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<span class="kw">let </span><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:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> for <font color="Olive" title="b1">W1</font>, <font color="Olive" title="b2">W3</font>, <font color="Olive" title="b3">W2</font> being   <a href="rlsub_1.html#M1" title="RLSUB_1:mode.1">Subspace</a> of <font color="Maroon" title="c1">V</font>  st <font color="Olive" title="b1">W1</font> is   <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="Olive" title="b2">W3</font> holds <br/><font color="Olive" title="b1">W1</font> <a href="rlsub_2.html#K1" title="RLSUB_2:func.1">+</a> <span class="p1">(<span class="default"><font color="Olive" title="b3">W2</font> <a href="rlsub_2.html#K2" title="RLSUB_2:func.2">/\</a> <font color="Olive" title="b2">W3</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><font color="Olive" title="b1">W1</font> <a href="rlsub_2.html#K1" title="RLSUB_2:func.1">+</a> <font color="Olive" title="b3">W2</font></span>)</span> <a href="rlsub_2.html#K2" title="RLSUB_2:func.2">/\</a> <font color="Olive" title="b2">W3</font></span><br/><span class="kw">let </span><font color="Maroon" title="c2">W1</font>, <font color="Maroon" title="c3">W3</font>, <font color="Maroon" title="c4">W2</font> be    <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:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> ( <font color="Maroon" title="c2">W1</font> is   <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="c3">W3</font> implies <font color="Maroon" title="c2">W1</font> <a href="rlsub_2.html#K1" title="RLSUB_2:func.1">+</a> <span class="p1">(<span class="default"><font color="Maroon" title="c4">W2</font> <a href="rlsub_2.html#K2" title="RLSUB_2:func.2">/\</a> <font color="Maroon" title="c3">W3</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><font color="Maroon" title="c2">W1</font> <a href="rlsub_2.html#K1" title="RLSUB_2:func.1">+</a> <font color="Maroon" title="c4">W2</font></span>)</span> <a href="rlsub_2.html#K2" title="RLSUB_2:func.2">/\</a> <font color="Maroon" title="c3">W3</font> )</span><br/>







<span class="kw">assume </span><a NAME="E1:33"/><span class="lab"><font color="Green" title="E29">A1</font></span>: 
<font color="Maroon" title="c2">W1</font> is   <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="c3">W3</font>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> <font color="Maroon" title="c2">W1</font> <a href="rlsub_2.html#K1" title="RLSUB_2:func.1">+</a> <span class="p1">(<span class="default"><font color="Maroon" title="c4">W2</font> <a href="rlsub_2.html#K2" title="RLSUB_2:func.2">/\</a> <font color="Maroon" title="c3">W3</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><font color="Maroon" title="c2">W1</font> <a href="rlsub_2.html#K1" title="RLSUB_2:func.1">+</a> <font color="Maroon" title="c4">W2</font></span>)</span> <a href="rlsub_2.html#K2" title="RLSUB_2:func.2">/\</a> <font color="Maroon" title="c3">W3</font></span><br/>

<span class="kw">thus </span><span class="p1">(<span class="default"><font color="Maroon" title="c2">W1</font> <a href="rlsub_2.html#K1" title="RLSUB_2:func.1">+</a> <font color="Maroon" title="c4">W2</font></span>)</span> <a href="rlsub_2.html#K2" title="RLSUB_2:func.2">/\</a> <font color="Maroon" title="c3">W3</font> = 
<font color="Maroon" title="c3">W3</font> <a href="rlsub_2.html#K2" title="RLSUB_2:func.2">/\</a> <span class="p1">(<span class="default"><font color="Maroon" title="c2">W1</font> <a href="rlsub_2.html#K1" title="RLSUB_2:func.1">+</a> <font color="Maroon" title="c4">W2</font></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="ref" href="rlsub_2.html#T18" target="_self" title="RLSUB_2:th.18">Th18</a></span>
<br/>.= 
<span class="p1">(<span class="default"><font color="Maroon" title="c2">W1</font> <a href="rlsub_2.html#K2" title="RLSUB_2:func.2">/\</a> <font color="Maroon" title="c3">W3</font></span>)</span> <a href="rlsub_2.html#K1" title="RLSUB_2:func.1">+</a> <span class="p1">(<span class="default"><font color="Maroon" title="c3">W3</font> <a href="rlsub_2.html#K2" title="RLSUB_2:func.2">/\</a> <font color="Maroon" title="c4">W2</font></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:33"><span class="lab"><font color="Green" title="E29">A1</font></span></a>, <a class="txt" href="rlsub_2.html#E40"><span class="lab"><font color="Green" title="E25">Lm9</font></span></a>, <a class="ref" href="rlsub_1.html#T38" title="RLSUB_1:th.38">RLSUB_1:38</a></span>
<br/>.= 
<font color="Maroon" title="c2">W1</font> <a href="rlsub_2.html#K1" title="RLSUB_2:func.1">+</a> <span class="p1">(<span class="default"><font color="Maroon" title="c3">W3</font> <a href="rlsub_2.html#K2" title="RLSUB_2:func.2">/\</a> <font color="Maroon" title="c4">W2</font></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:33"><span class="lab"><font color="Green" title="E29">A1</font></span></a>, <a class="ref" href="rlsub_2.html#T21" target="_self" title="RLSUB_2:th.21">Th21</a></span>
<br/>.= 
<font color="Maroon" title="c2">W1</font> <a href="rlsub_2.html#K1" title="RLSUB_2:func.1">+</a> <span class="p1">(<span class="default"><font color="Maroon" title="c4">W2</font> <a href="rlsub_2.html#K2" title="RLSUB_2:func.2">/\</a> <font color="Maroon" title="c3">W3</font></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="ref" href="rlsub_2.html#T18" target="_self" title="RLSUB_2:th.18">Th18</a></span>
; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> verum</span><br/>


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