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<b>let </b><font color="Maroon" title="c1">F</font> be   <a href="vectsp_1.html#NM2" title="VECTSP_1:NM.2">Field</a>;<br/><b>let </b><font color="Maroon" title="c2">VS</font> be  <a href="vectsp_1.html#V11" title="VECTSP_1:attr.11">strict</a> <a href="vectsp_1.html#NM6" title="VECTSP_1:NM.6">VectSp</a> of <font color="Maroon" title="c1">F</font>;<br/><b>let </b><font color="Maroon" title="c3">p</font>, <font color="Maroon" title="c4">q</font> be   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <span class="p1">(<span class="default"><a href="vectsp_8.html#K1" title="VECTSP_8:func.1">lattice</a> <font color="Maroon" title="c2">VS</font></span>)</span>;<br/><b>let </b><font color="Maroon" title="c5">H1</font>, <font color="Maroon" title="c6">H2</font> be    <a href="vectsp_4.html#M1" title="VECTSP_4:mode.1">Subspace</a> of <font color="Maroon" title="c2">VS</font>;<br/>







<b>consider </b><font color="Maroon" title="c7">H1</font> being  <a href="vectsp_1.html#V11" title="VECTSP_1:attr.11">strict</a>  <a href="vectsp_4.html#M1" title="VECTSP_4:mode.1">Subspace</a> of <font color="Maroon" title="c2">VS</font><b> such that </b><br/><a NAME="E2:11"/><i><font color="Green" title="E8">A1</font></i>: 
<font color="Maroon" title="c7">H1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c3">p</font>
 <b>by </b><i><a class="ref" href="vectsp_5.html#D3" title="VECTSP_5:def.3">VECTSP_5:def 3</a></i>;<br/>
<b>consider </b><font color="Maroon" title="c8">H2</font> being  <a href="vectsp_1.html#V11" title="VECTSP_1:attr.11">strict</a>  <a href="vectsp_4.html#M1" title="VECTSP_4:mode.1">Subspace</a> of <font color="Maroon" title="c2">VS</font><b> such that </b><br/><a NAME="E4:11"/><i><font color="Green" title="E9">A2</font></i>: 
<font color="Maroon" title="c8">H2</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c4">q</font>
 <b>by </b><i><a class="ref" href="vectsp_5.html#D3" title="VECTSP_5:def.3">VECTSP_5:def 3</a></i>;<br/>
<font color="Maroon" title="c3">p</font> <a href="lattices.html#K3" title="LATTICES:func.3">"\/"</a> <font color="Maroon" title="c4">q</font> = 
<span class="p1">(<span class="default"><a href="vectsp_5.html#K5" title="VECTSP_5:func.5">SubJoin</a> <font color="Maroon" title="c2">VS</font></span>)</span> <a href="binop_1.html#K1" title="BINOP_1:func.1">.</a> <font color="Maroon" title="c3">p</font>,<font color="Maroon" title="c4">q</font>
<b>by </b><i><a class="ref" href="lattices.html#D1" title="LATTICES:def.1">LATTICES:def 1</a></i>
<br/>.= 
<font color="Maroon" title="c7">H1</font> <a href="vectsp_5.html#K1" title="VECTSP_5:func.1">+</a> <font color="Maroon" title="c8">H2</font>
<b>by </b><i><a class="txt" href="vectsp_8.html#E2:11"><i><font color="Green" title="E8">A1</font></i></a>, <a class="txt" href="vectsp_8.html#E4:11"><i><font color="Green" title="E9">A2</font></i></a>, <a class="ref" href="vectsp_5.html#D7" title="VECTSP_5:def.7">VECTSP_5:def 7</a></i>
;<br/>
<b>hence </b><a NAME="E6:11"/>
( <font color="Maroon" title="c3">p</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c5">H1</font> &amp; <font color="Maroon" title="c4">q</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c6">H2</font> implies <font color="Maroon" title="c3">p</font> <a href="lattices.html#K3" title="LATTICES:func.3">"\/"</a> <font color="Maroon" title="c4">q</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c5">H1</font> <a href="vectsp_5.html#K1" title="VECTSP_5:func.1">+</a> <font color="Maroon" title="c6">H2</font> )
 <b>by </b><i><a class="txt" href="vectsp_8.html#E2:11"><i><font color="Green" title="E8">A1</font></i></a>, <a class="txt" href="vectsp_8.html#E4:11"><i><font color="Green" title="E9">A2</font></i></a></i>;<br/>


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