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<span class="kw">let </span><font color="Maroon" title="c1">V</font> be  non  <a href="struct_0.html#V2" title="STRUCT_0:attr.2">empty</a>   <a href="clvect_1.html#L1" title="CLVECT_1:struct.1">CLSStruct</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">a</font> being  <a href="cfunct_1.html#NM1" title="CFUNCT_1:NM.1">Complex</a><br/> for <font color="Olive" title="b2">L</font> being   <a href="convex4.html#M1" title="CONVEX4:mode.1">C_Linear_Combination</a> of <font color="Maroon" title="c1">V</font> holds  <font color="Olive" title="b1">a</font> <a href="clvect_1.html#K1" title="CLVECT_1:func.1">*</a> <span class="p1">(<span class="default"><a href="rlvect_2.html#K1" title="RLVECT_2:func.1">vector</a> <span class="p2">(<span class="default"><a href="convex4.html#K15" title="CONVEX4:func.15">LC_CLSpace</a> <font color="Maroon" title="c1">V</font></span>)</span>,<font color="Olive" title="b2">L</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b1">a</font> <a href="convex4.html#K7" title="CONVEX4:func.7">*</a> <font color="Olive" title="b2">L</font></span><br/><span class="kw">let </span><font color="Maroon" title="c2">a</font> be   <a href="cfunct_1.html#NM1" title="CFUNCT_1:NM.1">Complex</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">L</font> being   <a href="convex4.html#M1" title="CONVEX4:mode.1">C_Linear_Combination</a> of <font color="Maroon" title="c1">V</font> holds  <font color="Maroon" title="c2">a</font> <a href="clvect_1.html#K1" title="CLVECT_1:func.1">*</a> <span class="p1">(<span class="default"><a href="rlvect_2.html#K1" title="RLVECT_2:func.1">vector</a> <span class="p2">(<span class="default"><a href="convex4.html#K15" title="CONVEX4:func.15">LC_CLSpace</a> <font color="Maroon" title="c1">V</font></span>)</span>,<font color="Olive" title="b1">L</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c2">a</font> <a href="convex4.html#K7" title="CONVEX4:func.7">*</a> <font color="Olive" title="b1">L</font></span><br/><span class="kw">let </span><font color="Maroon" title="c3">L</font> be    <a href="convex4.html#M1" title="CONVEX4:mode.1">C_Linear_Combination</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">a</font> <a href="clvect_1.html#K1" title="CLVECT_1:func.1">*</a> <span class="p1">(<span class="default"><a href="rlvect_2.html#K1" title="RLVECT_2:func.1">vector</a> <span class="p2">(<span class="default"><a href="convex4.html#K15" title="CONVEX4:func.15">LC_CLSpace</a> <font color="Maroon" title="c1">V</font></span>)</span>,<font color="Maroon" title="c3">L</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c2">a</font> <a href="convex4.html#K7" title="CONVEX4:func.7">*</a> <font color="Maroon" title="c3">L</font></span><br/>





<a NAME="E1:60"/>
<font color="Maroon" title="c3">L</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <span class="p1">(<span class="default"><a href="convex4.html#K15" title="CONVEX4:func.15">LC_CLSpace</a> <font color="Maroon" title="c1">V</font></span>)</span>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="convex4.html#D12" target="_self" title="CONVEX4:def.12">Def12</a></span>;<br/>
<a NAME="E2:60"/><span class="kw">then </span>
<font color="Maroon" title="c3">L</font> <a href="struct_0.html#R1" title="STRUCT_0:pred.1">in</a>  <a href="convex4.html#K15" title="CONVEX4:func.15">LC_CLSpace</a> <font color="Maroon" title="c1">V</font>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="struct_0.html#D5" title="STRUCT_0:def.5">STRUCT_0:def 5</a></span>;<br/>
<a NAME="E3:60"/><span class="kw">then </span><span class="lab"><font color="Green" title="E39">A1</font></span>: 
<span class="p1">(<span class="default"><a href="convex4.html#K14" title="CONVEX4:func.14">C_LCMult</a> <font color="Maroon" title="c1">V</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p1"><a href="domain_1.html#K1" title="DOMAIN_1:func.1">[</a><span class="default"><font color="Maroon" title="c2">a</font>,<span class="p2">(<span class="default"><a href="rlvect_2.html#K1" title="RLVECT_2:func.1">vector</a> <span class="p3">(<span class="default"><a href="convex4.html#K15" title="CONVEX4:func.15">LC_CLSpace</a> <font color="Maroon" title="c1">V</font></span>)</span>,<font color="Maroon" title="c3">L</font></span>)</span></span><a href="domain_1.html#K1" title="DOMAIN_1:func.1">]</a></span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="convex4.html#K14" title="CONVEX4:func.14">C_LCMult</a> <font color="Maroon" title="c1">V</font></span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <span class="p1"><a href="domain_1.html#K1" title="DOMAIN_1:func.1">[</a><span class="default"><font color="Maroon" title="c2">a</font>,<span class="p2">(<span class="default"><a href="convex4.html#K12" title="CONVEX4:func.12">@</a> <font color="Maroon" title="c3">L</font></span>)</span></span><a href="domain_1.html#K1" title="DOMAIN_1:func.1">]</a></span>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="rlvect_2.html#D1" title="RLVECT_2:def.1">RLVECT_2:def 1</a></span>;<br/>
<a NAME="E4:60"/>
 <a href="convex4.html#K11" title="CONVEX4:func.11">@</a> <span class="p1">(<span class="default"><a href="convex4.html#K12" title="CONVEX4:func.12">@</a> <font color="Maroon" title="c3">L</font></span>)</span> <a href="convex4.html#R1" title="CONVEX4:pred.1">=</a> <font color="Maroon" title="c3">L</font>
 
;<br/>
<span class="kw">hence </span><a NAME="E5:60"/>
<font color="Maroon" title="c2">a</font> <a href="clvect_1.html#K1" title="CLVECT_1:func.1">*</a> <span class="p1">(<span class="default"><a href="rlvect_2.html#K1" title="RLVECT_2:func.1">vector</a> <span class="p2">(<span class="default"><a href="convex4.html#K15" title="CONVEX4:func.15">LC_CLSpace</a> <font color="Maroon" title="c1">V</font></span>)</span>,<font color="Maroon" title="c3">L</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c2">a</font> <a href="convex4.html#K7" title="CONVEX4:func.7">*</a> <font color="Maroon" title="c3">L</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E3:60"><span class="lab"><font color="Green" title="E39">A1</font></span></a>, <a class="ref" href="convex4.html#D16" target="_self" title="CONVEX4:def.16">Def16</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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