<?xml version="1.0"?>
<div class="add">

<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">V1</font> being   <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">f</font> being   <a href="ranknull.html#NM1" title="RANKNULL:NM.1">linear-transformation</a> of <font color="Olive" title="b1">V1</font>,<font color="Olive" title="b1">V1</font><br/>  for <font color="Olive" title="b3">L</font> being   <a href="vectsp_1.html#NM6" title="VECTSP_1:NM.6">Scalar</a> of <font color="Maroon" title="c1">K</font><br/>  for <font color="Olive" title="b4">I</font> being    <a href="vectsp_5.html#M1" title="VECTSP_5:mode.1">Linear_Compl</a> of  <a href="vectsp11.html#K2" title="VECTSP11:func.2">UnionKers</a> <span class="p1">(<span class="default"><font color="Olive" title="b2">f</font> <a href="matrlin.html#K3" title="MATRLIN:func.3">+</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="algstr_0.html#K4" title="ALGSTR_0:func.4">-</a> <font color="Olive" title="b3">L</font></span>)</span> <a href="matrlin.html#K4" title="MATRLIN:func.4">*</a> <span class="p3">(<span class="default"><a href="struct_0.html#K3" title="STRUCT_0:func.3">id</a> <font color="Olive" title="b1">V1</font></span>)</span></span>)</span></span>)</span><br/>  for <font color="Olive" title="b5">fI</font> being   <a href="ranknull.html#NM1" title="RANKNULL:NM.1">linear-transformation</a> of <font color="Olive" title="b4">I</font>,<font color="Olive" title="b4">I</font>  st <font color="Olive" title="b5">fI</font> <a href="funct_2.html#R1" title="FUNCT_2:pred.1">=</a> <font color="Olive" title="b2">f</font> <a href="matrlin2.html#K8" title="MATRLIN2:func.8">|</a> <font color="Olive" title="b4">I</font> holds <br/> for <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="b4">I</font>  st <font color="Olive" title="b5">fI</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Olive" title="b6">v</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b3">L</font> <a href="vectsp_1.html#K3" title="VECTSP_1:func.3">*</a> <font color="Olive" title="b6">v</font> holds <br/><font color="Olive" title="b6">v</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="struct_0.html#K4" title="STRUCT_0:func.4">0.</a> <font color="Olive" title="b1">V1</font></span><br/><span class="kw">let </span><font color="Maroon" title="c2">V1</font> be   <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">f</font> being   <a href="ranknull.html#NM1" title="RANKNULL:NM.1">linear-transformation</a> of <font color="Maroon" title="c2">V1</font>,<font color="Maroon" title="c2">V1</font><br/>  for <font color="Olive" title="b2">L</font> being   <a href="vectsp_1.html#NM6" title="VECTSP_1:NM.6">Scalar</a> of <font color="Maroon" title="c1">K</font><br/>  for <font color="Olive" title="b3">I</font> being    <a href="vectsp_5.html#M1" title="VECTSP_5:mode.1">Linear_Compl</a> of  <a href="vectsp11.html#K2" title="VECTSP11:func.2">UnionKers</a> <span class="p1">(<span class="default"><font color="Olive" title="b1">f</font> <a href="matrlin.html#K3" title="MATRLIN:func.3">+</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="algstr_0.html#K4" title="ALGSTR_0:func.4">-</a> <font color="Olive" title="b2">L</font></span>)</span> <a href="matrlin.html#K4" title="MATRLIN:func.4">*</a> <span class="p3">(<span class="default"><a href="struct_0.html#K3" title="STRUCT_0:func.3">id</a> <font color="Maroon" title="c2">V1</font></span>)</span></span>)</span></span>)</span><br/>  for <font color="Olive" title="b4">fI</font> being   <a href="ranknull.html#NM1" title="RANKNULL:NM.1">linear-transformation</a> of <font color="Olive" title="b3">I</font>,<font color="Olive" title="b3">I</font>  st <font color="Olive" title="b4">fI</font> <a href="funct_2.html#R1" title="FUNCT_2:pred.1">=</a> <font color="Olive" title="b1">f</font> <a href="matrlin2.html#K8" title="MATRLIN2:func.8">|</a> <font color="Olive" title="b3">I</font> holds <br/> for <font color="Olive" title="b5">v</font> being   <a href="vectsp_1.html#NM8" title="VECTSP_1:NM.8">Vector</a> of <font color="Olive" title="b3">I</font>  st <font color="Olive" title="b4">fI</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Olive" title="b5">v</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b2">L</font> <a href="vectsp_1.html#K3" title="VECTSP_1:func.3">*</a> <font color="Olive" title="b5">v</font> holds <br/><font color="Olive" title="b5">v</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="struct_0.html#K4" title="STRUCT_0:func.4">0.</a> <font color="Maroon" title="c2">V1</font></span><br/><span class="kw">let </span><font color="Maroon" title="c3">f</font> be   <a href="ranknull.html#NM1" title="RANKNULL:NM.1">linear-transformation</a> of <font color="Maroon" title="c2">V1</font>,<font color="Maroon" title="c2">V1</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">L</font> being   <a href="vectsp_1.html#NM6" title="VECTSP_1:NM.6">Scalar</a> of <font color="Maroon" title="c1">K</font><br/>  for <font color="Olive" title="b2">I</font> being    <a href="vectsp_5.html#M1" title="VECTSP_5:mode.1">Linear_Compl</a> of  <a href="vectsp11.html#K2" title="VECTSP11:func.2">UnionKers</a> <span class="p1">(<span class="default"><font color="Maroon" title="c3">f</font> <a href="matrlin.html#K3" title="MATRLIN:func.3">+</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="algstr_0.html#K4" title="ALGSTR_0:func.4">-</a> <font color="Olive" title="b1">L</font></span>)</span> <a href="matrlin.html#K4" title="MATRLIN:func.4">*</a> <span class="p3">(<span class="default"><a href="struct_0.html#K3" title="STRUCT_0:func.3">id</a> <font color="Maroon" title="c2">V1</font></span>)</span></span>)</span></span>)</span><br/>  for <font color="Olive" title="b3">fI</font> being   <a href="ranknull.html#NM1" title="RANKNULL:NM.1">linear-transformation</a> of <font color="Olive" title="b2">I</font>,<font color="Olive" title="b2">I</font>  st <font color="Olive" title="b3">fI</font> <a href="funct_2.html#R1" title="FUNCT_2:pred.1">=</a> <font color="Maroon" title="c3">f</font> <a href="matrlin2.html#K8" title="MATRLIN2:func.8">|</a> <font color="Olive" title="b2">I</font> holds <br/> for <font color="Olive" title="b4">v</font> being   <a href="vectsp_1.html#NM8" title="VECTSP_1:NM.8">Vector</a> of <font color="Olive" title="b2">I</font>  st <font color="Olive" title="b3">fI</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Olive" title="b4">v</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b1">L</font> <a href="vectsp_1.html#K3" title="VECTSP_1:func.3">*</a> <font color="Olive" title="b4">v</font> holds <br/><font color="Olive" title="b4">v</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="struct_0.html#K4" title="STRUCT_0:func.4">0.</a> <font color="Maroon" title="c2">V1</font></span><br/><span class="kw">let </span><font color="Maroon" title="c4">L</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">  for <font color="Olive" title="b1">I</font> being    <a href="vectsp_5.html#M1" title="VECTSP_5:mode.1">Linear_Compl</a> of  <a href="vectsp11.html#K2" title="VECTSP11:func.2">UnionKers</a> <span class="p1">(<span class="default"><font color="Maroon" title="c3">f</font> <a href="matrlin.html#K3" title="MATRLIN:func.3">+</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="algstr_0.html#K4" title="ALGSTR_0:func.4">-</a> <font color="Maroon" title="c4">L</font></span>)</span> <a href="matrlin.html#K4" title="MATRLIN:func.4">*</a> <span class="p3">(<span class="default"><a href="struct_0.html#K3" title="STRUCT_0:func.3">id</a> <font color="Maroon" title="c2">V1</font></span>)</span></span>)</span></span>)</span><br/>  for <font color="Olive" title="b2">fI</font> being   <a href="ranknull.html#NM1" title="RANKNULL:NM.1">linear-transformation</a> of <font color="Olive" title="b1">I</font>,<font color="Olive" title="b1">I</font>  st <font color="Olive" title="b2">fI</font> <a href="funct_2.html#R1" title="FUNCT_2:pred.1">=</a> <font color="Maroon" title="c3">f</font> <a href="matrlin2.html#K8" title="MATRLIN2:func.8">|</a> <font color="Olive" title="b1">I</font> holds <br/> for <font color="Olive" title="b3">v</font> being   <a href="vectsp_1.html#NM8" title="VECTSP_1:NM.8">Vector</a> of <font color="Olive" title="b1">I</font>  st <font color="Olive" title="b2">fI</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Olive" title="b3">v</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c4">L</font> <a href="vectsp_1.html#K3" title="VECTSP_1:func.3">*</a> <font color="Olive" title="b3">v</font> holds <br/><font color="Olive" title="b3">v</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="struct_0.html#K4" title="STRUCT_0:func.4">0.</a> <font color="Maroon" title="c2">V1</font></span><br/>







<span class="kw">set </span><font color="Maroon" title="c5">V</font> = <font color="Maroon" title="c2">V1</font>;<br/>
<span class="kw">set </span><font color="Maroon" title="c6">fi</font> = <font color="Maroon" title="c3">f</font> <a href="matrlin.html#K3" title="MATRLIN:func.3">+</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="algstr_0.html#K4" title="ALGSTR_0:func.4">-</a> <font color="Maroon" title="c4">L</font></span>)</span> <a href="matrlin.html#K4" title="MATRLIN:func.4">*</a> <span class="p2">(<span class="default"><a href="struct_0.html#K3" title="STRUCT_0:func.3">id</a> <font color="Maroon" title="c2">V1</font></span>)</span></span>)</span>;<br/>
<span class="kw">let </span><font color="Maroon" title="c7">I</font> be    <a href="vectsp_5.html#M1" title="VECTSP_5:mode.1">Linear_Compl</a> of  <a href="vectsp11.html#K2" title="VECTSP11:func.2">UnionKers</a> <span class="p1">(<span class="default"><font color="Maroon" title="c3">f</font> <a href="matrlin.html#K3" title="MATRLIN:func.3">+</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="algstr_0.html#K4" title="ALGSTR_0:func.4">-</a> <font color="Maroon" title="c4">L</font></span>)</span> <a href="matrlin.html#K4" title="MATRLIN:func.4">*</a> <span class="p3">(<span class="default"><a href="struct_0.html#K3" title="STRUCT_0:func.3">id</a> <font color="Maroon" title="c2">V1</font></span>)</span></span>)</span></span>)</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">fI</font> being   <a href="ranknull.html#NM1" title="RANKNULL:NM.1">linear-transformation</a> of <font color="Maroon" title="c7">I</font>,<font color="Maroon" title="c7">I</font>  st <font color="Olive" title="b1">fI</font> <a href="funct_2.html#R1" title="FUNCT_2:pred.1">=</a> <font color="Maroon" title="c3">f</font> <a href="matrlin2.html#K8" title="MATRLIN2:func.8">|</a> <font color="Maroon" title="c7">I</font> holds <br/> for <font color="Olive" title="b2">v</font> being   <a href="vectsp_1.html#NM8" title="VECTSP_1:NM.8">Vector</a> of <font color="Maroon" title="c7">I</font>  st <font color="Olive" title="b1">fI</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Olive" title="b2">v</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c4">L</font> <a href="vectsp_1.html#K3" title="VECTSP_1:func.3">*</a> <font color="Olive" title="b2">v</font> holds <br/><font color="Olive" title="b2">v</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="struct_0.html#K4" title="STRUCT_0:func.4">0.</a> <font color="Maroon" title="c2">V1</font></span><br/><span class="kw">let </span><font color="Maroon" title="c8">fI</font> be   <a href="ranknull.html#NM1" title="RANKNULL:NM.1">linear-transformation</a> of <font color="Maroon" title="c7">I</font>,<font color="Maroon" title="c7">I</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="c8">fI</font> <a href="funct_2.html#R1" title="FUNCT_2:pred.1">=</a> <font color="Maroon" title="c3">f</font> <a href="matrlin2.html#K8" title="MATRLIN2:func.8">|</a> <font color="Maroon" title="c7">I</font> implies  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="c7">I</font>  st <font color="Maroon" title="c8">fI</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Olive" title="b1">v</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c4">L</font> <a href="vectsp_1.html#K3" title="VECTSP_1:func.3">*</a> <font color="Olive" title="b1">v</font> holds <br/><font color="Olive" title="b1">v</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="struct_0.html#K4" title="STRUCT_0:func.4">0.</a> <font color="Maroon" title="c2">V1</font> )</span><br/>



<span class="kw">assume </span><a NAME="E1:47"/><span class="lab"><font color="Green" title="E33">A1</font></span>: 
<font color="Maroon" title="c8">fI</font> <a href="funct_2.html#R1" title="FUNCT_2:pred.1">=</a> <font color="Maroon" title="c3">f</font> <a href="matrlin2.html#K8" title="MATRLIN2:func.8">|</a> <font color="Maroon" title="c7">I</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="c7">I</font>  st <font color="Maroon" title="c8">fI</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Olive" title="b1">v</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c4">L</font> <a href="vectsp_1.html#K3" title="VECTSP_1:func.3">*</a> <font color="Olive" title="b1">v</font> holds <br/><font color="Olive" title="b1">v</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="struct_0.html#K4" title="STRUCT_0:func.4">0.</a> <font color="Maroon" title="c2">V1</font></span><br/>

<span class="kw">let </span><font color="Maroon" title="c9">v</font> be   <a href="vectsp_1.html#NM8" title="VECTSP_1:NM.8">Vector</a> of <font color="Maroon" title="c7">I</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="c8">fI</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c9">v</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c4">L</font> <a href="vectsp_1.html#K3" title="VECTSP_1:func.3">*</a> <font color="Maroon" title="c9">v</font> implies <font color="Maroon" title="c9">v</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="struct_0.html#K4" title="STRUCT_0:func.4">0.</a> <font color="Maroon" title="c2">V1</font> )</span><br/>

<span class="kw">assume </span><a NAME="E2:47"/><span class="lab"><font color="Green" title="E34">A2</font></span>: 
<font color="Maroon" title="c8">fI</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c9">v</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c4">L</font> <a href="vectsp_1.html#K3" title="VECTSP_1:func.3">*</a> <font color="Maroon" title="c9">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">v</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="struct_0.html#K4" title="STRUCT_0:func.4">0.</a> <font color="Maroon" title="c2">V1</font></span><br/>

<span class="kw">reconsider </span><font color="Maroon" title="c10">v1</font> = <font color="Maroon" title="c9">v</font> as   <a href="vectsp_1.html#NM8" title="VECTSP_1:NM.8">Vector</a> of <font color="Maroon" title="c2">V1</font> <span class="kw">by</span> <span class="lab"><a class="ref" href="vectsp_4.html#T10" onmouseover="rs('vectsp_4/T10')" onmouseout="rh()">VECTSP_4:10</a></span>;<br/>
<span class="lab"><font color="Green" title="E35">A3</font></span>: <font color="Maroon" title="c3">f</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c9">v</font> = 
<font color="Maroon" title="c8">fI</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c9">v</font>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:47"><span class="lab"><font color="Green" title="E33">A1</font></span></a>, <a class="ref" href="funct_1.html#T49" onmouseover="rs('funct_1/T49')" onmouseout="rh()">FUNCT_1:49</a></span>
<br/>.= 
<font color="Maroon" title="c4">L</font> <a href="vectsp_1.html#K3" title="VECTSP_1:func.3">*</a> <font color="Maroon" title="c10">v1</font>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:47"><span class="lab"><font color="Green" title="E34">A2</font></span></a>, <a class="ref" href="vectsp_4.html#T14" onmouseover="rs('vectsp_4/T14')" onmouseout="rh()">VECTSP_4:14</a></span>
;<br/>
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c3">f</font> <a href="matrlin.html#K3" title="MATRLIN:func.3">+</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="algstr_0.html#K4" title="ALGSTR_0:func.4">-</a> <font color="Maroon" title="c4">L</font></span>)</span> <a href="matrlin.html#K4" title="MATRLIN:func.4">*</a> <span class="p4">(<span class="default"><a href="struct_0.html#K3" title="STRUCT_0:func.3">id</a> <font color="Maroon" title="c2">V1</font></span>)</span></span>)</span></span>)</span> <a href="matrlin2.html#K8" title="MATRLIN2:func.8">|</a> <font color="Maroon" title="c7">I</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c10">v1</font> = 
<span class="p1">(<span class="default"><font color="Maroon" title="c3">f</font> <a href="matrlin.html#K3" title="MATRLIN:func.3">+</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="algstr_0.html#K4" title="ALGSTR_0:func.4">-</a> <font color="Maroon" title="c4">L</font></span>)</span> <a href="matrlin.html#K4" title="MATRLIN:func.4">*</a> <span class="p3">(<span class="default"><a href="struct_0.html#K3" title="STRUCT_0:func.3">id</a> <font color="Maroon" title="c2">V1</font></span>)</span></span>)</span></span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c10">v1</font>
<span class="kw">by</span> <span class="lab"><a class="ref" href="funct_1.html#T49" onmouseover="rs('funct_1/T49')" onmouseout="rh()">FUNCT_1:49</a></span>
<br/>.= 
<span class="p1">(<span class="default"><font color="Maroon" title="c3">f</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c10">v1</font></span>)</span> <a href="rlvect_1.html#K3" title="RLVECT_1:func.3">+</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="algstr_0.html#K4" title="ALGSTR_0:func.4">-</a> <font color="Maroon" title="c4">L</font></span>)</span> <a href="matrlin.html#K4" title="MATRLIN:func.4">*</a> <span class="p3">(<span class="default"><a href="struct_0.html#K3" title="STRUCT_0:func.3">id</a> <font color="Maroon" title="c2">V1</font></span>)</span></span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c10">v1</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="c3">f</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c10">v1</font></span>)</span> <a href="rlvect_1.html#K3" title="RLVECT_1:func.3">+</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="algstr_0.html#K4" title="ALGSTR_0:func.4">-</a> <font color="Maroon" title="c4">L</font></span>)</span> <a href="vectsp_1.html#K3" title="VECTSP_1:func.3">*</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="struct_0.html#K3" title="STRUCT_0:func.3">id</a> <font color="Maroon" title="c2">V1</font></span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c10">v1</font></span>)</span></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="ref" href="matrlin.html#D4" onmouseover="rs('matrlin/D4')" onmouseout="rh()">MATRLIN:def 4</a></span>
<br/>.= 
<span class="p1">(<span class="default"><font color="Maroon" title="c4">L</font> <a href="vectsp_1.html#K3" title="VECTSP_1:func.3">*</a> <font color="Maroon" title="c10">v1</font></span>)</span> <a href="rlvect_1.html#K3" title="RLVECT_1:func.3">+</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="algstr_0.html#K4" title="ALGSTR_0:func.4">-</a> <font color="Maroon" title="c4">L</font></span>)</span> <a href="vectsp_1.html#K3" title="VECTSP_1:func.3">*</a> <font color="Maroon" title="c10">v1</font></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E4:47"><span class="lab"><font color="Green" title="E35">A3</font></span></a></span>
<br/>.= 
<span class="p1">(<span class="default"><font color="Maroon" title="c4">L</font> <a href="rlvect_1.html#K3" title="RLVECT_1:func.3">+</a> <span class="p2">(<span class="default"><a href="algstr_0.html#K4" title="ALGSTR_0:func.4">-</a> <font color="Maroon" title="c4">L</font></span>)</span></span>)</span> <a href="vectsp_1.html#K3" title="VECTSP_1:func.3">*</a> <font color="Maroon" title="c10">v1</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="p1">(<span class="default"><a href="struct_0.html#K4" title="STRUCT_0:func.4">0.</a> <font color="Maroon" title="c1">K</font></span>)</span> <a href="vectsp_1.html#K3" title="VECTSP_1:func.3">*</a> <font color="Maroon" title="c10">v1</font>
<span class="kw">by</span> <span class="lab"><a class="ref" href="vectsp_1.html#T19" onmouseover="rs('vectsp_1/T19')" onmouseout="rh()">VECTSP_1:19</a></span>
<br/>.= 
 <a href="struct_0.html#K4" title="STRUCT_0:func.4">0.</a> <font color="Maroon" title="c2">V1</font>
<span class="kw">by</span> <span class="lab"><a class="ref" href="vectsp_1.html#T14" onmouseover="rs('vectsp_1/T14')" onmouseout="rh()">VECTSP_1:14</a></span>
;<br/>
<a NAME="E6:47"/><span class="kw">then </span><span class="lab"><font color="Green" title="E36">A4</font></span>: 
<font color="Maroon" title="c10">v1</font> <a href="struct_0.html#R1" title="STRUCT_0:pred.1">in</a>  <a href="ranknull.html#K1" title="RANKNULL:func.1">ker</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c3">f</font> <a href="matrlin.html#K3" title="MATRLIN:func.3">+</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="algstr_0.html#K4" title="ALGSTR_0:func.4">-</a> <font color="Maroon" title="c4">L</font></span>)</span> <a href="matrlin.html#K4" title="MATRLIN:func.4">*</a> <span class="p4">(<span class="default"><a href="struct_0.html#K3" title="STRUCT_0:func.3">id</a> <font color="Maroon" title="c2">V1</font></span>)</span></span>)</span></span>)</span> <a href="matrlin2.html#K8" title="MATRLIN2:func.8">|</a> <font color="Maroon" title="c7">I</font></span>)</span>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="ranknull.html#T10" onmouseover="rs('ranknull/T10')" onmouseout="rh()">RANKNULL:10</a></span>;<br/>
<a NAME="E7:47"/>
<span class="p1">(<span class="default"><font color="Maroon" title="c3">f</font> <a href="matrlin.html#K3" title="MATRLIN:func.3">+</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="algstr_0.html#K4" title="ALGSTR_0:func.4">-</a> <font color="Maroon" title="c4">L</font></span>)</span> <a href="matrlin.html#K4" title="MATRLIN:func.4">*</a> <span class="p3">(<span class="default"><a href="struct_0.html#K3" title="STRUCT_0:func.3">id</a> <font color="Maroon" title="c2">V1</font></span>)</span></span>)</span></span>)</span> <a href="matrlin2.html#K8" title="MATRLIN2:func.8">|</a> <font color="Maroon" title="c7">I</font> is  <a href="funct_1.html#V2" title="FUNCT_1:attr.2">one-to-one</a> 
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="vectsp11.html#T36" target="_self" onmouseover="rs('vectsp11/T36')" onmouseout="rh()">Th36</a></span>;<br/>
<a NAME="E8:47"/><span class="kw">then </span>
 <a href="ranknull.html#K1" title="RANKNULL:func.1">ker</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c3">f</font> <a href="matrlin.html#K3" title="MATRLIN:func.3">+</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="algstr_0.html#K4" title="ALGSTR_0:func.4">-</a> <font color="Maroon" title="c4">L</font></span>)</span> <a href="matrlin.html#K4" title="MATRLIN:func.4">*</a> <span class="p4">(<span class="default"><a href="struct_0.html#K3" title="STRUCT_0:func.3">id</a> <font color="Maroon" title="c2">V1</font></span>)</span></span>)</span></span>)</span> <a href="matrlin2.html#K8" title="MATRLIN2:func.8">|</a> <font color="Maroon" title="c7">I</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="vectsp_4.html#K1" title="VECTSP_4:func.1">(0).</a> <font color="Maroon" title="c7">I</font>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="matrlin2.html#T43" onmouseover="rs('matrlin2/T43')" onmouseout="rh()">MATRLIN2:43</a></span>;<br/>
<span class="kw">hence </span><font color="Maroon" title="c9">v</font> = 
 <a href="struct_0.html#K4" title="STRUCT_0:func.4">0.</a> <font color="Maroon" title="c7">I</font>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E6:47"><span class="lab"><font color="Green" title="E36">A4</font></span></a>, <a class="ref" href="vectsp_4.html#T35" onmouseover="rs('vectsp_4/T35')" onmouseout="rh()">VECTSP_4:35</a></span>
<br/>.= 
 <a href="struct_0.html#K4" title="STRUCT_0:func.4">0.</a> <font color="Maroon" title="c2">V1</font>
<span class="kw">by</span> <span class="lab"><a class="ref" href="vectsp_4.html#T11" onmouseover="rs('vectsp_4/T11')" onmouseout="rh()">VECTSP_4:11</a></span>
;<br/> <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>
