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<b>let </b><font color="Maroon" title="c1">H</font> be  non <a href="struct_0.html#V2" title="STRUCT_0:attr.2">empty</a>  <a href="orders_2.html#L1" title="ORDERS_2:struct.1">RelStr</a> ;<br/>

<b>assume </b><a NAME="E1:124"/><i><font color="Green" title="E73">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="E2:124"/><b>then </b><i><font color="Green" title="E74">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/>
<a NAME="E3:124"/><i><font color="Green" title="E75">A3</font></i>: 
<font color="Maroon" title="c1">H</font> is <a href="yellow_0.html#V2" title="YELLOW_0:attr.2">upper-bounded</a>
 
<b>by </b><i><a class="txt" href="waybel_1.html#E1:124"><i><font color="Green" title="E73">A1</font></i></a>, <a class="ref" href="waybel_1.html#T71" target="_self" title="WAYBEL_1:th.71">Th71</a></i>;<br/>
<b>let </b><font color="Maroon" title="c2">b</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="E4:124"/>
<span class="p1">(<span class="default"><a href="yellow_0.html#K4" title="YELLOW_0:func.4">Top</a> <font color="Maroon" title="c1">H</font></span>)</span> <a href="waybel_1.html#K6" title="WAYBEL_1:func.6">=&gt;</a> <font color="Maroon" title="c2">b</font> <a href="orders_2.html#R1" title="ORDERS_2:pred.1">&lt;=</a> <span class="p1">(<span class="default"><a href="yellow_0.html#K4" title="YELLOW_0:func.4">Top</a> <font color="Maroon" title="c1">H</font></span>)</span> <a href="waybel_1.html#K6" title="WAYBEL_1:func.6">=&gt;</a> <font color="Maroon" title="c2">b</font>
 
<b>by </b><i><a class="txt" href="waybel_1.html#E2:124"><i><font color="Green" title="E74">A2</font></i></a>, <a class="ref" href="orders_2.html#T24" title="ORDERS_2:th.24">ORDERS_2:24</a></i>;<br/>
<a NAME="E5:124"/><b>then </b>
<span class="p1">(<span class="default"><a href="yellow_0.html#K4" title="YELLOW_0:func.4">Top</a> <font color="Maroon" title="c1">H</font></span>)</span> <a href="lattice3.html#K11" title="LATTICE3:func.11">"/\"</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="yellow_0.html#K4" title="YELLOW_0:func.4">Top</a> <font color="Maroon" title="c1">H</font></span>)</span> <a href="waybel_1.html#K6" title="WAYBEL_1:func.6">=&gt;</a> <font color="Maroon" title="c2">b</font></span>)</span> <a href="orders_2.html#R1" title="ORDERS_2:pred.1">&lt;=</a> <font color="Maroon" title="c2">b</font>
 
<b>by </b><i><a class="txt" href="waybel_1.html#E1:124"><i><font color="Green" title="E73">A1</font></i></a>, <a class="ref" href="waybel_1.html#T70" target="_self" title="WAYBEL_1:th.70">Th70</a></i>;<br/>
<a NAME="E6:124"/><b>then </b><i><font color="Green" title="E76">A4</font></i>: 
<span class="p1">(<span class="default"><a href="yellow_0.html#K4" title="YELLOW_0:func.4">Top</a> <font color="Maroon" title="c1">H</font></span>)</span> <a href="waybel_1.html#K6" title="WAYBEL_1:func.6">=&gt;</a> <font color="Maroon" title="c2">b</font> <a href="orders_2.html#R1" title="ORDERS_2:pred.1">&lt;=</a> <font color="Maroon" title="c2">b</font>
 
<b>by </b><i><a class="txt" href="waybel_1.html#E2:124"><i><font color="Green" title="E74">A2</font></i></a>, <a class="txt" href="waybel_1.html#E3:124"><i><font color="Green" title="E75">A3</font></i></a>, <a class="ref" href="waybel_1.html#T5" target="_self" title="WAYBEL_1:th.5">Th5</a></i>;<br/>
<a NAME="E7:124"/>
<span class="p1">(<span class="default"><a href="yellow_0.html#K4" title="YELLOW_0:func.4">Top</a> <font color="Maroon" title="c1">H</font></span>)</span> <a href="waybel_1.html#K6" title="WAYBEL_1:func.6">=&gt;</a> <font color="Maroon" title="c2">b</font> <a href="orders_2.html#NR2" title="ORDERS_2:NR.2">&gt;=</a> <font color="Maroon" title="c2">b</font>
 
<b>by </b><i><a class="txt" href="waybel_1.html#E1:124"><i><font color="Green" title="E73">A1</font></i></a>, <a class="ref" href="waybel_1.html#T75" target="_self" title="WAYBEL_1:th.75">Th75</a></i>;<br/>
<b>hence </b><a NAME="E8:124"/>
<font color="Maroon" title="c2">b</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="yellow_0.html#K4" title="YELLOW_0:func.4">Top</a> <font color="Maroon" title="c1">H</font></span>)</span> <a href="waybel_1.html#K6" title="WAYBEL_1:func.6">=&gt;</a> <font color="Maroon" title="c2">b</font>
 <b>by </b><i><a class="txt" href="waybel_1.html#E2:124"><i><font color="Green" title="E74">A2</font></i></a>, <a class="txt" href="waybel_1.html#E6:124"><i><font color="Green" title="E76">A4</font></i></a>, <a class="ref" href="orders_2.html#T25" title="ORDERS_2:th.25">ORDERS_2:25</a></i>;<br/>


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