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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="E1:117"/><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="E2:117"/><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>consider </b><font color="Maroon" title="c2">a</font> being   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Maroon" title="c1">H</font>;<br/>
<b>take </b><font color="Maroon" title="c3">x</font> = <font color="Maroon" title="c2">a</font> <a href="waybel_1.html#K6" title="WAYBEL_1:func.6">=&gt;</a> <font color="Maroon" title="c2">a</font>; <i><font color="Red">:: according to </font></i><a class="ref" href="yellow_0.html#D5" title="YELLOW_0:def.5">YELLOW_0:def 5</a><br/>

<b>let </b><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>; <i><font color="Red">:: according to </font></i><a class="ref" href="lattice3.html#D9" title="LATTICE3:def.9">LATTICE3:def 9</a><br/>

<b>assume </b><a NAME="E4:117"/>
<font color="Maroon" title="c4">y</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c1">H</font>
 ;<br/>

<a NAME="E5:117"/>
<font color="Maroon" title="c2">a</font> <a href="orders_2.html#NR2" title="ORDERS_2:NR.2">&gt;=</a> <font color="Maroon" title="c2">a</font> <a href="lattice3.html#K11" title="LATTICE3:func.11">"/\"</a> <font color="Maroon" title="c4">y</font>
 
<b>by </b><i><a class="txt" href="waybel_1.html#E2:117"><i><font color="Green" title="E72">A2</font></i></a>, <a class="ref" href="yellow_0.html#T23" title="YELLOW_0:th.23">YELLOW_0:23</a></i>;<br/>
<b>hence </b><a NAME="E6:117"/>
<font color="Maroon" title="c3">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#E1:117"><i><font color="Green" title="E71">A1</font></i></a>, <a class="ref" href="waybel_1.html#T70" target="_self" title="WAYBEL_1:th.70">Th70</a></i>;<br/>


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