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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> ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> ( <font color="Maroon" title="c1">H</font> <a href="waybel_1.html#NR13" title="WAYBEL_1:NR.13">is_a_Heyting_algebra</a>  implies for <font color="Olive" title="b1">a</font> being  <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Maroon" title="c1">H</font> holds   <a href="yellow_0.html#K4" title="YELLOW_0:func.4">Top</a> <font color="Maroon" title="c1">H</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b1">a</font> <a href="waybel_1.html#K6" title="WAYBEL_1:func.6">=&gt;</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> )</span><br/>

<b>assume </b><a NAME="E1:123"/><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> 
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> for <font color="Olive" title="b1">a</font> being  <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Maroon" title="c1">H</font> holds   <a href="yellow_0.html#K4" title="YELLOW_0:func.4">Top</a> <font color="Maroon" title="c1">H</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b1">a</font> <a href="waybel_1.html#K6" title="WAYBEL_1:func.6">=&gt;</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></span><br/>

<a NAME="E2:123"/><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/>
<b>let </b><font color="Maroon" title="c2">a</font> be   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Maroon" title="c1">H</font>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide">  <a href="yellow_0.html#K4" title="YELLOW_0:func.4">Top</a> <font color="Maroon" title="c1">H</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c2">a</font> <a href="waybel_1.html#K6" title="WAYBEL_1:func.6">=&gt;</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></span><br/>

<a NAME="E3:123"/>
<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#E1:123"><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/>
<a NAME="E4:123"/><b>then </b>
<font color="Maroon" title="c2">a</font> <a href="orders_2.html#R1" title="ORDERS_2:pred.1">&lt;=</a>  <a href="yellow_0.html#K4" title="YELLOW_0:func.4">Top</a> <font color="Maroon" title="c1">H</font>
 
<b>by </b><i><a class="txt" href="waybel_1.html#E2:123"><i><font color="Green" title="E74">A2</font></i></a>, <a class="ref" href="yellow_0.html#T45" title="YELLOW_0:th.45">YELLOW_0:45</a></i>;<br/>
<b>hence </b><a NAME="E5:123"/>
 <a href="yellow_0.html#K4" title="YELLOW_0:func.4">Top</a> <font color="Maroon" title="c1">H</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c2">a</font> <a href="waybel_1.html#K6" title="WAYBEL_1:func.6">=&gt;</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>
 <b>by </b><i><a class="txt" href="waybel_1.html#E1:123"><i><font color="Green" title="E73">A1</font></i></a>, <a class="ref" href="waybel_1.html#T72" target="_self" title="WAYBEL_1:th.72">Th72</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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