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<span class="kw">let </span><font color="Maroon" title="c1">K</font> be   <a href="vectsp_1.html#NM5" title="VECTSP_1:NM.5">Field</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">V</font> being   non  <a href="struct_0.html#V7" title="STRUCT_0:attr.7">trivial</a>  <a href="vectsp_1.html#NM9" title="VECTSP_1:NM.9">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#NM6" title="VECTSP_1:NM.6">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#NM8" title="VECTSP_1:NM.8">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#K3" title="MATRLIN:func.3">+</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#K3" title="MATRLIN:func.3">+</a> <font color="Olive" title="b3">f2</font> &amp; (  for <font color="Olive" title="b6">w</font> being   <a href="vectsp_1.html#NM8" title="VECTSP_1:NM.8">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#K3" title="MATRLIN:func.3">+</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/><span class="kw">let </span><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#NM9" title="VECTSP_1:NM.9">VectSp</a> of <font color="Maroon" title="c1">K</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">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#NM6" title="VECTSP_1:NM.6">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#NM8" title="VECTSP_1:NM.8">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#K3" title="MATRLIN:func.3">+</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#K3" title="MATRLIN:func.3">+</a> <font color="Olive" title="b2">f2</font> &amp; (  for <font color="Olive" title="b5">w</font> being   <a href="vectsp_1.html#NM8" title="VECTSP_1:NM.8">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#K3" title="MATRLIN:func.3">+</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/><span class="kw">let </span><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" 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="vectsp_1.html#NM6" title="VECTSP_1:NM.6">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#NM8" title="VECTSP_1:NM.8">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#K3" title="MATRLIN:func.3">+</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#K3" title="MATRLIN:func.3">+</a> <font color="Maroon" title="c4">f2</font> &amp; (  for <font color="Olive" title="b3">w</font> being   <a href="vectsp_1.html#NM8" title="VECTSP_1:NM.8">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#K3" title="MATRLIN:func.3">+</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/><span class="kw">let </span><font color="Maroon" title="c5">L1</font>, <font color="Maroon" title="c6">L2</font> be   <a href="vectsp_1.html#NM6" title="VECTSP_1:NM.6">Scalar</a> of <font color="Maroon" title="c1">K</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="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#NM8" title="VECTSP_1:NM.8">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#K3" title="MATRLIN:func.3">+</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#K3" title="MATRLIN:func.3">+</a> <font color="Maroon" title="c4">f2</font> &amp; (  for <font color="Olive" title="b1">w</font> being   <a href="vectsp_1.html#NM8" title="VECTSP_1:NM.8">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#K3" title="MATRLIN:func.3">+</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="kw">set </span><font color="Maroon" title="c7">g</font> = <font color="Maroon" title="c3">f1</font> <a href="matrlin.html#K3" title="MATRLIN:func.3">+</a> <font color="Maroon" title="c4">f2</font>;<br/>
<span class="kw">assume </span><span class="kw">that </span><br/><a NAME="E1:17"/><span class="lab"><font color="Green" title="E13">A1</font></span>: 
<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>
 <span class="kw">and </span><br/><a NAME="E2:17"/><span class="lab"><font color="Green" title="E14">A2</font></span>: 
<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" 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">v</font> being   <a href="vectsp_1.html#NM8" title="VECTSP_1:NM.8">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#K3" title="MATRLIN:func.3">+</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#K3" title="MATRLIN:func.3">+</a> <font color="Maroon" title="c4">f2</font> &amp; (  for <font color="Olive" title="b1">w</font> being   <a href="vectsp_1.html#NM8" title="VECTSP_1:NM.8">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#K3" title="MATRLIN:func.3">+</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="kw">given </span><font color="Maroon" title="c8">v</font> being   <a href="vectsp_1.html#NM8" title="VECTSP_1:NM.8">Vector</a> of <font color="Maroon" title="c2">V</font><span class="kw"> such that </span><a NAME="E4:17"/><span class="lab"><font color="Green" title="E15">A3</font></span>: 
<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>
 <span class="kw">and </span><br/><a NAME="E5:17"/><span class="lab"><font color="Green" title="E16">A4</font></span>: 
<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>
 <span class="kw">and </span><br/><a NAME="E6:17"/><span class="lab"><font color="Green" title="E17">A5</font></span>: 
<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" 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="c3">f1</font> <a href="matrlin.html#K3" title="MATRLIN:func.3">+</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#K3" title="MATRLIN:func.3">+</a> <font color="Maroon" title="c4">f2</font> &amp; (  for <font color="Olive" title="b1">w</font> being   <a href="vectsp_1.html#NM8" title="VECTSP_1:NM.8">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#K3" title="MATRLIN:func.3">+</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="lab"><font color="Green" title="E18">A6</font></span>: <span class="p1">(<span class="default"><font color="Maroon" title="c3">f1</font> <a href="matrlin.html#K3" title="MATRLIN:func.3">+</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>
<span class="kw">by</span> <span class="lab"><a class="ref" href="matrlin.html#D3" onmouseover="rs('matrlin/D3')" onmouseout="rh()">MATRLIN:def 3</a></span>
<br/>.= 
<span class="p1">(<span class="default"><font color="Maroon" title="c5">L1</font> <a href="vectsp_1.html#K3" title="VECTSP_1: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>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:17"><span class="lab"><font color="Green" title="E13">A1</font></span></a>, <a class="txt" href="#E4:17"><span class="lab"><font color="Green" title="E15">A3</font></span></a>, <a class="ref" href="vectsp11.html#D3" target="_self" onmouseover="rs('vectsp11/D3')" onmouseout="rh()">Def3</a></span>
<br/>.= 
<span class="p1">(<span class="default"><font color="Maroon" title="c5">L1</font> <a href="vectsp_1.html#K3" title="VECTSP_1: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="c6">L2</font> <a href="vectsp_1.html#K3" title="VECTSP_1:func.3">*</a> <font color="Maroon" title="c8">v</font></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:17"><span class="lab"><font color="Green" title="E14">A2</font></span></a>, <a class="txt" href="#E5:17"><span class="lab"><font color="Green" title="E16">A4</font></span></a>, <a class="ref" href="vectsp11.html#D3" target="_self" onmouseover="rs('vectsp11/D3')" onmouseout="rh()">Def3</a></span>
<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#K3" title="VECTSP_1:func.3">*</a> <font color="Maroon" title="c8">v</font>
<span class="kw">by</span> <span class="lab"><a class="ref" href="vectsp_1.html#D15" onmouseover="rs('vectsp_1/D15')" onmouseout="rh()">VECTSP_1:def 15</a></span>
;<br/>
<span class="kw">hence </span><a NAME="E8:17"/><span class="lab"><font color="Green" title="E19">A7</font></span>: 
<font color="Maroon" title="c3">f1</font> <a href="matrlin.html#K3" title="MATRLIN:func.3">+</a> <font color="Maroon" title="c4">f2</font> is  <a href="vectsp11.html#V1" title="VECTSP11:attr.1">with_eigenvalues</a> 
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E6:17"><span class="lab"><font color="Green" title="E17">A5</font></span></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"> ( <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#K3" title="MATRLIN:func.3">+</a> <font color="Maroon" title="c4">f2</font> &amp; (  for <font color="Olive" title="b1">w</font> being   <a href="vectsp_1.html#NM8" title="VECTSP_1:NM.8">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#K3" title="MATRLIN:func.3">+</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="kw">hence </span><a NAME="E9:17"/><span class="lab"><font color="Green" title="E20">A8</font></span>: 
<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#K3" title="MATRLIN:func.3">+</a> <font color="Maroon" title="c4">f2</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E6:17"><span class="lab"><font color="Green" title="E17">A5</font></span></a>, <a class="txt" href="#E7:17"><span class="lab"><font color="Green" title="E18">A6</font></span></a>, <a class="ref" href="vectsp11.html#D2" target="_self" onmouseover="rs('vectsp11/D2')" onmouseout="rh()">Def2</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">  for <font color="Olive" title="b1">w</font> being   <a href="vectsp_1.html#NM8" title="VECTSP_1:NM.8">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#K3" title="MATRLIN:func.3">+</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="kw">let </span><font color="Maroon" title="c9">w</font> be   <a href="vectsp_1.html#NM8" title="VECTSP_1:NM.8">Vector</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="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#K3" title="MATRLIN:func.3">+</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="kw">assume </span><span class="kw">that </span><br/><a NAME="E10:17"/><span class="lab"><font color="Green" title="E21">A9</font></span>: 
<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>
 <span class="kw">and </span><br/><a NAME="E11:17"/><span class="lab"><font color="Green" title="E22">A10</font></span>: 
<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" 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="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#K3" title="MATRLIN:func.3">+</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#K3" title="MATRLIN:func.3">+</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>
<span class="kw">by</span> <span class="lab"><a class="ref" href="matrlin.html#D3" onmouseover="rs('matrlin/D3')" onmouseout="rh()">MATRLIN:def 3</a></span>
<br/>.= 
<span class="p1">(<span class="default"><font color="Maroon" title="c5">L1</font> <a href="vectsp_1.html#K3" title="VECTSP_1: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>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:17"><span class="lab"><font color="Green" title="E13">A1</font></span></a>, <a class="txt" href="#E10:17"><span class="lab"><font color="Green" title="E21">A9</font></span></a>, <a class="ref" href="vectsp11.html#D3" target="_self" onmouseover="rs('vectsp11/D3')" onmouseout="rh()">Def3</a></span>
<br/>.= 
<span class="p1">(<span class="default"><font color="Maroon" title="c5">L1</font> <a href="vectsp_1.html#K3" title="VECTSP_1: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="c6">L2</font> <a href="vectsp_1.html#K3" title="VECTSP_1:func.3">*</a> <font color="Maroon" title="c9">w</font></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:17"><span class="lab"><font color="Green" title="E14">A2</font></span></a>, <a class="txt" href="#E11:17"><span class="lab"><font color="Green" title="E22">A10</font></span></a>, <a class="ref" href="vectsp11.html#D3" target="_self" onmouseover="rs('vectsp11/D3')" onmouseout="rh()">Def3</a></span>
<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#K3" title="VECTSP_1:func.3">*</a> <font color="Maroon" title="c9">w</font>
<span class="kw">by</span> <span class="lab"><a class="ref" href="vectsp_1.html#D15" onmouseover="rs('vectsp_1/D15')" onmouseout="rh()">VECTSP_1:def 15</a></span>
;<br/>
<span class="kw">hence </span><a NAME="E13:17"/>
<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#K3" title="MATRLIN:func.3">+</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 class="kw">by</span> <span class="lab"><a class="txt" href="#E8:17"><span class="lab"><font color="Green" title="E19">A7</font></span></a>, <a class="txt" href="#E9:17"><span class="lab"><font color="Green" title="E20">A8</font></span></a>, <a class="ref" href="vectsp11.html#D3" target="_self" onmouseover="rs('vectsp11/D3')" onmouseout="rh()">Def3</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/>


</div>
