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<b>let </b><font color="Maroon" title="c1">K</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 non <a href="struct_0.html#V7" title="STRUCT_0:attr.7">trivial</a> <a href="vectsp_1.html#NM7" title="VECTSP_1:NM.7">VectSp</a> of <font color="Maroon" title="c1">K</font><br/> for <font color="Olive" title="b2">f1</font>, <font color="Olive" title="b3">f2</font> being <a href="vectsp11.html#V1" title="VECTSP11:attr.1">with_eigenvalues</a> <a href="struct_0.html#NM6" title="STRUCT_0:NM.6">Function</a> of <font color="Olive" title="b1">V</font>,<font color="Olive" title="b1">V</font><br/> for <font color="Olive" title="b4">L1</font>, <font color="Olive" title="b5">L2</font> being  <a href="vectsp_1.html#NM4" title="VECTSP_1:NM.4">Scalar</a> of <font color="Maroon" title="c1">K</font>  st <font color="Olive" title="b4">L1</font> is    <a href="vectsp11.html#M1" title="VECTSP11:mode.1">eigenvalue</a> of <font color="Olive" title="b2">f1</font> &amp; <font color="Olive" title="b5">L2</font> is    <a href="vectsp11.html#M1" title="VECTSP11:mode.1">eigenvalue</a> of <font color="Olive" title="b3">f2</font> &amp;  ex <font color="Olive" title="b6">v</font> being  <a href="vectsp_1.html#NM6" title="VECTSP_1:NM.6">Vector</a> of <font color="Olive" title="b1">V</font> st <br/>( <font color="Olive" title="b6">v</font> is    <a href="vectsp11.html#M2" title="VECTSP11:mode.2">eigenvector</a> of <font color="Olive" title="b2">f1</font>,<font color="Olive" title="b4">L1</font> &amp; <font color="Olive" title="b6">v</font> is    <a href="vectsp11.html#M2" title="VECTSP11:mode.2">eigenvector</a> of <font color="Olive" title="b3">f2</font>,<font color="Olive" title="b5">L2</font> &amp; <font color="Olive" title="b6">v</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a>  <a href="struct_0.html#K4" title="STRUCT_0:func.4">0.</a> <font color="Olive" title="b1">V</font> ) holds <br/>( <font color="Olive" title="b2">f1</font> <a href="matrlin.html#K5" title="MATRLIN:func.5">+</a> <font color="Olive" title="b3">f2</font> is <a href="vectsp11.html#V1" title="VECTSP11:attr.1">with_eigenvalues</a> &amp; <font color="Olive" title="b4">L1</font> <a href="rlvect_1.html#K3" title="RLVECT_1:func.3">+</a> <font color="Olive" title="b5">L2</font> is    <a href="vectsp11.html#M1" title="VECTSP11:mode.1">eigenvalue</a> of <font color="Olive" title="b2">f1</font> <a href="matrlin.html#K5" title="MATRLIN:func.5">+</a> <font color="Olive" title="b3">f2</font> &amp; ( for <font color="Olive" title="b6">w</font> being  <a href="vectsp_1.html#NM6" title="VECTSP_1:NM.6">Vector</a> of <font color="Olive" title="b1">V</font>  st <font color="Olive" title="b6">w</font> is    <a href="vectsp11.html#M2" title="VECTSP11:mode.2">eigenvector</a> of <font color="Olive" title="b2">f1</font>,<font color="Olive" title="b4">L1</font> &amp; <font color="Olive" title="b6">w</font> is    <a href="vectsp11.html#M2" title="VECTSP11:mode.2">eigenvector</a> of <font color="Olive" title="b3">f2</font>,<font color="Olive" title="b5">L2</font> holds <br/><font color="Olive" title="b6">w</font> is    <a href="vectsp11.html#M2" title="VECTSP11:mode.2">eigenvector</a> of <font color="Olive" title="b2">f1</font> <a href="matrlin.html#K5" title="MATRLIN:func.5">+</a> <font color="Olive" title="b3">f2</font>,<font color="Olive" title="b4">L1</font> <a href="rlvect_1.html#K3" title="RLVECT_1:func.3">+</a> <font color="Olive" title="b5">L2</font> ) )</span><br/><b>let </b><font color="Maroon" title="c2">V</font> be  non <a href="struct_0.html#V7" title="STRUCT_0:attr.7">trivial</a> <a href="vectsp_1.html#NM7" title="VECTSP_1:NM.7">VectSp</a> of <font color="Maroon" title="c1">K</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">f1</font>, <font color="Olive" title="b2">f2</font> being <a href="vectsp11.html#V1" title="VECTSP11:attr.1">with_eigenvalues</a> <a href="struct_0.html#NM6" title="STRUCT_0:NM.6">Function</a> of <font color="Maroon" title="c2">V</font>,<font color="Maroon" title="c2">V</font><br/> for <font color="Olive" title="b3">L1</font>, <font color="Olive" title="b4">L2</font> being  <a href="vectsp_1.html#NM4" title="VECTSP_1:NM.4">Scalar</a> of <font color="Maroon" title="c1">K</font>  st <font color="Olive" title="b3">L1</font> is    <a href="vectsp11.html#M1" title="VECTSP11:mode.1">eigenvalue</a> of <font color="Olive" title="b1">f1</font> &amp; <font color="Olive" title="b4">L2</font> is    <a href="vectsp11.html#M1" title="VECTSP11:mode.1">eigenvalue</a> of <font color="Olive" title="b2">f2</font> &amp;  ex <font color="Olive" title="b5">v</font> being  <a href="vectsp_1.html#NM6" title="VECTSP_1:NM.6">Vector</a> of <font color="Maroon" title="c2">V</font> st <br/>( <font color="Olive" title="b5">v</font> is    <a href="vectsp11.html#M2" title="VECTSP11:mode.2">eigenvector</a> of <font color="Olive" title="b1">f1</font>,<font color="Olive" title="b3">L1</font> &amp; <font color="Olive" title="b5">v</font> is    <a href="vectsp11.html#M2" title="VECTSP11:mode.2">eigenvector</a> of <font color="Olive" title="b2">f2</font>,<font color="Olive" title="b4">L2</font> &amp; <font color="Olive" title="b5">v</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a>  <a href="struct_0.html#K4" title="STRUCT_0:func.4">0.</a> <font color="Maroon" title="c2">V</font> ) holds <br/>( <font color="Olive" title="b1">f1</font> <a href="matrlin.html#K5" title="MATRLIN:func.5">+</a> <font color="Olive" title="b2">f2</font> is <a href="vectsp11.html#V1" title="VECTSP11:attr.1">with_eigenvalues</a> &amp; <font color="Olive" title="b3">L1</font> <a href="rlvect_1.html#K3" title="RLVECT_1:func.3">+</a> <font color="Olive" title="b4">L2</font> is    <a href="vectsp11.html#M1" title="VECTSP11:mode.1">eigenvalue</a> of <font color="Olive" title="b1">f1</font> <a href="matrlin.html#K5" title="MATRLIN:func.5">+</a> <font color="Olive" title="b2">f2</font> &amp; ( for <font color="Olive" title="b5">w</font> being  <a href="vectsp_1.html#NM6" title="VECTSP_1:NM.6">Vector</a> of <font color="Maroon" title="c2">V</font>  st <font color="Olive" title="b5">w</font> is    <a href="vectsp11.html#M2" title="VECTSP11:mode.2">eigenvector</a> of <font color="Olive" title="b1">f1</font>,<font color="Olive" title="b3">L1</font> &amp; <font color="Olive" title="b5">w</font> is    <a href="vectsp11.html#M2" title="VECTSP11:mode.2">eigenvector</a> of <font color="Olive" title="b2">f2</font>,<font color="Olive" title="b4">L2</font> holds <br/><font color="Olive" title="b5">w</font> is    <a href="vectsp11.html#M2" title="VECTSP11:mode.2">eigenvector</a> of <font color="Olive" title="b1">f1</font> <a href="matrlin.html#K5" title="MATRLIN:func.5">+</a> <font color="Olive" title="b2">f2</font>,<font color="Olive" title="b3">L1</font> <a href="rlvect_1.html#K3" title="RLVECT_1:func.3">+</a> <font color="Olive" title="b4">L2</font> ) )</span><br/><b>let </b><font color="Maroon" title="c3">f1</font>, <font color="Maroon" title="c4">f2</font> be  <a href="vectsp11.html#V1" title="VECTSP11:attr.1">with_eigenvalues</a> <a href="struct_0.html#NM6" title="STRUCT_0:NM.6">Function</a> of <font color="Maroon" title="c2">V</font>,<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"> for <font color="Olive" title="b1">L1</font>, <font color="Olive" title="b2">L2</font> being  <a href="vectsp_1.html#NM4" title="VECTSP_1:NM.4">Scalar</a> of <font color="Maroon" title="c1">K</font>  st <font color="Olive" title="b1">L1</font> is    <a href="vectsp11.html#M1" title="VECTSP11:mode.1">eigenvalue</a> of <font color="Maroon" title="c3">f1</font> &amp; <font color="Olive" title="b2">L2</font> is    <a href="vectsp11.html#M1" title="VECTSP11:mode.1">eigenvalue</a> of <font color="Maroon" title="c4">f2</font> &amp;  ex <font color="Olive" title="b3">v</font> being  <a href="vectsp_1.html#NM6" title="VECTSP_1:NM.6">Vector</a> of <font color="Maroon" title="c2">V</font> st <br/>( <font color="Olive" title="b3">v</font> is    <a href="vectsp11.html#M2" title="VECTSP11:mode.2">eigenvector</a> of <font color="Maroon" title="c3">f1</font>,<font color="Olive" title="b1">L1</font> &amp; <font color="Olive" title="b3">v</font> is    <a href="vectsp11.html#M2" title="VECTSP11:mode.2">eigenvector</a> of <font color="Maroon" title="c4">f2</font>,<font color="Olive" title="b2">L2</font> &amp; <font color="Olive" title="b3">v</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a>  <a href="struct_0.html#K4" title="STRUCT_0:func.4">0.</a> <font color="Maroon" title="c2">V</font> ) holds <br/>( <font color="Maroon" title="c3">f1</font> <a href="matrlin.html#K5" title="MATRLIN:func.5">+</a> <font color="Maroon" title="c4">f2</font> is <a href="vectsp11.html#V1" title="VECTSP11:attr.1">with_eigenvalues</a> &amp; <font color="Olive" title="b1">L1</font> <a href="rlvect_1.html#K3" title="RLVECT_1:func.3">+</a> <font color="Olive" title="b2">L2</font> is    <a href="vectsp11.html#M1" title="VECTSP11:mode.1">eigenvalue</a> of <font color="Maroon" title="c3">f1</font> <a href="matrlin.html#K5" title="MATRLIN:func.5">+</a> <font color="Maroon" title="c4">f2</font> &amp; ( for <font color="Olive" title="b3">w</font> being  <a href="vectsp_1.html#NM6" title="VECTSP_1:NM.6">Vector</a> of <font color="Maroon" title="c2">V</font>  st <font color="Olive" title="b3">w</font> is    <a href="vectsp11.html#M2" title="VECTSP11:mode.2">eigenvector</a> of <font color="Maroon" title="c3">f1</font>,<font color="Olive" title="b1">L1</font> &amp; <font color="Olive" title="b3">w</font> is    <a href="vectsp11.html#M2" title="VECTSP11:mode.2">eigenvector</a> of <font color="Maroon" title="c4">f2</font>,<font color="Olive" title="b2">L2</font> holds <br/><font color="Olive" title="b3">w</font> is    <a href="vectsp11.html#M2" title="VECTSP11:mode.2">eigenvector</a> of <font color="Maroon" title="c3">f1</font> <a href="matrlin.html#K5" title="MATRLIN:func.5">+</a> <font color="Maroon" title="c4">f2</font>,<font color="Olive" title="b1">L1</font> <a href="rlvect_1.html#K3" title="RLVECT_1:func.3">+</a> <font color="Olive" title="b2">L2</font> ) )</span><br/><b>let </b><font color="Maroon" title="c5">L1</font>, <font color="Maroon" title="c6">L2</font> be   <a href="vectsp_1.html#NM4" title="VECTSP_1:NM.4">Scalar</a> of <font color="Maroon" title="c1">K</font>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> ( <font color="Maroon" title="c5">L1</font> is    <a href="vectsp11.html#M1" title="VECTSP11:mode.1">eigenvalue</a> of <font color="Maroon" title="c3">f1</font> &amp; <font color="Maroon" title="c6">L2</font> is    <a href="vectsp11.html#M1" title="VECTSP11:mode.1">eigenvalue</a> of <font color="Maroon" title="c4">f2</font> &amp;  ex <font color="Olive" title="b1">v</font> being  <a href="vectsp_1.html#NM6" title="VECTSP_1:NM.6">Vector</a> of <font color="Maroon" title="c2">V</font> st <br/>( <font color="Olive" title="b1">v</font> is    <a href="vectsp11.html#M2" title="VECTSP11:mode.2">eigenvector</a> of <font color="Maroon" title="c3">f1</font>,<font color="Maroon" title="c5">L1</font> &amp; <font color="Olive" title="b1">v</font> is    <a href="vectsp11.html#M2" title="VECTSP11:mode.2">eigenvector</a> of <font color="Maroon" title="c4">f2</font>,<font color="Maroon" title="c6">L2</font> &amp; <font color="Olive" title="b1">v</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a>  <a href="struct_0.html#K4" title="STRUCT_0:func.4">0.</a> <font color="Maroon" title="c2">V</font> ) implies ( <font color="Maroon" title="c3">f1</font> <a href="matrlin.html#K5" title="MATRLIN:func.5">+</a> <font color="Maroon" title="c4">f2</font> is <a href="vectsp11.html#V1" title="VECTSP11:attr.1">with_eigenvalues</a> &amp; <font color="Maroon" title="c5">L1</font> <a href="rlvect_1.html#K3" title="RLVECT_1:func.3">+</a> <font color="Maroon" title="c6">L2</font> is    <a href="vectsp11.html#M1" title="VECTSP11:mode.1">eigenvalue</a> of <font color="Maroon" title="c3">f1</font> <a href="matrlin.html#K5" title="MATRLIN:func.5">+</a> <font color="Maroon" title="c4">f2</font> &amp; ( for <font color="Olive" title="b1">w</font> being  <a href="vectsp_1.html#NM6" title="VECTSP_1:NM.6">Vector</a> of <font color="Maroon" title="c2">V</font>  st <font color="Olive" title="b1">w</font> is    <a href="vectsp11.html#M2" title="VECTSP11:mode.2">eigenvector</a> of <font color="Maroon" title="c3">f1</font>,<font color="Maroon" title="c5">L1</font> &amp; <font color="Olive" title="b1">w</font> is    <a href="vectsp11.html#M2" title="VECTSP11:mode.2">eigenvector</a> of <font color="Maroon" title="c4">f2</font>,<font color="Maroon" title="c6">L2</font> holds <br/><font color="Olive" title="b1">w</font> is    <a href="vectsp11.html#M2" title="VECTSP11:mode.2">eigenvector</a> of <font color="Maroon" title="c3">f1</font> <a href="matrlin.html#K5" title="MATRLIN:func.5">+</a> <font color="Maroon" title="c4">f2</font>,<font color="Maroon" title="c5">L1</font> <a href="rlvect_1.html#K3" title="RLVECT_1:func.3">+</a> <font color="Maroon" title="c6">L2</font> ) ) )</span><br/>







<b>set </b><font color="Maroon" title="c7">g</font> = <font color="Maroon" title="c3">f1</font> <a href="matrlin.html#K5" title="MATRLIN:func.5">+</a> <font color="Maroon" title="c4">f2</font>;<br/>
<b>assume </b><a NAME="E1:17"/><i><font color="Green" title="E14">A1</font></i>: 
( <font color="Maroon" title="c5">L1</font> is    <a href="vectsp11.html#M1" title="VECTSP11:mode.1">eigenvalue</a> of <font color="Maroon" title="c3">f1</font> &amp; <font color="Maroon" title="c6">L2</font> is    <a href="vectsp11.html#M1" title="VECTSP11:mode.1">eigenvalue</a> of <font color="Maroon" title="c4">f2</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">v</font> being  <a href="vectsp_1.html#NM6" title="VECTSP_1:NM.6">Vector</a> of <font color="Maroon" title="c2">V</font>  holds <br/>(  not <font color="Olive" title="b1">v</font> is    <a href="vectsp11.html#M2" title="VECTSP11:mode.2">eigenvector</a> of <font color="Maroon" title="c3">f1</font>,<font color="Maroon" title="c5">L1</font> or  not <font color="Olive" title="b1">v</font> is    <a href="vectsp11.html#M2" title="VECTSP11:mode.2">eigenvector</a> of <font color="Maroon" title="c4">f2</font>,<font color="Maroon" title="c6">L2</font> or  not <font color="Olive" title="b1">v</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a>  <a href="struct_0.html#K4" title="STRUCT_0:func.4">0.</a> <font color="Maroon" title="c2">V</font> ) or ( <font color="Maroon" title="c3">f1</font> <a href="matrlin.html#K5" title="MATRLIN:func.5">+</a> <font color="Maroon" title="c4">f2</font> is <a href="vectsp11.html#V1" title="VECTSP11:attr.1">with_eigenvalues</a> &amp; <font color="Maroon" title="c5">L1</font> <a href="rlvect_1.html#K3" title="RLVECT_1:func.3">+</a> <font color="Maroon" title="c6">L2</font> is    <a href="vectsp11.html#M1" title="VECTSP11:mode.1">eigenvalue</a> of <font color="Maroon" title="c3">f1</font> <a href="matrlin.html#K5" title="MATRLIN:func.5">+</a> <font color="Maroon" title="c4">f2</font> &amp; ( for <font color="Olive" title="b1">w</font> being  <a href="vectsp_1.html#NM6" title="VECTSP_1:NM.6">Vector</a> of <font color="Maroon" title="c2">V</font>  st <font color="Olive" title="b1">w</font> is    <a href="vectsp11.html#M2" title="VECTSP11:mode.2">eigenvector</a> of <font color="Maroon" title="c3">f1</font>,<font color="Maroon" title="c5">L1</font> &amp; <font color="Olive" title="b1">w</font> is    <a href="vectsp11.html#M2" title="VECTSP11:mode.2">eigenvector</a> of <font color="Maroon" title="c4">f2</font>,<font color="Maroon" title="c6">L2</font> holds <br/><font color="Olive" title="b1">w</font> is    <a href="vectsp11.html#M2" title="VECTSP11:mode.2">eigenvector</a> of <font color="Maroon" title="c3">f1</font> <a href="matrlin.html#K5" title="MATRLIN:func.5">+</a> <font color="Maroon" title="c4">f2</font>,<font color="Maroon" title="c5">L1</font> <a href="rlvect_1.html#K3" title="RLVECT_1:func.3">+</a> <font color="Maroon" title="c6">L2</font> ) ) )</span><br/>

<b>given </b><font color="Maroon" title="c8">v</font> being   <a href="vectsp_1.html#NM6" title="VECTSP_1:NM.6">Vector</a> of <font color="Maroon" title="c2">V</font><b> such that </b><a NAME="E3:17"/><i><font color="Green" title="E15">A2</font></i>: 
( <font color="Maroon" title="c8">v</font> is    <a href="vectsp11.html#M2" title="VECTSP11:mode.2">eigenvector</a> of <font color="Maroon" title="c3">f1</font>,<font color="Maroon" title="c5">L1</font> &amp; <font color="Maroon" title="c8">v</font> is    <a href="vectsp11.html#M2" title="VECTSP11:mode.2">eigenvector</a> of <font color="Maroon" title="c4">f2</font>,<font color="Maroon" title="c6">L2</font> &amp; <font color="Maroon" title="c8">v</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a>  <a href="struct_0.html#K4" title="STRUCT_0:func.4">0.</a> <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="c3">f1</font> <a href="matrlin.html#K5" title="MATRLIN:func.5">+</a> <font color="Maroon" title="c4">f2</font> is <a href="vectsp11.html#V1" title="VECTSP11:attr.1">with_eigenvalues</a> &amp; <font color="Maroon" title="c5">L1</font> <a href="rlvect_1.html#K3" title="RLVECT_1:func.3">+</a> <font color="Maroon" title="c6">L2</font> is    <a href="vectsp11.html#M1" title="VECTSP11:mode.1">eigenvalue</a> of <font color="Maroon" title="c3">f1</font> <a href="matrlin.html#K5" title="MATRLIN:func.5">+</a> <font color="Maroon" title="c4">f2</font> &amp; ( for <font color="Olive" title="b1">w</font> being  <a href="vectsp_1.html#NM6" title="VECTSP_1:NM.6">Vector</a> of <font color="Maroon" title="c2">V</font>  st <font color="Olive" title="b1">w</font> is    <a href="vectsp11.html#M2" title="VECTSP11:mode.2">eigenvector</a> of <font color="Maroon" title="c3">f1</font>,<font color="Maroon" title="c5">L1</font> &amp; <font color="Olive" title="b1">w</font> is    <a href="vectsp11.html#M2" title="VECTSP11:mode.2">eigenvector</a> of <font color="Maroon" title="c4">f2</font>,<font color="Maroon" title="c6">L2</font> holds <br/><font color="Olive" title="b1">w</font> is    <a href="vectsp11.html#M2" title="VECTSP11:mode.2">eigenvector</a> of <font color="Maroon" title="c3">f1</font> <a href="matrlin.html#K5" title="MATRLIN:func.5">+</a> <font color="Maroon" title="c4">f2</font>,<font color="Maroon" title="c5">L1</font> <a href="rlvect_1.html#K3" title="RLVECT_1:func.3">+</a> <font color="Maroon" title="c6">L2</font> ) )</span><br/>

<i><font color="Green" title="E16">A3</font></i>: <span class="p1">(<span class="default"><font color="Maroon" title="c3">f1</font> <a href="matrlin.html#K5" title="MATRLIN:func.5">+</a> <font color="Maroon" title="c4">f2</font></span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c8">v</font> = 
<span class="p1">(<span class="default"><font color="Maroon" title="c3">f1</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c8">v</font></span>)</span> <a href="rlvect_1.html#K3" title="RLVECT_1:func.3">+</a> <span class="p1">(<span class="default"><font color="Maroon" title="c4">f2</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c8">v</font></span>)</span>
<b>by </b><i><a class="ref" href="matrlin.html#D5" title="MATRLIN:def.5">MATRLIN:def 5</a></i>
<br/>.= 
<span class="p1">(<span class="default"><font color="Maroon" title="c5">L1</font> <a href="vectsp_1.html#K4" title="VECTSP_1:func.4">*</a> <font color="Maroon" title="c8">v</font></span>)</span> <a href="rlvect_1.html#K3" title="RLVECT_1:func.3">+</a> <span class="p1">(<span class="default"><font color="Maroon" title="c4">f2</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c8">v</font></span>)</span>
<b>by </b><i><a class="txt" href="#E1:17"><i><font color="Green" title="E14">A1</font></i></a>, <a class="txt" href="#E3:17"><i><font color="Green" title="E15">A2</font></i></a>, <a class="ref" href="vectsp11.html#D3" target="_self" title="VECTSP11:def.3">Def3</a></i>
<br/>.= 
<span class="p1">(<span class="default"><font color="Maroon" title="c5">L1</font> <a href="vectsp_1.html#K4" title="VECTSP_1:func.4">*</a> <font color="Maroon" title="c8">v</font></span>)</span> <a href="rlvect_1.html#K3" title="RLVECT_1:func.3">+</a> <span class="p1">(<span class="default"><font color="Maroon" title="c6">L2</font> <a href="vectsp_1.html#K4" title="VECTSP_1:func.4">*</a> <font color="Maroon" title="c8">v</font></span>)</span>
<b>by </b><i><a class="txt" href="#E1:17"><i><font color="Green" title="E14">A1</font></i></a>, <a class="txt" href="#E3:17"><i><font color="Green" title="E15">A2</font></i></a>, <a class="ref" href="vectsp11.html#D3" target="_self" title="VECTSP11:def.3">Def3</a></i>
<br/>.= 
<span class="p1">(<span class="default"><font color="Maroon" title="c5">L1</font> <a href="rlvect_1.html#K3" title="RLVECT_1:func.3">+</a> <font color="Maroon" title="c6">L2</font></span>)</span> <a href="vectsp_1.html#K4" title="VECTSP_1:func.4">*</a> <font color="Maroon" title="c8">v</font>
<b>by </b><i><a class="ref" href="vectsp_1.html#D26" title="VECTSP_1:def.26">VECTSP_1:def 26</a></i>
;<br/>
<b>hence </b><a NAME="E5:17"/><i><font color="Green" title="E17">A4</font></i>: 
<font color="Maroon" title="c3">f1</font> <a href="matrlin.html#K5" title="MATRLIN:func.5">+</a> <font color="Maroon" title="c4">f2</font> is <a href="vectsp11.html#V1" title="VECTSP11:attr.1">with_eigenvalues</a>
 <b>by </b><i><a class="txt" href="#E3:17"><i><font color="Green" title="E15">A2</font></i></a>, <a class="ref" href="vectsp11.html#D1" target="_self" title="VECTSP11:def.1">Def1</a></i>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> ( <font color="Maroon" title="c5">L1</font> <a href="rlvect_1.html#K3" title="RLVECT_1:func.3">+</a> <font color="Maroon" title="c6">L2</font> is    <a href="vectsp11.html#M1" title="VECTSP11:mode.1">eigenvalue</a> of <font color="Maroon" title="c3">f1</font> <a href="matrlin.html#K5" title="MATRLIN:func.5">+</a> <font color="Maroon" title="c4">f2</font> &amp; ( for <font color="Olive" title="b1">w</font> being  <a href="vectsp_1.html#NM6" title="VECTSP_1:NM.6">Vector</a> of <font color="Maroon" title="c2">V</font>  st <font color="Olive" title="b1">w</font> is    <a href="vectsp11.html#M2" title="VECTSP11:mode.2">eigenvector</a> of <font color="Maroon" title="c3">f1</font>,<font color="Maroon" title="c5">L1</font> &amp; <font color="Olive" title="b1">w</font> is    <a href="vectsp11.html#M2" title="VECTSP11:mode.2">eigenvector</a> of <font color="Maroon" title="c4">f2</font>,<font color="Maroon" title="c6">L2</font> holds <br/><font color="Olive" title="b1">w</font> is    <a href="vectsp11.html#M2" title="VECTSP11:mode.2">eigenvector</a> of <font color="Maroon" title="c3">f1</font> <a href="matrlin.html#K5" title="MATRLIN:func.5">+</a> <font color="Maroon" title="c4">f2</font>,<font color="Maroon" title="c5">L1</font> <a href="rlvect_1.html#K3" title="RLVECT_1:func.3">+</a> <font color="Maroon" title="c6">L2</font> ) )</span><br/>

<b>thus </b><a NAME="E6:17"/><i><font color="Green" title="E18">A5</font></i>: 
<font color="Maroon" title="c5">L1</font> <a href="rlvect_1.html#K3" title="RLVECT_1:func.3">+</a> <font color="Maroon" title="c6">L2</font> is    <a href="vectsp11.html#M1" title="VECTSP11:mode.1">eigenvalue</a> of <font color="Maroon" title="c3">f1</font> <a href="matrlin.html#K5" title="MATRLIN:func.5">+</a> <font color="Maroon" title="c4">f2</font>
 <b>by </b><i><a class="txt" href="#E3:17"><i><font color="Green" title="E15">A2</font></i></a>, <a class="txt" href="#E4:17"><i><font color="Green" title="E16">A3</font></i></a>, <a class="txt" href="#E5:17"><i><font color="Green" title="E17">A4</font></i></a>, <a class="ref" href="vectsp11.html#D2" target="_self" title="VECTSP11:def.2">Def2</a></i>; <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">w</font> being  <a href="vectsp_1.html#NM6" title="VECTSP_1:NM.6">Vector</a> of <font color="Maroon" title="c2">V</font>  st <font color="Olive" title="b1">w</font> is    <a href="vectsp11.html#M2" title="VECTSP11:mode.2">eigenvector</a> of <font color="Maroon" title="c3">f1</font>,<font color="Maroon" title="c5">L1</font> &amp; <font color="Olive" title="b1">w</font> is    <a href="vectsp11.html#M2" title="VECTSP11:mode.2">eigenvector</a> of <font color="Maroon" title="c4">f2</font>,<font color="Maroon" title="c6">L2</font> holds <br/><font color="Olive" title="b1">w</font> is    <a href="vectsp11.html#M2" title="VECTSP11:mode.2">eigenvector</a> of <font color="Maroon" title="c3">f1</font> <a href="matrlin.html#K5" title="MATRLIN:func.5">+</a> <font color="Maroon" title="c4">f2</font>,<font color="Maroon" title="c5">L1</font> <a href="rlvect_1.html#K3" title="RLVECT_1:func.3">+</a> <font color="Maroon" title="c6">L2</font></span><br/>

<b>let </b><font color="Maroon" title="c9">w</font> be   <a href="vectsp_1.html#NM6" title="VECTSP_1:NM.6">Vector</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="c9">w</font> is    <a href="vectsp11.html#M2" title="VECTSP11:mode.2">eigenvector</a> of <font color="Maroon" title="c3">f1</font>,<font color="Maroon" title="c5">L1</font> &amp; <font color="Maroon" title="c9">w</font> is    <a href="vectsp11.html#M2" title="VECTSP11:mode.2">eigenvector</a> of <font color="Maroon" title="c4">f2</font>,<font color="Maroon" title="c6">L2</font> implies <font color="Maroon" title="c9">w</font> is    <a href="vectsp11.html#M2" title="VECTSP11:mode.2">eigenvector</a> of <font color="Maroon" title="c3">f1</font> <a href="matrlin.html#K5" title="MATRLIN:func.5">+</a> <font color="Maroon" title="c4">f2</font>,<font color="Maroon" title="c5">L1</font> <a href="rlvect_1.html#K3" title="RLVECT_1:func.3">+</a> <font color="Maroon" title="c6">L2</font> )</span><br/>

<b>assume </b><a NAME="E7:17"/><i><font color="Green" title="E19">A6</font></i>: 
( <font color="Maroon" title="c9">w</font> is    <a href="vectsp11.html#M2" title="VECTSP11:mode.2">eigenvector</a> of <font color="Maroon" title="c3">f1</font>,<font color="Maroon" title="c5">L1</font> &amp; <font color="Maroon" title="c9">w</font> is    <a href="vectsp11.html#M2" title="VECTSP11:mode.2">eigenvector</a> of <font color="Maroon" title="c4">f2</font>,<font color="Maroon" title="c6">L2</font> )
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> <font color="Maroon" title="c9">w</font> is    <a href="vectsp11.html#M2" title="VECTSP11:mode.2">eigenvector</a> of <font color="Maroon" title="c3">f1</font> <a href="matrlin.html#K5" title="MATRLIN:func.5">+</a> <font color="Maroon" title="c4">f2</font>,<font color="Maroon" title="c5">L1</font> <a href="rlvect_1.html#K3" title="RLVECT_1:func.3">+</a> <font color="Maroon" title="c6">L2</font></span><br/>

<span class="p1">(<span class="default"><font color="Maroon" title="c3">f1</font> <a href="matrlin.html#K5" title="MATRLIN:func.5">+</a> <font color="Maroon" title="c4">f2</font></span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c9">w</font> = 
<span class="p1">(<span class="default"><font color="Maroon" title="c3">f1</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c9">w</font></span>)</span> <a href="rlvect_1.html#K3" title="RLVECT_1:func.3">+</a> <span class="p1">(<span class="default"><font color="Maroon" title="c4">f2</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c9">w</font></span>)</span>
<b>by </b><i><a class="ref" href="matrlin.html#D5" title="MATRLIN:def.5">MATRLIN:def 5</a></i>
<br/>.= 
<span class="p1">(<span class="default"><font color="Maroon" title="c5">L1</font> <a href="vectsp_1.html#K4" title="VECTSP_1:func.4">*</a> <font color="Maroon" title="c9">w</font></span>)</span> <a href="rlvect_1.html#K3" title="RLVECT_1:func.3">+</a> <span class="p1">(<span class="default"><font color="Maroon" title="c4">f2</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c9">w</font></span>)</span>
<b>by </b><i><a class="txt" href="#E1:17"><i><font color="Green" title="E14">A1</font></i></a>, <a class="txt" href="#E7:17"><i><font color="Green" title="E19">A6</font></i></a>, <a class="ref" href="vectsp11.html#D3" target="_self" title="VECTSP11:def.3">Def3</a></i>
<br/>.= 
<span class="p1">(<span class="default"><font color="Maroon" title="c5">L1</font> <a href="vectsp_1.html#K4" title="VECTSP_1:func.4">*</a> <font color="Maroon" title="c9">w</font></span>)</span> <a href="rlvect_1.html#K3" title="RLVECT_1:func.3">+</a> <span class="p1">(<span class="default"><font color="Maroon" title="c6">L2</font> <a href="vectsp_1.html#K4" title="VECTSP_1:func.4">*</a> <font color="Maroon" title="c9">w</font></span>)</span>
<b>by </b><i><a class="txt" href="#E1:17"><i><font color="Green" title="E14">A1</font></i></a>, <a class="txt" href="#E7:17"><i><font color="Green" title="E19">A6</font></i></a>, <a class="ref" href="vectsp11.html#D3" target="_self" title="VECTSP11:def.3">Def3</a></i>
<br/>.= 
<span class="p1">(<span class="default"><font color="Maroon" title="c5">L1</font> <a href="rlvect_1.html#K3" title="RLVECT_1:func.3">+</a> <font color="Maroon" title="c6">L2</font></span>)</span> <a href="vectsp_1.html#K4" title="VECTSP_1:func.4">*</a> <font color="Maroon" title="c9">w</font>
<b>by </b><i><a class="ref" href="vectsp_1.html#D26" title="VECTSP_1:def.26">VECTSP_1:def 26</a></i>
;<br/>
<b>hence </b><a NAME="E9:17"/>
<font color="Maroon" title="c9">w</font> is    <a href="vectsp11.html#M2" title="VECTSP11:mode.2">eigenvector</a> of <font color="Maroon" title="c3">f1</font> <a href="matrlin.html#K5" title="MATRLIN:func.5">+</a> <font color="Maroon" title="c4">f2</font>,<font color="Maroon" title="c5">L1</font> <a href="rlvect_1.html#K3" title="RLVECT_1:func.3">+</a> <font color="Maroon" title="c6">L2</font>
 <b>by </b><i><a class="txt" href="#E5:17"><i><font color="Green" title="E17">A4</font></i></a>, <a class="txt" href="#E6:17"><i><font color="Green" title="E18">A5</font></i></a>, <a class="ref" href="vectsp11.html#D3" target="_self" title="VECTSP11:def.3">Def3</a></i>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> verum</span><br/>


</div>
