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<b>let </b><font color="Maroon">c<sub>1</sub></font> be   <a href="vectsp_1.html#NM2">Field</a>;<br/><b>let </b><font color="Maroon">c<sub>2</sub></font> be  <a href="matrlin.html#V2">finite-dimensional</a> <a href="vectsp_1.html#NM6">VectSp</a> of <font color="Maroon">c<sub>1</sub></font>;<br/><b>let </b><font color="Maroon">c<sub>3</sub></font> be   <a href="nat_1.html#NM1">Nat</a>;<br/>





<b>assume </b><a NAME="E1:36"/><i><font color="Green">E34</font></i>: 
( 1 <a href="xxreal_0.html#R1">&lt;=</a> <font color="Maroon">c<sub>3</sub></font> &amp; <font color="Maroon">c<sub>3</sub></font> <a href="nat_1.html#K1">+</a> 1 <a href="xxreal_0.html#NR3" target="_self">&lt;</a>  <a href="vectsp_9.html#K1">dim</a> <font color="Maroon">c<sub>2</sub></font> )
 ;<br/>

<a NAME="E2:36"/><b>then </b><i><font color="Green">E35</font></i>: 
<font color="Maroon">c<sub>3</sub></font> <a href="xxreal_0.html#R1">&lt;=</a>  <a href="vectsp_9.html#K1">dim</a> <font color="Maroon">c<sub>2</sub></font>
 
<b>by </b><i><a class="ref" href="nat_1.html#T38">NAT_1:38</a></i>;<br/>
<b>set </b><font color="Maroon">c<sub>4</sub></font> =  <a href="pencil_4.html#K7" target="_self">GrassmannSpace</a> <font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>3</sub></font>,<span class="p1">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="nat_1.html#K1">+</a> 1</span>)</span>;<br/>
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="36_1"><b>now </b></a><div class="add"><b>thus </b><a NAME="E1:36_1"/>
not  <a href="pencil_4.html#K7" target="_self">GrassmannSpace</a> <font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>3</sub></font>,<span class="p1">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="nat_1.html#K1">+</a> 1</span>)</span> is <a href="struct_0.html#V3">empty</a>
 <b>by </b><i><a class="ref" href="pencil_4.html#T27" target="_self">Th27</a>, <a class="txt" href="pencil_4.html#E2:36"><i><font color="Green">E35</font></i></a></i>;<br/><b>thus </b><a NAME="E2:36_1"/>
not  <a href="pencil_4.html#K7" target="_self">GrassmannSpace</a> <font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>3</sub></font>,<span class="p1">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="nat_1.html#K1">+</a> 1</span>)</span> is <a href="pencil_1.html#V3">void</a>
 <b>by </b><i><a class="ref" href="pencil_4.html#T28" target="_self">Th28</a>, <a class="txt" href="pencil_4.html#E1:36"><i><font color="Green">E34</font></i></a></i>;<br/><a NAME="E3:36_1"/>
<font color="Maroon">c<sub>3</sub></font> <a href="xxreal_0.html#NR3" target="_self">&lt;</a> <font color="Maroon">c<sub>3</sub></font> <a href="nat_1.html#K1">+</a> 1
 <b>by </b><i><a class="ref" href="nat_1.html#T38">NAT_1:38</a></i>;<br/><b>hence </b><a NAME="E4:36_1"/>
not  <a href="pencil_4.html#K7" target="_self">GrassmannSpace</a> <font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>3</sub></font>,<span class="p1">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="nat_1.html#K1">+</a> 1</span>)</span> is <a href="pencil_1.html#V4">degenerated</a>
 <b>by </b><i><a class="ref" href="pencil_4.html#T29" target="_self">Th29</a>, <a class="txt" href="pencil_4.html#E1:36"><i><font color="Green">E34</font></i></a></i>;<br/><a NAME="E5:36_1"/>
<font color="Maroon">c<sub>3</sub></font> <a href="xxreal_0.html#NR3" target="_self">&lt;</a> <font color="Maroon">c<sub>3</sub></font> <a href="nat_1.html#K1">+</a> 1
 <b>by </b><i><a class="ref" href="nat_1.html#T38">NAT_1:38</a></i>;<br/><b>hence </b><a NAME="E6:36_1"/>
 <a href="pencil_4.html#K7" target="_self">GrassmannSpace</a> <font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>3</sub></font>,<span class="p1">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="nat_1.html#K1">+</a> 1</span>)</span> is <a href="pencil_1.html#V5">with_non_trivial_blocks</a>
 <b>by </b><i><a class="ref" href="pencil_4.html#T30" target="_self">Th30</a>, <a class="txt" href="pencil_4.html#E1:36"><i><font color="Green">E34</font></i></a></i>;<br/><b>thus </b><a NAME="E7:36_1"/>
 <a href="pencil_4.html#K7" target="_self">GrassmannSpace</a> <font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>3</sub></font>,<span class="p1">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="nat_1.html#K1">+</a> 1</span>)</span> is <a href="pencil_1.html#V6">identifying_close_blocks</a>
 <b>by </b><i><a class="ref" href="pencil_4.html#T31" target="_self">Th31</a>, <a class="txt" href="pencil_4.html#E1:36"><i><font color="Green">E34</font></i></a></i>;<br/></div><b>end;</b></div>
<b>hence </b><a NAME="E4:36"/>
 <a href="pencil_4.html#K7" target="_self">GrassmannSpace</a> <font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>3</sub></font>,<span class="p1">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="nat_1.html#K1">+</a> 1</span>)</span> is   <a href="pencil_1.html#NM2">PLS</a>
 ;<br/>


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