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<b>let </b><font color="Maroon">c<sub>1</sub></font> be  <a href="orders_2.html#V4">antisymmetric</a> <a href="lattice3.html#V2">with_infima</a>  <a href="orders_2.html#L1">RelStr</a> ;<br/><b>let </b><font color="Maroon">c<sub>2</sub></font> be   <a href="struct_0.html#NM2">Subset</a> of <font color="Maroon">c<sub>1</sub></font>;<br/><b>let </b><font color="Maroon">c<sub>3</sub></font> be  non <a href="xboole_0.html#V1">empty</a> <a href="struct_0.html#NM2">Subset</a> of <font color="Maroon">c<sub>1</sub></font>;<br/><b>let </b><font color="Maroon">c<sub>4</sub></font> be   <a href="struct_0.html#NM1">Element</a> of <font color="Maroon">c<sub>1</sub></font>; <i><font color="Red">:: according to </font></i><a class="ref" href="yellow_4.html#D2" target="_self">YELLOW_4:def 2</a><br/>







<b>assume </b><a NAME="E1:46"/><i><font color="Green">E13</font></i>: 
<font color="Maroon">c<sub>4</sub></font> <a href="hidden.html#R2">in</a> <font color="Maroon">c<sub>2</sub></font>
 ;<br/>

<b>consider </b><font color="Maroon">c<sub>5</sub></font> being    <a href="hidden.html#M1">set</a> <b> such that </b><br/><a NAME="E3:46"/><i><font color="Green">E14</font></i>: 
<font color="Maroon">c<sub>5</sub></font> <a href="hidden.html#R2">in</a> <font color="Maroon">c<sub>3</sub></font>
 <b>by </b><i><a class="ref" href="xboole_0.html#D1">XBOOLE_0:def 1</a></i>;<br/>
<b>reconsider </b><font color="Maroon">c<sub>6</sub></font> = <font color="Maroon">c<sub>5</sub></font> as    <a href="struct_0.html#M1">Element</a> of <font color="Maroon">c<sub>3</sub></font> <b>by </b><i><a class="txt" href="yellow_4.html#E3:46"><i><font color="Green">E14</font></i></a></i>;<br/>
<b>take </b>
<font color="Maroon">c<sub>4</sub></font> <a href="lattice3.html#K12">"/\"</a> <font color="Maroon">c<sub>6</sub></font>
;<br/>

<b>thus </b><a NAME="E5:46"/>
<font color="Maroon">c<sub>4</sub></font> <a href="lattice3.html#K12">"/\"</a> <font color="Maroon">c<sub>6</sub></font> <a href="hidden.html#R2">in</a> <font color="Maroon">c<sub>2</sub></font> <a href="yellow_4.html#K4" target="_self">"/\"</a> <font color="Maroon">c<sub>3</sub></font>
 <b>by </b><i><a class="txt" href="yellow_4.html#E1:46"><i><font color="Green">E13</font></i></a></i>;<br/>

<b>thus </b><a NAME="E6:46"/>
<font color="Maroon">c<sub>4</sub></font> <a href="lattice3.html#K12">"/\"</a> <font color="Maroon">c<sub>6</sub></font> <a href="orders_2.html#R1">&lt;=</a> <font color="Maroon">c<sub>4</sub></font>
 <b>by </b><i><a class="ref" href="yellow_0.html#T23">YELLOW_0:23</a></i>;<br/>


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