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<b>let </b><font color="Maroon" title="c1">H</font> be  non <a href="struct_0.html#V3" title="STRUCT_0:attr.3">empty</a>  <a href="orders_2.html#L1" title="ORDERS_2:struct.1">RelStr</a> ;<br/>

<b>assume </b><a NAME="E1:116"/><i><font color="Green" title="E71">A1</font></i>: 
<font color="Maroon" title="c1">H</font> <a href="waybel_1.html#NR13" title="WAYBEL_1:NR.13">is_a_Heyting_algebra</a> 
 ;<br/>

<a NAME="E2:116"/><b>then </b><i><font color="Green" title="E72">A2</font></i>: 
<font color="Maroon" title="c1">H</font> is   <a href="waybel_0.html#NM8" title="WAYBEL_0:NM.8">LATTICE</a>
 
<b>by </b><i><a class="ref" href="waybel_1.html#D19" target="_self" title="WAYBEL_1:def.19">Def19</a></i>;<br/>
<b>let </b><font color="Maroon" title="c2">x</font>, <font color="Maroon" title="c3">a</font>, <font color="Maroon" title="c4">y</font> be   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Maroon" title="c1">H</font>;<br/>

<a NAME="E3:116"/>
<span class="p1"><a href="waybel_1.html#K1" title="WAYBEL_1:func.1">[</a><span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c3">a</font> <a href="waybel_1.html#K5" title="WAYBEL_1:func.5">=&gt;</a> </span>)</span>,<span class="p2">(<span class="default"><font color="Maroon" title="c3">a</font> <a href="waybel_1.html#K4" title="WAYBEL_1:func.4">"/\"</a> </span>)</span></span><a href="waybel_1.html#K1" title="WAYBEL_1:func.1">]</a></span> is <a href="waybel_1.html#V3" title="WAYBEL_1:attr.3">Galois</a>
 
<b>by </b><i><a class="txt" href="waybel_1.html#E1:116"><i><font color="Green" title="E71">A1</font></i></a>, <a class="ref" href="waybel_1.html#D20" target="_self" title="WAYBEL_1:def.20">Def20</a></i>;<br/>
<a NAME="E4:116"/><b>then </b>
( <font color="Maroon" title="c2">x</font> <a href="orders_2.html#NR2" title="ORDERS_2:NR.2">&gt;=</a> <span class="p1">(<span class="default"><font color="Maroon" title="c3">a</font> <a href="waybel_1.html#K4" title="WAYBEL_1:func.4">"/\"</a> </span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c4">y</font> iff <span class="p1">(<span class="default"><font color="Maroon" title="c3">a</font> <a href="waybel_1.html#K5" title="WAYBEL_1:func.5">=&gt;</a> </span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c2">x</font> <a href="orders_2.html#NR2" title="ORDERS_2:NR.2">&gt;=</a> <font color="Maroon" title="c4">y</font> )
 
<b>by </b><i><a class="txt" href="waybel_1.html#E2:116"><i><font color="Green" title="E72">A2</font></i></a>, <a class="ref" href="waybel_1.html#T9" target="_self" title="WAYBEL_1:th.9">Th9</a></i>;<br/>
<b>hence </b><a NAME="E5:116"/>
( <font color="Maroon" title="c2">x</font> <a href="orders_2.html#NR2" title="ORDERS_2:NR.2">&gt;=</a> <font color="Maroon" title="c3">a</font> <a href="lattice3.html#K11" title="LATTICE3:func.11">"/\"</a> <font color="Maroon" title="c4">y</font> iff <font color="Maroon" title="c3">a</font> <a href="waybel_1.html#K6" title="WAYBEL_1:func.6">=&gt;</a> <font color="Maroon" title="c2">x</font> <a href="orders_2.html#NR2" title="ORDERS_2:NR.2">&gt;=</a> <font color="Maroon" title="c4">y</font> )
 <b>by </b><i><a class="ref" href="waybel_1.html#D18" target="_self" title="WAYBEL_1:def.18">Def18</a></i>;<br/>


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