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<b>let </b><font color="Maroon" title="c1">F</font> be   <a href="vectsp_1.html#NM3" title="VECTSP_1:NM.3">Field</a>;<br/><b>let </b><font color="Maroon" title="c2">V</font> be  <a href="matrlin.html#V2" title="MATRLIN:attr.2">finite-dimensional</a> <a href="vectsp_1.html#NM7" title="VECTSP_1:NM.7">VectSp</a> of <font color="Maroon" title="c1">F</font>;<br/><b>let </b><font color="Maroon" title="c3">m</font> be   <a href="nat_1.html#NM1" title="NAT_1:NM.1">Nat</a>;<br/>





<b>assume </b><a NAME="E1:36"/><i><font color="Green" title="E32">A1</font></i>: 
( 1 <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a> <font color="Maroon" title="c3">m</font> &amp; <font color="Maroon" title="c3">m</font> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 1 <a href="xxreal_0.html#NR3" title="XXREAL_0:NR.3">&lt;</a>  <a href="vectsp_9.html#K1" title="VECTSP_9:func.1">dim</a> <font color="Maroon" title="c2">V</font> )
 ;<br/>

<a NAME="E2:36"/><b>then </b><i><font color="Green" title="E33">A2</font></i>: 
<font color="Maroon" title="c3">m</font> <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a>  <a href="vectsp_9.html#K1" title="VECTSP_9:func.1">dim</a> <font color="Maroon" title="c2">V</font>
 
<b>by </b><i><a class="ref" href="nat_1.html#T13" title="NAT_1:th.13">NAT_1:13</a></i>;<br/>
<b>set </b><font color="Maroon" title="c4">S</font> =  <a href="pencil_4.html#K7" title="PENCIL_4:func.7">GrassmannSpace</a> <font color="Maroon" title="c2">V</font>,<font color="Maroon" title="c3">m</font>,<span class="p1">(<span class="default"><font color="Maroon" title="c3">m</font> <a href="nat_1.html#K1" title="NAT_1:func.1">+</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" title="PENCIL_4:func.7">GrassmannSpace</a> <font color="Maroon" title="c2">V</font>,<font color="Maroon" title="c3">m</font>,<span class="p1">(<span class="default"><font color="Maroon" title="c3">m</font> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 1</span>)</span> is <a href="struct_0.html#V2" title="STRUCT_0:attr.2">empty</a>
 <b>by </b><i><a class="txt" href="pencil_4.html#E2:36"><i><font color="Green" title="E33">A2</font></i></a>, <a class="ref" href="pencil_4.html#T27" target="_self" title="PENCIL_4:th.27">Th27</a></i>;<br/><b>thus </b><a NAME="E2:36_1"/>
not  <a href="pencil_4.html#K7" title="PENCIL_4:func.7">GrassmannSpace</a> <font color="Maroon" title="c2">V</font>,<font color="Maroon" title="c3">m</font>,<span class="p1">(<span class="default"><font color="Maroon" title="c3">m</font> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 1</span>)</span> is <a href="pencil_1.html#V3" title="PENCIL_1:attr.3">void</a>
 <b>by </b><i><a class="txt" href="pencil_4.html#E1:36"><i><font color="Green" title="E32">A1</font></i></a>, <a class="ref" href="pencil_4.html#T28" target="_self" title="PENCIL_4:th.28">Th28</a></i>;<br/><a NAME="E3:36_1"/>
<font color="Maroon" title="c3">m</font> <a href="xxreal_0.html#NR3" title="XXREAL_0:NR.3">&lt;</a> <font color="Maroon" title="c3">m</font> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 1
 <b>by </b><i><a class="ref" href="nat_1.html#T13" title="NAT_1:th.13">NAT_1:13</a></i>;<br/><b>hence </b><a NAME="E4:36_1"/>
not  <a href="pencil_4.html#K7" title="PENCIL_4:func.7">GrassmannSpace</a> <font color="Maroon" title="c2">V</font>,<font color="Maroon" title="c3">m</font>,<span class="p1">(<span class="default"><font color="Maroon" title="c3">m</font> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 1</span>)</span> is <a href="pencil_1.html#V4" title="PENCIL_1:attr.4">degenerated</a>
 <b>by </b><i><a class="txt" href="pencil_4.html#E1:36"><i><font color="Green" title="E32">A1</font></i></a>, <a class="ref" href="pencil_4.html#T29" target="_self" title="PENCIL_4:th.29">Th29</a></i>;<br/><a NAME="E5:36_1"/>
<font color="Maroon" title="c3">m</font> <a href="xxreal_0.html#NR3" title="XXREAL_0:NR.3">&lt;</a> <font color="Maroon" title="c3">m</font> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 1
 <b>by </b><i><a class="ref" href="nat_1.html#T13" title="NAT_1:th.13">NAT_1:13</a></i>;<br/><b>hence </b><a NAME="E6:36_1"/>
 <a href="pencil_4.html#K7" title="PENCIL_4:func.7">GrassmannSpace</a> <font color="Maroon" title="c2">V</font>,<font color="Maroon" title="c3">m</font>,<span class="p1">(<span class="default"><font color="Maroon" title="c3">m</font> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 1</span>)</span> is <a href="pencil_1.html#V5" title="PENCIL_1:attr.5">with_non_trivial_blocks</a>
 <b>by </b><i><a class="txt" href="pencil_4.html#E1:36"><i><font color="Green" title="E32">A1</font></i></a>, <a class="ref" href="pencil_4.html#T30" target="_self" title="PENCIL_4:th.30">Th30</a></i>;<br/><b>thus </b><a NAME="E7:36_1"/>
 <a href="pencil_4.html#K7" title="PENCIL_4:func.7">GrassmannSpace</a> <font color="Maroon" title="c2">V</font>,<font color="Maroon" title="c3">m</font>,<span class="p1">(<span class="default"><font color="Maroon" title="c3">m</font> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 1</span>)</span> is <a href="pencil_1.html#V6" title="PENCIL_1:attr.6">identifying_close_blocks</a>
 <b>by </b><i><a class="txt" href="pencil_4.html#E1:36"><i><font color="Green" title="E32">A1</font></i></a>, <a class="ref" href="pencil_4.html#T31" target="_self" title="PENCIL_4:th.31">Th31</a></i>;<br/></div><b>end;</b></div>
<b>hence </b><a NAME="E4:36"/>
 <a href="pencil_4.html#K7" title="PENCIL_4:func.7">GrassmannSpace</a> <font color="Maroon" title="c2">V</font>,<font color="Maroon" title="c3">m</font>,<span class="p1">(<span class="default"><font color="Maroon" title="c3">m</font> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 1</span>)</span> is   <a href="pencil_1.html#NM2" title="PENCIL_1:NM.2">PLS</a>
 ;<br/>


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