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<span class="kw">let </span><font color="Maroon" title="c2">V</font> be   <a href="rlvect_1.html#NM2" title="RLVECT_1:NM.2">RealLinearSpace</a>; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide">  for <font color="Olive" title="b1">A</font> being   <a href="struct_0.html#NM2" title="STRUCT_0:NM.2">Subset</a> of <font color="Maroon" title="c2">V</font><br/>  for <font color="Olive" title="b2">L1</font>, <font color="Olive" title="b3">L2</font> being    <a href="rlvect_2.html#M1" title="RLVECT_2:mode.1">Linear_Combination</a> of <font color="Maroon" title="c2">V</font>  st <font color="Olive" title="b2">L1</font> is    <a href="rlvect_2.html#M2" title="RLVECT_2:mode.2">Linear_Combination</a> of <font color="Olive" title="b1">A</font> &amp; <font color="Olive" title="b3">L2</font> is    <a href="rlvect_2.html#M2" title="RLVECT_2:mode.2">Linear_Combination</a> of <font color="Olive" title="b1">A</font> holds <br/><font color="Olive" title="b2">L1</font> <a href="rlvect_2.html#K10" title="RLVECT_2:func.10">-</a> <font color="Olive" title="b3">L2</font> is    <a href="rlvect_2.html#M2" title="RLVECT_2:mode.2">Linear_Combination</a> of <font color="Olive" title="b1">A</font></span><br/><span class="kw">let </span><font color="Maroon" title="c3">A</font> be   <a href="struct_0.html#NM2" title="STRUCT_0:NM.2">Subset</a> of <font color="Maroon" title="c2">V</font>; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide">  for <font color="Olive" title="b1">L1</font>, <font color="Olive" title="b2">L2</font> being    <a href="rlvect_2.html#M1" title="RLVECT_2:mode.1">Linear_Combination</a> of <font color="Maroon" title="c2">V</font>  st <font color="Olive" title="b1">L1</font> is    <a href="rlvect_2.html#M2" title="RLVECT_2:mode.2">Linear_Combination</a> of <font color="Maroon" title="c3">A</font> &amp; <font color="Olive" title="b2">L2</font> is    <a href="rlvect_2.html#M2" title="RLVECT_2:mode.2">Linear_Combination</a> of <font color="Maroon" title="c3">A</font> holds <br/><font color="Olive" title="b1">L1</font> <a href="rlvect_2.html#K10" title="RLVECT_2:func.10">-</a> <font color="Olive" title="b2">L2</font> is    <a href="rlvect_2.html#M2" title="RLVECT_2:mode.2">Linear_Combination</a> of <font color="Maroon" title="c3">A</font></span><br/><span class="kw">let </span><font color="Maroon" title="c4">L1</font>, <font color="Maroon" title="c5">L2</font> be    <a href="rlvect_2.html#M1" title="RLVECT_2:mode.1">Linear_Combination</a> of <font color="Maroon" title="c2">V</font>; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> ( <font color="Maroon" title="c4">L1</font> is    <a href="rlvect_2.html#M2" title="RLVECT_2:mode.2">Linear_Combination</a> of <font color="Maroon" title="c3">A</font> &amp; <font color="Maroon" title="c5">L2</font> is    <a href="rlvect_2.html#M2" title="RLVECT_2:mode.2">Linear_Combination</a> of <font color="Maroon" title="c3">A</font> implies <font color="Maroon" title="c4">L1</font> <a href="rlvect_2.html#K10" title="RLVECT_2:func.10">-</a> <font color="Maroon" title="c5">L2</font> is    <a href="rlvect_2.html#M2" title="RLVECT_2:mode.2">Linear_Combination</a> of <font color="Maroon" title="c3">A</font> )</span><br/>







<span class="kw">assume </span><span class="kw">that </span><br/><a NAME="E1:67"/><span class="lab"><font color="Green" title="E41">A1</font></span>: 
<font color="Maroon" title="c4">L1</font> is    <a href="rlvect_2.html#M2" title="RLVECT_2:mode.2">Linear_Combination</a> of <font color="Maroon" title="c3">A</font>
 <span class="kw">and </span><br/><a NAME="E2:67"/><span class="lab"><font color="Green" title="E42">A2</font></span>: 
<font color="Maroon" title="c5">L2</font> is    <a href="rlvect_2.html#M2" title="RLVECT_2:mode.2">Linear_Combination</a> of <font color="Maroon" title="c3">A</font>
 ; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> <font color="Maroon" title="c4">L1</font> <a href="rlvect_2.html#K10" title="RLVECT_2:func.10">-</a> <font color="Maroon" title="c5">L2</font> is    <a href="rlvect_2.html#M2" title="RLVECT_2:mode.2">Linear_Combination</a> of <font color="Maroon" title="c3">A</font></span><br/>

<a NAME="E3:67"/>
 <a href="rlvect_2.html#K9" title="RLVECT_2:func.9">-</a> <font color="Maroon" title="c5">L2</font> is    <a href="rlvect_2.html#M2" title="RLVECT_2:mode.2">Linear_Combination</a> of <font color="Maroon" title="c3">A</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:67"><span class="lab"><font color="Green" title="E42">A2</font></span></a>, <a class="ref" href="rlvect_2.html#T44" target="_self" onmouseover="rs('rlvect_2/T44')" onmouseout="rh()">Th44</a></span>;<br/>
<span class="kw">hence </span><a NAME="E4:67"/>
<font color="Maroon" title="c4">L1</font> <a href="rlvect_2.html#K10" title="RLVECT_2:func.10">-</a> <font color="Maroon" title="c5">L2</font> is    <a href="rlvect_2.html#M2" title="RLVECT_2:mode.2">Linear_Combination</a> of <font color="Maroon" title="c3">A</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:67"><span class="lab"><font color="Green" title="E41">A1</font></span></a>, <a class="ref" href="rlvect_2.html#T38" target="_self" onmouseover="rs('rlvect_2/T38')" onmouseout="rh()">Th38</a></span>; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> verum</span><br/>


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