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<b>let </b><font color="Maroon">c<sub>1</sub></font> be   <a href="vectsp_1.html#NM2">Field</a>;<br/><b>let </b><font color="Maroon">c<sub>2</sub></font> be  <a href="vectsp_1.html#V11">strict</a> <a href="vectsp_1.html#NM6">VectSp</a> of <font color="Maroon">c<sub>1</sub></font>;<br/><b>let </b><font color="Maroon">c<sub>3</sub></font>, <font color="Maroon">c<sub>4</sub></font> be   <a href="struct_0.html#NM1">Element</a> of <span class="p1">(<span class="default"><a href="vectsp_8.html#K1" target="_self">lattice</a> <font color="Maroon">c<sub>2</sub></font></span>)</span>;<br/><b>let </b><font color="Maroon">c<sub>5</sub></font>, <font color="Maroon">c<sub>6</sub></font> be    <a href="vectsp_4.html#M1">Subspace</a> of <font color="Maroon">c<sub>2</sub></font>;<br/>







<b>consider </b><font color="Maroon">c<sub>7</sub></font> being  <a href="vectsp_1.html#V11">strict</a>  <a href="vectsp_4.html#M1">Subspace</a> of <font color="Maroon">c<sub>2</sub></font><b> such that </b><br/><a NAME="E2:12"/><i><font color="Green">E9</font></i>: 
<font color="Maroon">c<sub>7</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>3</sub></font>
 <b>by </b><i><a class="ref" href="vectsp_5.html#D3">VECTSP_5:def 3</a></i>;<br/>
<b>consider </b><font color="Maroon">c<sub>8</sub></font> being  <a href="vectsp_1.html#V11">strict</a>  <a href="vectsp_4.html#M1">Subspace</a> of <font color="Maroon">c<sub>2</sub></font><b> such that </b><br/><a NAME="E4:12"/><i><font color="Green">E10</font></i>: 
<font color="Maroon">c<sub>8</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>4</sub></font>
 <b>by </b><i><a class="ref" href="vectsp_5.html#D3">VECTSP_5:def 3</a></i>;<br/>
<font color="Maroon">c<sub>3</sub></font> <a href="lattices.html#K4">"/\"</a> <font color="Maroon">c<sub>4</sub></font> = 
the <a href="lattices.html#U1">L_meet</a> of <span class="p1">(<span class="default"><a href="vectsp_8.html#K1" target="_self">lattice</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="binop_1.html#K2">.</a> <font color="Maroon">c<sub>3</sub></font>,<font color="Maroon">c<sub>4</sub></font>
<b>by </b><i><a class="ref" href="lattices.html#D2">LATTICES:def 2</a></i>
<br/>.= 
<span class="p1">(<span class="default"><a href="vectsp_5.html#K6">SubMeet</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="binop_1.html#K1">.</a> <font color="Maroon">c<sub>3</sub></font>,<font color="Maroon">c<sub>4</sub></font>

<br/>.= 
<font color="Maroon">c<sub>7</sub></font> <a href="vectsp_5.html#K2">/\</a> <font color="Maroon">c<sub>8</sub></font>
<b>by </b><i><a class="txt" href="vectsp_8.html#E2:12"><i><font color="Green">E9</font></i></a>, <a class="txt" href="vectsp_8.html#E4:12"><i><font color="Green">E10</font></i></a>, <a class="ref" href="vectsp_5.html#D8">VECTSP_5:def 8</a></i>
;<br/>
<b>hence </b><a NAME="E6:12"/>
( <font color="Maroon">c<sub>3</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>5</sub></font> &amp; <font color="Maroon">c<sub>4</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>6</sub></font> implies <font color="Maroon">c<sub>3</sub></font> <a href="lattices.html#K4">"/\"</a> <font color="Maroon">c<sub>4</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>5</sub></font> <a href="vectsp_5.html#K2">/\</a> <font color="Maroon">c<sub>6</sub></font> )
 <b>by </b><i><a class="txt" href="vectsp_8.html#E2:12"><i><font color="Green">E9</font></i></a>, <a class="txt" href="vectsp_8.html#E4:12"><i><font color="Green">E10</font></i></a></i>;<br/>


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