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<b>let </b><font color="Maroon" title="c1">K</font> be   <a href="funcsdom.html#NM1" title="FUNCSDOM:NM.1">Ring</a>;<br/><b>let </b><font color="Maroon" title="c2">V</font> be   <a href="vectsp_2.html#NM6" title="VECTSP_2:NM.6">LeftMod</a> of <font color="Maroon" title="c1">K</font>;<br/><b>let </b><font color="Maroon" title="c3">a1</font>, <font color="Maroon" title="c4">a2</font> be   <a href="vectsp_1.html#NM6" title="VECTSP_1:NM.6">Vector</a> of <font color="Maroon" title="c2">V</font>;<br/><b>let </b><font color="Maroon" title="c5">W</font> be    <a href="vectsp_4.html#M1" title="VECTSP_4:mode.1">Subspace</a> of <font color="Maroon" title="c2">V</font>;<br/>









<a NAME="E1:37"/>
( <font color="Maroon" title="c4">a2</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c3">a1</font> <a href="vectsp_4.html#K3" title="VECTSP_4:func.3">+</a> <font color="Maroon" title="c5">W</font> iff <font color="Maroon" title="c3">a1</font> <a href="vectsp_4.html#K3" title="VECTSP_4:func.3">+</a> <font color="Maroon" title="c5">W</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c4">a2</font> <a href="vectsp_4.html#K3" title="VECTSP_4:func.3">+</a> <font color="Maroon" title="c5">W</font> )
 
<b>by </b><i><a class="ref" href="vectsp_4.html#T70" title="VECTSP_4:th.70">VECTSP_4:70</a></i>;<br/>
<b>hence </b><a NAME="E2:37"/>
( <font color="Maroon" title="c3">a1</font> <a href="vectsp_4.html#K3" title="VECTSP_4:func.3">+</a> <font color="Maroon" title="c5">W</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c4">a2</font> <a href="vectsp_4.html#K3" title="VECTSP_4:func.3">+</a> <font color="Maroon" title="c5">W</font> iff <font color="Maroon" title="c3">a1</font> <a href="rlvect_1.html#K5" title="RLVECT_1:func.5">-</a> <font color="Maroon" title="c4">a2</font> <a href="struct_0.html#R1" title="STRUCT_0:pred.1">in</a> <font color="Maroon" title="c5">W</font> )
 <b>by </b><i><a class="ref" href="lmod_7.html#T17" target="_self" title="LMOD_7:th.17">Th17</a></i>;<br/>


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