><font color="Green">E35</font></i>: 
<font color="Maroon">H</font> is   <a href="waybel_0.html#NM8">LATTICE</a>
 
<b>by </b><i/>;<br/>
<b>let </b><font color="Maroon">x</font> be   <a href="struct_0.html#NM1">Element</a> of <font color="Maroon">H</font>, <font color="Maroon">a</font> be   <a href="struct_0.html#NM1">Element</a> of <font color="Maroon">H</font>, <font color="Maroon">y</font> be   <a href="struct_0.html#NM1">Element</a> of <font color="Maroon">H</font>;<br/>

<a NAME="E3:116"/>
<span class="p1"><a href="waybel_1.html#K1" target="_self">[</a><span class="default"><span class="p2">(<span class="default"><font color="Maroon">a</font> <a href="waybel_1.html#K5" target="_self">=&gt;</a> </span>)</span>,<span class="p2">(<span class="default"><font color="Maroon">a</font> <a href="waybel_1.html#K4" target="_self">"/\"</a> </span>)</span></span><a href="waybel_1.html#K1" target="_self">]</a></span> is <a href="waybel_1.html#V3" target="_self">Galois</a>
 
<b>by </b><i>, </i>;<br/>
<a NAME="E4:116"/><b>then </b>
( <font color="Maroon">x</font> <a href="orders_2.html#NR2" target="_self">&gt;=</a> <span class="p1">(<span class="default"><font color="Maroon">a</font> <a href="waybel_1.html#K4" target="_self">"/\"</a> </span>)</span> <a href="funct_2.html#K3">.</a> <font color="Maroon">y</font> iff <span class="p1">(<span class="default"><font color="Maroon">a</font> <a href="waybel_1.html#K5" target="_self">=&gt;</a> </span>)</span> <a href="funct_2.html#K3">.</a> <font color="Maroon">x</font> <a href="orders_2.html#NR2" target="_self">&gt;=</a> <font color="Maroon">y</font> )
 
<b>by </b><i><a class="ref" href="waybel_1.html#D9" target="_self">Def9</a>, </i>;<br/>
<b>hence </b><a NAME="E5:116"/>
( <font color="Maroon">x</font> <a href="orders_2.html#NR2" target="_self">&gt;=</a> <font color="Maroon">a</font> <a href="lattice3.html#K11">"/\"</a> <font color="Maroon">y</font> iff <font color="Maroon">a</font> <a href="waybel_1.html#K6" target="_self">=&gt;</a> <font color="Maroon">x</font> <a href="orders_2.html#NR2" target="_self">&gt;=</a> <font color="Maroon">y</font> )
 <b>by </b><i/>;<br/>


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