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<b>let </b><font color="Maroon">c<sub>1</sub></font>, <font color="Maroon">c<sub>2</sub></font>, <font color="Maroon">c<sub>3</sub></font> be   <a href="struct_0.html#NM1">Element</a> of <a href="real_lat.html#K3" target="_self">Real_Lattice</a> ;<br/>





<b>set </b><font color="Maroon">c<sub>4</sub></font> = <font color="Maroon">c<sub>2</sub></font> <a href="lattices.html#K4">"/\"</a> <font color="Maroon">c<sub>3</sub></font>;<br/>
<b>thus </b><i><font color="Green">E14</font></i>: <a href="real_lat.html#K1" target="_self">minreal</a>  <a href="binop_1.html#K1">.</a> <font color="Maroon">c<sub>1</sub></font>,<span class="p1">(<span class="default"><a href="real_lat.html#K1" target="_self">minreal</a>  <a href="binop_1.html#K1">.</a> <font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>3</sub></font></span>)</span> = 
<span class="p1">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="lattices.html#K4">"/\"</a> <font color="Maroon">c<sub>3</sub></font></span>)</span> <a href="lattices.html#K4">"/\"</a> <font color="Maroon">c<sub>1</sub></font>
<b>by </b><i><a class="ref" href="lattices.html#D2">LATTICES:def 2</a></i>
<br/>.= 
<a href="real_lat.html#K1" target="_self">minreal</a>  <a href="binop_1.html#K1">.</a> <span class="p1">(<span class="default"><a href="real_lat.html#K1" target="_self">minreal</a>  <a href="binop_1.html#K1">.</a> <font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>3</sub></font></span>)</span>,<font color="Maroon">c<sub>1</sub></font>

;<br/>

<b>thus </b><a href="real_lat.html#K1" target="_self">minreal</a>  <a href="binop_1.html#K1">.</a> <font color="Maroon">c<sub>1</sub></font>,<span class="p1">(<span class="default"><a href="real_lat.html#K1" target="_self">minreal</a>  <a href="binop_1.html#K1">.</a> <font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>3</sub></font></span>)</span> = 
<font color="Maroon">c<sub>1</sub></font> <a href="lattices.html#K4">"/\"</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="lattices.html#K4">"/\"</a> <font color="Maroon">c<sub>3</sub></font></span>)</span>

<br/>.= 
<span class="p1">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="lattices.html#K4">"/\"</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="lattices.html#K4">"/\"</a> <font color="Maroon">c<sub>3</sub></font>
<b>by </b><i><a class="txt" href="real_lat.html#E9"><i><font color="Green">Lemma7</font></i></a></i>
<br/>.= 
<a href="real_lat.html#K1" target="_self">minreal</a>  <a href="binop_1.html#K1">.</a> <span class="p1">(<span class="default"><a href="real_lat.html#K1" target="_self">minreal</a>  <a href="binop_1.html#K1">.</a> <font color="Maroon">c<sub>1</sub></font>,<font color="Maroon">c<sub>2</sub></font></span>)</span>,<font color="Maroon">c<sub>3</sub></font>

;<br/>

<b>thus </b><a href="real_lat.html#K1" target="_self">minreal</a>  <a href="binop_1.html#K1">.</a> <font color="Maroon">c<sub>1</sub></font>,<span class="p1">(<span class="default"><a href="real_lat.html#K1" target="_self">minreal</a>  <a href="binop_1.html#K1">.</a> <font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>3</sub></font></span>)</span> = 
<font color="Maroon">c<sub>1</sub></font> <a href="lattices.html#K4">"/\"</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="lattices.html#K4">"/\"</a> <font color="Maroon">c<sub>3</sub></font></span>)</span>

<br/>.= 
<span class="p1">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="lattices.html#K4">"/\"</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="lattices.html#K4">"/\"</a> <font color="Maroon">c<sub>3</sub></font>
<b>by </b><i><a class="txt" href="real_lat.html#E9"><i><font color="Green">Lemma7</font></i></a></i>
<br/>.= 
<a href="real_lat.html#K1" target="_self">minreal</a>  <a href="binop_1.html#K1">.</a> <span class="p1">(<span class="default"><a href="real_lat.html#K1" target="_self">minreal</a>  <a href="binop_1.html#K1">.</a> <font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>1</sub></font></span>)</span>,<font color="Maroon">c<sub>3</sub></font>

;<br/>

<b>thus </b><i><font color="Green">E15</font></i>: <a href="real_lat.html#K1" target="_self">minreal</a>  <a href="binop_1.html#K1">.</a> <font color="Maroon">c<sub>1</sub></font>,<span class="p1">(<span class="default"><a href="real_lat.html#K1" target="_self">minreal</a>  <a href="binop_1.html#K1">.</a> <font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>3</sub></font></span>)</span> = 
<font color="Maroon">c<sub>1</sub></font> <a href="lattices.html#K4">"/\"</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="lattices.html#K4">"/\"</a> <font color="Maroon">c<sub>3</sub></font></span>)</span>

<br/>.= 
<span class="p1">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="lattices.html#K4">"/\"</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="lattices.html#K4">"/\"</a> <font color="Maroon">c<sub>2</sub></font>
<b>by </b><i><a class="txt" href="real_lat.html#E9"><i><font color="Green">Lemma7</font></i></a></i>
<br/>.= 
<a href="real_lat.html#K1" target="_self">minreal</a>  <a href="binop_1.html#K1">.</a> <span class="p1">(<span class="default"><a href="real_lat.html#K1" target="_self">minreal</a>  <a href="binop_1.html#K1">.</a> <font color="Maroon">c<sub>3</sub></font>,<font color="Maroon">c<sub>1</sub></font></span>)</span>,<font color="Maroon">c<sub>2</sub></font>

;<br/>

<b>thus </b><a NAME="E5:16"/>
<a href="real_lat.html#K1" target="_self">minreal</a>  <a href="binop_1.html#K1">.</a> <font color="Maroon">c<sub>1</sub></font>,<span class="p1">(<span class="default"><a href="real_lat.html#K1" target="_self">minreal</a>  <a href="binop_1.html#K1">.</a> <font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>3</sub></font></span>)</span> <a href="hidden.html#R1">=</a> <a href="real_lat.html#K1" target="_self">minreal</a>  <a href="binop_1.html#K1">.</a> <span class="p1">(<span class="default"><a href="real_lat.html#K1" target="_self">minreal</a>  <a href="binop_1.html#K1">.</a> <font color="Maroon">c<sub>3</sub></font>,<font color="Maroon">c<sub>2</sub></font></span>)</span>,<font color="Maroon">c<sub>1</sub></font>
 <b>by </b><i><a class="txt" href="real_lat.html#E1:16"><i><font color="Green">E14</font></i></a>, <a class="ref" href="real_lat.html#T9" target="_self">Th9</a></i>;<br/>

<b>thus </b><a NAME="E6:16"/>
<a href="real_lat.html#K1" target="_self">minreal</a>  <a href="binop_1.html#K1">.</a> <font color="Maroon">c<sub>1</sub></font>,<span class="p1">(<span class="default"><a href="real_lat.html#K1" target="_self">minreal</a>  <a href="binop_1.html#K1">.</a> <font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>3</sub></font></span>)</span> <a href="hidden.html#R1">=</a> <a href="real_lat.html#K1" target="_self">minreal</a>  <a href="binop_1.html#K1">.</a> <span class="p1">(<span class="default"><a href="real_lat.html#K1" target="_self">minreal</a>  <a href="binop_1.html#K1">.</a> <font color="Maroon">c<sub>1</sub></font>,<font color="Maroon">c<sub>3</sub></font></span>)</span>,<font color="Maroon">c<sub>2</sub></font>
 <b>by </b><i><a class="txt" href="real_lat.html#E4:16"><i><font color="Green">E15</font></i></a>, <a class="ref" href="real_lat.html#T9" target="_self">Th9</a></i>;<br/>


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