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<b>let </b><font color="Maroon" title="c1">F</font> be   <a href="vectsp_1.html#NM3" title="VECTSP_1:NM.3">Field</a>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> for <font color="Olive" title="b1">V</font> being  <a href="vectsp_1.html#NM7" title="VECTSP_1:NM.7">VectSp</a> of <font color="Maroon" title="c1">F</font><br/> for <font color="Olive" title="b2">W1</font>, <font color="Olive" title="b3">W2</font> being   <a href="vectsp_4.html#M1" title="VECTSP_4:mode.1">Subspace</a> of <font color="Olive" title="b1">V</font>  st <font color="Olive" title="b1">V</font> <a href="vectsp_5.html#R1" title="VECTSP_5:pred.1">is_the_direct_sum_of</a> <font color="Olive" title="b2">W1</font>,<font color="Olive" title="b3">W2</font> holds <br/><font color="Olive" title="b3">W2</font> is    <a href="vectsp_5.html#M1" title="VECTSP_5:mode.1">Linear_Compl</a> of <font color="Olive" title="b2">W1</font></span><br/><b>let </b><font color="Maroon" title="c2">V</font> be   <a href="vectsp_1.html#NM7" title="VECTSP_1:NM.7">VectSp</a> of <font color="Maroon" title="c1">F</font>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> for <font color="Olive" title="b1">W1</font>, <font color="Olive" title="b2">W2</font> being   <a href="vectsp_4.html#M1" title="VECTSP_4:mode.1">Subspace</a> of <font color="Maroon" title="c2">V</font>  st <font color="Maroon" title="c2">V</font> <a href="vectsp_5.html#R1" title="VECTSP_5:pred.1">is_the_direct_sum_of</a> <font color="Olive" title="b1">W1</font>,<font color="Olive" title="b2">W2</font> holds <br/><font color="Olive" title="b2">W2</font> is    <a href="vectsp_5.html#M1" title="VECTSP_5:mode.1">Linear_Compl</a> of <font color="Olive" title="b1">W1</font></span><br/><b>let </b><font color="Maroon" title="c3">W1</font>, <font color="Maroon" title="c4">W2</font> be    <a href="vectsp_4.html#M1" title="VECTSP_4:mode.1">Subspace</a> of <font color="Maroon" title="c2">V</font>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> ( <font color="Maroon" title="c2">V</font> <a href="vectsp_5.html#R1" title="VECTSP_5:pred.1">is_the_direct_sum_of</a> <font color="Maroon" title="c3">W1</font>,<font color="Maroon" title="c4">W2</font> implies <font color="Maroon" title="c4">W2</font> is    <a href="vectsp_5.html#M1" title="VECTSP_5:mode.1">Linear_Compl</a> of <font color="Maroon" title="c3">W1</font> )</span><br/>







<b>assume </b><a NAME="E1:48"/>
<font color="Maroon" title="c2">V</font> <a href="vectsp_5.html#R1" title="VECTSP_5:pred.1">is_the_direct_sum_of</a> <font color="Maroon" title="c3">W1</font>,<font color="Maroon" title="c4">W2</font>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> <font color="Maroon" title="c4">W2</font> is    <a href="vectsp_5.html#M1" title="VECTSP_5:mode.1">Linear_Compl</a> of <font color="Maroon" title="c3">W1</font></span><br/>

<a NAME="E2:48"/><b>then </b>
<font color="Maroon" title="c2">V</font> <a href="vectsp_5.html#R1" title="VECTSP_5:pred.1">is_the_direct_sum_of</a> <font color="Maroon" title="c4">W2</font>,<font color="Maroon" title="c3">W1</font>
 
<b>by </b><i><a class="txt" href="vectsp_5.html#E66"><i><font color="Green" title="E36">Lm17</font></i></a></i>;<br/>
<b>hence </b><a NAME="E3:48"/>
<font color="Maroon" title="c4">W2</font> is    <a href="vectsp_5.html#M1" title="VECTSP_5:mode.1">Linear_Compl</a> of <font color="Maroon" title="c3">W1</font>
 <b>by </b><i><a class="ref" href="vectsp_5.html#D5" target="_self" title="VECTSP_5:def.5">Def5</a></i>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> verum</span><br/>


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