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<b>let </b><font color="Maroon" title="c1">V</font> be   <a href="rlvect_1.html#NM2" title="RLVECT_1:NM.2">RealLinearSpace</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">W1</font>, <font color="Olive" title="b2">W2</font> being <a href="rlvect_1.html#V1" title="RLVECT_1:attr.1">strict</a>  <a href="rlsub_1.html#M1" title="RLSUB_1:mode.1">Subspace</a> of <font color="Maroon" title="c1">V</font> holds <br/> ( <font color="Olive" title="b1">W1</font> <a href="rlsub_2.html#K1" title="RLSUB_2:func.1">+</a> <font color="Olive" title="b2">W2</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b2">W2</font> iff <font color="Olive" title="b1">W1</font> <a href="rlsub_2.html#K2" title="RLSUB_2:func.2">/\</a> <font color="Olive" title="b2">W2</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b1">W1</font> )</span><br/><b>let </b><font color="Maroon" title="c2">W1</font>, <font color="Maroon" title="c3">W2</font> be  <a href="rlvect_1.html#V1" title="RLVECT_1:attr.1">strict</a>  <a href="rlsub_1.html#M1" title="RLSUB_1:mode.1">Subspace</a> of <font color="Maroon" title="c1">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">W1</font> <a href="rlsub_2.html#K1" title="RLSUB_2:func.1">+</a> <font color="Maroon" title="c3">W2</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c3">W2</font> iff <font color="Maroon" title="c2">W1</font> <a href="rlsub_2.html#K2" title="RLSUB_2:func.2">/\</a> <font color="Maroon" title="c3">W2</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c2">W1</font> )</span><br/>



<a NAME="E1:30"/>
( ( <font color="Maroon" title="c2">W1</font> <a href="rlsub_2.html#K1" title="RLSUB_2:func.1">+</a> <font color="Maroon" title="c3">W2</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c3">W2</font> implies <font color="Maroon" title="c2">W1</font> is    <a href="rlsub_1.html#M1" title="RLSUB_1:mode.1">Subspace</a> of <font color="Maroon" title="c3">W2</font> ) &amp; ( <font color="Maroon" title="c2">W1</font> is    <a href="rlsub_1.html#M1" title="RLSUB_1:mode.1">Subspace</a> of <font color="Maroon" title="c3">W2</font> implies <font color="Maroon" title="c2">W1</font> <a href="rlsub_2.html#K1" title="RLSUB_2:func.1">+</a> <font color="Maroon" title="c3">W2</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c3">W2</font> ) &amp; ( <font color="Maroon" title="c2">W1</font> <a href="rlsub_2.html#K2" title="RLSUB_2:func.2">/\</a> <font color="Maroon" title="c3">W2</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c2">W1</font> implies <font color="Maroon" title="c2">W1</font> is    <a href="rlsub_1.html#M1" title="RLSUB_1:mode.1">Subspace</a> of <font color="Maroon" title="c3">W2</font> ) &amp; ( <font color="Maroon" title="c2">W1</font> is    <a href="rlsub_1.html#M1" title="RLSUB_1:mode.1">Subspace</a> of <font color="Maroon" title="c3">W2</font> implies <font color="Maroon" title="c2">W1</font> <a href="rlsub_2.html#K2" title="RLSUB_2:func.2">/\</a> <font color="Maroon" title="c3">W2</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c2">W1</font> ) )
 
<b>by </b><i><a class="ref" href="rlsub_2.html#T12" target="_self" title="RLSUB_2:th.12">Th12</a>, <a class="ref" href="rlsub_2.html#T21" target="_self" title="RLSUB_2:th.21">Th21</a></i>;<br/>
<b>hence </b><a NAME="E2:30"/>
( <font color="Maroon" title="c2">W1</font> <a href="rlsub_2.html#K1" title="RLSUB_2:func.1">+</a> <font color="Maroon" title="c3">W2</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c3">W2</font> iff <font color="Maroon" title="c2">W1</font> <a href="rlsub_2.html#K2" title="RLSUB_2:func.2">/\</a> <font color="Maroon" title="c3">W2</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c2">W1</font> )
 ; <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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