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<b>let </b><font color="Maroon">a1</font> be   <a href="struct_0.html#NM1">Element</a> of <font color="Maroon">L</font>, <font color="Maroon">a2</font> be   <a href="struct_0.html#NM1">Element</a> of <font color="Maroon">L</font>;<br/>

<b>given </b><font color="Maroon">a</font> being   <a href="struct_0.html#NM1">Element</a> of <font color="Maroon">L</font><b> such that </b><a NAME="E1:38_1_1"/><i><font color="Green">E24</font></i>: 
( <font color="Maroon">X</font> <a href="lattice3.html#R2">is_&lt;=_than</a> <font color="Maroon">a</font> &amp; ( for <font color="Olive">b</font> being  <a href="struct_0.html#NM1">Element</a> of <font color="Maroon">L</font>  st <font color="Maroon">X</font> <a href="lattice3.html#R2">is_&lt;=_than</a> <font color="Olive">b</font> holds <br/><font color="Olive">b</font> <a href="orders_2.html#NR2" target="_self">&gt;=</a> <font color="Maroon">a</font> ) &amp; ( for <font color="Olive">c</font> being  <a href="struct_0.html#NM1">Element</a> of <font color="Maroon">L</font>  st <font color="Maroon">X</font> <a href="lattice3.html#R2">is_&lt;=_than</a> <font color="Olive">c</font> &amp; ( for <font color="Olive">b</font> being  <a href="struct_0.html#NM1">Element</a> of <font color="Maroon">L</font>  st <font color="Maroon">X</font> <a href="lattice3.html#R2">is_&lt;=_than</a> <font color="Olive">b</font> holds <br/><font color="Olive">b</font> <a href="orders_2.html#NR2" target="_self">&gt;=</a> <font color="Olive">c</font> ) holds <br/><font color="Olive">c</font> <a href="hidden.html#R1">=</a> <font color="Maroon">a</font> ) )
 ; <i><font color="Red">:: according to </font></i><a class="ref" href="yellow_0.html#D7" target="_self">YELLOW_0:def 7</a><br/>

<b>assume </b><a NAME="E2:38_1_1"/><i><font color="Green">E29</font></i>: 
( <font color="Maroon">X</font> <a href="lattice3.html#R2">is_&lt;=_than</a> <font color="Maroon">a1</font> &amp; ( for <font color="Olive">a</font> being  <a href="struct_0.html#NM1">Element</a> of <font color="Maroon">L</font>  st <font color="Maroon">X</font> <a href="lattice3.html#R2">is_&lt;=_than</a> <font color="Olive">a</font> holds <br/><font color="Maroon">a1</font> <a href="orders_2.html#R1">&lt;=</a> <font color="Olive">a</font> ) &amp; <font color="Maroon">X</font> <a href="lattice3.html#R2">is_&lt;=_than</a> <font color="Maroon">a2</font> &amp; ( for <font color="Olive">a</font> being  <a href="struct_0.html#NM1">Element</a> of <font color="Maroon">L</font>  st <font color="Maroon">X</font> <a href="lattice3.html#R2">is_&lt;=_than</a> <font color="Olive">a</font> holds <br/><font color="Maroon">a2</font> <a href="orders_2.html#R1">&lt;=</a> <font color="Olive">a</font> ) &amp; not <font color="Maroon">a1</font> <a href="hidden.html#R1">=</a> <font color="Maroon">a2</font> )
 ;<br/>

<a NAME="E3:38_1_1"/><b>then </b>
( <font color="Maroon">a1</font> <a href="hidden.html#R1">=</a> <font color="Maroon">a</font> &amp; <font color="Maroon">a2</font> <a href="hidden.html#R1">=</a> <font color="Maroon">a</font> )
 
<b>by </b><i/>;<br/>
<b>hence </b><a NAME="E4:38_1_1"/>
contradiction
 <b>by </b><i/>;<br/>


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