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<b>let </b><font color="Maroon" title="c1">n</font> be   <a href="nat_1.html#NM1" title="NAT_1:NM.1">Nat</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">K</font> being  <a href="vectsp_1.html#NM3" title="VECTSP_1:NM.3">Field</a><br/> for <font color="Olive" title="b2">V1</font> being  <a href="vectsp_1.html#NM7" title="VECTSP_1:NM.7">VectSp</a> of <font color="Olive" title="b1">K</font><br/> for <font color="Olive" title="b3">f</font> being  <a href="ranknull.html#NM1" title="RANKNULL:NM.1">linear-transformation</a> of <font color="Olive" title="b2">V1</font>,<font color="Olive" title="b2">V1</font><br/> for <font color="Olive" title="b4">L</font> being  <a href="vectsp_1.html#NM4" title="VECTSP_1:NM.4">Scalar</a> of <font color="Olive" title="b1">K</font>  st <font color="Maroon" title="c1">n</font> <a href="xxreal_0.html#NR2" title="XXREAL_0:NR.2">&gt;=</a> 1 holds <br/> ex <font color="Olive" title="b5">h</font> being  <a href="ranknull.html#NM1" title="RANKNULL:NM.1">linear-transformation</a> of <font color="Olive" title="b2">V1</font>,<font color="Olive" title="b2">V1</font> st <br/>( <span class="p1">(<span class="default"><font color="Olive" title="b3">f</font> <a href="matrlin2.html#K8" title="MATRLIN2:func.8">+</a> <span class="p2">(<span class="default"><font color="Olive" title="b4">L</font> <a href="matrlin2.html#K9" title="MATRLIN2:func.9">*</a> <span class="p3">(<span class="default"><a href="matrlin2.html#K7" title="MATRLIN2:func.7">id</a> <font color="Olive" title="b2">V1</font></span>)</span></span>)</span></span>)</span> <a href="vectsp11.html#K2" title="VECTSP11:func.2">|^</a> <font color="Maroon" title="c1">n</font> <a href="funct_2.html#R2" title="FUNCT_2:pred.2">=</a> <span class="p1">(<span class="default"><font color="Olive" title="b3">f</font> <a href="matrlin2.html#K10" title="MATRLIN2:func.10">*</a> <font color="Olive" title="b5">h</font></span>)</span> <a href="matrlin2.html#K8" title="MATRLIN2:func.8">+</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Olive" title="b4">L</font> <a href="matrlin2.html#K9" title="MATRLIN2:func.9">*</a> <span class="p3">(<span class="default"><a href="matrlin2.html#K7" title="MATRLIN2:func.7">id</a> <font color="Olive" title="b2">V1</font></span>)</span></span>)</span> <a href="vectsp11.html#K2" title="VECTSP11:func.2">|^</a> <font color="Maroon" title="c1">n</font></span>)</span> &amp; ( for <font color="Olive" title="b6">i</font> being  <a href="nat_1.html#NM1" title="NAT_1:NM.1">Nat</a> holds  <span class="p1">(<span class="default"><font color="Olive" title="b3">f</font> <a href="vectsp11.html#K2" title="VECTSP11:func.2">|^</a> <font color="Olive" title="b6">i</font></span>)</span> <a href="matrlin2.html#K10" title="MATRLIN2:func.10">*</a> <font color="Olive" title="b5">h</font> <a href="funct_2.html#R2" title="FUNCT_2:pred.2">=</a> <font color="Olive" title="b5">h</font> <a href="matrlin2.html#K10" title="MATRLIN2:func.10">*</a> <span class="p1">(<span class="default"><font color="Olive" title="b3">f</font> <a href="vectsp11.html#K2" title="VECTSP11:func.2">|^</a> <font color="Olive" title="b6">i</font></span>)</span> ) )</span><br/><b>let </b><font color="Maroon" title="c2">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">V1</font> being  <a href="vectsp_1.html#NM7" title="VECTSP_1:NM.7">VectSp</a> of <font color="Maroon" title="c2">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#NM4" title="VECTSP_1:NM.4">Scalar</a> of <font color="Maroon" title="c2">K</font>  st <font color="Maroon" title="c1">n</font> <a href="xxreal_0.html#NR2" title="XXREAL_0:NR.2">&gt;=</a> 1 holds <br/> ex <font color="Olive" title="b4">h</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> st <br/>( <span class="p1">(<span class="default"><font color="Olive" title="b2">f</font> <a href="matrlin2.html#K8" title="MATRLIN2:func.8">+</a> <span class="p2">(<span class="default"><font color="Olive" title="b3">L</font> <a href="matrlin2.html#K9" title="MATRLIN2:func.9">*</a> <span class="p3">(<span class="default"><a href="matrlin2.html#K7" title="MATRLIN2:func.7">id</a> <font color="Olive" title="b1">V1</font></span>)</span></span>)</span></span>)</span> <a href="vectsp11.html#K2" title="VECTSP11:func.2">|^</a> <font color="Maroon" title="c1">n</font> <a href="funct_2.html#R2" title="FUNCT_2:pred.2">=</a> <span class="p1">(<span class="default"><font color="Olive" title="b2">f</font> <a href="matrlin2.html#K10" title="MATRLIN2:func.10">*</a> <font color="Olive" title="b4">h</font></span>)</span> <a href="matrlin2.html#K8" title="MATRLIN2:func.8">+</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Olive" title="b3">L</font> <a href="matrlin2.html#K9" title="MATRLIN2:func.9">*</a> <span class="p3">(<span class="default"><a href="matrlin2.html#K7" title="MATRLIN2:func.7">id</a> <font color="Olive" title="b1">V1</font></span>)</span></span>)</span> <a href="vectsp11.html#K2" title="VECTSP11:func.2">|^</a> <font color="Maroon" title="c1">n</font></span>)</span> &amp; ( for <font color="Olive" title="b5">i</font> being  <a href="nat_1.html#NM1" title="NAT_1:NM.1">Nat</a> holds  <span class="p1">(<span class="default"><font color="Olive" title="b2">f</font> <a href="vectsp11.html#K2" title="VECTSP11:func.2">|^</a> <font color="Olive" title="b5">i</font></span>)</span> <a href="matrlin2.html#K10" title="MATRLIN2:func.10">*</a> <font color="Olive" title="b4">h</font> <a href="funct_2.html#R2" title="FUNCT_2:pred.2">=</a> <font color="Olive" title="b4">h</font> <a href="matrlin2.html#K10" title="MATRLIN2:func.10">*</a> <span class="p1">(<span class="default"><font color="Olive" title="b2">f</font> <a href="vectsp11.html#K2" title="VECTSP11:func.2">|^</a> <font color="Olive" title="b5">i</font></span>)</span> ) )</span><br/><b>let </b><font color="Maroon" title="c3">V1</font> be   <a href="vectsp_1.html#NM7" title="VECTSP_1:NM.7">VectSp</a> of <font color="Maroon" title="c2">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">f</font> being  <a href="ranknull.html#NM1" title="RANKNULL:NM.1">linear-transformation</a> of <font color="Maroon" title="c3">V1</font>,<font color="Maroon" title="c3">V1</font><br/> for <font color="Olive" title="b2">L</font> being  <a href="vectsp_1.html#NM4" title="VECTSP_1:NM.4">Scalar</a> of <font color="Maroon" title="c2">K</font>  st <font color="Maroon" title="c1">n</font> <a href="xxreal_0.html#NR2" title="XXREAL_0:NR.2">&gt;=</a> 1 holds <br/> ex <font color="Olive" title="b3">h</font> being  <a href="ranknull.html#NM1" title="RANKNULL:NM.1">linear-transformation</a> of <font color="Maroon" title="c3">V1</font>,<font color="Maroon" title="c3">V1</font> st <br/>( <span class="p1">(<span class="default"><font color="Olive" title="b1">f</font> <a href="matrlin2.html#K8" title="MATRLIN2:func.8">+</a> <span class="p2">(<span class="default"><font color="Olive" title="b2">L</font> <a href="matrlin2.html#K9" title="MATRLIN2:func.9">*</a> <span class="p3">(<span class="default"><a href="matrlin2.html#K7" title="MATRLIN2:func.7">id</a> <font color="Maroon" title="c3">V1</font></span>)</span></span>)</span></span>)</span> <a href="vectsp11.html#K2" title="VECTSP11:func.2">|^</a> <font color="Maroon" title="c1">n</font> <a href="funct_2.html#R2" title="FUNCT_2:pred.2">=</a> <span class="p1">(<span class="default"><font color="Olive" title="b1">f</font> <a href="matrlin2.html#K10" title="MATRLIN2:func.10">*</a> <font color="Olive" title="b3">h</font></span>)</span> <a href="matrlin2.html#K8" title="MATRLIN2:func.8">+</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Olive" title="b2">L</font> <a href="matrlin2.html#K9" title="MATRLIN2:func.9">*</a> <span class="p3">(<span class="default"><a href="matrlin2.html#K7" title="MATRLIN2:func.7">id</a> <font color="Maroon" title="c3">V1</font></span>)</span></span>)</span> <a href="vectsp11.html#K2" title="VECTSP11:func.2">|^</a> <font color="Maroon" title="c1">n</font></span>)</span> &amp; ( for <font color="Olive" title="b4">i</font> being  <a href="nat_1.html#NM1" title="NAT_1:NM.1">Nat</a> holds  <span class="p1">(<span class="default"><font color="Olive" title="b1">f</font> <a href="vectsp11.html#K2" title="VECTSP11:func.2">|^</a> <font color="Olive" title="b4">i</font></span>)</span> <a href="matrlin2.html#K10" title="MATRLIN2:func.10">*</a> <font color="Olive" title="b3">h</font> <a href="funct_2.html#R2" title="FUNCT_2:pred.2">=</a> <font color="Olive" title="b3">h</font> <a href="matrlin2.html#K10" title="MATRLIN2:func.10">*</a> <span class="p1">(<span class="default"><font color="Olive" title="b1">f</font> <a href="vectsp11.html#K2" title="VECTSP11:func.2">|^</a> <font color="Olive" title="b4">i</font></span>)</span> ) )</span><br/><b>let </b><font color="Maroon" title="c4">f</font> be   <a href="ranknull.html#NM1" title="RANKNULL:NM.1">linear-transformation</a> of <font color="Maroon" title="c3">V1</font>,<font color="Maroon" title="c3">V1</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">L</font> being  <a href="vectsp_1.html#NM4" title="VECTSP_1:NM.4">Scalar</a> of <font color="Maroon" title="c2">K</font>  st <font color="Maroon" title="c1">n</font> <a href="xxreal_0.html#NR2" title="XXREAL_0:NR.2">&gt;=</a> 1 holds <br/> ex <font color="Olive" title="b2">h</font> being  <a href="ranknull.html#NM1" title="RANKNULL:NM.1">linear-transformation</a> of <font color="Maroon" title="c3">V1</font>,<font color="Maroon" title="c3">V1</font> st <br/>( <span class="p1">(<span class="default"><font color="Maroon" title="c4">f</font> <a href="matrlin2.html#K8" title="MATRLIN2:func.8">+</a> <span class="p2">(<span class="default"><font color="Olive" title="b1">L</font> <a href="matrlin2.html#K9" title="MATRLIN2:func.9">*</a> <span class="p3">(<span class="default"><a href="matrlin2.html#K7" title="MATRLIN2:func.7">id</a> <font color="Maroon" title="c3">V1</font></span>)</span></span>)</span></span>)</span> <a href="vectsp11.html#K2" title="VECTSP11:func.2">|^</a> <font color="Maroon" title="c1">n</font> <a href="funct_2.html#R2" title="FUNCT_2:pred.2">=</a> <span class="p1">(<span class="default"><font color="Maroon" title="c4">f</font> <a href="matrlin2.html#K10" title="MATRLIN2:func.10">*</a> <font color="Olive" title="b2">h</font></span>)</span> <a href="matrlin2.html#K8" title="MATRLIN2:func.8">+</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Olive" title="b1">L</font> <a href="matrlin2.html#K9" title="MATRLIN2:func.9">*</a> <span class="p3">(<span class="default"><a href="matrlin2.html#K7" title="MATRLIN2:func.7">id</a> <font color="Maroon" title="c3">V1</font></span>)</span></span>)</span> <a href="vectsp11.html#K2" title="VECTSP11:func.2">|^</a> <font color="Maroon" title="c1">n</font></span>)</span> &amp; ( for <font color="Olive" title="b3">i</font> being  <a href="nat_1.html#NM1" title="NAT_1:NM.1">Nat</a> holds  <span class="p1">(<span class="default"><font color="Maroon" title="c4">f</font> <a href="vectsp11.html#K2" title="VECTSP11:func.2">|^</a> <font color="Olive" title="b3">i</font></span>)</span> <a href="matrlin2.html#K10" title="MATRLIN2:func.10">*</a> <font color="Olive" title="b2">h</font> <a href="funct_2.html#R2" title="FUNCT_2:pred.2">=</a> <font color="Olive" title="b2">h</font> <a href="matrlin2.html#K10" title="MATRLIN2:func.10">*</a> <span class="p1">(<span class="default"><font color="Maroon" title="c4">f</font> <a href="vectsp11.html#K2" title="VECTSP11:func.2">|^</a> <font color="Olive" title="b3">i</font></span>)</span> ) )</span><br/><b>let </b><font color="Maroon" title="c5">L</font> be   <a href="vectsp_1.html#NM4" title="VECTSP_1:NM.4">Scalar</a> of <font color="Maroon" title="c2">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="c1">n</font> <a href="xxreal_0.html#NR2" title="XXREAL_0:NR.2">&gt;=</a> 1 implies  ex <font color="Olive" title="b1">h</font> being  <a href="ranknull.html#NM1" title="RANKNULL:NM.1">linear-transformation</a> of <font color="Maroon" title="c3">V1</font>,<font color="Maroon" title="c3">V1</font> st <br/>( <span class="p1">(<span class="default"><font color="Maroon" title="c4">f</font> <a href="matrlin2.html#K8" title="MATRLIN2:func.8">+</a> <span class="p2">(<span class="default"><font color="Maroon" title="c5">L</font> <a href="matrlin2.html#K9" title="MATRLIN2:func.9">*</a> <span class="p3">(<span class="default"><a href="matrlin2.html#K7" title="MATRLIN2:func.7">id</a> <font color="Maroon" title="c3">V1</font></span>)</span></span>)</span></span>)</span> <a href="vectsp11.html#K2" title="VECTSP11:func.2">|^</a> <font color="Maroon" title="c1">n</font> <a href="funct_2.html#R2" title="FUNCT_2:pred.2">=</a> <span class="p1">(<span class="default"><font color="Maroon" title="c4">f</font> <a href="matrlin2.html#K10" title="MATRLIN2:func.10">*</a> <font color="Olive" title="b1">h</font></span>)</span> <a href="matrlin2.html#K8" title="MATRLIN2:func.8">+</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c5">L</font> <a href="matrlin2.html#K9" title="MATRLIN2:func.9">*</a> <span class="p3">(<span class="default"><a href="matrlin2.html#K7" title="MATRLIN2:func.7">id</a> <font color="Maroon" title="c3">V1</font></span>)</span></span>)</span> <a href="vectsp11.html#K2" title="VECTSP11:func.2">|^</a> <font color="Maroon" title="c1">n</font></span>)</span> &amp; ( for <font color="Olive" title="b2">i</font> being  <a href="nat_1.html#NM1" title="NAT_1:NM.1">Nat</a> holds  <span class="p1">(<span class="default"><font color="Maroon" title="c4">f</font> <a href="vectsp11.html#K2" title="VECTSP11:func.2">|^</a> <font color="Olive" title="b2">i</font></span>)</span> <a href="matrlin2.html#K10" title="MATRLIN2:func.10">*</a> <font color="Olive" title="b1">h</font> <a href="funct_2.html#R2" title="FUNCT_2:pred.2">=</a> <font color="Olive" title="b1">h</font> <a href="matrlin2.html#K10" title="MATRLIN2:func.10">*</a> <span class="p1">(<span class="default"><font color="Maroon" title="c4">f</font> <a href="vectsp11.html#K2" title="VECTSP11:func.2">|^</a> <font color="Olive" title="b2">i</font></span>)</span> ) ) )</span><br/>









<b>set </b><font color="Maroon" title="c6">g</font> = <font color="Maroon" title="c5">L</font> <a href="matrlin2.html#K9" title="MATRLIN2:func.9">*</a> <span class="p1">(<span class="default"><a href="matrlin2.html#K7" title="MATRLIN2:func.7">id</a> <font color="Maroon" title="c3">V1</font></span>)</span>;<br/>
<b>defpred </b><font color="Maroon">S<sub>1</sub></font>[  <a href="nat_1.html#NM1" title="NAT_1:NM.1">Nat</a>] <b>means </b> ex <font color="Olive" title="b1">h</font> being  <a href="ranknull.html#NM1" title="RANKNULL:NM.1">linear-transformation</a> of <font color="Maroon" title="c3">V1</font>,<font color="Maroon" title="c3">V1</font> st <br/>( <span class="p1">(<span class="default"><font color="Maroon" title="c4">f</font> <a href="matrlin2.html#K8" title="MATRLIN2:func.8">+</a> <span class="p2">(<span class="default"><font color="Maroon" title="c5">L</font> <a href="matrlin2.html#K9" title="MATRLIN2:func.9">*</a> <span class="p3">(<span class="default"><a href="matrlin2.html#K7" title="MATRLIN2:func.7">id</a> <font color="Maroon" title="c3">V1</font></span>)</span></span>)</span></span>)</span> <a href="vectsp11.html#K2" title="VECTSP11:func.2">|^</a> $1 <a href="funct_2.html#R2" title="FUNCT_2:pred.2">=</a> <span class="p1">(<span class="default"><font color="Maroon" title="c4">f</font> <a href="matrlin2.html#K10" title="MATRLIN2:func.10">*</a> <font color="Olive" title="b1">h</font></span>)</span> <a href="matrlin2.html#K8" title="MATRLIN2:func.8">+</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c5">L</font> <a href="matrlin2.html#K9" title="MATRLIN2:func.9">*</a> <span class="p3">(<span class="default"><a href="matrlin2.html#K7" title="MATRLIN2:func.7">id</a> <font color="Maroon" title="c3">V1</font></span>)</span></span>)</span> <a href="vectsp11.html#K2" title="VECTSP11:func.2">|^</a> $1</span>)</span> &amp; ( for <font color="Olive" title="b2">i</font> being  <a href="nat_1.html#NM1" title="NAT_1:NM.1">Nat</a> holds  <span class="p1">(<span class="default"><font color="Maroon" title="c4">f</font> <a href="vectsp11.html#K2" title="VECTSP11:func.2">|^</a> <font color="Olive" title="b2">i</font></span>)</span> <a href="matrlin2.html#K10" title="MATRLIN2:func.10">*</a> <font color="Olive" title="b1">h</font> <a href="funct_2.html#R2" title="FUNCT_2:pred.2">=</a> <font color="Olive" title="b1">h</font> <a href="matrlin2.html#K10" title="MATRLIN2:func.10">*</a> <span class="p1">(<span class="default"><font color="Maroon" title="c4">f</font> <a href="vectsp11.html#K2" title="VECTSP11:func.2">|^</a> <font color="Olive" title="b2">i</font></span>)</span> ) );<br/>
<a NAME="E1:56"/><i><font color="Green" title="E43">A1</font></i>: 
<font color="Maroon">S<sub>1</sub></font>[1]
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="56_1"><b>proof </b></a><div class="add">

<b>take </b><font color="Maroon" title="c7">h</font> =  <a href="matrlin2.html#K7" title="MATRLIN2:func.7">id</a> <font color="Maroon" title="c3">V1</font>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> ( <span class="p1">(<span class="default"><font color="Maroon" title="c4">f</font> <a href="matrlin2.html#K8" title="MATRLIN2:func.8">+</a> <span class="p2">(<span class="default"><font color="Maroon" title="c5">L</font> <a href="matrlin2.html#K9" title="MATRLIN2:func.9">*</a> <span class="p3">(<span class="default"><a href="matrlin2.html#K7" title="MATRLIN2:func.7">id</a> <font color="Maroon" title="c3">V1</font></span>)</span></span>)</span></span>)</span> <a href="vectsp11.html#K2" title="VECTSP11:func.2">|^</a> 1 <a href="funct_2.html#R2" title="FUNCT_2:pred.2">=</a> <span class="p1">(<span class="default"><font color="Maroon" title="c4">f</font> <a href="matrlin2.html#K10" title="MATRLIN2:func.10">*</a> <font color="Maroon" title="c7">h</font></span>)</span> <a href="matrlin2.html#K8" title="MATRLIN2:func.8">+</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c5">L</font> <a href="matrlin2.html#K9" title="MATRLIN2:func.9">*</a> <span class="p3">(<span class="default"><a href="matrlin2.html#K7" title="MATRLIN2:func.7">id</a> <font color="Maroon" title="c3">V1</font></span>)</span></span>)</span> <a href="vectsp11.html#K2" title="VECTSP11:func.2">|^</a> 1</span>)</span> &amp; ( for <font color="Olive" title="b1">i</font> being  <a href="nat_1.html#NM1" title="NAT_1:NM.1">Nat</a> holds  <span class="p1">(<span class="default"><font color="Maroon" title="c4">f</font> <a href="vectsp11.html#K2" title="VECTSP11:func.2">|^</a> <font color="Olive" title="b1">i</font></span>)</span> <a href="matrlin2.html#K10" title="MATRLIN2:func.10">*</a> <font color="Maroon" title="c7">h</font> <a href="funct_2.html#R2" title="FUNCT_2:pred.2">=</a> <font color="Maroon" title="c7">h</font> <a href="matrlin2.html#K10" title="MATRLIN2:func.10">*</a> <span class="p1">(<span class="default"><font color="Maroon" title="c4">f</font> <a href="vectsp11.html#K2" title="VECTSP11:func.2">|^</a> <font color="Olive" title="b1">i</font></span>)</span> ) )</span><br/>

<b>thus </b><span class="p1">(<span class="default"><font color="Maroon" title="c4">f</font> <a href="matrlin2.html#K8" title="MATRLIN2:func.8">+</a> <span class="p2">(<span class="default"><font color="Maroon" title="c5">L</font> <a href="matrlin2.html#K9" title="MATRLIN2:func.9">*</a> <span class="p3">(<span class="default"><a href="matrlin2.html#K7" title="MATRLIN2:func.7">id</a> <font color="Maroon" title="c3">V1</font></span>)</span></span>)</span></span>)</span> <a href="vectsp11.html#K2" title="VECTSP11:func.2">|^</a> 1 = 
<font color="Maroon" title="c4">f</font> <a href="matrlin2.html#K8" title="MATRLIN2:func.8">+</a> <span class="p1">(<span class="default"><font color="Maroon" title="c5">L</font> <a href="matrlin2.html#K9" title="MATRLIN2:func.9">*</a> <span class="p2">(<span class="default"><a href="matrlin2.html#K7" title="MATRLIN2:func.7">id</a> <font color="Maroon" title="c3">V1</font></span>)</span></span>)</span>
<b>by </b><i><a class="ref" href="vectsp11.html#T19" target="_self" title="VECTSP11:th.19">Th19</a></i>
<br/>.= 
<span class="p1">(<span class="default"><font color="Maroon" title="c4">f</font> <a href="vectsp11.html#K2" title="VECTSP11:func.2">|^</a> <span class="p2">(<span class="default">1 <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> <a href="card_1.html#NK1" title="CARD_1:NK.1">0</a> </span>)</span></span>)</span> <a href="matrlin2.html#K8" title="MATRLIN2:func.8">+</a> <span class="p1">(<span class="default"><font color="Maroon" title="c5">L</font> <a href="matrlin2.html#K9" title="MATRLIN2:func.9">*</a> <span class="p2">(<span class="default"><a href="matrlin2.html#K7" title="MATRLIN2:func.7">id</a> <font color="Maroon" title="c3">V1</font></span>)</span></span>)</span>
<b>by </b><i><a class="ref" href="vectsp11.html#T19" target="_self" title="VECTSP11:th.19">Th19</a></i>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c4">f</font> <a href="vectsp11.html#K2" title="VECTSP11:func.2">|^</a> 1</span>)</span> <a href="matrlin2.html#K10" title="MATRLIN2:func.10">*</a> <span class="p2">(<span class="default"><font color="Maroon" title="c4">f</font> <a href="vectsp11.html#K2" title="VECTSP11:func.2">|^</a> <a href="card_1.html#NK1" title="CARD_1:NK.1">0</a> </span>)</span></span>)</span> <a href="matrlin2.html#K8" title="MATRLIN2:func.8">+</a> <span class="p1">(<span class="default"><font color="Maroon" title="c5">L</font> <a href="matrlin2.html#K9" title="MATRLIN2:func.9">*</a> <span class="p2">(<span class="default"><a href="matrlin2.html#K7" title="MATRLIN2:func.7">id</a> <font color="Maroon" title="c3">V1</font></span>)</span></span>)</span>
<b>by </b><i><a class="ref" href="vectsp11.html#T20" target="_self" title="VECTSP11:th.20">Th20</a></i>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c4">f</font> <a href="vectsp11.html#K2" title="VECTSP11:func.2">|^</a> 1</span>)</span> <a href="matrlin2.html#K10" title="MATRLIN2:func.10">*</a> <font color="Maroon" title="c7">h</font></span>)</span> <a href="matrlin2.html#K8" title="MATRLIN2:func.8">+</a> <span class="p1">(<span class="default"><font color="Maroon" title="c5">L</font> <a href="matrlin2.html#K9" title="MATRLIN2:func.9">*</a> <span class="p2">(<span class="default"><a href="matrlin2.html#K7" title="MATRLIN2:func.7">id</a> <font color="Maroon" title="c3">V1</font></span>)</span></span>)</span>
<b>by </b><i><a class="ref" href="vectsp11.html#T18" target="_self" title="VECTSP11:th.18">Th18</a></i>
<br/>.= 
<span class="p1">(<span class="default"><font color="Maroon" title="c4">f</font> <a href="matrlin2.html#K10" title="MATRLIN2:func.10">*</a> <font color="Maroon" title="c7">h</font></span>)</span> <a href="matrlin2.html#K8" title="MATRLIN2:func.8">+</a> <span class="p1">(<span class="default"><font color="Maroon" title="c5">L</font> <a href="matrlin2.html#K9" title="MATRLIN2:func.9">*</a> <span class="p2">(<span class="default"><a href="matrlin2.html#K7" title="MATRLIN2:func.7">id</a> <font color="Maroon" title="c3">V1</font></span>)</span></span>)</span>
<b>by </b><i><a class="ref" href="vectsp11.html#T19" target="_self" title="VECTSP11:th.19">Th19</a></i>
<br/>.= 
<span class="p1">(<span class="default"><font color="Maroon" title="c4">f</font> <a href="matrlin2.html#K10" title="MATRLIN2:func.10">*</a> <font color="Maroon" title="c7">h</font></span>)</span> <a href="matrlin2.html#K8" title="MATRLIN2:func.8">+</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c5">L</font> <a href="matrlin2.html#K9" title="MATRLIN2:func.9">*</a> <span class="p3">(<span class="default"><a href="matrlin2.html#K7" title="MATRLIN2:func.7">id</a> <font color="Maroon" title="c3">V1</font></span>)</span></span>)</span> <a href="vectsp11.html#K2" title="VECTSP11:func.2">|^</a> 1</span>)</span>
<b>by </b><i><a class="ref" href="vectsp11.html#T19" target="_self" title="VECTSP11:th.19">Th19</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">i</font> being  <a href="nat_1.html#NM1" title="NAT_1:NM.1">Nat</a> holds  <span class="p1">(<span class="default"><font color="Maroon" title="c4">f</font> <a href="vectsp11.html#K2" title="VECTSP11:func.2">|^</a> <font color="Olive" title="b1">i</font></span>)</span> <a href="matrlin2.html#K10" title="MATRLIN2:func.10">*</a> <font color="Maroon" title="c7">h</font> <a href="funct_2.html#R2" title="FUNCT_2:pred.2">=</a> <font color="Maroon" title="c7">h</font> <a href="matrlin2.html#K10" title="MATRLIN2:func.10">*</a> <span class="p1">(<span class="default"><font color="Maroon" title="c4">f</font> <a href="vectsp11.html#K2" title="VECTSP11:func.2">|^</a> <font color="Olive" title="b1">i</font></span>)</span></span><br/>

<b>let </b><font color="Maroon" title="c8">i</font> be   <a href="nat_1.html#NM1" title="NAT_1:NM.1">Nat</a>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> <span class="p1">(<span class="default"><font color="Maroon" title="c4">f</font> <a href="vectsp11.html#K2" title="VECTSP11:func.2">|^</a> <font color="Maroon" title="c8">i</font></span>)</span> <a href="matrlin2.html#K10" title="MATRLIN2:func.10">*</a> <font color="Maroon" title="c7">h</font> <a href="funct_2.html#R2" title="FUNCT_2:pred.2">=</a> <font color="Maroon" title="c7">h</font> <a href="matrlin2.html#K10" title="MATRLIN2:func.10">*</a> <span class="p1">(<span class="default"><font color="Maroon" title="c4">f</font> <a href="vectsp11.html#K2" title="VECTSP11:func.2">|^</a> <font color="Maroon" title="c8">i</font></span>)</span></span><br/>

<b>thus </b><span class="p1">(<span class="default"><font color="Maroon" title="c4">f</font> <a href="vectsp11.html#K2" title="VECTSP11:func.2">|^</a> <font color="Maroon" title="c8">i</font></span>)</span> <a href="matrlin2.html#K10" title="MATRLIN2:func.10">*</a> <font color="Maroon" title="c7">h</font> = 
<span class="p1">(<span class="default"><font color="Maroon" title="c4">f</font> <a href="vectsp11.html#K2" title="VECTSP11:func.2">|^</a> <font color="Maroon" title="c8">i</font></span>)</span> <a href="matrlin2.html#K10" title="MATRLIN2:func.10">*</a> <span class="p1">(<span class="default"><font color="Maroon" title="c4">f</font> <a href="vectsp11.html#K2" title="VECTSP11:func.2">|^</a> <a href="card_1.html#NK1" title="CARD_1:NK.1">0</a> </span>)</span>
<b>by </b><i><a class="ref" href="vectsp11.html#T18" target="_self" title="VECTSP11:th.18">Th18</a></i>
<br/>.= 
<font color="Maroon" title="c4">f</font> <a href="vectsp11.html#K2" title="VECTSP11:func.2">|^</a> <span class="p1">(<span class="default"><font color="Maroon" title="c8">i</font> <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> <a href="card_1.html#NK1" title="CARD_1:NK.1">0</a> </span>)</span>
<b>by </b><i><a class="ref" href="vectsp11.html#T20" target="_self" title="VECTSP11:th.20">Th20</a></i>
<br/>.= 
<span class="p1">(<span class="default"><font color="Maroon" title="c4">f</font> <a href="vectsp11.html#K2" title="VECTSP11:func.2">|^</a> <a href="card_1.html#NK1" title="CARD_1:NK.1">0</a> </span>)</span> <a href="matrlin2.html#K10" title="MATRLIN2:func.10">*</a> <span class="p1">(<span class="default"><font color="Maroon" title="c4">f</font> <a href="vectsp11.html#K2" title="VECTSP11:func.2">|^</a> <font color="Maroon" title="c8">i</font></span>)</span>
<b>by </b><i><a class="ref" href="vectsp11.html#T20" target="_self" title="VECTSP11:th.20">Th20</a></i>
<br/>.= 
<font color="Maroon" title="c7">h</font> <a href="matrlin2.html#K10" title="MATRLIN2:func.10">*</a> <span class="p1">(<span class="default"><font color="Maroon" title="c4">f</font> <a href="vectsp11.html#K2" title="VECTSP11:func.2">|^</a> <font color="Maroon" title="c8">i</font></span>)</span>
<b>by </b><i><a class="ref" href="vectsp11.html#T18" target="_self" title="VECTSP11:th.18">Th18</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><b>end;</b></div>
<a NAME="E2:56"/><i><font color="Green" title="E44">A2</font></i>: 
for <font color="Olive" title="b1">n</font> being  <a href="nat_1.html#NM1" title="NAT_1:NM.1">Nat</a>  st 1 <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a> <font color="Olive" title="b1">n</font> &amp; <font color="Maroon">S<sub>1</sub></font>[<font color="Olive" title="b1">n</font>] holds <br/><font color="Maroon">S<sub>1</sub></font>[<font color="Olive" title="b1">n</font> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 1]
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="56_2"><b>proof </b></a><div class="add">

<b>let </b><font color="Maroon" title="c7">n</font> be   <a href="nat_1.html#NM1" title="NAT_1:NM.1">Nat</a>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> ( 1 <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a> <font color="Maroon" title="c7">n</font> &amp; <font color="Maroon">S<sub>1</sub></font>[<font color="Maroon" title="c7">n</font>] implies <font color="Maroon">S<sub>1</sub></font>[<font color="Maroon" title="c7">n</font> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 1] )</span><br/>

<b>assume </b><a NAME="E1:56_2"/>
1 <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a> <font color="Maroon" title="c7">n</font>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> (  not <font color="Maroon">S<sub>1</sub></font>[<font color="Maroon" title="c7">n</font>] or <font color="Maroon">S<sub>1</sub></font>[<font color="Maroon" title="c7">n</font> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 1] )</span><br/>

<b>assume </b><a NAME="E2:56_2"/>
<font color="Maroon">S<sub>1</sub></font>[<font color="Maroon" title="c7">n</font>]
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> <font color="Maroon">S<sub>1</sub></font>[<font color="Maroon" title="c7">n</font> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 1]</span><br/>

<b>then consider </b><font color="Maroon" title="c8">h</font> being   <a href="ranknull.html#NM1" title="RANKNULL:NM.1">linear-transformation</a> of <font color="Maroon" title="c3">V1</font>,<font color="Maroon" title="c3">V1</font><b> such that </b><br/><a NAME="E4:56_2"/><i><font color="Green" title="E45">A3</font></i>: 
<span class="p1">(<span class="default"><font color="Maroon" title="c4">f</font> <a href="matrlin2.html#K8" title="MATRLIN2:func.8">+</a> <span class="p2">(<span class="default"><font color="Maroon" title="c5">L</font> <a href="matrlin2.html#K9" title="MATRLIN2:func.9">*</a> <span class="p3">(<span class="default"><a href="matrlin2.html#K7" title="MATRLIN2:func.7">id</a> <font color="Maroon" title="c3">V1</font></span>)</span></span>)</span></span>)</span> <a href="vectsp11.html#K2" title="VECTSP11:func.2">|^</a> <font color="Maroon" title="c7">n</font> <a href="funct_2.html#R2" title="FUNCT_2:pred.2">=</a> <span class="p1">(<span class="default"><font color="Maroon" title="c4">f</font> <a href="matrlin2.html#K10" title="MATRLIN2:func.10">*</a> <font color="Maroon" title="c8">h</font></span>)</span> <a href="matrlin2.html#K8" title="MATRLIN2:func.8">+</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c5">L</font> <a href="matrlin2.html#K9" title="MATRLIN2:func.9">*</a> <span class="p3">(<span class="default"><a href="matrlin2.html#K7" title="MATRLIN2:func.7">id</a> <font color="Maroon" title="c3">V1</font></span>)</span></span>)</span> <a href="vectsp11.html#K2" title="VECTSP11:func.2">|^</a> <font color="Maroon" title="c7">n</font></span>)</span>
 <b>and </b><br/><a NAME="E5:56_2"/><i><font color="Green" title="E46">A4</font></i>: 
for <font color="Olive" title="b1">i</font> being  <a href="nat_1.html#NM1" title="NAT_1:NM.1">Nat</a> holds  <span class="p1">(<span class="default"><font color="Maroon" title="c4">f</font> <a href="vectsp11.html#K2" title="VECTSP11:func.2">|^</a> <font color="Olive" title="b1">i</font></span>)</span> <a href="matrlin2.html#K10" title="MATRLIN2:func.10">*</a> <font color="Maroon" title="c8">h</font> <a href="funct_2.html#R2" title="FUNCT_2:pred.2">=</a> <font color="Maroon" title="c8">h</font> <a href="matrlin2.html#K10" title="MATRLIN2:func.10">*</a> <span class="p1">(<span class="default"><font color="Maroon" title="c4">f</font> <a href="vectsp11.html#K2" title="VECTSP11:func.2">|^</a> <font color="Olive" title="b1">i</font></span>)</span>
 ;<br/>
<b>take </b><font color="Maroon" title="c9">H</font> = <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c4">f</font> <a href="matrlin2.html#K10" title="MATRLIN2:func.10">*</a> <font color="Maroon" title="c8">h</font></span>)</span> <a href="matrlin2.html#K8" title="MATRLIN2:func.8">+</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon" title="c5">L</font> <a href="matrlin2.html#K9" title="MATRLIN2:func.9">*</a> <span class="p4">(<span class="default"><a href="matrlin2.html#K7" title="MATRLIN2:func.7">id</a> <font color="Maroon" title="c3">V1</font></span>)</span></span>)</span> <a href="vectsp11.html#K2" title="VECTSP11:func.2">|^</a> <font color="Maroon" title="c7">n</font></span>)</span></span>)</span> <a href="matrlin2.html#K8" title="MATRLIN2:func.8">+</a> <span class="p1">(<span class="default"><font color="Maroon" title="c5">L</font> <a href="matrlin2.html#K9" title="MATRLIN2:func.9">*</a> <font color="Maroon" title="c8">h</font></span>)</span>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> ( <span class="p1">(<span class="default"><font color="Maroon" title="c4">f</font> <a href="matrlin2.html#K8" title="MATRLIN2:func.8">+</a> <span class="p2">(<span class="default"><font color="Maroon" title="c5">L</font> <a href="matrlin2.html#K9" title="MATRLIN2:func.9">*</a> <span class="p3">(<span class="default"><a href="matrlin2.html#K7" title="MATRLIN2:func.7">id</a> <font color="Maroon" title="c3">V1</font></span>)</span></span>)</span></span>)</span> <a href="vectsp11.html#K2" title="VECTSP11:func.2">|^</a> <span class="p1">(<span class="default"><font color="Maroon" title="c7">n</font> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 1</span>)</span> <a href="funct_2.html#R2" title="FUNCT_2:pred.2">=</a> <span class="p1">(<span class="default"><font color="Maroon" title="c4">f</font> <a href="matrlin2.html#K10" title="MATRLIN2:func.10">*</a> <font color="Maroon" title="c9">H</font></span>)</span> <a href="matrlin2.html#K8" title="MATRLIN2:func.8">+</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c5">L</font> <a href="matrlin2.html#K9" title="MATRLIN2:func.9">*</a> <span class="p3">(<span class="default"><a href="matrlin2.html#K7" title="MATRLIN2:func.7">id</a> <font color="Maroon" title="c3">V1</font></span>)</span></span>)</span> <a href="vectsp11.html#K2" title="VECTSP11:func.2">|^</a> <span class="p2">(<span class="default"><font color="Maroon" title="c7">n</font> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 1</span>)</span></span>)</span> &amp; ( for <font color="Olive" title="b1">i</font> being  <a href="nat_1.html#NM1" title="NAT_1:NM.1">Nat</a> holds  <span class="p1">(<span class="default"><font color="Maroon" title="c4">f</font> <a href="vectsp11.html#K2" title="VECTSP11:func.2">|^</a> <font color="Olive" title="b1">i</font></span>)</span> <a href="matrlin2.html#K10" title="MATRLIN2:func.10">*</a> <font color="Maroon" title="c9">H</font> <a href="funct_2.html#R2" title="FUNCT_2:pred.2">=</a> <font color="Maroon" title="c9">H</font> <a href="matrlin2.html#K10" title="MATRLIN2:func.10">*</a> <span class="p1">(<span class="default"><font color="Maroon" title="c4">f</font> <a href="vectsp11.html#K2" title="VECTSP11:func.2">|^</a> <font color="Olive" title="b1">i</font></span>)</span> ) )</span><br/>

<a NAME="E6:56_2"/><i><font color="Green" title="E47">A5</font></i>: 
 <a href="relat_1.html#K2" title="RELAT_1:func.2">rng</a> <span class="p1">(<span class="default"><font color="Maroon" title="c4">f</font> <a href="matrlin2.html#K10" title="MATRLIN2:func.10">*</a> <font color="Maroon" title="c8">h</font></span>)</span> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a>  <a href="struct_0.html#K2" title="STRUCT_0:func.2">[#]</a> <font color="Maroon" title="c3">V1</font>
 
<b>by </b><i><a class="ref" href="relset_1.html#T12" title="RELSET_1:th.12">RELSET_1:12</a></i>;<br/>
<b>thus </b><span class="p1">(<span class="default"><font color="Maroon" title="c4">f</font> <a href="matrlin2.html#K8" title="MATRLIN2:func.8">+</a> <span class="p2">(<span class="default"><font color="Maroon" title="c5">L</font> <a href="matrlin2.html#K9" title="MATRLIN2:func.9">*</a> <span class="p3">(<span class="default"><a href="matrlin2.html#K7" title="MATRLIN2:func.7">id</a> <font color="Maroon" title="c3">V1</font></span>)</span></span>)</span></span>)</span> <a href="vectsp11.html#K2" title="VECTSP11:func.2">|^</a> <span class="p1">(<span class="default"><font color="Maroon" title="c7">n</font> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 1</span>)</span> = 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c4">f</font> <a href="matrlin2.html#K8" title="MATRLIN2:func.8">+</a> <span class="p3">(<span class="default"><font color="Maroon" title="c5">L</font> <a href="matrlin2.html#K9" title="MATRLIN2:func.9">*</a> <span class="p4">(<span class="default"><a href="matrlin2.html#K7" title="MATRLIN2:func.7">id</a> <font color="Maroon" title="c3">V1</font></span>)</span></span>)</span></span>)</span> <a href="vectsp11.html#K2" title="VECTSP11:func.2">|^</a> 1</span>)</span> <a href="matrlin2.html#K10" title="MATRLIN2:func.10">*</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c4">f</font> <a href="matrlin2.html#K8" title="MATRLIN2:func.8">+</a> <span class="p3">(<span class="default"><font color="Maroon" title="c5">L</font> <a href="matrlin2.html#K9" title="MATRLIN2:func.9">*</a> <span class="p4">(<span class="default"><a href="matrlin2.html#K7" title="MATRLIN2:func.7">id</a> <font color="Maroon" title="c3">V1</font></span>)</span></span>)</span></span>)</span> <a href="vectsp11.html#K2" title="VECTSP11:func.2">|^</a> <font color="Maroon" title="c7">n</font></span>)</span>
<b>by </b><i><a class="ref" href="vectsp11.html#T20" target="_self" title="VECTSP11:th.20">Th20</a></i>
<br/>.= 
<span class="p1">(<span class="default"><font color="Maroon" title="c4">f</font> <a href="matrlin2.html#K8" title="MATRLIN2:func.8">+</a> <span class="p2">(<span class="default"><font color="Maroon" title="c5">L</font> <a href="matrlin2.html#K9" title="MATRLIN2:func.9">*</a> <span class="p3">(<span class="default"><a href="matrlin2.html#K7" title="MATRLIN2:func.7">id</a> <font color="Maroon" title="c3">V1</font></span>)</span></span>)</span></span>)</span> <a href="matrlin2.html#K10" title="MATRLIN2:func.10">*</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c4">f</font> <a href="matrlin2.html#K10" title="MATRLIN2:func.10">*</a> <font color="Maroon" title="c8">h</font></span>)</span> <a href="matrlin2.html#K8" title="MATRLIN2:func.8">+</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon" title="c5">L</font> <a href="matrlin2.html#K9" title="MATRLIN2:func.9">*</a> <span class="p4">(<span class="default"><a href="matrlin2.html#K7" title="MATRLIN2:func.7">id</a> <font color="Maroon" title="c3">V1</font></span>)</span></span>)</span> <a href="vectsp11.html#K2" title="VECTSP11:func.2">|^</a> <font color="Maroon" title="c7">n</font></span>)</span></span>)</span>
<b>by </b><i><a class="txt" href="#E4:56_2"><i><font color="Green" title="E45">A3</font></i></a>, <a class="ref" href="vectsp11.html#T19" target="_self" title="VECTSP11:th.19">Th19</a></i>
<br/>.= 
<span class="p1">(<span class="default"><font color="Maroon" title="c4">f</font> <a href="matrlin2.html#K10" title="MATRLIN2:func.10">*</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon" title="c4">f</font> <a href="matrlin2.html#K10" title="MATRLIN2:func.10">*</a> <font color="Maroon" title="c8">h</font></span>)</span> <a href="matrlin2.html#K8" title="MATRLIN2:func.8">+</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon" title="c5">L</font> <a href="matrlin2.html#K9" title="MATRLIN2:func.9">*</a> <span class="p5">(<span class="default"><a href="matrlin2.html#K7" title="MATRLIN2:func.7">id</a> <font color="Maroon" title="c3">V1</font></span>)</span></span>)</span> <a href="vectsp11.html#K2" title="VECTSP11:func.2">|^</a> <font color="Maroon" title="c7">n</font></span>)</span></span>)</span></span>)</span> <a href="matrlin2.html#K8" title="MATRLIN2:func.8">+</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c5">L</font> <a href="matrlin2.html#K9" title="MATRLIN2:func.9">*</a> <span class="p3">(<span class="default"><a href="matrlin2.html#K7" title="MATRLIN2:func.7">id</a> <font color="Maroon" title="c3">V1</font></span>)</span></span>)</span> <a href="matrlin2.html#K10" title="MATRLIN2:func.10">*</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon" title="c4">f</font> <a href="matrlin2.html#K10" title="MATRLIN2:func.10">*</a> <font color="Maroon" title="c8">h</font></span>)</span> <a href="matrlin2.html#K8" title="MATRLIN2:func.8">+</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon" title="c5">L</font> <a href="matrlin2.html#K9" title="MATRLIN2:func.9">*</a> <span class="p5">(<span class="default"><a href="matrlin2.html#K7" title="MATRLIN2:func.7">id</a> <font color="Maroon" title="c3">V1</font></span>)</span></span>)</span> <a href="vectsp11.html#K2" title="VECTSP11:func.2">|^</a> <font color="Maroon" title="c7">n</font></span>)</span></span>)</span></span>)</span>
<b>by </b><i><a class="txt" href="vectsp11.html#E48"><i><font color="Green" title="E37">Lm6</font></i></a></i>
<br/>.= 
<span class="p1">(<span class="default"><font color="Maroon" title="c4">f</font> <a href="matrlin2.html#K10" title="MATRLIN2:func.10">*</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon" title="c4">f</font> <a href="matrlin2.html#K10" title="MATRLIN2:func.10">*</a> <font color="Maroon" title="c8">h</font></span>)</span> <a href="matrlin2.html#K8" title="MATRLIN2:func.8">+</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon" title="c5">L</font> <a href="matrlin2.html#K9" title="MATRLIN2:func.9">*</a> <span class="p5">(<span class="default"><a href="matrlin2.html#K7" title="MATRLIN2:func.7">id</a> <font color="Maroon" title="c3">V1</font></span>)</span></span>)</span> <a href="vectsp11.html#K2" title="VECTSP11:func.2">|^</a> <font color="Maroon" title="c7">n</font></span>)</span></span>)</span></span>)</span> <a href="matrlin2.html#K8" title="MATRLIN2:func.8">+</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon" title="c5">L</font> <a href="matrlin2.html#K9" title="MATRLIN2:func.9">*</a> <span class="p4">(<span class="default"><a href="matrlin2.html#K7" title="MATRLIN2:func.7">id</a> <font color="Maroon" title="c3">V1</font></span>)</span></span>)</span> <a href="matrlin2.html#K10" title="MATRLIN2:func.10">*</a> <span class="p3">(<span class="default"><font color="Maroon" title="c4">f</font> <a href="matrlin2.html#K10" title="MATRLIN2:func.10">*</a> <font color="Maroon" title="c8">h</font></span>)</span></span>)</span> <a href="matrlin2.html#K8" title="MATRLIN2:func.8">+</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon" title="c5">L</font> <a href="matrlin2.html#K9" title="MATRLIN2:func.9">*</a> <span class="p4">(<span class="default"><a href="matrlin2.html#K7" title="MATRLIN2:func.7">id</a> <font color="Maroon" title="c3">V1</font></span>)</span></span>)</span> <a href="matrlin2.html#K10" title="MATRLIN2:func.10">*</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon" title="c5">L</font> <a href="matrlin2.html#K9" title="MATRLIN2:func.9">*</a> <span class="p5">(<span class="default"><a href="matrlin2.html#K7" title="MATRLIN2:func.7">id</a> <font color="Maroon" title="c3">V1</font></span>)</span></span>)</span> <a href="vectsp11.html#K2" title="VECTSP11:func.2">|^</a> <font color="Maroon" title="c7">n</font></span>)</span></span>)</span></span>)</span>
<b>by </b><i><a class="txt" href="vectsp11.html#E49"><i><font color="Green" title="E38">Lm7</font></i></a></i>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c4">f</font> <a href="matrlin2.html#K10" title="MATRLIN2:func.10">*</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon" title="c4">f</font> <a href="matrlin2.html#K10" title="MATRLIN2:func.10">*</a> <font color="Maroon" title="c8">h</font></span>)</span> <a href="matrlin2.html#K8" title="MATRLIN2:func.8">+</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><font color="Maroon" title="c5">L</font> <a href="matrlin2.html#K9" title="MATRLIN2:func.9">*</a> <span class="p0">(<span class="default"><a href="matrlin2.html#K7" title="MATRLIN2:func.7">id</a> <font color="Maroon" title="c3">V1</font></span>)</span></span>)</span> <a href="vectsp11.html#K2" title="VECTSP11:func.2">|^</a> <font color="Maroon" title="c7">n</font></span>)</span></span>)</span></span>)</span> <a href="matrlin2.html#K8" title="MATRLIN2:func.8">+</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon" title="c5">L</font> <a href="matrlin2.html#K9" title="MATRLIN2:func.9">*</a> <span class="p4">(<span class="default"><a href="matrlin2.html#K7" title="MATRLIN2:func.7">id</a> <font color="Maroon" title="c3">V1</font></span>)</span></span>)</span> <a href="matrlin2.html#K10" title="MATRLIN2:func.10">*</a> <span class="p3">(<span class="default"><font color="Maroon" title="c4">f</font> <a href="matrlin2.html#K10" title="MATRLIN2:func.10">*</a> <font color="Maroon" title="c8">h</font></span>)</span></span>)</span></span>)</span> <a href="matrlin2.html#K8" title="MATRLIN2:func.8">+</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c5">L</font> <a href="matrlin2.html#K9" title="MATRLIN2:func.9">*</a> <span class="p3">(<span class="default"><a href="matrlin2.html#K7" title="MATRLIN2:func.7">id</a> <font color="Maroon" title="c3">V1</font></span>)</span></span>)</span> <a href="matrlin2.html#K10" title="MATRLIN2:func.10">*</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon" title="c5">L</font> <a href="matrlin2.html#K9" title="MATRLIN2:func.9">*</a> <span class="p4">(<span class="default"><a href="matrlin2.html#K7" title="MATRLIN2:func.7">id</a> <font color="Maroon" title="c3">V1</font></span>)</span></span>)</span> <a href="vectsp11.html#K2" title="VECTSP11:func.2">|^</a> <font color="Maroon" title="c7">n</font></span>)</span></span>)</span>
<b>by </b><i><a class="txt" href="vectsp11.html#E50"><i><font color="Green" title="E39">Lm8</font></i></a></i>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c4">f</font> <a href="matrlin2.html#K10" title="MATRLIN2:func.10">*</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon" title="c4">f</font> <a href="matrlin2.html#K10" title="MATRLIN2:func.10">*</a> <font color="Maroon" title="c8">h</font></span>)</span> <a href="matrlin2.html#K8" title="MATRLIN2:func.8">+</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><font color="Maroon" title="c5">L</font> <a href="matrlin2.html#K9" title="MATRLIN2:func.9">*</a> <span class="p0">(<span class="default"><a href="matrlin2.html#K7" title="MATRLIN2:func.7">id</a> <font color="Maroon" title="c3">V1</font></span>)</span></span>)</span> <a href="vectsp11.html#K2" title="VECTSP11:func.2">|^</a> <font color="Maroon" title="c7">n</font></span>)</span></span>)</span></span>)</span> <a href="matrlin2.html#K8" title="MATRLIN2:func.8">+</a> <span class="p2">(<span class="default"><font color="Maroon" title="c5">L</font> <a href="matrlin2.html#K9" title="MATRLIN2:func.9">*</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="matrlin2.html#K7" title="MATRLIN2:func.7">id</a> <font color="Maroon" title="c3">V1</font></span>)</span> <a href="matrlin2.html#K10" title="MATRLIN2:func.10">*</a> <span class="p4">(<span class="default"><font color="Maroon" title="c4">f</font> <a href="matrlin2.html#K10" title="MATRLIN2:func.10">*</a> <font color="Maroon" title="c8">h</font></span>)</span></span>)</span></span>)</span></span>)</span> <a href="matrlin2.html#K8" title="MATRLIN2:func.8">+</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c5">L</font> <a href="matrlin2.html#K9" title="MATRLIN2:func.9">*</a> <span class="p3">(<span class="default"><a href="matrlin2.html#K7" title="MATRLIN2:func.7">id</a> <font color="Maroon" title="c3">V1</font></span>)</span></span>)</span> <a href="matrlin2.html#K10" title="MATRLIN2:func.10">*</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon" title="c5">L</font> <a href="matrlin2.html#K9" title="MATRLIN2:func.9">*</a> <span class="p4">(<span class="default"><a href="matrlin2.html#K7" title="MATRLIN2:func.7">id</a> <font color="Maroon" title="c3">V1</font></span>)</span></span>)</span> <a href="vectsp11.html#K2" title="VECTSP11:func.2">|^</a> <font color="Maroon" title="c7">n</font></span>)</span></span>)</span>
<b>by </b><i><a class="txt" href="vectsp11.html#E46"><i><font color="Green" title="E35">Lm4</font></i></a></i>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c4">f</font> <a href="matrlin2.html#K10" title="MATRLIN2:func.10">*</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon" title="c4">f</font> <a href="matrlin2.html#K10" title="MATRLIN2:func.10">*</a> <font color="Maroon" title="c8">h</font></span>)</span> <a href="matrlin2.html#K8" title="MATRLIN2:func.8">+</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><font color="Maroon" title="c5">L</font> <a href="matrlin2.html#K9" title="MATRLIN2:func.9">*</a> <span class="p0">(<span class="default"><a href="matrlin2.html#K7" title="MATRLIN2:func.7">id</a> <font color="Maroon" title="c3">V1</font></span>)</span></span>)</span> <a href="vectsp11.html#K2" title="VECTSP11:func.2">|^</a> <font color="Maroon" title="c7">n</font></span>)</span></span>)</span></span>)</span> <a href="matrlin2.html#K8" title="MATRLIN2:func.8">+</a> <span class="p2">(<span class="default"><font color="Maroon" title="c5">L</font> <a href="matrlin2.html#K9" title="MATRLIN2:func.9">*</a> <span class="p3">(<span class="default"><font color="Maroon" title="c4">f</font> <a href="matrlin2.html#K10" title="MATRLIN2:func.10">*</a> <font color="Maroon" title="c8">h</font></span>)</span></span>)</span></span>)</span> <a href="matrlin2.html#K8" title="MATRLIN2:func.8">+</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c5">L</font> <a href="matrlin2.html#K9" title="MATRLIN2:func.9">*</a> <span class="p3">(<span class="default"><a href="matrlin2.html#K7" title="MATRLIN2:func.7">id</a> <font color="Maroon" title="c3">V1</font></span>)</span></span>)</span> <a href="matrlin2.html#K10" title="MATRLIN2:func.10">*</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon" title="c5">L</font> <a href="matrlin2.html#K9" title="MATRLIN2:func.9">*</a> <span class="p4">(<span class="default"><a href="matrlin2.html#K7" title="MATRLIN2:func.7">id</a> <font color="Maroon" title="c3">V1</font></span>)</span></span>)</span> <a href="vectsp11.html#K2" title="VECTSP11:func.2">|^</a> <font color="Maroon" title="c7">n</font></span>)</span></span>)</span>
<b>by </b><i><a class="txt" href="#E6:56_2"><i><font color="Green" title="E47">A5</font></i></a>, <a class="ref" href="relat_1.html#T79" title="RELAT_1:th.79">RELAT_1:79</a></i>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c4">f</font> <a href="matrlin2.html#K10" title="MATRLIN2:func.10">*</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon" title="c4">f</font> <a href="matrlin2.html#K10" title="MATRLIN2:func.10">*</a> <font color="Maroon" title="c8">h</font></span>)</span> <a href="matrlin2.html#K8" title="MATRLIN2:func.8">+</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><font color="Maroon" title="c5">L</font> <a href="matrlin2.html#K9" title="MATRLIN2:func.9">*</a> <span class="p0">(<span class="default"><a href="matrlin2.html#K7" title="MATRLIN2:func.7">id</a> <font color="Maroon" title="c3">V1</font></span>)</span></span>)</span> <a href="vectsp11.html#K2" title="VECTSP11:func.2">|^</a> <font color="Maroon" title="c7">n</font></span>)</span></span>)</span></span>)</span> <a href="matrlin2.html#K8" title="MATRLIN2:func.8">+</a> <span class="p2">(<span class="default"><font color="Maroon" title="c4">f</font> <a href="matrlin2.html#K10" title="MATRLIN2:func.10">*</a> <span class="p3">(<span class="default"><font color="Maroon" title="c5">L</font> <a href="matrlin2.html#K9" title="MATRLIN2:func.9">*</a> <font color="Maroon" title="c8">h</font></span>)</span></span>)</span></span>)</span> <a href="matrlin2.html#K8" title="MATRLIN2:func.8">+</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c5">L</font> <a href="matrlin2.html#K9" title="MATRLIN2:func.9">*</a> <span class="p3">(<span class="default"><a href="matrlin2.html#K7" title="MATRLIN2:func.7">id</a> <font color="Maroon" title="c3">V1</font></span>)</span></span>)</span> <a href="matrlin2.html#K10" title="MATRLIN2:func.10">*</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon" title="c5">L</font> <a href="matrlin2.html#K9" title="MATRLIN2:func.9">*</a> <span class="p4">(<span class="default"><a href="matrlin2.html#K7" title="MATRLIN2:func.7">id</a> <font color="Maroon" title="c3">V1</font></span>)</span></span>)</span> <a href="vectsp11.html#K2" title="VECTSP11:func.2">|^</a> <font color="Maroon" title="c7">n</font></span>)</span></span>)</span>
<b>by </b><i><a class="txt" href="vectsp11.html#E47"><i><font color="Green" title="E36">Lm5</font></i></a></i>
<br/>.= 
<span class="p1">(<span class="default"><font color="Maroon" title="c4">f</font> <a href="matrlin2.html#K10" title="MATRLIN2:func.10">*</a> <font color="Maroon" title="c9">H</font></span>)</span> <a href="matrlin2.html#K8" title="MATRLIN2:func.8">+</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c5">L</font> <a href="matrlin2.html#K9" title="MATRLIN2:func.9">*</a> <span class="p3">(<span class="default"><a href="matrlin2.html#K7" title="MATRLIN2:func.7">id</a> <font color="Maroon" title="c3">V1</font></span>)</span></span>)</span> <a href="matrlin2.html#K10" title="MATRLIN2:func.10">*</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon" title="c5">L</font> <a href="matrlin2.html#K9" title="MATRLIN2:func.9">*</a> <span class="p4">(<span class="default"><a href="matrlin2.html#K7" title="MATRLIN2:func.7">id</a> <font color="Maroon" title="c3">V1</font></span>)</span></span>)</span> <a href="vectsp11.html#K2" title="VECTSP11:func.2">|^</a> <font color="Maroon" title="c7">n</font></span>)</span></span>)</span>
<b>by </b><i><a class="txt" href="vectsp11.html#E49"><i><font color="Green" title="E38">Lm7</font></i></a></i>
<br/>.= 
<span class="p1">(<span class="default"><font color="Maroon" title="c4">f</font> <a href="matrlin2.html#K10" title="MATRLIN2:func.10">*</a> <font color="Maroon" title="c9">H</font></span>)</span> <a href="matrlin2.html#K8" title="MATRLIN2:func.8">+</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon" title="c5">L</font> <a href="matrlin2.html#K9" title="MATRLIN2:func.9">*</a> <span class="p4">(<span class="default"><a href="matrlin2.html#K7" title="MATRLIN2:func.7">id</a> <font color="Maroon" title="c3">V1</font></span>)</span></span>)</span> <a href="vectsp11.html#K2" title="VECTSP11:func.2">|^</a> 1</span>)</span> <a href="matrlin2.html#K10" title="MATRLIN2:func.10">*</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon" title="c5">L</font> <a href="matrlin2.html#K9" title="MATRLIN2:func.9">*</a> <span class="p4">(<span class="default"><a href="matrlin2.html#K7" title="MATRLIN2:func.7">id</a> <font color="Maroon" title="c3">V1</font></span>)</span></span>)</span> <a href="vectsp11.html#K2" title="VECTSP11:func.2">|^</a> <font color="Maroon" title="c7">n</font></span>)</span></span>)</span>
<b>by </b><i><a class="ref" href="vectsp11.html#T19" target="_self" title="VECTSP11:th.19">Th19</a></i>
<br/>.= 
<span class="p1">(<span class="default"><font color="Maroon" title="c4">f</font> <a href="matrlin2.html#K10" title="MATRLIN2:func.10">*</a> <font color="Maroon" title="c9">H</font></span>)</span> <a href="matrlin2.html#K8" title="MATRLIN2:func.8">+</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c5">L</font> <a href="matrlin2.html#K9" title="MATRLIN2:func.9">*</a> <span class="p3">(<span class="default"><a href="matrlin2.html#K7" title="MATRLIN2:func.7">id</a> <font color="Maroon" title="c3">V1</font></span>)</span></span>)</span> <a href="vectsp11.html#K2" title="VECTSP11:func.2">|^</a> <span class="p2">(<span class="default"><font color="Maroon" title="c7">n</font> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 1</span>)</span></span>)</span>
<b>by </b><i><a class="ref" href="vectsp11.html#T20" target="_self" title="VECTSP11:th.20">Th20</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">i</font> being  <a href="nat_1.html#NM1" title="NAT_1:NM.1">Nat</a> holds  <span class="p1">(<span class="default"><font color="Maroon" title="c4">f</font> <a href="vectsp11.html#K2" title="VECTSP11:func.2">|^</a> <font color="Olive" title="b1">i</font></span>)</span> <a href="matrlin2.html#K10" title="MATRLIN2:func.10">*</a> <font color="Maroon" title="c9">H</font> <a href="funct_2.html#R2" title="FUNCT_2:pred.2">=</a> <font color="Maroon" title="c9">H</font> <a href="matrlin2.html#K10" title="MATRLIN2:func.10">*</a> <span class="p1">(<span class="default"><font color="Maroon" title="c4">f</font> <a href="vectsp11.html#K2" title="VECTSP11:func.2">|^</a> <font color="Olive" title="b1">i</font></span>)</span></span><br/>

<b>let </b><font color="Maroon" title="c10">i</font> be   <a href="nat_1.html#NM1" title="NAT_1:NM.1">Nat</a>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> <span class="p1">(<span class="default"><font color="Maroon" title="c4">f</font> <a href="vectsp11.html#K2" title="VECTSP11:func.2">|^</a> <font color="Maroon" title="c10">i</font></span>)</span> <a href="matrlin2.html#K10" title="MATRLIN2:func.10">*</a> <font color="Maroon" title="c9">H</font> <a href="funct_2.html#R2" title="FUNCT_2:pred.2">=</a> <font color="Maroon" title="c9">H</font> <a href="matrlin2.html#K10" title="MATRLIN2:func.10">*</a> <span class="p1">(<span class="default"><font color="Maroon" title="c4">f</font> <a href="vectsp11.html#K2" title="VECTSP11:func.2">|^</a> <font color="Maroon" title="c10">i</font></span>)</span></span><br/>

<i><font color="Green" title="E48">A6</font></i>: <span class="p1">(<span class="default"><font color="Maroon" title="c4">f</font> <a href="vectsp11.html#K2" title="VECTSP11:func.2">|^</a> <font color="Maroon" title="c10">i</font></span>)</span> <a href="matrlin2.html#K10" title="MATRLIN2:func.10">*</a> <span class="p1">(<span class="default"><font color="Maroon" title="c5">L</font> <a href="matrlin2.html#K9" title="MATRLIN2:func.9">*</a> <font color="Maroon" title="c8">h</font></span>)</span> = 
<font color="Maroon" title="c5">L</font> <a href="matrlin2.html#K9" title="MATRLIN2:func.9">*</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c4">f</font> <a href="vectsp11.html#K2" title="VECTSP11:func.2">|^</a> <font color="Maroon" title="c10">i</font></span>)</span> <a href="matrlin2.html#K10" title="MATRLIN2:func.10">*</a> <font color="Maroon" title="c8">h</font></span>)</span>
<b>by </b><i><a class="txt" href="vectsp11.html#E47"><i><font color="Green" title="E36">Lm5</font></i></a></i>
<br/>.= 
<font color="Maroon" title="c5">L</font> <a href="matrlin2.html#K9" title="MATRLIN2:func.9">*</a> <span class="p1">(<span class="default"><font color="Maroon" title="c8">h</font> <a href="matrlin2.html#K10" title="MATRLIN2:func.10">*</a> <span class="p2">(<span class="default"><font color="Maroon" title="c4">f</font> <a href="vectsp11.html#K2" title="VECTSP11:func.2">|^</a> <font color="Maroon" title="c10">i</font></span>)</span></span>)</span>
<b>by </b><i><a class="txt" href="#E5:56_2"><i><font color="Green" title="E46">A4</font></i></a></i>
<br/>.= 
<span class="p1">(<span class="default"><font color="Maroon" title="c5">L</font> <a href="matrlin2.html#K9" title="MATRLIN2:func.9">*</a> <font color="Maroon" title="c8">h</font></span>)</span> <a href="matrlin2.html#K10" title="MATRLIN2:func.10">*</a> <span class="p1">(<span class="default"><font color="Maroon" title="c4">f</font> <a href="vectsp11.html#K2" title="VECTSP11:func.2">|^</a> <font color="Maroon" title="c10">i</font></span>)</span>
<b>by </b><i><a class="txt" href="vectsp11.html#E46"><i><font color="Green" title="E35">Lm4</font></i></a></i>
;<br/>
<i><font color="Green" title="E49">A7</font></i>: <span class="p1">(<span class="default"><font color="Maroon" title="c4">f</font> <a href="vectsp11.html#K2" title="VECTSP11:func.2">|^</a> <font color="Maroon" title="c10">i</font></span>)</span> <a href="matrlin2.html#K10" title="MATRLIN2:func.10">*</a> <span class="p1">(<span class="default"><font color="Maroon" title="c4">f</font> <a href="matrlin2.html#K10" title="MATRLIN2:func.10">*</a> <font color="Maroon" title="c8">h</font></span>)</span> = 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c4">f</font> <a href="vectsp11.html#K2" title="VECTSP11:func.2">|^</a> <font color="Maroon" title="c10">i</font></span>)</span> <a href="matrlin2.html#K10" title="MATRLIN2:func.10">*</a> <font color="Maroon" title="c4">f</font></span>)</span> <a href="matrlin2.html#K10" title="MATRLIN2:func.10">*</a> <font color="Maroon" title="c8">h</font>
<b>by </b><i><a class="ref" href="relat_1.html#T55" title="RELAT_1:th.55">RELAT_1:55</a></i>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c4">f</font> <a href="vectsp11.html#K2" title="VECTSP11:func.2">|^</a> <font color="Maroon" title="c10">i</font></span>)</span> <a href="matrlin2.html#K10" title="MATRLIN2:func.10">*</a> <span class="p2">(<span class="default"><font color="Maroon" title="c4">f</font> <a href="vectsp11.html#K2" title="VECTSP11:func.2">|^</a> 1</span>)</span></span>)</span> <a href="matrlin2.html#K10" title="MATRLIN2:func.10">*</a> <font color="Maroon" title="c8">h</font>
<b>by </b><i><a class="ref" href="vectsp11.html#T19" target="_self" title="VECTSP11:th.19">Th19</a></i>
<br/>.= 
<span class="p1">(<span class="default"><font color="Maroon" title="c4">f</font> <a href="vectsp11.html#K2" title="VECTSP11:func.2">|^</a> <span class="p2">(<span class="default"><font color="Maroon" title="c10">i</font> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 1</span>)</span></span>)</span> <a href="matrlin2.html#K10" title="MATRLIN2:func.10">*</a> <font color="Maroon" title="c8">h</font>
<b>by </b><i><a class="ref" href="vectsp11.html#T20" target="_self" title="VECTSP11:th.20">Th20</a></i>
<br/>.= 
<font color="Maroon" title="c8">h</font> <a href="matrlin2.html#K10" title="MATRLIN2:func.10">*</a> <span class="p1">(<span class="default"><font color="Maroon" title="c4">f</font> <a href="vectsp11.html#K2" title="VECTSP11:func.2">|^</a> <span class="p2">(<span class="default"><font color="Maroon" title="c10">i</font> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 1</span>)</span></span>)</span>
<b>by </b><i><a class="txt" href="#E5:56_2"><i><font color="Green" title="E46">A4</font></i></a></i>
<br/>.= 
<font color="Maroon" title="c8">h</font> <a href="matrlin2.html#K10" title="MATRLIN2:func.10">*</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c4">f</font> <a href="vectsp11.html#K2" title="VECTSP11:func.2">|^</a> 1</span>)</span> <a href="matrlin2.html#K10" title="MATRLIN2:func.10">*</a> <span class="p2">(<span class="default"><font color="Maroon" title="c4">f</font> <a href="vectsp11.html#K2" title="VECTSP11:func.2">|^</a> <font color="Maroon" title="c10">i</font></span>)</span></span>)</span>
<b>by </b><i><a class="ref" href="vectsp11.html#T20" target="_self" title="VECTSP11:th.20">Th20</a></i>
<br/>.= 
<span class="p1">(<span class="default"><font color="Maroon" title="c8">h</font> <a href="matrlin2.html#K10" title="MATRLIN2:func.10">*</a> <span class="p2">(<span class="default"><font color="Maroon" title="c4">f</font> <a href="vectsp11.html#K2" title="VECTSP11:func.2">|^</a> 1</span>)</span></span>)</span> <a href="matrlin2.html#K10" title="MATRLIN2:func.10">*</a> <span class="p1">(<span class="default"><font color="Maroon" title="c4">f</font> <a href="vectsp11.html#K2" title="VECTSP11:func.2">|^</a> <font color="Maroon" title="c10">i</font></span>)</span>
<b>by </b><i><a class="ref" href="relat_1.html#T55" title="RELAT_1:th.55">RELAT_1:55</a></i>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c4">f</font> <a href="vectsp11.html#K2" title="VECTSP11:func.2">|^</a> 1</span>)</span> <a href="matrlin2.html#K10" title="MATRLIN2:func.10">*</a> <font color="Maroon" title="c8">h</font></span>)</span> <a href="matrlin2.html#K10" title="MATRLIN2:func.10">*</a> <span class="p1">(<span class="default"><font color="Maroon" title="c4">f</font> <a href="vectsp11.html#K2" title="VECTSP11:func.2">|^</a> <font color="Maroon" title="c10">i</font></span>)</span>
<b>by </b><i><a class="txt" href="#E5:56_2"><i><font color="Green" title="E46">A4</font></i></a></i>
<br/>.= 
<span class="p1">(<span class="default"><font color="Maroon" title="c4">f</font> <a href="matrlin2.html#K10" title="MATRLIN2:func.10">*</a> <font color="Maroon" title="c8">h</font></span>)</span> <a href="matrlin2.html#K10" title="MATRLIN2:func.10">*</a> <span class="p1">(<span class="default"><font color="Maroon" title="c4">f</font> <a href="vectsp11.html#K2" title="VECTSP11:func.2">|^</a> <font color="Maroon" title="c10">i</font></span>)</span>
<b>by </b><i><a class="ref" href="vectsp11.html#T19" target="_self" title="VECTSP11:th.19">Th19</a></i>
;<br/>
<i><font color="Green" title="E50">A8</font></i>: <span class="p1">(<span class="default"><font color="Maroon" title="c4">f</font> <a href="vectsp11.html#K2" title="VECTSP11:func.2">|^</a> <font color="Maroon" title="c10">i</font></span>)</span> <a href="matrlin2.html#K10" title="MATRLIN2:func.10">*</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c5">L</font> <a href="matrlin2.html#K9" title="MATRLIN2:func.9">*</a> <span class="p3">(<span class="default"><a href="matrlin2.html#K7" title="MATRLIN2:func.7">id</a> <font color="Maroon" title="c3">V1</font></span>)</span></span>)</span> <a href="vectsp11.html#K2" title="VECTSP11:func.2">|^</a> <font color="Maroon" title="c7">n</font></span>)</span> = 
<span class="p1">(<span class="default"><font color="Maroon" title="c4">f</font> <a href="vectsp11.html#K2" title="VECTSP11:func.2">|^</a> <font color="Maroon" title="c10">i</font></span>)</span> <a href="matrlin2.html#K10" title="MATRLIN2:func.10">*</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="group_1.html#K4" title="GROUP_1:func.4">power</a> <font color="Maroon" title="c2">K</font></span>)</span> <a href="laplace.html#K1" title="LAPLACE:func.1">.</a> <font color="Maroon" title="c5">L</font>,<font color="Maroon" title="c7">n</font></span>)</span> <a href="matrlin2.html#K9" title="MATRLIN2:func.9">*</a> <span class="p2">(<span class="default"><a href="matrlin2.html#K7" title="MATRLIN2:func.7">id</a> <font color="Maroon" title="c3">V1</font></span>)</span></span>)</span>
<b>by </b><i><a class="txt" href="vectsp11.html#E51"><i><font color="Green" title="E40">Lm9</font></i></a></i>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="group_1.html#K4" title="GROUP_1:func.4">power</a> <font color="Maroon" title="c2">K</font></span>)</span> <a href="laplace.html#K1" title="LAPLACE:func.1">.</a> <font color="Maroon" title="c5">L</font>,<font color="Maroon" title="c7">n</font></span>)</span> <a href="matrlin2.html#K9" title="MATRLIN2:func.9">*</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c4">f</font> <a href="vectsp11.html#K2" title="VECTSP11:func.2">|^</a> <font color="Maroon" title="c10">i</font></span>)</span> <a href="matrlin2.html#K10" title="MATRLIN2:func.10">*</a> <span class="p2">(<span class="default"><a href="matrlin2.html#K7" title="MATRLIN2:func.7">id</a> <font color="Maroon" title="c3">V1</font></span>)</span></span>)</span>
<b>by </b><i><a class="txt" href="vectsp11.html#E47"><i><font color="Green" title="E36">Lm5</font></i></a></i>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="group_1.html#K4" title="GROUP_1:func.4">power</a> <font color="Maroon" title="c2">K</font></span>)</span> <a href="laplace.html#K1" title="LAPLACE:func.1">.</a> <font color="Maroon" title="c5">L</font>,<font color="Maroon" title="c7">n</font></span>)</span> <a href="matrlin2.html#K9" title="MATRLIN2:func.9">*</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c4">f</font> <a href="vectsp11.html#K2" title="VECTSP11:func.2">|^</a> <font color="Maroon" title="c10">i</font></span>)</span> <a href="matrlin2.html#K10" title="MATRLIN2:func.10">*</a> <span class="p2">(<span class="default"><font color="Maroon" title="c4">f</font> <a href="vectsp11.html#K2" title="VECTSP11:func.2">|^</a> <a href="card_1.html#NK1" title="CARD_1:NK.1">0</a> </span>)</span></span>)</span>
<b>by </b><i><a class="ref" href="vectsp11.html#T18" target="_self" title="VECTSP11:th.18">Th18</a></i>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="group_1.html#K4" title="GROUP_1:func.4">power</a> <font color="Maroon" title="c2">K</font></span>)</span> <a href="laplace.html#K1" title="LAPLACE:func.1">.</a> <font color="Maroon" title="c5">L</font>,<font color="Maroon" title="c7">n</font></span>)</span> <a href="matrlin2.html#K9" title="MATRLIN2:func.9">*</a> <span class="p1">(<span class="default"><font color="Maroon" title="c4">f</font> <a href="vectsp11.html#K2" title="VECTSP11:func.2">|^</a> <span class="p2">(<span class="default"><font color="Maroon" title="c10">i</font> <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> <a href="card_1.html#NK1" title="CARD_1:NK.1">0</a> </span>)</span></span>)</span>
<b>by </b><i><a class="ref" href="vectsp11.html#T20" target="_self" title="VECTSP11:th.20">Th20</a></i>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="group_1.html#K4" title="GROUP_1:func.4">power</a> <font color="Maroon" title="c2">K</font></span>)</span> <a href="laplace.html#K1" title="LAPLACE:func.1">.</a> <font color="Maroon" title="c5">L</font>,<font color="Maroon" title="c7">n</font></span>)</span> <a href="matrlin2.html#K9" title="MATRLIN2:func.9">*</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c4">f</font> <a href="vectsp11.html#K2" title="VECTSP11:func.2">|^</a> <a href="card_1.html#NK1" title="CARD_1:NK.1">0</a> </span>)</span> <a href="matrlin2.html#K10" title="MATRLIN2:func.10">*</a> <span class="p2">(<span class="default"><font color="Maroon" title="c4">f</font> <a href="vectsp11.html#K2" title="VECTSP11:func.2">|^</a> <font color="Maroon" title="c10">i</font></span>)</span></span>)</span>
<b>by </b><i><a class="ref" href="vectsp11.html#T20" target="_self" title="VECTSP11:th.20">Th20</a></i>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="group_1.html#K4" title="GROUP_1:func.4">power</a> <font color="Maroon" title="c2">K</font></span>)</span> <a href="laplace.html#K1" title="LAPLACE:func.1">.</a> <font color="Maroon" title="c5">L</font>,<font color="Maroon" title="c7">n</font></span>)</span> <a href="matrlin2.html#K9" title="MATRLIN2:func.9">*</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="matrlin2.html#K7" title="MATRLIN2:func.7">id</a> <font color="Maroon" title="c3">V1</font></span>)</span> <a href="matrlin2.html#K10" title="MATRLIN2:func.10">*</a> <span class="p2">(<span class="default"><font color="Maroon" title="c4">f</font> <a href="vectsp11.html#K2" title="VECTSP11:func.2">|^</a> <font color="Maroon" title="c10">i</font></span>)</span></span>)</span>
<b>by </b><i><a class="ref" href="vectsp11.html#T18" target="_self" title="VECTSP11:th.18">Th18</a></i>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="group_1.html#K4" title="GROUP_1:func.4">power</a> <font color="Maroon" title="c2">K</font></span>)</span> <a href="laplace.html#K1" title="LAPLACE:func.1">.</a> <font color="Maroon" title="c5">L</font>,<font color="Maroon" title="c7">n</font></span>)</span> <a href="matrlin2.html#K9" title="MATRLIN2:func.9">*</a> <span class="p2">(<span class="default"><a href="matrlin2.html#K7" title="MATRLIN2:func.7">id</a> <font color="Maroon" title="c3">V1</font></span>)</span></span>)</span> <a href="matrlin2.html#K10" title="MATRLIN2:func.10">*</a> <span class="p1">(<span class="default"><font color="Maroon" title="c4">f</font> <a href="vectsp11.html#K2" title="VECTSP11:func.2">|^</a> <font color="Maroon" title="c10">i</font></span>)</span>
<b>by </b><i><a class="txt" href="vectsp11.html#E46"><i><font color="Green" title="E35">Lm4</font></i></a></i>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c5">L</font> <a href="matrlin2.html#K9" title="MATRLIN2:func.9">*</a> <span class="p3">(<span class="default"><a href="matrlin2.html#K7" title="MATRLIN2:func.7">id</a> <font color="Maroon" title="c3">V1</font></span>)</span></span>)</span> <a href="vectsp11.html#K2" title="VECTSP11:func.2">|^</a> <font color="Maroon" title="c7">n</font></span>)</span> <a href="matrlin2.html#K10" title="MATRLIN2:func.10">*</a> <span class="p1">(<span class="default"><font color="Maroon" title="c4">f</font> <a href="vectsp11.html#K2" title="VECTSP11:func.2">|^</a> <font color="Maroon" title="c10">i</font></span>)</span>
<b>by </b><i><a class="txt" href="vectsp11.html#E51"><i><font color="Green" title="E40">Lm9</font></i></a></i>
;<br/>
<b>thus </b><span class="p1">(<span class="default"><font color="Maroon" title="c4">f</font> <a href="vectsp11.html#K2" title="VECTSP11:func.2">|^</a> <font color="Maroon" title="c10">i</font></span>)</span> <a href="matrlin2.html#K10" title="MATRLIN2:func.10">*</a> <font color="Maroon" title="c9">H</font> = 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c4">f</font> <a href="vectsp11.html#K2" title="VECTSP11:func.2">|^</a> <font color="Maroon" title="c10">i</font></span>)</span> <a href="matrlin2.html#K10" title="MATRLIN2:func.10">*</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon" title="c4">f</font> <a href="matrlin2.html#K10" title="MATRLIN2:func.10">*</a> <font color="Maroon" title="c8">h</font></span>)</span> <a href="matrlin2.html#K8" title="MATRLIN2:func.8">+</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon" title="c5">L</font> <a href="matrlin2.html#K9" title="MATRLIN2:func.9">*</a> <span class="p5">(<span class="default"><a href="matrlin2.html#K7" title="MATRLIN2:func.7">id</a> <font color="Maroon" title="c3">V1</font></span>)</span></span>)</span> <a href="vectsp11.html#K2" title="VECTSP11:func.2">|^</a> <font color="Maroon" title="c7">n</font></span>)</span></span>)</span></span>)</span> <a href="matrlin2.html#K8" title="MATRLIN2:func.8">+</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c5">L</font> <a href="matrlin2.html#K9" title="MATRLIN2:func.9">*</a> <font color="Maroon" title="c8">h</font></span>)</span> <a href="matrlin2.html#K10" title="MATRLIN2:func.10">*</a> <span class="p2">(<span class="default"><font color="Maroon" title="c4">f</font> <a href="vectsp11.html#K2" title="VECTSP11:func.2">|^</a> <font color="Maroon" title="c10">i</font></span>)</span></span>)</span>
<b>by </b><i><a class="txt" href="#E8:56_2"><i><font color="Green" title="E48">A6</font></i></a>, <a class="txt" href="vectsp11.html#E49"><i><font color="Green" title="E38">Lm7</font></i></a></i>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon" title="c4">f</font> <a href="matrlin2.html#K10" title="MATRLIN2:func.10">*</a> <font color="Maroon" title="c8">h</font></span>)</span> <a href="matrlin2.html#K10" title="MATRLIN2:func.10">*</a> <span class="p3">(<span class="default"><font color="Maroon" title="c4">f</font> <a href="vectsp11.html#K2" title="VECTSP11:func.2">|^</a> <font color="Maroon" title="c10">i</font></span>)</span></span>)</span> <a href="matrlin2.html#K8" title="MATRLIN2:func.8">+</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon" title="c5">L</font> <a href="matrlin2.html#K9" title="MATRLIN2:func.9">*</a> <span class="p5">(<span class="default"><a href="matrlin2.html#K7" title="MATRLIN2:func.7">id</a> <font color="Maroon" title="c3">V1</font></span>)</span></span>)</span> <a href="vectsp11.html#K2" title="VECTSP11:func.2">|^</a> <font color="Maroon" title="c7">n</font></span>)</span> <a href="matrlin2.html#K10" title="MATRLIN2:func.10">*</a> <span class="p3">(<span class="default"><font color="Maroon" title="c4">f</font> <a href="vectsp11.html#K2" title="VECTSP11:func.2">|^</a> <font color="Maroon" title="c10">i</font></span>)</span></span>)</span></span>)</span> <a href="matrlin2.html#K8" title="MATRLIN2:func.8">+</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c5">L</font> <a href="matrlin2.html#K9" title="MATRLIN2:func.9">*</a> <font color="Maroon" title="c8">h</font></span>)</span> <a href="matrlin2.html#K10" title="MATRLIN2:func.10">*</a> <span class="p2">(<span class="default"><font color="Maroon" title="c4">f</font> <a href="vectsp11.html#K2" title="VECTSP11:func.2">|^</a> <font color="Maroon" title="c10">i</font></span>)</span></span>)</span>
<b>by </b><i><a class="txt" href="#E9:56_2"><i><font color="Green" title="E49">A7</font></i></a>, <a class="txt" href="#E10:56_2"><i><font color="Green" title="E50">A8</font></i></a>, <a class="txt" href="vectsp11.html#E49"><i><font color="Green" title="E38">Lm7</font></i></a></i>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon" title="c4">f</font> <a href="matrlin2.html#K10" title="MATRLIN2:func.10">*</a> <font color="Maroon" title="c8">h</font></span>)</span> <a href="matrlin2.html#K8" title="MATRLIN2:func.8">+</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon" title="c5">L</font> <a href="matrlin2.html#K9" title="MATRLIN2:func.9">*</a> <span class="p5">(<span class="default"><a href="matrlin2.html#K7" title="MATRLIN2:func.7">id</a> <font color="Maroon" title="c3">V1</font></span>)</span></span>)</span> <a href="vectsp11.html#K2" title="VECTSP11:func.2">|^</a> <font color="Maroon" title="c7">n</font></span>)</span></span>)</span> <a href="matrlin2.html#K10" title="MATRLIN2:func.10">*</a> <span class="p2">(<span class="default"><font color="Maroon" title="c4">f</font> <a href="vectsp11.html#K2" title="VECTSP11:func.2">|^</a> <font color="Maroon" title="c10">i</font></span>)</span></span>)</span> <a href="matrlin2.html#K8" title="MATRLIN2:func.8">+</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c5">L</font> <a href="matrlin2.html#K9" title="MATRLIN2:func.9">*</a> <font color="Maroon" title="c8">h</font></span>)</span> <a href="matrlin2.html#K10" title="MATRLIN2:func.10">*</a> <span class="p2">(<span class="default"><font color="Maroon" title="c4">f</font> <a href="vectsp11.html#K2" title="VECTSP11:func.2">|^</a> <font color="Maroon" title="c10">i</font></span>)</span></span>)</span>
<b>by </b><i><a class="txt" href="vectsp11.html#E48"><i><font color="Green" title="E37">Lm6</font></i></a></i>
<br/>.= 
<font color="Maroon" title="c9">H</font> <a href="matrlin2.html#K10" title="MATRLIN2:func.10">*</a> <span class="p1">(<span class="default"><font color="Maroon" title="c4">f</font> <a href="vectsp11.html#K2" title="VECTSP11:func.2">|^</a> <font color="Maroon" title="c10">i</font></span>)</span>
<b>by </b><i><a class="txt" href="vectsp11.html#E48"><i><font color="Green" title="E37">Lm6</font></i></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><b>end;</b></div>
<a NAME="E3:56"/>
for <font color="Olive" title="b1">n</font> being  <a href="nat_1.html#NM1" title="NAT_1:NM.1">Nat</a>  st 1 <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a> <font color="Olive" title="b1">n</font> holds <br/><font color="Maroon">S<sub>1</sub></font>[<font color="Olive" title="b1">n</font>]
 
<b>from </b><i><a class="ref" href="nat_1.html#S8" title="NAT_1:sch.8">NAT_1:sch 8</a>(<a class="txt" href="#E1:56"><i><font color="Green" title="E43">A1</font></i></a>, <a class="txt" href="#E2:56"><i><font color="Green" title="E44">A2</font></i></a>);<br/></i>
<b>hence </b><a NAME="E4:56"/>
( <font color="Maroon" title="c1">n</font> <a href="xxreal_0.html#NR2" title="XXREAL_0:NR.2">&gt;=</a> 1 implies  ex <font color="Olive" title="b1">h</font> being  <a href="ranknull.html#NM1" title="RANKNULL:NM.1">linear-transformation</a> of <font color="Maroon" title="c3">V1</font>,<font color="Maroon" title="c3">V1</font> st <br/>( <span class="p1">(<span class="default"><font color="Maroon" title="c4">f</font> <a href="matrlin2.html#K8" title="MATRLIN2:func.8">+</a> <span class="p2">(<span class="default"><font color="Maroon" title="c5">L</font> <a href="matrlin2.html#K9" title="MATRLIN2:func.9">*</a> <span class="p3">(<span class="default"><a href="matrlin2.html#K7" title="MATRLIN2:func.7">id</a> <font color="Maroon" title="c3">V1</font></span>)</span></span>)</span></span>)</span> <a href="vectsp11.html#K2" title="VECTSP11:func.2">|^</a> <font color="Maroon" title="c1">n</font> <a href="funct_2.html#R2" title="FUNCT_2:pred.2">=</a> <span class="p1">(<span class="default"><font color="Maroon" title="c4">f</font> <a href="matrlin2.html#K10" title="MATRLIN2:func.10">*</a> <font color="Olive" title="b1">h</font></span>)</span> <a href="matrlin2.html#K8" title="MATRLIN2:func.8">+</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c5">L</font> <a href="matrlin2.html#K9" title="MATRLIN2:func.9">*</a> <span class="p3">(<span class="default"><a href="matrlin2.html#K7" title="MATRLIN2:func.7">id</a> <font color="Maroon" title="c3">V1</font></span>)</span></span>)</span> <a href="vectsp11.html#K2" title="VECTSP11:func.2">|^</a> <font color="Maroon" title="c1">n</font></span>)</span> &amp; ( for <font color="Olive" title="b2">i</font> being  <a href="nat_1.html#NM1" title="NAT_1:NM.1">Nat</a> holds  <span class="p1">(<span class="default"><font color="Maroon" title="c4">f</font> <a href="vectsp11.html#K2" title="VECTSP11:func.2">|^</a> <font color="Olive" title="b2">i</font></span>)</span> <a href="matrlin2.html#K10" title="MATRLIN2:func.10">*</a> <font color="Olive" title="b1">h</font> <a href="funct_2.html#R2" title="FUNCT_2:pred.2">=</a> <font color="Olive" title="b1">h</font> <a href="matrlin2.html#K10" title="MATRLIN2:func.10">*</a> <span class="p1">(<span class="default"><font color="Maroon" title="c4">f</font> <a href="vectsp11.html#K2" title="VECTSP11:func.2">|^</a> <font color="Olive" title="b2">i</font></span>)</span> ) ) )
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> verum</span><br/>


</div>
